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Ismail",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/10013.jpg",keywords:"Thermodynamics, Heat Transfer Analyses, Geothermal Power Generation, Economics, Geothermal Systems, Geothermal Heat Pump, Green Energy Buildings, Exploration Methods, Geologic Fundamentals, Geotechnical, Geothermal System Materials, Sustainability",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 29th 2020",dateEndSecondStepPublish:"November 26th 2020",dateEndThirdStepPublish:"January 25th 2021",dateEndFourthStepPublish:"April 15th 2021",dateEndFifthStepPublish:"June 14th 2021",remainingDaysToSecondStep:"3 months",secondStepPassed:!0,currentStepOfPublishingProcess:4,editedByType:null,kuFlag:!1,biosketch:"Leading research investigator in a collaborative project (2007-2010) with Goldcorp-Musselwhite Canada Ltd. and Engineering of Lakehead University, owner of a Ph.D. degree in Mechanical Engineering from McMaster University, Hamilton, Ontario, Canada and postdoctoral researcher (2004 to 2005) at McMaster University.",coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"62122",title:"Dr.",name:"Basel",middleName:"I.",surname:"Ismail",slug:"basel-ismail",fullName:"Basel Ismail",profilePictureURL:"https://mts.intechopen.com/storage/users/62122/images/system/62122.jpg",biography:"Dr. B. Ismail is currently an Associate Professor and Chairman of the Department of Mechanical Engineering, Lakehead University, Thunder Bay, Ontario, Canada. In 2004, Prof. Ismail earned his Ph.D. degree in Mechanical Engineering from McMaster University, Hamilton, Ontario, Canada. From 2004 to 2005, he worked as a Postdoctoral researcher at McMaster University. His specialty is in engineering heat transfer, engineering thermodynamics, and energy conversion and storage engineering. Dr. Ismail’s research activities are theoretical and applied in nature. Currently, his research areas of interest are focused on green engineering technologies related to alternative and renewable energy systems for power generation, heating and cooling. Dr. Ismail was the leading research investigator in a collaborative project (2007-2010) with Goldcorp-Musselwhite Canada Ltd. and Engineering of Lakehead University. 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From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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\n
1. Introduction
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In recent years, T-S (Takagi-Sugeno) model-based fuzzy control has attracted wide attention, essentially because the fuzzy model is an effective and flexible tool for the control of nonlinear systems [1–8]. Through the application of sector nonlinearity approach, local approximation in fuzzy partition spaces or other different approximation methods, T-S fuzzy models will be used to approximate or exactly represent a nonlinear system in a compact set of state variables. The merit of the model is that the consequent part of a fuzzy rule is a linear dynamic subsystem, which makes it possible to apply the classical and mature linear systems theory to nonlinear systems. Further, by using the fuzzy inference method, the overall fuzzy model will be obtained. A fuzzy controller is designed via the method titled ‘parallel distributed compensation (PDC)’ [3–6], the main idea of which is that for each linear subsystem, the corresponding linear controller is carried out. Finally, the overall nonlinear controller is obtained via fuzzy blending of each individual linear controller. Based on the above content,, T-S fuzzy model has been widely studied, and many results have been obtained [1–8]. In practical applications, time delay often occurs in many dynamic systems such as biological systems, network systems, etc. It is shown that the existence of delays usually becomes the source of instability and deteriorating performance of systems [3–8]. In general, when delay-dependent results were calculated, the emergence of the inner product between two vectors often makes the process of calculation more complicated. In order to avoid it, some model transformations were utilized in many papers, unfortunately, which will arouse the generation of an inequality, resulting in possible conservatism. On the other hand, due to the influence of many factors such as finite word length, truncation errors in numerical computation and electronic component parameter change, the parameters of the controller in a certain degree will change, which lead to imprecision in controller implementation. In this case, some small perturbations of the controllers’ coefficients will make the designed controllers sensitive, even worse, destabilize the closed-loop control system [9]. So the problem of non-fragile control has been important issues. Recently, the research of non-fragile control has been paid much attention, and a series of productions have been obtained [10–13].
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As we know, bilinear models have been widely used in many physical systems, biotechnology, socioeconomics and dynamical processes in other engineering fields [14, 15]. Bilinear model is a special nonlinear model, the nonlinear part of which consists of the bilinear function of the state and input. Compared with a linear model, the bilinear models have two main advantages. One is that the bilinear model can better approximate a nonlinear system. Another is that because of nonlinearity of it, many real physical processes may be appropriately modeled as bilinear systems. A famous example of a bilinear system is the population of biological species, which can be showed by \n\n\n\n\n\nd\nθ\n\n\nd\nt\n\n\n\n=\nθ\nv\n\n\n. In this equation, v is the birth rate minus death rate, and θ denotes the population. Obviously, the equation cannot be approximated by a linear model [14].
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Most of the existing results focus on the stability analysis and synthesis based on T-S fuzzy model with linear local model. However, when a nonlinear system has of complex nonlinearities, the constructed T-S model will consist of a number of fuzzy local models. This will lead to very heavy computational burden. According to the advantages of bilinear systems and T-S fuzzy control, so many researchers paid their attentions to the T-S fuzzy models with bilinear rule consequence [16–18]. From these papers, it is evident that the T-S fuzzy bilinear model may be suitable for some classes of nonlinear plants. In Ref. [16], a nonlinear system was transformed into a bilinear model via Taylor’s series expansion, and the stability of T-S fuzzy bilinear model was studied. Moreover, the result was stretched into the complex fuzzy system with state time delay [17]. Ref. [18] presented robust stabilization for a class of discrete-time fuzzy bilinear system. Very recently, a class of nonlinear systems is described by T-S fuzzy models with nonlinear local models in Ref. [19], and in this paper, the scholars put forward a new fuzzy control scheme with local nonlinear feedbacks, the advantage of which over the existing methods is that a fewer fuzzy rules and less computational burden. The non-fragile guaranteed cost controller was designed for a class of T-S discrete-time fuzzy bilinear systems in Ref. [20]. However, in Refs. [19, 20], the time-delay effects on the system is not considered. Ref. [17] is only considered the fuzzy system with the delay in the state and the derivatives of time-delay, \n\n\n\n\nd\n˙\n\n\n(\nt\n)\n<\n1\n\n\n is required. Refs. [21–23] dealt with the uncertain fuzzy systems with time-delay in different ways. It should be pointed out that all the aforementioned works did not take into account the effect of the control input delays on the systems. The results therein are not applicable to systems with input delay. Recently, some controller design approaches have been presented for systems with input delay, see [2, 3, 4, 18, 24–32] for fuzzy T-S systems and [8, 15, 33, 34] for non-fuzzy systems and the references therein. All of these results are required to know the exact delay values in the implementation. T-S fuzzy stochastic systems with state time-vary or distributed delays were studied in Refs. [35–39]. The researches of fractional order T-S fuzzy systems on robust stability, stability analysis about “0 < α < 1”, and decentralized stabilization in multiple time delays were presented in Refs. [40–42], respectively. For different delay types, the corresponding adaptive fuzzy controls for nonlinear systems were proposed in Refs. [33, 43, 44]. In Refs. [45, 46], to achieve small control amplitude, a new T-S fuzzy hyperbolic model was developed, moreover, Ref. [46] considered the input delay of the novel model. In Ref. [25, 47], the problems of observer-based fuzzy control design for T-S fuzzy systems were concerned.
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So far, the problem of non-fragile guaranteed cost control for fuzzy system with local bilinear model with different time-varying state and input delays has not been discussed.
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In this paper, the problem of delay-dependent non-fragile guaranteed cost control is studied for the fuzzy time-varying delay systems with local bilinear model and different state and input delays. Based on the PDC scheme, new delay-dependent stabilization conditions for the closed-loop fuzzy systems are derived. No model transformation is involved in the derivation. The merit of the proposed conditions lies in its reduced conservatism, which is achieved by circumventing the utilization of some bounding inequalities for the cross-product between two vectors as in Ref. [17]. The three main contributions of this paper are the following: (1) a non-fragile guaranteed cost controller is presented for the fuzzy system with time-varying delay in both state and input; (2) some free-weighting matrices are introduced in the derivation process, where the constraint of the derivatives of time-delay, \n\n\n\n\nd\n˙\n\n\n(\nt\n)\n<\n1\n\n\n and \n\n\n\n\nh\n˙\n\n\n(\nt\n)\n<\n1\n\n\n, is eliminated; and (3) the delay-dependent stability conditions for the fuzzy system are described by LMIs. Finally, simulation examples are given to illustrate the effectiveness of the obtained results.
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The paper is organized as follows. Section 2 introduces the fuzzy delay system with local bilinear model, and non-fragile controller law for such system is designed based on the parallel distributed compensation approach in Section 3. Results of non-fragile guaranteed cost control are given in Section 4. Two simulation examples are used to illustrate the effectiveness of the proposed method in Section 5, which is followed by conclusions in Section 6.
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Notation: Throughout this paper, the notation P > 0(P ≥ 0) stands for P being real symmetric and positive definite (or positive semi-definite). In symmetric block matrices, the asterisk (*) refers to a term that is induced by symmetry, and diag{….} denotes a block-diagonal matrix. The superscript T means matrix transposition. The notion \n\n\n\n∑\n\ni\n,\nj\n=\n1\n\ns\n\n\n\n is an abbreviation of \n\n\n\n∑\n\ni\n=\n1\n\ns\n\n\n∑\n\nj\n=\n1\n\ns\n\n\n\n. Matrices, if the dimensions are not explicitly stated, are assumed to have compatible dimensions for algebraic operations.
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2. System description and assumptions
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In this section, we introduce the T-S fuzzy time-delay system with local bilinear model. The ith rule of the fuzzy system is represented by the following form:
where Fij is the fuzzy set, s is the number of fuzzy rules, x(t) ∈ Rn is the state vector, and u(t) ∈ R is the control input, ϑ1(t), ϑ2(t),…,ϑv(t) are the premise variables. It is assumed that the premise variables do not depend on the input u(t). \n\n\n\nA\ni\n\n,\n\nA\n\nd\ni\n\n\n,\n\nN\ni\n\n,\n\nN\n\nd\ni\n\n\n∈\n\nR\n\nn\n×\nn\n\n\n,\n\nB\ni\n\n,\n\nB\n\nh\ni\n\n\n∈\n\nR\n\nn\n×\n1\n\n\n\n\n denote the system matrices with appropriate dimensions. d(t) is a time-varying differentiable function that satisfies 0 ≤ d(t) ≤ τ1, 0 ≤ h(t) ≤ τ2, where τ1, τ2 are real positive constants as the upper bound of the time-varying delay. It is also assumed that \n\n\n\n\nd\n˙\n\n\n(\nt\n)\n≤\n\nσ\n1\n\n\n\n, \n\n\n\n\nh\n˙\n\n\n(\nt\n)\n≤\n\nσ\n2\n\n\n\n, and σ1, σ2 are known constants. The initial conditions φ(t), ϕ(t) are continuous functions of t, \n\n\nt\n∈\n[\n-\nτ\n,\n\n0\n]\n,\nτ\n=\nmin\n(\n\nτ\n1\n\n,\n\nτ\n2\n\n)\n\n\n.
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Remark 1: The fuzzy system with time-varying state and input delays will be investigated in this paper, which is different from the system in Ref. [17]. In Ref. [17], only state time-varying delay is considered. And also, here, we assume that the derivative of time-varying delay is less than or equal to a known constant that may be greater than 1; the assumption on time-varying delay in Ref. [17] is relaxed.
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By using singleton fuzzifier, product inferred and weighted defuzzifier, the fuzzy system can be expressed by the following globe model:
\n\n\n\n\nh\ni\n\n(\nϑ\n(\nt\n)\n)\n=\n\nω\ni\n\n(\nϑ\n(\nt\n)\n)\n/\n\n\n∑\n\ni\n=\n1\n\ns\n\n\n\nω\ni\n\n(\nϑ\n(\nt\n)\n)\n\n\n,\n\nω\ni\n\n(\nϑ\n(\nt\n)\n)\n=\n\n\n∏\n\nj\n=\n1\n\nv\n\n\n\nμ\n\ni\nj\n\n\n\n\n(\nϑ\n(\nt\n)\n)\n\n\n, μij (ϑ(t)) is the grade of membership of ϑi(t) in Fij. In this paper, it is assumed that \n\n\n\nω\ni\n\n(\nϑ\n(\nt\n)\n)\n≥\n0\n,\n\n\n∑\n\ni\n=\n1\n\ns\n\n\n\nω\ni\n\n(\nϑ\n(\nt\n)\n)\n>\n0\n\n\n\n\n for all t. Then, we have the following conditions hi(ϑ(t)) ≥ 0, \n\n\n\n\n∑\n\ni\n=\n1\n\ns\n\n\n\nh\ni\n\n(\nϑ\n(\nt\n)\n)\n=\n1\n\n\n\n\n for all t. In the consequent, we use abbreviation hi, hhi, xd(t), ud(t), xh(t), uh(t), to replace hi(ϑ(t)), hi(ϑ(t − h(t))), x(t − d(t)), u(t − d(t)), x(t − h(t)), u(t − h(t)), respectively, for convenience.
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The objective of this paper is to design a state-feedback non-fragile guaranteed cost control law for the fuzzy system (2).
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3. Non-fragile guaranteed cost controller design
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Extending the design concept in Ref. [17], we give the following non-fragile fuzzy control law:
where ρ > 0 is a scalar to be assigned, and Ki ∈ Rl×n is a local controller gain to be determined. ΔKi represents the additive controller gain perturbations of the form ΔKi = HiFi(t)Eki with Hi and Eki being known constant matrices, and Fi(t) the uncertain parameter matrix satisfying \n\n\n\nF\ni\n\n\n\n\nT\n\n(\nt\n)\n\nF\ni\n\n(\nt\n)\n≤\nI\n\n\n.\n\n\nsin\n\nθ\ni\n\n=\n\n\n\n\n\n\nK\n¯\n\n\ni\n\nx\n(\nt\n)\n\n\n\n\n1\n+\n\nx\nT\n\n\n\n\nK\n¯\n\n\ni\nT\n\n\n\n\nK\n¯\n\n\ni\n\nx\n\n\n\n\n\n\n\n, \n\n\ncos\n\nθ\ni\n\n=\n\n\n1\n\n\n\n1\n+\n\nx\nT\n\n\n\n\nK\n¯\n\n\ni\nT\n\n\n\n\nK\n¯\n\n\ni\n\nx\n\n\n\n\n\n\n\n, \n\n\n\nθ\ni\n\n∈\n[\n−\n\n\nπ\n2\n\n\n,\n\n\nπ\n2\n\n\n]\n\n\n, \n\n\n\n\n\nK\n¯\n\n\ni\n\n=\n\nK\ni\n\n+\nΔ\n\nK\ni\n\n(\nt\n)\n=\n\nK\ni\n\n+\n\nH\ni\n\n\nF\ni\n\n(\nt\n)\n\nE\n\nk\ni\n\n\n\n\n.
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The overall fuzzy control law can be represented by
where \n\n\nsin\n\nϕ\nl\n\n=\n\n\n\n\n\n\nK\n˜\n\n\nl\n\n\nx\nh\n\n(\nt\n)\n\n\n\n\n1\n+\n\nx\nh\nT\n\n\n\n\nK\n˜\n\n\nl\nT\n\n\n\n\nK\n˜\n\n\nl\n\n\nx\nh\n\n\n\n\n\n\n\n\n, \n\n\ncos\n\nϕ\nl\n\n=\n\n\n1\n\n\n\n1\n+\n\nx\nh\nT\n\n\n\n\nK\n˜\n\n\nl\nT\n\n\n\n\nK\n˜\n\n\nl\n\n\nx\nh\n\n\n\n\n\n\n\n\n, \n\n\n\nϕ\nl\n\n∈\n[\n−\n\n\nπ\n2\n\n\n,\n\n\nπ\n2\n\n\n]\n\n\n, \n\n\n\n\n\nK\n˜\n\n\nl\n\n=\n\nK\nl\n\n+\nΔ\n\nK\nl\n\n(\nt\n−\nh\n(\nt\n)\n)\n=\n\nK\nl\n\n+\n\nH\nl\n\n\nF\nl\n\n(\nt\n−\nh\n(\nt\n)\n)\n\nE\n\nk\nl\n\n\n\n\n.
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So, it is natural and necessary to make an assumption that the functions hi are well defined all t ∈ [−τ2, 0], and satisfy the following properties:
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\n\n\n\n\nh\ni\n\n(\nϑ\n(\nt\n−\nh\n(\nt\n)\n)\n)\n≥\n0\n\n\n, for i = 1,2,…,s, and \n\n\n\n∑\n\ni\n=\n1\n\ns\n\n\nh\ni\n\n(\nϑ\n(\nt\n−\nh\n(\nt\n)\n)\n)\n=\n1\n\n\n.
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By substituting Eq. (5) into Eq. (2), the closed-loop system can be given by
Definition 1. The fuzzy non-fragile control law u(t) is said to be non-fragile guaranteed cost if for the system (2), there exist control laws (4) and (5) and a scalar J0 such that the closed-loop system (6) is asymptotically stable and the closed-loop value of the cost function (7) satisfies J ≤ J0.
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4. Analysis of stability for the closed-loop system
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Firstly, the following lemmas are presented which will be used in the paper.
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Lemma 1 [20]: Given any matrices Mand N with appropriate dimensions such that ε > 0, we have MTN + NT M ≤ εMTM + ε−1NTN.
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Lemma 2 [21]: Given constant matrices G, Eand a symmetric constant matrix Sof appropriate dimensions. The inequality S + GFE + ETFTGT < 0 holds, where F(t) satisfies FT(t) F(t) ≤ I if and only if, for some ε > 0, S + εGGT+ ε−1ETE < 0.
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The following theorem gives the sufficient conditions for the existence of the non-fragile guaranteed cost controller for system (6) with additive controller gain perturbations.
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Theorem 1.Consider system (6) associated with cost function (7). For given scalars ρ > 0, τ1 > 0, τ2 > 0, σ1 > 0, σ2 > 0, if there exist matrices P > 0, Q1 > 0, Q2 > 0, R1 > 0, R2 > 0, Ki, i = 1, 2,…, s, X1, X2, X3, X4, Y1, Y2, Y3, Y4, and scalar ε > 0 satisfying the inequalities (8), the system (6) is asymptotically stable and the control law (5) is a fuzzy non-fragile guaranteed cost control law, moreover,
Define the free-weighting matrices as \n\n\nX\n=\n\n\n[\n\n\n\n\n\nX\n1\nT\n\n\n\n\n\n\nX\n2\nT\n\n\n\n\n\n\nX\n3\nT\n\n\n\n\n\n\nX\n4\nT\n\n\n\n\n\n]\n\nT\n\n\n\n, \n\n\nY\n=\n\n\n[\n\n\n\n\n\nY\n1\nT\n\n\n\n\n\n\nY\n2\nT\n\n\n\n\n\n\nY\n3\nT\n\n\n\n\n\n\nY\n4\nT\n\n\n\n\n\n]\n\nT\n\n,\n\n\n\n\n\nZ\n=\n\n\n[\n\n\n\n\n\nZ\n1\nT\n\n\n\n\n\n\nZ\n2\nT\n\n\n\n\n\n\nZ\n3\nT\n\n\n\n\n\n\nZ\n4\nT\n\n\n\n\n\n]\n\nT\n\n\n\n, where Xk ∈ Rn×n, Yk ∈ Rn×n, Zk ∈ Rn×n, k = 1, 2, 3, 4 will be determined later.
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Using the Leibniz-Newton formula and system equation (6), we have the following identical equations:
where \n\n\nη\n(\nt\n)\n=\n\n\n[\n\nx\nT\n\n(\nt\n)\n,\n\n\nx\nd\nT\n\n(\nt\n)\n,\n\n\nx\nh\nT\n\n(\nt\n)\n,\n\n\n\n\nx\n˙\n\n\nT\n\n(\nt\n)\n]\n\nT\n\n\n\n.
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Applying Lemma 1, we have the following inequalities:
In light of the inequality \n\n\n\n\n\nK\n¯\n\n\ni\nT\n\nW\n\n\n\nK\n¯\n\n\nj\n\n\n\n+\n\n\n\nK\n¯\n\n\nj\nT\n\nW\n\n\n\nK\n¯\n\n\ni\n\n\n\n≤\n\n\n\nK\n¯\n\n\ni\nT\n\nW\n\n\n\nK\n¯\n\n\ni\n\n\n\n+\n\n\n\nK\n¯\n\n\nj\nT\n\nW\n\n\n\nK\n¯\n\n\nj\n\n\n\n\n\n, we have
Because of V (x(t),t) ≥ 0 and \n\n\n\n\nV\n˙\n\n\n(\nx\n(\nt\n)\n,\nt\n)\n<\n0\n\n\n, thus \n\n\n\n\n\nlim\n\n\nT\n→\n∞\n\n\n\nV\n(\nx\n(\nT\n)\n,\nT\n)\n=\nc\n,\n\n\n where c is a nonnegative constant. Therefore, the following inequality can be obtained:
Remark 2: In the derivation of Theorem 1, the free-weighting matrices Xk ∈ Rn×n, Yk ∈ Rn×n, k = 1, 2, 3, 4 are introduced, the purpose of which is to reduce conservatism in the existing delay-dependent stabilization conditions, see Ref. [17].
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In the following section, we shall turn the conditions given in Theorem 1 into linear matrix inequalities (LMIs). Under the assumptions that Y1, Y2, Y3, Y4 are non-singular, we can define the matrix \n\n\n\nY\ni\n\n\n\n\n\n−\nT\n\n\n=\nλ\nZ\n\n\n, i = 1, 2, 3, 4, Z = P−1,λ > 0.
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Pre- and post-multiply (8) and (9) with \n\n\nΘ\n=\nd\ni\na\ng\n{\n\nY\n1\n\n−\n1\n\n\n,\n\nY\n2\n\n−\n1\n\n\n,\n\nY\n3\n\n−\n1\n\n\n,\n\nY\n4\n\n−\n1\n\n\n,\n\nY\n4\n\n−\n1\n\n\n,\n\nY\n4\n\n−\n1\n\n\n}\n\n\n and \n\n\n\nΘ\nT\n\n=\nd\ni\na\ng\n{\n\nY\n1\n\n−\nT\n\n\n,\n\nY\n2\n\n−\nT\n\n\n,\n\nY\n3\n\n−\nT\n\n\n,\n\nY\n4\n\n−\nT\n\n\n,\n\nY\n4\n\n−\nT\n\n\n,\n\nY\n4\n\n−\nT\n\n\n}\n\n\n, respectively, and letting \n\n\n\n\n\nQ\n¯\n\n\n1\n\n=\n\nY\n1\n\n\n\n\n\n−\n1\n\n\n\nQ\n1\n\n\nY\n1\n\n\n\n\n\n−\nT\n\n\n\n\n, \n\n\n\n\n\nQ\n¯\n\n\n2\n\n=\n\nY\n1\n\n\n\n\n\n−\n1\n\n\n\nQ\n2\n\n\nY\n1\n\n\n\n\n\n−\nT\n\n\n\n\n, \n\n\n\n\n\nR\n¯\n\n\nk\n\n=\n\nY\n4\n\n\n\n\n\n−\n1\n\n\n\nR\nk\n\n\nY\n4\n\n\n\n\n\n−\nT\n\n\n,\nk\n=\n1\n,\n2\n,\n\n\n\n\nX\n¯\n\n\n\ni\n\n=\n\nY\ni\n\n\n\n\n\n−\n1\n\n\n\nX\ni\n\n\nY\ni\n\n\n\n\n\n−\nT\n\n\n,\n\n\n\nZ\n¯\n\n\ni\n\n=\n\nY\ni\n\n\n\n\n\n−\n1\n\n\n\nZ\ni\n\n\nY\ni\n\n\n\n\n\n−\nT\n\n\n\n\n, i = 1, 2, 3, 4, we obtain the following inequality (18), which is equivalent to (8):
Obviously, the closed-loop fuzzy system (6) is asymptotically stable, if for some scalars λ > 0, there exist matrices \n\n\nZ\n>\n0\n,\n\n\nQ\n¯\n\n\n>\n0\n,\n\n\nR\n¯\n\n\n>\n0\n\n\n and \n\n\n\n\n\nX\n¯\n\n\n1\n\n,\n\n\n\nX\n¯\n\n\n2\n\n,\n\n\n\nX\n¯\n\n\n3\n\n,\n\n\n\nK\n¯\n\n\ni\n\n,\ni\n=\n1\n,\n2\n,\n..\n,\ns\n\n\n satisfying the inequality (19).
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Theorem 2.Consider the system (6) associated with cost function (7). For given scalars ρ > 0, τ1 > 0, τ2 > 0, σ1 > 0, σ2 > 0 and λ > 0, δ > 0, if there exist matrices \n\n\nZ\n>\n0\n,\n\n\n\nQ\n¯\n\n\n1\n\n>\n0\n,\n\n\n\nR\n¯\n\n\n1\n\n>\n0\n,\n\n\n\nQ\n¯\n\n\n2\n\n>\n0\n,\n\n\n\nR\n¯\n\n\n2\n\n>\n0\n\n\n and \n\n\n\n\n\nX\n¯\n\n\n1\n\n,\n\n\n\nX\n¯\n\n\n2\n\n,\n\n\n\nX\n¯\n\n\n3\n\n,\n\n\n\nX\n¯\n\n\n4\n\n,\n\n\n Mi, i = 1,2,…,s and scalar ε > 0 satisfying the following LMI (20), the system (6) is asymptotically stable and the control law (5) is a fuzzy non-fragile guaranteed cost control law
where \n\n\nΔ\n\n\n\nK\n˜\n\n\ni\n\n=\nΔ\n\nK\ni\n\n(\nt\n−\nd\n(\nt\n)\n)\n\n\n.
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Therefore, it follows from Theorem 1 that the system (6) is asymptotically stable and the control law (5) is a fuzzy non-fragile guaranteed cost control law. Thus, we complete the proof.
Similar to Ref. [23], we supposed that there exist positive scalars α1, α2, α3, α4, α5, such that \n\n\n\nZ\n\n−\n1\n\n\n≤\n\nα\n1\n\nI\n,\n\n1\n\n\nλ\n2\n\n\n\nP\n\n\n\nQ\n¯\n\n\n1\n\nP\n≤\n\nα\n2\n\nI\n,\n\n1\n\n\nλ\n2\n\n\n\nP\n\n\n\nQ\n¯\n\n\n2\n\nP\n≤\n\nα\n3\n\nI\n,\n\n1\n\n\nλ\n2\n\n\n\nP\n\n\n\nR\n¯\n\n\n1\n\nP\n≤\n\nα\n4\n\nI\n,\n\n1\n\n\nλ\n2\n\n\n\nP\n\n\n\nR\n¯\n\n\n2\n\nP\n≤\n\nα\n5\n\nI\n\n\n.
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Then, define \n\n\n\nS\n\nQ\n1\n\n\n=\n\n\n\nQ\n¯\n\n\n1\n\n\n\n\n\n−\n1\n\n\n,\n\nS\n\nQ\n2\n\n\n=\n\n\n\nQ\n¯\n\n\n2\n\n\n\n\n\n−\n1\n\n\n,\n\nS\n\nR\n1\n\n\n=\n\n\n\nR\n¯\n\n\n1\n\n\n\n\n\n−\n1\n\n\n,\n\nS\n\nR\n2\n\n\n=\n\n\n\nR\n¯\n\n\n2\n\n\n\n\n\n−\n1\n\n\n\n\n, by Schur complement lemma, we have the following inequalities:
Using the idea of the cone complement linear algorithm in Ref. [24], we can obtain the solution of the minimization problem of upper bound of the value of the cost function as follows:
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\n\n\n\n\nminimize\n\n{\n\nt\nr\na\nc\ne\n(\nP\nZ\n+\n\nS\n\nQ\n1\n\n\n\n\n\nQ\n¯\n\n\n1\n\n+\n\nS\n\nQ\n2\n\n\n\n\n\nQ\n¯\n\n\n2\n\n+\n\nS\n\nR\n1\n\n\n\n\n\nR\n¯\n\n\n1\n\n+\n\nS\n\nR\n2\n\n\n\n\n\nR\n¯\n\n\n2\n\n+\n\nα\n1\n\n\nx\nT\n\n(\n0\n)\nx\n(\n0\n)\n+\n\nα\n2\n\n\n\n\n∫\n\n−\nd\n(\n0\n)\n\n0\n\n\n\nx\nT\n\n(\ns\n)\nx\n(\ns\n)\n\n\n\nd\ns\n\n\n\n\n\n\n+\n\nα\n4\n\n\n\n\n∫\n\n−\n\nτ\n1\n\n\n0\n\n\n\n\n\n∫\nθ\n0\n\n\n\n\n\nx\n˙\n\n\nT\n\n(\ns\n)\n\n\nx\n˙\n\n\n(\ns\n)\nd\ns\nd\nθ\n\n\n\n\n\n\n+\n\nα\n3\n\n\n\n\n∫\n\n−\nh\n(\n0\n)\n\n0\n\n\n\nx\nT\n\n(\ns\n)\nx\n(\ns\n)\n\n\n\nd\ns\n+\n\nα\n5\n\n\n\n\n∫\n\n−\n\nτ\n2\n\n\n0\n\n\n\n\n\n∫\nθ\n0\n\n\n\n\n\n\n\nx\n˙\n\n\nT\n\n(\ns\n)\n\n\nx\n˙\n\n\n(\ns\n)\nd\ns\nd\nθ\n\n}\n\n\n\n\n\n\n\n\n\n\n\nsubject to (20),(23), \nε\n>0,\n\n\n\nQ\n¯\n\n\n1\n\n>\n0\n,\n\n\n\nQ\n¯\n\n\n2\n\n>\n0\n,\n\n\n\nR\n¯\n\n\n1\n\n>\n0\n,\n\n\n\nR\n¯\n\n\n2\n\n>\n0\n,\nZ\n>\n0\n,\n\nα\ni\n\n>\n0\n,\ni\n=\n1\n,\n…\n,\n5\n\n\n\n\n\n\nE24
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Using the following cone complement linearization (CCL) algorithm [24] can iteratively solve the minimization problem (24). □
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\n
\n
5. Simulation examples
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In this section, the proposed approach is applied to the Van de Vusse system to verify its effectiveness.
\n
Example: Consider the dynamics of an isothermal continuous stirred tank reactor for the Van de Vusse
From the system equation (25), some equilibrium points are tabulated in Table 1. According to these equilibrium points, [xeue], which are also chosen as the desired operating points, \n\n\n[\n\n\nx\n′\n\ne\n\n\n\n\nu\n′\n\ne\n\n]\n\n\n, we can use the similar modeling method that is described in Ref. [16].
The cost function associated with this system is given with \n\n\nS\n=\n\n[\n\n\n\n\n1\n\n\n0\n\n\n\n\n0\n\n\n1\n\n\n\n\n]\n\n,\nW\n=\n1\n\n\n. The controller gain perturbation ΔK of the additive form is give with H1 = H2 = H3 = 0.1, Ek1 = [0.05 −0.01], Ek2 = [0.02 0.01], Ek3 = [−0.01 0].
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The membership functions of state x1 are shown in Figure 1.
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Figure 1.
Membership functions.
\n
Then, solving LMIs (23) and (24) for ρ = 0.45, λ = 1.02 and \n\n\nδ\n=\n0.11\n,\n\nτ\n1\n\n=\n\nτ\n2\n\n=\n2\n,\n\nσ\n1\n\n=\n0\n,\n\nσ\n2\n\n=\n0\n\n\n gives the following feasible solution:
Figures 2–4 illustrate the simulation results of applying the non-fragile fuzzy controller to the system (25) with \n\n\n\n\nx\n′\n\ne\n\n=\n\n\n[\n\n\n\n\n3\n.6626\n\n\n\n\n2\n.5443\n\n\n\n\n]\n\nT\n\n\n\n and \n\n\n\n\nu\n′\n\ne\n\n=\n77\n.7272\n\n\n under initial condition ϕ(t) = [1.2 −1.8]T, t ∈ [−2 0]. It can be seen that with the fuzzy control law, the closed-loop system is asymptotically stable and an upper bound of the guaranteed cost is J0 = 292.0399. The simulation results show that the fuzzy non-fragile guaranteed controller proposed in this paper is effective.
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Figure 2.
State responses of x1(t).
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Figure 3.
State responses of x2(t).
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Figure 4.
Control trajectory of system.
\n
\n
\n
6. Conclusions
\n
In this paper, the problem of non-fragile guaranteed cost control for a class of fuzzy time-varying delay systems with local bilinear models has been explored. By utilizing the Lyapunov stability theory and LMI technique, sufficient conditions for the delay-dependent asymptotically stability of the closed-loop T-S fuzzy local bilinear system have been obtained. Moreover, the designed fuzzy controller has guaranteed the cost function-bound constraint. Finally, the effectiveness of the developed approach has been demonstrated by the simulation example. The robust non-fragile guaranteed cost control and robust non-fragile H-infinite control based on fuzzy bilinear model will be further investigated in the future work.
\n
\n
Acknowledgments
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This work is supported by NSFC Nos. 60974139 and 61573013.
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\n',keywords:"fuzzy control, non-fragile guaranteed cost control, delay-dependent, linear matrix inequality (LMI), T-S fuzzy bilinear model",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/56382.pdf",chapterXML:"https://mts.intechopen.com/source/xml/56382.xml",downloadPdfUrl:"/chapter/pdf-download/56382",previewPdfUrl:"/chapter/pdf-preview/56382",totalDownloads:851,totalViews:121,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:"November 1st 2016",dateReviewed:"May 16th 2017",datePrePublished:null,datePublished:"August 30th 2017",dateFinished:null,readingETA:"0",abstract:"This paper focuses on the non-fragile guaranteed cost control problem for a class of Takagi-Sugeno (T-S) fuzzy time-varying delay systems with local bilinear models and different state and input delays. A non-fragile guaranteed cost state-feedback controller is designed such that the closed-loop T-S fuzzy local bilinear control system is delay-dependent asymptotically stable, and the closed-loop fuzzy system performance is constrained to a certain upper bound when the additive controller gain perturbations exist. By employing the linear matrix inequality (LMI) technique, sufficient conditions are established for the existence of desired non-fragile guaranteed cost controllers. The simulation examples show that the proposed approach is effective and feasible.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/56382",risUrl:"/chapter/ris/56382",book:{slug:"modern-fuzzy-control-systems-and-its-applications"},signatures:"Junmin Li, Jinsha Li and Ruirui Duan",authors:[{id:"153140",title:"Prof.",name:"Junmin",middleName:null,surname:"Li",fullName:"Junmin Li",slug:"junmin-li",email:"jmli@mail.xidian.edu.cn",position:null,institution:{name:"Xi'an University of Science and Technology",institutionURL:null,country:{name:"China"}}},{id:"200134",title:"Dr.",name:"Guo",middleName:null,surname:"Zhang",fullName:"Guo Zhang",slug:"guo-zhang",email:"gzhang@126.com",position:null,institution:null},{id:"200136",title:"Dr.",name:"Jinsha",middleName:null,surname:"Li",fullName:"Jinsha Li",slug:"jinsha-li",email:"jinsha@126.com",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. System description and assumptions",level:"1"},{id:"sec_3",title:"3. Non-fragile guaranteed cost controller design",level:"1"},{id:"sec_4",title:"4. Analysis of stability for the closed-loop system",level:"1"},{id:"sec_5",title:"5. Simulation examples",level:"1"},{id:"sec_6",title:"6. Conclusions",level:"1"},{id:"sec_7",title:"Acknowledgments",level:"1"}],chapterReferences:[{id:"B1",body:'Pang CT, Lur YY. On the stability of Takagi-Sugeno fuzzy systems with time-varying uncertainties. IEEE Transactions on Fuzzy Systems. 2008;16:162–170\n'},{id:"B2",body:'Zhou SS, Lam J, Zheng WX. Control design for fuzzy systems based on relaxed non-quadratic stability and H∞ performance conditions. IEEE Transactions on Fuzzy Systems. 2007;15:188–198\n'},{id:"B3",body:'Zhou SS, Li T. Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov-Krasovskii function. Fuzzy Sets and Systems. 2005;151:139–153\n'},{id:"B4",body:'Gao HJ, Liu X, Lam J. 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Stabilization for state/input delay systems via static and integral output feedback. Automatica. 2010;46:2000–2007\n'},{id:"B28",body:'Kim JH. Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays. International Journal of Control, Automation, and Systems. 2009;7:357–364\n'},{id:"B29",body:'Li L, Liu XD. New approach on robust stability for uncertain T–S fuzzy systems with state and input delays. Chaos, Solitons and Fractals. 2009;40:2329–2339\n'},{id:"B30",body:'Yu KW, Lien CH. Robust H-infinite control for uncertain T–S fuzzy systems with state and input delays. Chaos, Solitons and Fractals. 2008;37:150–156\n'},{id:"B31",body:'Yue D, Lam J. Non-fragile guaranteed cost control for uncertain descriptor systems with time-varying state and input delays. Optimal Control Applications and Methods. 2005;26:85–105\n'},{id:"B32",body:'Zhang G, Li JM. Non-fragile guaranteed cost control of discrete-time fuzzy bilinear system with time-delay. Journal of Dynamic Systems, Measurement and Control. 2014;136:044502–044504\n'},{id:"B33",body:'Yue HY, Li JM. Output-feedback adaptive fuzzy control for a class of nonlinear systems with input delay and unknown control directions. Journal of the Franklin Institute. 2013;350:129–154\n'},{id:"B34",body:'Yue HY, Li JM. Adaptive fuzzy tracking control for a class of perturbed nonlinear time-varying delays systems with unknown control direction. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems. 2013;21:497–531\n'},{id:"B35",body:'Wang RJ, Lin WW, Wang WJ. Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems. IEEE Transactions on Systems, Man, Cybernetics, Part B. 2004;34:1288–1292\n'},{id:"B36",body:'Xia ZL, Li JM, Li JR. Delay-dependent fuzzy static output feedback control for discrete-time fuzzy stochastic systems with distributed time-varying delays. ISA Transaction. 2012;51:702–712\n'},{id:"B37",body:'Xia ZL, Li JM. Switching fuzzy filtering for nonlinear stochastic delay systems using piecewise Lyapunov-Krasovskii function. International Journal of Fuzzy Systems. 2012;14:530–539\n'},{id:"B38",body:'Li JR, Li JM, Xia ZL. Delay-dependent generalized H2 fuzzy static-output-feedback control for discrete T-S fuzzy bilinear stochastic systems with mixed delays. Journal of Intelligent and Fuzzy Systems. 2013;25:863–880\n'},{id:"B39",body:'Xia ZL, Li JM, Li JR. Passivity-based resilient adaptive control for fuzzy stochastic delay systems with Markovian switching. Journal of the Franklin Institute-Engineering and Applied Mathematics. 2014;351:3818–3836\n'},{id:"B40",body:'Li JM, Li YT. Robust stability and stabilization of fractional order systems based on uncertain T-S fuzzy model with the fractional order. Journal of Computational and Nonlinear Dynamics. 2013;8:041005\n'},{id:"B41",body:'Li YT, Li JM. Stability analysis of fractional order systems based on T-S fuzzy model with the fractional order α: 0<α<1. Nonlinear Dynamics. 2014;78:2909–2919\n'},{id:"B42",body:'Li YT, Li JM. Decentralized stabilization of fractional order T-S fuzzy interconnected systems with multiple time delays. Journal of Intelligent and Fuzzy Systems. 2016;30:319–331\n'},{id:"B43",body:'Li JM, Yue HY. Adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time-varying delays. Applied Mathematics and Computation. 2015;256:514–528\n'},{id:"B44",body:'Yue HY, Yu SQ. Adaptive fuzzy tracking control for a class of stochastic nonlinearly parameterized systems with distributed input delay. Journal of the Franklin Institute-Engineering and Applied Mathematics. 2016;353:713–734\n'},{id:"B45",body:'Duan RR, Li JM, Zhang YN, Yang Y, Chen GP. Stability analysis and H-inf control of discrete T-S fuzzy hyperbolic systems. International Journal of Applied Mathematics and Computer Science. 2016;26:133–145\n'},{id:"B46",body:'Wang JX, Li JM. Stability analysis and feedback control of T-S fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay. Iranian Journal of Fuzzy Systems. 2016;13:111–134\n'},{id:"B47",body:'Li JR, Li JM, Xia ZL. Observer-based fuzzy control design for discrete time T-S fuzzy bilinear systems. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems. 2013;21:435–454\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Junmin Li",address:"jmli@mail.xidian.edu.cn",affiliation:'
School of Mathematics and Statistics, Xidian University, Xi’an, PR China
School of Mathematics and Statistics, Xidian University, Xi’an, PR China
'}],corrections:null},book:{id:"5883",title:"Modern Fuzzy Control Systems and Its Applications",subtitle:null,fullTitle:"Modern Fuzzy Control Systems and Its Applications",slug:"modern-fuzzy-control-systems-and-its-applications",publishedDate:"August 30th 2017",bookSignature:"S. 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1. Introduction
Ethiopia is not only rich in sheep population but also rich in sheep genetic diversity, which developed by natural selection and potential genetic resources of sheep breeds [1]. In the highlands of the country, about 75% of sheep population are found, while the remaining 25% are distributed in the lowlands [2]. Sheep production is a major component of the livestock sector in Ethiopia, owing to the large population of 30.70 million sheep are estimated to be found in the country, out of which about 72.14% are females, and about 27.86% are males [3]. The small ruminants account for 40% of cash income earned by farm households, 19% of the total value of subsistence food derived from all livestock production, and 25% of total domestic meat consumption [4]. Smallholder sheep production is the major source of food security serving a diverse function, including cash income, savings, fertilizer, socio-cultural functions and fiber production. Sheep are particularly important for farmers in the subalpine highlands and pastoralist/agropastoralist where crop production is unreliable. Moreover, despites its socio-cultural importance, sheep resources significantly contributed for foreign currency earning accounting for the live animal exports [1].
The cool highland sheep production systems in most highland areas are characterized by erratic and unevenly distributed rainfall, recurrent drought, and scarcity in livestock feeds and feed that is poor in quality [5]. In those production environments, the role of sheep in supporting the livelihood of smallholder farmers is increasing due to recurrent crop failure [5, 6]. However, the sheep flocks are managed under traditional extensive systems with no or minimal inputs and improved technologies, which results in low productivity. They depend on natural pasture and fibrous crop residues for their survival, growth and reproduction. The available natural pasture lands are overloaded with livestock beyond optimum carrying capacity that has resulted in overgrazing and land degradation [7, 8]. This indicated the critical need of supplemental feed during the feed-deficient period and wise management of communal and private natural pasture grazing. A limited supply of nutrients in the sheep’s diet can lead to weight loss, low fertility, high mortality, increased risk of disease and poor wool growth. Sheep need a balanced diet containing energy (fat and carbohydrates), protein, vitamins, minerals, and water. Sheep and goat production in Ethiopia suffers feed shortages at all levels with an estimated 40% deficit in the national feed balance. This is aggravated by seasonal availability of forage and crop residues in the highlands and by recurrent and prolonged drought in the lowlands.
Therefore, the study was accomplished on, assessment of productive performance through on-station feedlot based and natural pasture grazing weight gain performance and carcass yield characteristics evaluation of indigenous Wollo highland sheep breed and their F1 crossbreds with 75% Awassi and pure indigenous Washera breed rams.
The specific objectives of the study are:
to evaluate on-station feedlot weight gain and carcass yield characteristics of Wollo highland sheep and their F1 crossbreds of Awassi and Washera sheep breeds.
to assess natural grass grazing value as basal diet for the study breeds supplemented by concentrated feed.
2. Material and methods
2.1 Description of the study area
This research was conducted from 2018 to 2019 in the two selected areas of Dessie Zuria and Kutaber districts in South Wollo Zone of Amhara Region, Ethiopia. The geographical location of South Wollo Zone is delimited with North Shewa and Oromia region in the Southern part, East Gojjam in the West, South Gondar in the Northwest, North Wollo in the North, Afar Region in the Northeast and Argobba district of the Oromia Zone in the Eastern part (Figure 1).
2.2 Experimental design and treatments
A 3 × 2 factorial experimental design arrangement of three genotype and two feeding type factors with six treatment levels (three genotypes by two feeding type’s combinations) and six replications were used. The three genotypes belonging to 50% Awassi F1 crosses, 50% Washera F1 crosses and 100% local Wollo highland lambs were grouped in to three by their genotypes and in to two by their feeding types of supplemented and non-supplemented groups for each genotypes. The supplemented and non-supplemented feeding types randomly assigned for each 36 experimental animals.
Both supplemented and non-supplemented groups grazed for 8 hours/day as a basal diet with rotational grazing system and animal holding of 36 sheep/0.5 ha paddock/day. The supplemented group fed at the rate of 1% of their body weight/day of concentrate mix diet, whereas the non-supplemented group fed only natural pasture grazing area for 8 hours/day from 8:00 AM to 5:30 PM with a 1 hour rest from 12:30 AM to 1:30 PM and had free access of drinking water.
2.3 Experimental animals grazing management
The grazing land characterized by both annual and perennial grass such as Cyperus rotundus, Dactylis glomerata Cynodon nlemfuensis, Cynodon dactylon, Cyperus polystachyos and Urochloa brizantha (Table 1). The size of natural pasture grazing area was 2.5 ha of land and that sub-divided into five paddocks with each individual paddock size was 0.5 ha.
Figure 1.
Description of the study area.
Local name
Scientific name
Growth form
Akirma
Cynodon nlemfuensis
Grass—perennial
Tult
Asarum canadense
Herb—annual
Sindedo
Urochloa brizantha
Grass—perennial
Serdo
Cynodon dactylon
Grass—annual
Gicha
Cyperus rotundus
Grass—annual
Gazia
Dactylis glomerata L.
Grass—perennial
Arintata
Trifolium repens
Herb—annual
Others
—
—
Muja
Snowdenia polystachya
Grass—annual
Gudign
Dichondra repens
Herb—annual
Ketema
Cyperus polystachyos
Grass—perennial
Bare land
—
—
Table 1.
Species composition of private owned natural pasture grass land.
2.4 Body weight gain and linear body measurements
Lambs were weighed at 15 days of interval for 1 year in the last week of each month using a 0.1 kg precision scale. Lambs were weighed at birth and fortnightly thereafter up to weaning. After weaning at the age of about 90 days they were weighed in 15 days interval together with the rest of the flock. Lamb body weights were adjusted by age.
The average daily weight gain (ADG) was calculated using the following formula at on-farm growth performance study:
ADG=dW2Kg+W1KgA∗1000E1
where ADG g = average daily gain in gram, W1 kg = birth weight or weight at the preceding age, W2 kg = weight at a given age, and A = age in days or days between weighing dates.
Average daily gain was calculated for the following stages of growth: (a) pre-weaning weight average daily gain (PreADG) ADG = birth to 90 days of age, (b) post-weaning weight average daily gain (PoADG) = birth to 365 days of age, and (c) weaning weight = at average body weight at 90 days.
Average daily weight gain of ram lambs in the on-station growth performance evaluation was also calculated using the following formula:
ADG=FWTKg+IWTKgAD∗100E2
where FWT = final body weight, IWT = initial body weight, and D = number of fattening days.
Linear body measurements were taken together with 3 months of interval measurements (from 3 months of age to 12 months). All body measurements were taken with a measuring tape in centimeter and measured to the nearest 0.5 cm. Linear body measurements traits were taken: (a) heart girth is the circumference of the chest posterior to the forelegs at right angles to the body axis, (b) wither height is the highest point measured as the vertical distance from the top of the shoulder to the ground, (c) body length is the distance between the crown and the sacrococcygeal joint, (d) tail width is directly behind the tuber ichiad, and (e) tail circumference is directly behind the tuber ichiad.
Model 1. On-station growth of initial and final body weight, average daily gain (ADG) of ram lambs (9 months–365 days of age):
Yijklm=μ+Bi+Fl+Bi×Flijm+eijklmE3
where Yijklm = average daily gain (ADG) and body weight change, μ = overall mean, Bi = fixed effect of the ith breed (i = Awassi F1 crossbred, Washera F1 crossbred and local Wollo highland breed), Fl = fixed effect of the feeding type (1 = supplemented, 2 = non-supplemented), (Bi × Fl)il = breed by feeding type interaction effect and eil = effect of the nth random error.
Model 2. Weight and linear body measurements of male lambs (90–365 days of age):
Yij=μ+Bi+Btj+eijE4
where Yij = body weight and linear body measurements at 90, 180, 270 and 365 days of age, μ = overall mean, Bi = fixed effect of the ith breed (i = Awassi F1 crossbred, Washera F1 crossbred and local Wollo highland breed), Btj = fixed effect of the jth birth type (j = single, twins), eij = effect of the oth random error.
Model 3. Body weight gain, carcass and non-carcass parameters:
Yijk=μ+Bi+Fj+Wk+eijk,E5
where Yijk = body weight gain, carcass and non-carcass parameter, μ = mean, Bi = effect of the ith breed (i = Awassi F1 crossbred, Washera F1 crossbred and local Wollo highland breed), Fj = the fixed effect of feeding type (j = supplemented, non-supplemented), Wk = the random effect of body weight (k = birth weight, pre-weaning weight ADG, weaning weight, post-weaning weight ADG and yearling weight, empty body weight, pre-slaughter weight), eijk = effect of the kth random error.
2.5 Data analysis
According to a 3 × 2 factorial statistical designs of the breed and diet as main effects and the PROC GLM of multivariate analysis package of the SAS Windows 9.0-2004 system used for those data fitted with the main factors of breed, feeding type, sex, birth type and parity effects on body weight gain response variable in the model. Initial body weight was also used as a covariate factor in the model to control the residual effects of initial body weight on consecutive rate of body weight gain. The dependent variables include body weight, average daily weight gain, survival rates, linear body measurements, reproductive traits and carcass yield characteristic parameters were considered in the GLM multivariate analysis of variance. The stepwise procedure of Pearson correlation of the SAS system was used to see the effects of association between body weight and linear body measurement traits. Tukey’s standardized range significance test was used to compare the different groups of mean.
3. Results
3.1 Effects of genotype and supplementation feed on ram lambs growth rate
Genotype and supplementation diet effect on ram lambs’ average body weight and their daily weight gain is presented in Table 2. Initial body weight had significant (p < 0.05) difference between genotypes and used in the covariate analysis model to avoid its residual effect on consecutive body weight gain and to quantify the genotype effect. However, it has non-significant difference within genotypes. The between and within genotype variations were continued throughout 10, 20 and 30 days experimental period except supplemented Washera F1 crossbreds and Wollo highland breed lambs and which were significantly higher than their non-supplemented group at 10 and 20 days treatment period, respectively. Despite the fact that at 30, 40, 50 and 60 days of feed treatment period the supplemented group of Wollo highland breed lambs had non-significant differences with both supplemented and non-supplemented Washera crossbred lambs and between breed variation eliminated. At 40 and 50 days, treatment period, except Wollo highland lambs the other genotypes have insignificant differences between supplemented and non-supplemented groups. Conversely, at 60 days of treatment period supplemented Wollo highland breed lambs had non-significant variation with both supplemented and non-supplemented Washera F1 crossbred lambs and vice versa. Awassi F1 crossbred lambs significantly (p < 0.05) higher average weight gain than both Wollo highland and Washera F1 cross ram lambs throughout the experimental period (Table 2).
Awassi genotype
Wollo genotype
Washera genotype
ABW (kg)
T1
T2
T1
T2
T1
T2
Sig.L
IBW
31.6 ± 1.0a
31.5 ± 0.8a
21.9 ± 0.7b
21.4 ± 0.5b
26.4 ± 0.7c
26.6 ± 0.7c
***
10 days
33.4 ± 0.9a
34.0 ± 0.9a
26.9 ± 0.9b
24.5 ± 0.9b
29.0 ± 0.5c
27.5 ± 0.5d
*
20 days
33.3 ± 1.1a
34.1 ± 1.1a
26.6 ± 1.1c
24.2 ± 1.1b
28.8 ± 0.6c
26.9 ± 0.6c
*
30 days
36.7 ± 1.3a
36.9 ± 1.3a
28.4 ± 1.3b,c
26.3 ± 1.3b
30.3 ± 0.7c
29.0 ± 0.7c
*
40 days
37.8 ± 1.3a
37.7 ± 1.3a
29.3 ± 1.3b
27.0 ± 1.3d
30.6 ± 0.7c
29.2 ± 0.7c
*
50 days
38.3 ± 1.7a
36.1 ± 1.7b
30.8 ± 1.7c,e
28.4 ± 1.7d
31.1 ± 0.9e
29.4 ± 0.9c,d
*
60 days
38.8 ± 1.8a
35.8 ± 1.8b
32.4 ± 1.7c
29.8 ± 1.8d
32.1 ± 1.0c
29.9 ± 1.0d
**
70 days
39.9 ± 1.8a
37.3 ± 1.8b
33.3 ± 1.8d
30.4 ± 1.8c
32.2 ± 1.0c,d
30.6 ± 1.0e,c
**
80 days
41.4 ± 1.8a
38.2 ± 1.8b
34.4 ± 1.8c
31.1 ± 1.8d
33.1 ± 1.0c
31.3 ± 1.0d
**
FBW
45.5 ± 1.4a
42.4 ± 1.4b
35.2 ± 1.3c
31.6 ± 1.4d
34.4 ± 0.7c
32.4 ± 0.7d
***
BWC
16.1 ± 1.1a
13.4 ± 1.1b
8.9 ± 1.1c
7.5 ± 1.1d
6.0 ± 0.6e
5.9 ± 0.6e
**
ADG (g)
178.5 ± 12.3a
148.3 ± 12.4b
98.4 ± 12.2c
83.5 ± 12.3d
66.6 ± 6.7e
65.2 ± 6.7e
**
Table 2.
Genotype and supplemented diet effect on ram lambs body weight gain.
P < 0.05, **P < 0.01, ***P < 0.001.
ABW, average body weight gain; FBW, final body weight gain; BWC, body weight change; ADG, average daily weight gain; T1, supplemented; T2, not-supplemented; superscript with the same letter is not significant and different letters has significant difference (across the row); SE, standard error of the mean.
The total body weight changes from initial to final body weight higher in supplemented Awassi crossbred lambs and followed by their non-supplemented group. Supplemented and non-supplemented Wollo highland lambs observed better growth performance than Washera F1 crossbreds. Therefore, on-station feed supplementation effect had fastest growth performance record with Awassi F1 crossbred lambs than Wollo highland and Washera F1 crossbred lambs. Supplemented Wollo highland lambs had faster growth rates than their non-supplemented group. Supplemented Washera crossbred lambs had a comparable body weight change to non-supplemented group.
Even though, Wollo highland breed had faster body weight change and average daily gain than Washera F1 crossbred lambs, the supplemented group of Washera crossbred lambs had higher final body weight gain than supplemented Wollo highland breed lambs. The final body weight of non-supplemented Washera crossbred lambs had higher than non-supplemented Wollo highland lambs.
3.2 Genotypes and supplementation effect on carcass characteristic performance
Carcass and non-carcass yield characteristics included, pre-slaughtered weight, slaughter body weight, empty body weight, fasting loss, hot carcass weight, cold carcass weight, total edible proportion, non-carcass organs, rib-eye area, fat and lean meat thickness and commercial yield were presented in Table 2.
Slaughtered and empty body weight bases of the supplemented and non-supplemented groups did not significant difference for each genotype. However, significant variations recorded between the three genotypes. Subsequent to 24 hours of fasting period (except water) the body weight losses and hot carcass weight had comparable value within breeds. However, Awassi crossbred lambs lost more than Washera crossbred and Wollo highland breed lambs. Even though Awassi F1 crossbred lambs lost higher body weight than others during fasting period, it is significantly (P < 0.05) higher hot carcass weight than Washera F1 crossbreds and Wollo highland ram lambs. Nevertheless, fasting loss and hot carcass weight have comparable value between supplemented and non-supplemented Wollo highland and Washera crossbred lambs.
Fat thickness of both supplemented and non-supplemented groups of Awassi crossbred lambs had significantly higher than Wollo highland and non-supplemented Washera crossbred lambs. Despite the fact that, supplemented Washera crossbred lambs, had comparable fat thickness with supplemented Awassi crossbred lambs. Awassi crosses had significantly higher a total non-carcass weight than both Washera and Wollo highland breed lambs, but did not show within breed difference. Between supplemented and non-supplemented Washera genotype and supplemented local Wollo highland breed did not have significant variation of total non-carcass components and non-supplemented Wollo highland lambs significantly lower than others.
Slaughtered body weight had strong positive and significant correlation with empty body weight, hot and cold carcass weight, rib-eye area (cm2), fat thickness (mm2) and slight positive correlation with lean thickness (mm2). However, it had inverse correlation with commercial yield % (cold carcass weight/slaughtered body weight × 100) carcass trait. Empty body weight has strong and positive correlation with cold and hot carcass weight, and rib-eye area (cm2). However, poor and positively associated with lean meat thickness (mm2).
Hot carcass weight had perfect positive significant correlation with rib-eye area (cm2) of lean meat composition, medium positive correlation with fat thickness and poorly correlated with amount of commercial yield (Table 3). The cold carcass weight trait has positive and intermediate correlation with rib-eye area and with lean meat thickness and poorly positive correlation with commercial yield feature. Likewise, rib-eye area carcass trait contents had medium positive association with fat thickness and lean meat thickness attribute. However, it had poor and positive correlation with commercial yield percentage composition, while fat thickness amount of the carcass had positive and medium correlation with lean meat thickness in the entire carcass, but negatively correlated with commercial yield percentage composition. In other ways lean meat content of the carcass had poor positive correlation with commercial yield of the whole carcass composition (Table 3).
Carcass traits
Awassi F1 crossbreds
Wollo highland breed
Washera F1 crossbreds
T1
T2
T1
T2
T1
T2
Sig. L
SBW (kg)
47.4 ± 0.8a
44.6 ± 0.6b
32.5 ± 1.4c
29.3 ± 1.1d
32.6 ± 0.5c
32.2 ± 0.5c
***
EBW(kg)
35.3 ± 1.3a
32.4 ± 1.3a
24.5 ± 1.7b
20.5 ± 1.7b
26.9 ± 0.9c
26.8 ± 0.9c
**
HCW (kg)
20.8 ± 1.6a
20.2 ± 1.6a
14.7 ± 1.2b
13.5 ± 1.2b
16.0 ± 0.5c
13.2 ± 0.5b
***
CCW (kg)
18.3 ± 1.4a
18.2 ± 1.4a
11.7 ± 1.0b
11.6 ± 1.0b
14.9 ± 0.4c
12.5 ± 0.4c,b
**
HCWDP (%)
43.9 ± 3.2a
45.3 ± 3.2b
45.2 ± 3.2b
46.1 ± 3.2b
49.1 ± 0.3c
41.0 ± 0.3d
*
CCWDP (%)
38.6 ± 2.9a
40.8 ± 2.9b
36 ± 5.2c
39.6 ± 5.2a,b
45.7 ± 1.8d
38.8 ± 1.8a
*
TEP (kg)
25.1 ± 1.8a
23.8 ± 1.8a
17.4 ± 1.6b
17.2 ± 1.6b
19.6 ± 0.7c
17.6 ± 0.7b
**
REA (cm2)
15.9 ± 0.2a
15.5 ± 0.2a
7.3 ± 0.1b
6.5 ± 0.1b
9.2 ± 0.1c
7.3 ± 0.1b
**
TNCW (kg)
14.5 ± 1.3a
12.2 ± 1.3a,b
10.8 ± 1.3b
6.9 ± 1.3c
10 ± 1.3b
12.9 ± 1.3b
*
FT (mm)
0.3 ± 0.1a
0.3 ± 0.1a
0.2 ± 0.0b
0.2 ± 0.0b
0.3 ± 0.2a
0.2 ± 0.2b
*
Table 3.
Analysis of variability for genotype and diet effects on carcass traits.
T1, supplemented; T2, non-supplemented; SBW, sloughter body weight; EBW, empty body weight; HCW, hot carcass weight; CCW, cold carcass weight; HCWDP, hot carcass weight dressing percentage; CCWDP, cold carcass weight dressing percentage; TEP, total edible propertion; REA, rib-eye area; TNCW, total non-carcass weight. Superscript with the same letter is not significant and different letters has significant difference.
3.4 Genotype and supplementation effects on carcass morphometric traits
Carcass morphometric characteristics of the present study were described by carcass length, lean meat weight, lean meat length, compactness index, chest width, shoulder width, and lean meat thickness presented in Table 4. Hence, the length of the carcass and lean meat had significantly higher for Awassi and followed by Washera crossbred lambs. Between the supplemented and non-supplemented groups of each genotypes, comparable carcass and lean meat length were recorded, however, significantly different between genotypes. Lean meat thickness significantly higher for both supplemented and non-supplemented Awassi F1 crossbred lambs. Between supplemented and non-supplemented groups of Wollo highland breed and Washera, crossbred lambs had significant difference.
Body weight (kg)
SBW
EBW
HCW
CCW
REA
LMT
EBW
0.87**
HCW
0.82**
0.77**
CCW
0.86**
0.79**
0.98***
REA (cm2)
0.82**
0.77**
0.99***
0.98***
LMT (mm2)
0.52*
0.50*
0.54*
0.554*
0.54*
CY (%)
−0.15
−0.01
0.42
0.36
0.42
0.08
Table 4.
Pearson correlation coefficient of carcass yield characterestics.
Correlation is significant at the 0.001 level (two-tailed).
Correlation is significant at the 0.01 level (two-tailed).
Correlation is significant at the 0.05 level (two-tailed).
SBW, slaughter body weight; EBW, empty body weight; HCW, hot carcass weight; CCW, cold carcass weight; REA, rib-eye area; LMT, lean meat thickness; CY, commercial yield.
The carcass composition of lean meat weight amount is significantly higher with Awassi crossbred lambs than Washera crossbred and Wollo highland breed lambs. Supplemented Wollo highland lambs and Washera crossbred lambs had proportional amount of lean meat weight. The carcass compactness index is measured by grams of lean meat per centimeters of its length. Carcass compactness index, chest and shoulder width had comparable records for all genotypes except chest width for Awassi genotype.
3.5 Genotype and supplementation feed effects on non-carcass fat distribution
The effects of genotype and supplementation diet effect on non-carcass fat distribution presented in Table 5. Thus, the non-carcass fat contents around the scrotal fat organ had not significant variation between supplemented and non supplemented group of each genotypes. However, between Wollo highland breed and Awassi crossbred lambs had a significant variation of scrotal fat contents. Likewise, Washera and Awassi crossbred lambs had significant differences between supplemented and non supplemented groups of scrotal fat contents. While, kidney fat composition of Awassi crossbred lambs and Wollo highland breed lambs had significantly lower than that of Washera crossbred lambs (Table 5).
Carcass morphometric traits
Awassi F1 crossbreds
Wollo highland breed
Washera F1 crossbreds
T1
T2
T1
T2
T1
T2
Carcass length (cm)
74.3 ± 1.2a
73.7 ± 1.2a
63.0 ± 1.9b
64.0 ± 1.9b
70.3 ± 2.2c
68.0 ± 2.2c
Lean meat thickness (mm)
12.5 ± 2.4a
11.0 ± 2.4a
9.0 ± 0.7b
6.4 ± 0.7c
12.0 ± 0.5a
6.3 ± 0.5c
Lean meat weight (kg)
0.7 ± 0.03a
0.7 ± 0.03a
0.5 ± 0.1b
0.5 ± 0.1b
0.6 ± 0.1b
0.5 ± 0.1b
Lean meat length (cm)
55.3 ± 1.2a
54.7 ± 1.2a
44.0 ± 1.9b
45.0 ± 1.9b
51.3 ± 2.2c
49. ± 2.2c
Compactness index (g/cm)
12.1 ± 0.8
12.0 ± 0.8
11.8 ± 0.8
11.9 ± 0.8
12.4 ± 0.9
10.5 ± 0.9
Chest width (cm)
13.9 ± 0.6a
13.7 ± 0.6a
9.2 ± 1.0b
8.1 ± 1.0b
10.9 ± 0.9b
8.8 ± 0.9b
Shoulder width (cm)
17.7 ± 0.6
18.1 ± 0.6
14.4 ± 0.6
14.2 ± 0.6
17.1 ± 0.6
15.0 ± 0.6
Table 5.
Between and within genotype carcass morphometric traits variability.
T1, supplemented; T2, non-supplemented; cm, centimeters, kg, kilograms, mm, millimeters, g, gram. Superscript with the same letter is not significant and different letters has significant difference.
Whereas, significant difference recorded between three genotypes of total non carcass fat contents. Both supplemented and non supplemented group of Awassi F1 crossbred lambs had higher composition of total non-carcass fat contents followed by Washera crossbred lambs. In general all supplemented groups were comprised of higher numerical value of non carcass fat composition, but not significantly different with non supplemented groups.
3.6 Genotype and feed effects on non-carcass edible and non-edible components
According to intellectual prohibited cultural and religious taboo of the local communities the edible components of non-carcass organs were presented as liver, tongue, heart, kidney, empty gastrointestinal part and tail fat were the most common. Hence, liver and heart weight had comparable value for Wollo highland and Washera crossbred lambs; however, Awassi crossbred had significantly higher amount of liver and heart weight. At the same time, non-significant record was observed between supplemented and non-supplemented groups of all genotypes. While the kidney and empty gastrointestinal weight had comparable value for all genotypes and feeding type factors, there was no significant difference both within and between genotypes and feeding types. Whereas the tail weight had comparable value between the three genotypes, Washera crossbred had a numerically higher quantity of tail weight than others (Table 6).
Non-carcass fat traits (g)
Wollo highland breed
Awassi F1 crossbreds
Washera F1 crossbreds
T1
T2
T1
T2
T1
T2
Scrotal fat
8.7 ± 2.9c
10.7 ± 2.1c
33 ± 6.7b
40 ± 6.7b
13.7 ± 4.4c
15.7 ± 4.4c
Pelvic fat
29.3 ± 3.5a
26.7 ± 3.5a
30.7 ± 3.1a
27.7 ± 3.1a
47.0 ± 10.6c
38.3 ± 10.6c
Kidney fat
25.3 ± 2.0a
23.3 ± 2.0a
60 ± 18a
63 ± 18.0a
171.0 ± 52.4c
89.3 ± 52.4c
Mesentery fat
55.3 ± 8.5a
43.3 ± 8.5a
414 ± 38.7b
317.7 ± 38.7b
233.3 ± 64.1c
145.0 ± 64.1c
Overall
117.7 ± 12.6a
103.6 ± 12.6a
537.7 ± 54.7c
448.4 ± 54.7d
465 ± 129.7c
288.3 ± 129.7b
Table 6.
Non-carcass fat distribution traits variability between and within genotypes.
T1, supplemented; T2, non-supplemented; g, grams. Superscript with the same letter is not significant and different letters has significant difference.
Except kidney weight of non-supplemented Awassi and Washera F1 crossbreds and supplemented Wollo highland breed lambs, the edible non-carcass components not significant variation between supplemented and non-supplemented groups. However, except kidney weight and GIT empty weight, genotype had significant variation on non-carcass edible components. Except tail fat weight composition, in all edible non-carcass components of the Awassi crossbred lambs had the largest portion (Table 6).
Wollo highland breed had a comparable tail fat composition with Awassi crossbred lambs. However, both genotype and supplementation diet did not had significant differences with kidney and empty gastrointestinal weight of supplemented and non-supplemented groups. Subsequently, the non-edible, non-carcass components were skin, head, testicle and genital organ, blood, bladder, pancreas, feet, digestive contents and spleen which prohibited by the local communities cultural and religious taboo.
4. Discussion
4.1 Genotype and supplemented diet effects on body weight gain and carcass traits
The availability and supply of animal feed in the tropics is not constant in terms of both quantity and quality particularly in arid and semiarid regions seasonal fluctuation in the growth rate of animal in these regions [9, 10]. This is particularly true in the study area, where the main source of animal feed is grazing on natural pasture. For this reason, to use whatever available resource more economically, it will be advantageous to identify those breeds of animals which are more efficient meat producers [11] or animals which have high performance in feed conversion efficiency to produce saleable products [11].
4.2 Effects of genotype and supplementation on body weight gain performance
Genotypes and supplementation feed effects on ram lambs’ body weight gain presented in Table 2. Initially the body weight gain of the three genotypes significantly different (p < 0.05) each other and the differences were come from breed effects but not significant differences within group in each treatment. To avoid the effects of initial body weight on the successive body weight gain, covariate analysis was used and the adjusted initial body weight at 26.56 kg of all genotypes. In the present study, significantly higher average daily weight gain observed on the supplemented group implied that they were adequately fed and their maintenance and growth nutrient requirements were satisfied compared with non-supplemented groups (grazing only).
The average daily weight gain (ADG), the rate of body weight change and final body weights of supplemented group of Awassi, and Washera F1 crossbred and Wollo highland breed ram lambs were significantly higher (p < 0.05) than non-supplemented groups. As a result, Awassi F1 crossbred lambs’ growth rate had significantly greater (p < 0.05) than both Wollo highland and Washera F1 crossbred ram lambs throughout the experimental period and followed by supplementing Wollo highland breed ram lambs. The reason behind this might be the genetic potential difference of the three genotypes affecting average daily weight gain efficiency with different extent. Therefore, genotype is the limiting factor affecting average daily weight gain of lambs and in agreement with reported by Hammell and Laforest [12] for Polled Dorset, Hampshire and Romanov breeds.
The total amount of body weight change and the rate of daily weight gain indicated Wollo highland breed lambs were significantly greater than both supplemented and non-supplemented groups of Washera F1 crossbred lambs. This indicated improved grazing management condition and supplementation diet of Wollo highland breed lambs can have comparable body weight gain potential with their Washera F1 crossbreds with the same management condition [13, 14, 15].
In general the Awassi F1 crossbred ram lambs have a promising growth performance with supplementation of local available concentrate feed. Hence, with controlled management condition of natural pasture grazing has contributed to better growth performance of ram lambs body weight gain. Furthermore, Washera F1 crossbreed lambs have an imperative body weight change and can be another alternative to enhance genetic potential of pure local Wollo highland breed, and in addition to this, inbreeding coefficient risk can be reduced. Moreover, cost-effective concentrate feed supplementation on natural pasture grazing need appropriate attention by fatteners, and other sheep producers. Together with this private controlled grazing management, system had also played a great role to improve the body weight gain of ram lambs through quality pasture production.
4.3 Effects of genotype and supplemented feed on carcass yield characteristics
Carcass composition used as tool to characterize breeds for possible identification of potential genetic resource for lean lamb production and also to identify management alternatives to suit different breeds [16]. Therefore, breed is known to influence not only carcass composition and quality but also carcass conformation as well, differences in carcass merits between breeds is likely to govern the choice and development of breeds for specific production objectives.
Slaughter and empty body weight between supplemented and non-supplemented groups variation not significant for all genotypes. The reason behind this might be less significant variation between supplemented and non-supplemented body weight before slaughter and relatively comparable amount of fasting loss. Nevertheless, significant variations between the three genotypes recorded, and which in agreement with Orr [17] and Lakew et al. [18]. Subsequent to 24 hours of fasting period, the body weight losses had a comparable amount for all genotypes and not significant variation observed. The loss of rumen contents through defecation and urination effects of fasting period not significantly different among genotypes (Table 7).
Non-carcass components
Awassi crosses (means)
Wollo highland breed (means)
Washera crosses (means)
T1
T2
T1
T2
T1
T2
SE
P-value
I. Edible non-carcass traits
Liver (g)
717.0a
541.3a
332.0b
384.3b
445.0c
453.0c
76.0
**
Tongue (g)
137.8a
143.2a
109.3b
114.3b
91.9c
89.8c
7.0
***
Heart (g)
190.3a
127.3a
61.3c
68.3c
68.3c
75.3c
25.5
**
Kidney (g)
63.3a
66.0b
64.3a,b
59.0c
54.0c
66.0b
31.4
*
GIT empty (g)
1900.0
1633.3
1611.3
2215.0
1779.3
1633.3
330
ns
Tail fat (g)
987.3
951.0
1106.7
920.0
1151.3
1213.3
100.9
ns
II. Non-edible non-carcass traits
Skin (g)
3600.0a
3766.7a
3700.0a
3133.3b
5100.0c
5033.3c
255.0
**
Head (g)
1773.3a
1733.3a
2110.0b
2206.7b
2660.0c
2763.3c
134.9
**
Testicle (g)
420.0a
420.0a
310.0b
310.0b
540.0a
430.0a
56.0
***
Blood (g)
1336.7a
1300.0a
873.3b
937.3b
2033.3c
1823.3c
181.3
**
Bladder (g)
67.3a
68.7a
57.3b
63.3b
72.3.0a
64.0a
2.3
**
Feet (g)
247.7a
249.7a
214.0a
194.7b
203.7b
217.7a
16.4
*
Digestive content (g)
8400.0c
8300c
4222.0a
5551.7b
3466.7a
4337.3a
725.2
**
Spleen (g)
41.7
44.0
32.7
45.0
33.7
30.3
4.7
ns
Table 7.
Genotype and diet effects on edible and non-edible non-carcass components.
T1, supplemented; T2, non-supplemented; ns, non-significant; GIT, gastrointestinal track and SE, standard error of the mean. Superscript with the same letter is not significant and different letters has significant difference.
Hot carcass weight has comparable value between supplemented and non-supplemented groups. However, between genotypes a significant variation (p < 0.001) reported and which in agreement with Orr [17] and Lakew et al. [18]. Therefore, Awassi F1 crossbred ram lambs significantly higher (p < 0.001) hot carcass weight than Wollo highland and Washera F1 crosses (Table 2). This is because of higher slaughtered body weight and higher average daily weight gain (ADG) effect and their comparable fasting loss. Assefu [19, 20] reported there was no breed effect in hot carcass weight between Horro and Washera breeds and which disagree with present study.
Cold carcass weight used as commercial carcass yield indicator trait used for productive performance tools to evaluate the productivity of a given meat animals. Awassi crossbred lambs’ cold carcass weight significantly (p < 0.05) greater than both Washera crosses and Wollo highland breed lambs. Within each genotype, cold carcass weight did not have significant difference because of the higher amount of chilling loss rate of supplemented groups (Table 7). This indicated that, the supplemented feed does not bring significant impact on cold carcass weight and agreement with Awgichew [10] for Menz and Horro breed lambs and Jorge et al. [21] for Chilote and Suffolk breeds in Chile Island. The chilling loss of cold carcass weight may vary between 1 and 7%, usually found close to 2.5% [22]. Moreover, sex, weight, fat covering of the carcass, temperature, and humidity in the cold storage chamber and the handling of the carcasses [23, 24] influence cold carcass characteristic.
Dressing percentage is described as the proportion of carcass weight to slaughtered body weight and it helps to assess meat productivity of the animals. Nutrition influences dressing percentage through variation in weight of mesentery contents and variation in actual organ weights [25, 26]. In agreement with the present finding, Awgichew [10] reported, regardless of the clear tendency of Horro lambs having a heavier hot and cold carcass weight, but did not differ significantly from Menz breed in dressing % and the loss of carcass moisture (shrinking %) after an overnight cooling. The present finding reported, hot carcass weight dressing percentage (HCCWDP) does not have significant difference both between and within genotype and which in agreement with Awgichew [10] and Jorge et al. [21]. Concurring with this report, an experimental trial conducted by Mazemder et al. [27] on grazing local sheep supplemented and with non-supplemented of 100, 200 and 300 g of concentrate feed/day; dressing percentage was similar among the treatments.
Rib-eye muscle area is mostly used as a tool to indicate the proportion of carcass muscling [28, 29]. In the present study the supplementation diet did not have a significant impact on rib-eye muscle area but numerical difference was observed. In line with the current finding, Gizaw [1] reported supplementation did not have significant effect on rib-eye muscle area in Somali goats fed hay and supplemented with different levels of peanut cake and wheat bran mixture. However, unlike this finding, Matiwas et al. [28] and Alemu [32] reported supplementation diet had a significant and positive effect on rib-eye muscle area. In concurrence with this finding, Matiwas et al. [31], Alemu [32]; Simret and Gizaw [30] reported rib-eye area had a significant variation between breeds. However, did not significant variation between supplemented and non-supplemented groups of Awassi crosses and Wollo highland breed lambs (Table 7). Nevertheless, supplemented and non-supplemented groups of Washera crossbreds had significant differences of rib-eye area composition. This fact is an indicator of better muscle development of supplementing Washera crosses than non-supplemented one. Hence, this rib-eye area muscle development is one of the merits to select Washera F1 crossbred lambs for meat production objective. Both supplemented and non-supplemented Wollo highland and non-supplemented Washera crossbred lambs have relatively comparable rib-eye area muscle development (Table 7).
Except dressing percentage, almost all carcass characteristic extent both supplemented and non-supplemented Awassi crossbred had significantly higher than Wollo highland and Washera F1 crossbred lambs. Hence, crossbreeding effect on genetic improvement practices using Awassi exotic breed had significant response associated with growth and carcass yield characteristic traits. As a result Awassi F1 crossbred lambs had potential effect on meat production improvement objective and advisable to be selected for further breed productivity improvement program.
4.4 Genotype and supplemented feed effects on non-carcass fat distribution
The effects of genotype and supplementation diet on non-carcass fat distribution was presented in Table 6. Thus, non-carcass fat contents around the scrotal organ had not significant variation between supplemented and non-supplemented groups of the three genotypes. However, between Wollo highland breed lambs and Awassi F1 crossbred lambs, significant variation of fat around scrotal organ observed. Likewise, between supplemented and non-supplemented groups of Washera and Awassi F1 crossbred lambs have significant difference fat around scrotal organ recorded. Subcutaneous fat content between Wollo highland and Awassi crossbred lambs had comparable value. However, Awassi crossbred and Wollo highland breed lambs significantly lower subcutaneous fat content than Washera crossbred lambs. The reason behind this, on fat deposition efficiency of Washera F1 crosses genotype effect has more noticeable than Awassi crosses and Wollo highland breed.
The current study showed mesentery fat, kidney fat and subcutaneous fat decreased in non-supplemented ram lambs fed on natural pasture forage diet only. The current result is in agreement with reported by Karim et al. [33] and Papi et al. [34] on the concept of lambs with high forage quality tended to deposit less subcutaneous and intestinal fat contents. Lambs fed a concentrate diet displayed considerably greater fat accumulation than lambs raised on forage based diets [35]. The reduced non-carcass fat attributed to lower energy intake from forage [33]. In addition, high starch consumption the supplemented concentrate diets produces higher amounts of propionate, which ultimately increases insulin secretion and stimulates fat synthesis [35]. In agreement with this finding, Ibrahim et al. [29], Salo et al. [36], Roberto et al. [37] and Abebe and Tamir [38] reported the total fat contents of non-carcass components were significantly affected by the type of diet used. However, in the current finding, in addition to the effects of diet, genotype effects also significant (P < 0.05) different on total non-carcass fat contents. Even though, supplemented Awassi and Washera crossbred lambs had comparable total non-carcass fat composition, Washera F1 crossbred lambs showed comparatively higher fat contents than Awassi F1 crossbreds in relation to their body weight difference.
4.5 Genotype and supplemented feed effects on edible and non-edible, non-carcass part
Accordingly, intellectual prohibited cultural and religious taboo of local communities, edible components of non-carcass organs, which presented as liver, tongue, heart, kidney, empty gastrointestinal content and tail fat are the most common and presented in Table 6. Hence, liver and heart weight comparable value between Wollo highland and Washera crossbred lambs; however, Awassi crossbred lambs had significantly (p < 0.05) higher than the other. The reason behind this might be larger body size and physiological appearance of the genotype. However, non-significant variation between supplemented and non-supplemented groups of all genotypes were recorded, while the kidney and intestine weight had a comparable amount for all genotypes and feeding type. Roughage part of animal feed obvious to feel rumen content and the the green forge grazing was equally accessible to all genotypes and which was the reason for comparable intestinal weight. Whereas the tail size had comparable value for Awassi crossbred and Wollo highland breed ram lambs, Washera crossbred lambs had a significantly (P < 0.05) larger tail size than other two genotypes. This also indicated that Washera F1 crossbred ram-lambs shown larger fat development nature and that might be because of largest tail weight.
In agreement with current finding, Riley et al. [39] and Teklu [40] were reported the majority of edible offal components was not affected (P > 0.05) by the supplemented feed. As a remarkable feature of Awassi crossbred lambs more advanced with liver, tongue and heart weight. This perceptible difference resulted from large body size and genotype effect. In concurrence with the current result, Riley et al. [39] indicated that differences in internal organs were more influenced by age, breed and sex of the animals rather than plane of nutrition, whereas kidney and empty gastrointestinal track weight cover the larger portions of edible non-carcass components compared with all genotypes, which aligned with Teklu [40]. This implies animals consume more feed, their stomach enlarged to accommodate the larger ingesta and thicker to resist the workload on it and this may increase the volume and weight of the gastrointestinal tract as a whole.
Except lung with trachea and spleen, all non-edible offal components were not affected by supplemented diet and indicating that variation of supplementation diet not influenced the non-edible non-carcass components. The non-edible non-carcass contents of head, digestive content and blood volume significant difference (p < 0.05) among genotypes and this might be slaughtered body weight differences and the inherent genotype effect. In agreement with the current study, Prasad and Kirton [41] reported live weight status of the animals could affect the production efficiency of carcass offal and considered as depressing factor for hot and cold carcass weight extent and their dressing percentage. However, the nutritional effect not significantly visible for most non-edible non-carcass component weight and which in agreement with Teklu [40] but disagree with Michael and Yaynshet [42]. In general the larger extent of non-carcass non-edible components could be reduced the edible carcass and non-carcass amount, hence, through breed selection task, need to be considered the non-carcass non-edible content of genotype.
5. Conclusion and recommendation
The study conducted at feedlot productive performance evaluation of Wollo highland sheep breed and their F1 crossbreeds of Awassi and Washera sheep in Ethiopia. The objectives of the research is grazing and feedlot based productive performance evaluation of Wollo highland sheep breed and their F1 crosses.
The average daily weight gain (ADG), total body weight change and final body weights of supplemented group Awassi F1 crossbred and Wollo highland ram lambs significantly higher than non-supplemented groups. Awassi F1 crossbred lambs growth performance significantly higher than Wollo highland and Washera F1 crossbred lambs and followed by supplemented Wollo highland breed lambs. Wollo highland breed had ability to increase their body weight compared with other selected indigenous breed types of the country and have potential value for fattening purpose and productive potential genetic improvement practice, as far as their nutritional requirement is maintained.
The effect of genotypes on average daily weight gain of Awassi crossbred ram lambs had the largest value of breed selection in the current study. Therefore, the effect of both genotype and supplementation diet have an advanced value for lamb body weight gain improvement practices. Moreover, cost effective concentrate feed supplementation on natural pasture controlled grazing have to give appropriate attention by smallholder sheep producers and fatteners.
Carcass composition used as a tool to characterize breeds for possible identification of potential genetic resource of lean meat type of lamb production and identify management alternatives to suit different breeds. Differences in carcass merits between genotypes are likely to govern the choice and development of breeds for specific production objective. Natural pasture controlled grazing management important alternative for productive and organic product improvement practices.
Supplementation diet does not have significant effect on hot carcass weight dressing percentage however, further research is important to confirm at different level of supplementation feeding trial. Cold carcass weight dressing percentage (CCWDP) has a significant difference between supplemented and non-supplemented groups of each of the three genotype in the present study and its important parameter for carcass productivity improvement practice.
Awassi F1 crossbred progenies designated for promising attributes for higher body weight gain and carcass yield characteristics productive trait and good fertility rate; however, further research verification activities suggested with different blood level of crossbred progenies performance evaluation. The genotype and supplementation diet effect has profound factors to enhance productive and farmers’ production objectives decision. Hence, researchers need to investigate farmers’ interest and potential of available breed type through genetic and phenotype performance study. Effective concentrate feed supplementation on controlled natural pasture grazing had significant impact on ram lambs productive performance improvement and it is crucial to create appropriate understanding for fatteners, traders and other sheep producers.
Acknowledgments
Mehamed Ali (private sheep farm owner) and Dessie Zuria District smallholder farmers have participated with allowed their sheep flocks for inventory purpose. Medhin G/Cherkos, Tadesse Mergiaw, Tilahun Gezahegn and Ayiten Mekete participated through data collection as enumerator. Addis Ababa (AAU) and Wollo University (WU) have participated in providing Research Grant. Department of Animal Production Study (DAPS) in Addis Ababa University, participated through assistance from the beginning to the end of data collection process and the whole thesis work.
Conflict of interest
The authors declare no conflict of interest.
Funding
The work of this research project has done by the funding support of Addis Ababa University thematic project, Minister of Education, and Wollo University collaboration.
Abbreviations
CSA
Central Statistics Authority
EPA
extension planning area
SPS
sanitary and phytosanitary standards
UNCTD
United Nations Conference on Trade and Development
\n',keywords:"body weight, carcass, Awassi and Washera, F1 crossbred and Wollo highland",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/72724.pdf",chapterXML:"https://mts.intechopen.com/source/xml/72724.xml",downloadPdfUrl:"/chapter/pdf-download/72724",previewPdfUrl:"/chapter/pdf-preview/72724",totalDownloads:130,totalViews:0,totalCrossrefCites:0,dateSubmitted:"November 26th 2019",dateReviewed:"March 31st 2020",datePrePublished:"July 6th 2020",datePublished:"January 14th 2021",dateFinished:"July 6th 2020",readingETA:"0",abstract:"In the study area, sheep flocks are managed under traditional extensive systems with no or minimal inputs and improved technologies, which results in low productivity. The available natural pasture lands are overloaded with livestock beyond optimum carrying capacity that has resulted in overgrazing and land degradation. This indicates the critical need of supplemental feed during feed-deficient period. The objective of the research was assessment of productive performance through on-station feedlot and natural pasture grazing effect on weight gain and carcass yield characteristics evaluation. The average daily weight gain (ADG), total body weight change and final body weights of supplemented groups significantly higher than (p < 0.05) non-supplemented groups. Hence, supplemented and non-supplemented Awassi crossbreds had higher daily weight gain and followed by supplemented Wollo highland group. Between genotypes, there is significant difference (p < 0.05) of rib-eye area, empty body weight, hot and cold carcass weight and cold carcass dressing percentage. Conversely, Wollo highland sheep has exhibited compensatory growth rate than others. Awassi crossbred lambs has higher weight gain and faster growth performance followed by Washera crossbred one. Therefore, local breed productive performance improvement practices have to continue and need adjustment of breeding strategies with a definite breeding plan.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/72724",risUrl:"/chapter/ris/72724",signatures:"Tadesse Amare Sisay, Gebeyehu Goshu Negia and Berhan Tamir Mersso",book:{id:"8468",title:"Sheep Farming",subtitle:"An Approach to Feed, Growth and Health",fullTitle:"Sheep Farming - An Approach to Feed, Growth and Health",slug:"sheep-farming-an-approach-to-feed-growth-and-health",publishedDate:"January 14th 2021",bookSignature:"António Monteiro",coverURL:"https://cdn.intechopen.com/books/images_new/8468.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",editors:[{id:"190314",title:"Prof.",name:"António",middleName:"Cardoso",surname:"Monteiro",slug:"antonio-monteiro",fullName:"António Monteiro"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"316037",title:"Ph.D.",name:"Tadesse",middleName:"Sisay",surname:"Amare",fullName:"Tadesse Amare",slug:"tadesse-amare",email:"workeamare@gmail.com",position:null,institution:{name:"Wollo University",institutionURL:null,country:{name:"Ethiopia"}}},{id:"316038",title:"Prof.",name:"Gebeyehu",middleName:null,surname:"Goshu Negia",fullName:"Gebeyehu Goshu Negia",slug:"gebeyehu-goshu-negia",email:"ggoshu2000@yahoo.com",position:null,institution:{name:"Addis Ababa University",institutionURL:null,country:{name:"Ethiopia"}}},{id:"317608",title:"Prof.",name:"Berhan",middleName:null,surname:"Tamir Mersso",fullName:"Berhan Tamir Mersso",slug:"berhan-tamir-mersso",email:"berhantamir@yahoo.com",position:null,institution:{name:"Addis Ababa University",institutionURL:null,country:{name:"Ethiopia"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Material and methods",level:"1"},{id:"sec_2_2",title:"2.1 Description of the study area",level:"2"},{id:"sec_3_2",title:"2.2 Experimental design and treatments",level:"2"},{id:"sec_4_2",title:"2.3 Experimental animals grazing management",level:"2"},{id:"sec_5_2",title:"2.4 Body weight gain and linear body measurements",level:"2"},{id:"sec_6_2",title:"2.5 Data analysis",level:"2"},{id:"sec_8",title:"3. Results",level:"1"},{id:"sec_8_2",title:"3.1 Effects of genotype and supplementation feed on ram lambs growth rate",level:"2"},{id:"sec_9_2",title:"3.2 Genotypes and supplementation effect on carcass characteristic performance",level:"2"},{id:"sec_10_2",title:"3.3 Carcass yield traits correlation coefficient analysis",level:"2"},{id:"sec_11_2",title:"3.4 Genotype and supplementation effects on carcass morphometric traits",level:"2"},{id:"sec_12_2",title:"3.5 Genotype and supplementation feed effects on non-carcass fat distribution",level:"2"},{id:"sec_13_2",title:"3.6 Genotype and feed effects on non-carcass edible and non-edible components",level:"2"},{id:"sec_15",title:"4. Discussion",level:"1"},{id:"sec_15_2",title:"4.1 Genotype and supplemented diet effects on body weight gain and carcass traits",level:"2"},{id:"sec_16_2",title:"4.2 Effects of genotype and supplementation on body weight gain performance",level:"2"},{id:"sec_17_2",title:"4.3 Effects of genotype and supplemented feed on carcass yield characteristics",level:"2"},{id:"sec_18_2",title:"4.4 Genotype and supplemented feed effects on non-carcass fat distribution",level:"2"},{id:"sec_19_2",title:"4.5 Genotype and supplemented feed effects on edible and non-edible, non-carcass part",level:"2"},{id:"sec_21",title:"5. Conclusion and recommendation",level:"1"},{id:"sec_22",title:"Acknowledgments",level:"1"},{id:"sec_25",title:"Conflict of interest",level:"1"},{id:"sec_22",title:"Funding",level:"1"},{id:"sec_25",title:"Abbreviations",level:"1"}],chapterReferences:[{id:"B1",body:'Gizaw S, Johan A, Olivier H, Hans K, Johann S, Dessie T, Van der Z, Herbert H. 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Journal of ABC Research Alert (JABCRA). 2014;2(1):12-15'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Tadesse Amare Sisay",address:"tadesse.amare2002@yahoo.com",affiliation:'
Department of Animal Science, College of Agriculture, Wollo University, Ethiopia
Department of Animal Production Studies, College of Veterinary Medicine and Agriculture, Addiss Ababa University, Ethiopia
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UK Research and Innovation (former Research Councils UK (RCUK) - including AHRC, BBSRC, ESRC, EPSRC, MRC, NERC, STFC.) Processing charges for books/book chapters can be covered through RCUK block grants which are allocated to most universities in the UK, which then handle the OA publication funding requests. It is at the discretion of the university whether it will approve the request.)
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