Control Configuration Selection for Nonlinear Systems

Abstract

Very popular research in the field of Modern control Engineering is design of controllers for nonlinear systems. It is obvious that all the real-world systems are multivariable and nonlinear in nature which is highly challenging to control these nonlinear systems as it exhibits complexity. In addition to these, all the real systems exhibit uncertainty due to slow or sudden changes in process parameters. Hence, the design of robust nonlinear controller should have an ability to handle these uncertainties. The design of controllers for nonlinear system needs proper selection of appropriate input–output pairing. This book chapter focus on the conventional and proposed method of control configuration selection for nonlinear systems.

1. Introduction

Research in nonlinear systems is developing rapidly and it is observed that useful results tend to appear. The classical approach in nonlinear system is linearization and thereby design of linear controllers. This classical approach is recommended when the nonlinearities are mild. Also, this approach is not recommended when the nonlinearities are pronounced more. For such case, variable transformation techniques are adopted and hence effective controllers are designed. The philosophy of nonlinear controller design is indicated using following four schemes: i. Local linearization, ii. Local linearization with adaptation, iii. Linearization using variable transformations and iv. Special purpose procedure.

Most of the nonlinear systems exhibit sustained oscillations for wide range of operating point. Investigation of stability for nonlinear systems is based on linearization of nonlinear system around the steady state. If the linearized system is stable at the vicinity, then it is concluded that the corresponding nonlinear system will be stable in the vicinity of the point.

There are four methods involved to analyse the dynamic behaviour of nonlinear systems. Rigorous analytical approach is used to characterise qualitatively the dynamics of nonlinear system. Analytical approach will evolve to the state of the nonlinear system. Exact linearization by variable transformation technique will first carry out the transformation, then dynamic analysis on linear transformed version and finally transforming back to original variables. Numerical analysis will processes the numerical values at specific points in time. Finally in approximate linearization method nonlinear system will be approximated to linear system.

Many researchers from ‘drive by wire’ cars to ‘fly by air’ flight control systems have shown interest in analysis and design of nonlinear control strategies. This growing interest in design of nonlinear control is due to improvement in linear control system and hard nonlinearities analysis. Hence researcher need to deal with model uncertainties and robust design.

Modern technology requires high speed and accurate robots. Inverted pendulum is an example of nonlinear system which finds application in positioning of robots and control of manipulators. As the nonlinear systems exhibit limit cycle, it is not ease to use Kalman test for checking controllability and observability. Also, stability is not simply location of poles as the system is having multiple stable/unstable equilibrium points.

In eighteenth century, nonlinear control was introduced to control steam engine by using centrifugal flyball governor reviewed by Jamshed Iqbal et al. [1]. Lyapunov [2] in 1892 proposed the stability for nonlinear system by finding stability of linear approximation of nonlinear system at equilibrium point is equivalent to analysing stability for nonlinear system at vicinity of equilibrium point. Two benchmark nonlinear system on Duffing’s research [3] in 1918 on nonlinear vibrations and van der pol findings [4] in 1926 on electronic oscillations representing nonlinear control systems. The various phenomenon in nonlinear systems is jump resonance, limit cycle, subharmonic oscillations and frequency entrainment. Control Engineering in 1930 [5], Poincare approximated servomechanisms to second order system using phase-plane method. During second world war, research in nonlinear control led to control of guided vehicles for defence. In the year 1940–1960, nonlinear systems are represented analytically using describing function and phase plane method [6]. Modern era for nonlinear control was developed in the year 1960. The key applications of nonlinear control are defence sector and industrial arena. As nonlinear real-world systems are multivariable, high dimensional, poorly modelled which is outside the boundary of classical control theory. Thus, nonlinear control falls under the modern control Engineering in which digital controllers are used Fuller 1979 [7, 8]. In 1970, scientist proposed dynamic system can be viewed as energy transformation mechanism. Sontag and Wang [9] in 1995 proposed input–output stability of nonlinear system using elementary subsystems. By the introduction of geometric control theory by Isidori [10] in 2013 to analyse the stability of nonlinear system. 1990s is considered as decade of ‘activation process’ in nonlinear control systems.

The aim of this chapter is to analysis the nonlinear system and nonlinear control. The rest of the chapter is carried out as follows: Section 2 discusses benchmark nonlinear system. Conventional method of input–output pairing is explained in Section 3. The proposed method of control structure selection and determination of input/output pairs are given in Section 4. At the end, conclusion is drawn.

2. Process description

A nonlinear system does not obey the principle of superposition. In this system, the response to sum of inputs is not equal to sum of individual responses. Also, response to step input of magnitude A is not equal to A times magnitude of step, step-down response is not equal to mirror image of step-up response. A sinusoidal input to nonlinear system will not lead to perfect sinusoidal response.

Most of the chemical processes are nonlinear. Some of the examples of nonlinear chemical process [11] are as follows:

1. The blending process

2. Stirred mixing tank process

3. Nonisothermal CSTR process - mildly nonlinear system [12]

4. pH neutralisation process–moderate to high nonlinear system and

5. Distillation column–highly non-linear system

2.1 The blending process

In the blending process shown in Figure 1, it is required to blend the pure material A and pure material B whose respective flowrates F_A and F_B. The objective of blending process is to control the flow rate and composition.

Figure 1.

Blending process.

Representing the mathematical modelling of blending process:

Total mass balance:

$$\mathrm{F}={\mathrm{F}}_{\mathrm{A}}+{\mathrm{F}}_{\mathrm{B}}$$E1

Component A mass balance:

$$\mathrm{x}={\mathrm{F}}_{\mathrm{A}}/{\mathrm{F}}_{\mathrm{A}}+{\mathrm{F}}_{\mathrm{B}}$$E2

On linearizing, the process transfer function is obtained as:

$$G_{11}\left(s\right)=\frac{R^{\prime }\left(s\right)}{W_1^{\prime }\left(s\right)}={10}^{-3}$$E3

$$G_{12}\left(s\right)=\frac{R^{\prime }\left(s\right)}{W_2^{\prime }\left(s\right)}={10}^{-3}$$E4

$$G_{21}\left(s\right)=\frac{X^{\prime }\left(s\right)}{W_1^{\prime }\left(s\right)}=\frac{-2.5\ast {10}^{-6}}{s+4\ast {10}^{-4}}$$E5

$$G_{22}\left(s\right)=\frac{X^{\prime }\left(s\right)}{W_2^{\prime }\left(s\right)}=\frac{-2.5\ast {10}^{-6}}{s+4\ast {10}^{-4}}$$E6

2.2 Stirred mixing tank reactor

The stirred mixing tank reactor is having two input variables: hot and cold stream flowrate and two output variables: liquid level and temperature of the liquid in the tank.

For this stirred mixing tank reactor in Figure 2, assume cross sectional area is uniform, liquid physical properties are constant. The mathematical model of the tank reactor is

Figure 2.

Stirred mixing tank reactor.

$$A_c\frac{\mathit{dh}}{\mathit{dt}}=F_H+F_C+F_D-k\surd h$$E7

$$\rho C_p{A}_c\frac{d\left(\mathit{hT}\right)}{\mathit{dt}}=\rho C_p$$E8

This process is considered as nonlinear because of square root term and product functions of h and T.

Process transfer function for stirred mixing tank reactor is:

$$G\left(s\right)=\left[\begin{array}{cc}\frac{0.7}{1+9s}& 0\\ \frac{2}{1+8s}& \frac{0.4}{1+9s}\end{array}\right]$$E9

2.3 CSTR process

One of the nonlinear chemical processes is nonisothermal CSTR shown in Figure 3.

Figure 3.

The nonisothermal CSTR.

In this process, irreversible chemical reaction takes place, where the feed material having composition C moles/volume enters the reactor at the temperature, T_f. Assuming the concentration and temperature are uniform throughout, exit temperature and composition are also same as within the reactor.

The mathematical model for this process is:

$$\frac{d{C}_A}{\mathit{dt}}=\frac{-1}{\theta }{c}_A-k_0{e}^{-\left(\frac{E}{\mathit{RT}}\right)}{c}_A+\frac{1}{\theta }{c}_{\mathit{Af}}$$E10

$$\frac{\mathit{dT}}{\mathit{dt}}=\frac{-1}{\theta }T+\beta k_0{e}^{-\left(\frac{E}{\mathit{RT}}\right)}{c}_A+\frac{1}{\theta }{T}_f-\chi$$E11

The CSTR process is having two manipulated variables and two controlled variables (reaction temperature and concentration). Based on mathematical model of CSTR process, it is observed that the nonlinearities are due to nonlinear function of temperature – involving exponential of temperature and products of concentration and function of temperature.

The process transfer function matrix of CSTR process is presented in Eq. (12):

$$\left(\begin{array}{c}{C}_A\\ T\end{array}\right)=\left(\begin{array}{cc}\frac{0.022e^{-0.33s}}{15s+1}& \frac{5e^{-0.33s}}{21s+1}\\ \frac{0.0056e^{-6s}}{21s+1}& \frac{5.9e^{-0.33s}}{21s+1}\end{array}\right)\left(\begin{array}{c}F\\ F_j\end{array}\right)$$E12

2.4 pH neutralisation process

Most of the pH processes exhibit nonlinear behaviour to degree of either mild or high. The pH neutralisation process is shown in Figure 4.

Figure 4.

pH neutralisation process.

The dynamic model of pH neutralisation system is derived using conservation and equilibrium relations. Assuming perfect mixing, constant density and complete solubility of the ions involved.

The following differential equations for the effluent reaction invariants can be derived:

$$A_1{h}_1\frac{{\mathit{dW}}_{a4}}{\mathit{dt}}=q_{1e}\left(W_{a1}-W_{a4}\right)+q_2\left(W_{a2}-W_{a4}\right)+q_3\left(W_{a3}-W_{a4}\right)$$E13

$$A_1{h}_1\frac{{\mathit{dW}}_{b4}}{\mathit{dt}}=q_{1e}\left(W_{b1}-W_{b4}\right)+q_2\left(W_{b2}-W_{b4}\right)+q_3\left(W_{b3}-W_{b4}\right)$$E14

The pH and level transmitters are modelled as first order transfer functions. The desired flow rates q₁ and q₃ serve as setpoints.

The process is treated as square MIMO systems where pH₂ and h₂ are to be controlled variables using Q₄ and Q₆ as the manipulated variables with Q₁ and Q₃ held constant.

The resulting process transfer function matrix is represented in the following Eq. (15).

$$\left(\begin{array}{c}{\mathrm{pH}}_2\\ h_2\end{array}\right)=\left(\begin{array}{cc}\frac{-0.32e^{-0.8s}}{2.36s+1}& \frac{0.32e^{-0.4s}}{2.03s+1}\\ \frac{0.42e^{-0.4s}}{3.32s+1}& \frac{0.41e^{-0.1s}}{2.07s+1}\end{array}\right)\left(\begin{array}{c}{Q}_4\\ Q_6\end{array}\right)$$E15

2.5 Distillation column

The design of binary distillation process shown in Figure 5 is a highly nonlinear chemical process.

Figure 5.

Binary distillation tower.

The potential manipulated variables of the distillation process are reflux (FR) and reboiler flow rate (FV) whereas distillate (XD) and bottom composition (XB) are the controlled variables here. This nonlinear system is having 3 input variables and 2 output variables.

The transfer functions are obtained for the distillation column is described by the following equation.

$$X_D\left(s\right)=\frac{0.0747e^{-3s}}{12s+1}{F}_R\left(s\right)-\frac{0.0667e^{-2s}}{15s+1}{F}_V\left(s\right)+\frac{0.7e^{-5s}}{14.4s+1}{X}_F\left(s\right)$$E16

$$X_B\left(s\right)=\frac{0.1173e^{-3.3s}}{11.7s+1}{F}_R\left(s\right)-\frac{0.1253e^{-2s}}{10.2s+1}{F}_V\left(s\right)+\frac{1.3e^{-5s}}{12s+1}{X}_F\left(s\right)$$E17

whose transfer function matrix Eq. (18) is described as:

$$\left(\begin{array}{c}{X}_D\left(s\right)\\ X_B\left(s\right)\end{array}\right)=\left(\begin{array}{cc}\frac{0.0747e^{-3s}}{12s+1}& \frac{-0.0667e^{-2s}}{15s+1}\\ \frac{0.1173e^{-3.3s}}{11.7s+1}& \frac{-0.1253e^{-2s}}{10.2s+1}\end{array}\right)\left(\begin{array}{c}{F}_R\left(s\right)\\ F_V\left(s\right)\end{array}\right)$$E18

3. Conventional method of loop pairing for nonlinear systems

For all the processes namely SISO and MIMO it is required to pair the input and output variables before designing the controller. Later the controller can be designed according to any one of such input–output pair. Further any one of this configuration will lead to better overall system performance.

For the linear systems, Relative Gain Array (RGA) is obtained based on transfer function models [11]. Interaction analysis using RGA is based on steady-state information. But for nonlinear systems, by assuming that process model is available, two approaches are used to obtain RGA.

1. Using steady state version of nonlinear model from first principles, it is possible to obtain the analytical expressions.

2. By linearizing the nonlinear model around a steady state using approximate K matrix.

3.1 RGA based loop pairing for blending process

RGA is computed using the steady state version of nonlinear model for this process.

For the blending process, two input variables are u₁ and u₂ and the two output variables are F and x.

$$\mathrm{F}={\mathrm{u}}_1+{\mathrm{u}}_2-\text{Linear}$$E19

$$\mathrm{X}={\mathrm{u}}_1/{\mathrm{u}}_1+{\mathrm{u}}_2-\text{Nonlinear}$$E20

For this 2x2 MIMO process, the elements of RGA is given by:

$$\lambda =\frac{{\left(\frac{\mathit{dF}}{d{u}_1}\right)}_{\mathit{\text{bothloopsopen}}}}{{\left(\frac{\mathit{dF}}{d{u}_1}\right)}_{\mathit{\text{secondloopclosed}}}}$$E21

From Eq. (19), when both loops open, ${\left(\frac{\mathit{dF}}{d{u}_1}\right)}_{\mathit{\text{bothloopsopen}}}=1.$

Upon closing the second loop, what value u₂ will take in order for any change in u₁, x is restored to desired steady state value x^*. Solving for u₂ in terms of u₁ and x^*.

$$u_2=\frac{u_1}{x}-x$$E22

Thus, when the second loop is closed, subs Eq. (22) in Eq. (19)

$$\mathrm{F}={\mathrm{u}}_{1+}\frac{u_1}{x}-x$$

$$\mathrm{F}=\frac{u_1}{x}$$E23

Differentiate F w.r.t u₁, we get ${\left(\frac{\mathit{dF}}{d{u}_1}\right)}_{\mathit{\text{secondloopclosed}}}=\frac{1}{x}$

Finally, $\lambda =\frac{1}{\frac{1}{x}}$

$$\lambda =x$$E24

Therefore, RGA for blending system is

$$\lambda =\left(\begin{array}{cc}x& 1-x\\ 1-x& x\end{array}\right)$$E25

where $x$ is the mole fraction of species A in the blend.

RGA depends on only one steady state operating point, $x$ whose value lies between 0 and 1.

Loop pairing for blending process:

1. When x* is closer to 1, recommended pairing is F-u₁ and m-u₂.

2. When product composition is closer to 1, recommended pairing is F-u₁ and m-u₂.

3. When product composition is closer to 0, recommended pairing is F-u₂ and m-u₁.

4. When x* = 0.5, which input variable is used to control which output variable.

3.2 RGA based loop pairing for stirred mixing tank reactor

Using the technique of approximating the nonlinear model around the steady state value, RGA is obtained for stirred mixing tank reactor.

Steady state gain matrix for the reactor is

$$K=G\left(0\right)=\frac{1}{k}\left[\begin{array}{cc}2\sqrt{h_s}& 2\sqrt{h_s}\\ \frac{\left(T_H-T_s\right)}{\sqrt{h_s}}& \frac{\left(T_C-T_s\right)}{\sqrt{h_s}}\end{array}\right]$$E26

Two output variables are y₁ – liquid level and y₂ – temperature

Two input variables are u₁ – hot stream flowrate and u₂ – cold stream flowrate

RGA for this system at steady state operating point T_S,

$$\Lambda =\left[\frac{T_C-T_s}{T_C-T_H}\frac{-\left(T||H-T_s\right)}{T_C-T_H}\frac{-\left(T||H-T_s\right)}{T_C-T_H}\frac{T_C-T_s}{T_C-T_H}\right]$$E27

For illustrations, numerical values of $T_C=15$°C and $T_H$=65°C

Condition 1: T_S > 40°C, (T_S = 55°C)

$$\Lambda =\left[\begin{array}{cc}0.8& 0.2\\ 0.2& 0.8\end{array}\right]$$E28

RGA recommends (u₁-y₁) and (u₂-y₂) pairing.

Condition 2: T_S < 40°C, (T_S = 25°C)

$$\Lambda =\left[\begin{array}{cc}0.2& 0.8\\ 0.8& 0.2\end{array}\right]$$E29

RGA recommends (u₂-y₁) and (u₁-y₂) pairing.

Condition 3: T_S = 40°C,

$$\Lambda =\left[\begin{array}{cc}0.5& 0.5\\ 0.5& 0.5\end{array}\right]$$E30

Here either pairing is equally bad.

Condition 4: T_S = T_H

$$\Lambda =\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$E31

Here we can achieve the perfect control.

3.3 RGA based loop pairing for mild, mild to high and high nonlinear process

RGA for mild, mild to high and high nonlinear processes are given in Table 1 based on steady state value of process transfer function matrix.

S.No	Process	Relative Gain Array
1	CSTR	$\left(\begin{array}{cc}1.2750& -0.2750\\ -0.2750& 1.2750\end{array}\right)$
2	pH	$\left(\begin{array}{cc}0.4940& 0.5060\\ 0.5060& 0.4940\end{array}\right)$
3	Distillation column	$\left(\begin{array}{cc}6.0937& -5.0937\\ -5.0937& 6.0937\end{array}\right)$

Table 1.

Conventional method of loop pairing for nonlinear chemical process.

It is clear that from RGA matrix for all the benchmark process, the desirable input–output pair is (y₁-m₁); (y₂-m₂).

4. Proposed loop pairing for the nonlinear process

The proposed method is based on finding the area under the closed loop undesired response and choosing the pair based on minimum area under the response [13, 14]. The controllers are designed using the method proposed by Panda [15] Figures 10 and 11.

4.1 Loop pairing for blending process

Case 1: Diagonal pairing

Based on the comparing the area tabulated in Table 2 under undesired response for both diagonal and off diagonal shown in Figures 6–9, the recommended input output pairing is 1–1/2–2 using the proposed method.

Figure 6.

Closed loop undesired response (y₁) for diagonal pairing.

Figure 7.

Closed loop undesired response (y₂) for diagonal pairing.

Figure 8.

Closed loop undesired response (y₁) for off diagonal pairing.

Figure 9.

Closed loop undesired response (y₂) for off diagonal pairing.

Figure 10.

Stirred mixing tank undesired response (y₁) for diagonal pairing.

Figure 11.

Stirred mixing tank undesired response (y₂) for diagonal pairing.

4.2 Loop pairing for stirred mixing tank process

Case1: Diagonal pairing:Figures 10 and 11

Case 2: off-diagonal pairing:Figures 12 and 13

Closed loop undesired response is shown in Figures 9–12 and area is compared in Table 3 conclude that off diagonal pairing is the recommended input output pairing.

Figure 12.

Stirred mixing tank undesired response (y₁) for off diagonal pairing.

Blending Process
(y1-u1); (y2-u2) pairing		(y2-u1); (y1-u2) pairing
y2	1.0393e-05	y2	−3.8772e-24
y1	6.6693e-05	y1	−9.0875e-06

Table 2.

Comparison of area under undesired response of blending process.

Mixing stirred tank reactor
(y1-u1); (y2-u2) pairing		(y2-u1); (y1-u2) pairing
y2	0.6568	y2	0
y1	0	y1	0.6325

Table 3.

Area under the undesired response.

Figure 13.

Stirred mixing tank undesired response (y₂) for off diagonal pairing.

4.3 Loop pairing of CSTR process

By assuming both the diagonal and off diagonal pairing, responses are obtained and its area under the responses are compared to find the desired input output pairing.

Case 1: Diagonal pairing: (y₁-m₁); (y₂-m₂) pairing

Figure 14 represents the closed loop undesired response, y₂ of CSTR process by assuming the diagonal pairing when there is change in input m₁ while m₂ = 0.

Figure 14.

Closed loop undesired response for diagonal pairing (y₂/m₁).

For CSTR process, the closed-loop undesired response, y₁ when there is change in m₂ for diagonal pairing of CSTR process is represented in Figure 15.

Figure 15.

Closed loop undesired response for diagonal pairing (y₁/m₂).

Case 2: Off-diagonal pairing: (y₂-m₁); (y₁-m₂) pairing

Figure 16 shows that for CSTR process, the closed loop undesired response y₂ for the change in m₂ by assuming off-diagonal pairing.

Figure 16.

Closed loop undesired response for off diagonal pairing (y₂/m₂).

The closed loop undesired response y₁ for the change in m₁ for off diagonal pairing in CSTR process is represented in Figure 17.

Figure 17.

Closed loop undesired response for off diagonal pairing (y₁/m₁).

4.4 Loop pairing of pH process

For the pH process, closed loop undesired responses are obtained for both diagonal and off-diagonal pairing as shown in Figures 18–21. The areas obtained under these curves are given in Table 4 and the same is compared to obtain the desired input–output pair based on minimum value.

Figure 18.

Closed loop undesired response for diagonal pairing (y₂/m₁).

Figure 19.

Closed loop undesired response for diagonal pairing (y₁/m₂).

Figure 20.

Closed loop undesired response for off diagonal pairing (y₂/m₂).

Figure 21.

Closed loop undesired response for off diagonal pairing (y₁/m₁).

Case 1: Diagonal pairing: (y₁-m₁); (y₂-m₂) pairing

Figure 18 represents the closed loop undesired response y₂ for the change in m₁ for diagonal pairing of pH process.

For diagonal pairing in pH process, closed loop undesired response y₁ for change in m₂ is shown in Figure 19.

Case 2: Off diagonal pairing (y₂-m₁); (y₁-m₂) pairing

For the pH process, the closed loop undesired response y₂ for change in m₂ is represented in Figure 20 for off-diagonal pairing.

For off diagonal pairing in pH process, Figure 21 represents the closed-loop undesired response y₁ for the change in m₁.

4.5 Loop pairing of distillation column

Similar to CSTR and pH process, the pairing for distillation column is also carried out to choose the correct input–output pairing.

Case 1: Diagonal pairing:

Closed loop undesired response for diagonal pairing of distillation column is represented in Figure 22.

Figure 22.

Closed loop undesired response for diagonal pairing (y₂/m₁).

Figure 23 shows that closed loop response of distillation column for diagonal pairing.

Figure 23.

Closed loop undesired response for diagonal pairing (y₁/m₂).

Case 2: Off- diagonal pairing

For the distillation column, closed loop undesired response y₂ for the change in m₂ for off diagonal pairing is shown in Figure 24.

Figure 24.

Closed loop undesired response for off diagonal pairing (y₂/m₂).

Figure 25 represents that the closed loop undesired response y₁ for off diagonal pairing of distillation column

Figure 25.

Closed loop undesired response for off diagonal pairing (y₁/m₁).

Similarly, Figures 22–25 represent undesired responses for distillation column and its area is given in Table 4.

From the Table 4, for the CSTR, pH and distillation column benchmark nonlinear chemical processes, it is clear that the minimum area is obtained only for (y₁-m₁); (y₂-m₂) pairing. Hence, desirable pairing for all these processes is (y₁-m₁); (y₂-m₂).

CSTR Process
(y1-m1); (y2-m2) pairing		(y2-m1);(y1-m2) pairing
$\left(y_2{m}_1\right)$	0.0036	$\left(y_2{m}_2\right)$	0.0637
$\left(y_1{m}_2\right)$	15.7309	$\left(y_1{m}_1\right)$	0.8989
pH Process
$\left(y_2{m}_1\right)$	0.3333	$\left(y_2{m}_2\right)$	0.2539
$\left(y_1{m}_2\right)$	0.8328	$\left(y_1{m}_1\right)$	1.0930
Distillation column
$\left(y_2{m}_1\right)$	51.0823	$\left(y_2{m}_2\right)$	29.0406
$\left(y_1{m}_2\right)$	26.0268	$\left(y_1{m}_1\right)$	45.7813

Table 4.

Proposed loop pairing - Comparison of areas under the load responses.

5. Conclusion

As real-world physical systems are nonlinear, it is required to control these nonlinear processes. In order to design the nonlinear controller, one needs to choose the proper input–output pair. This chapter discusses the conventional method of loop pairing for the class of benchmark nonlinear system. RGA is calculated based on steady state information for the nonlinear system. The proposed method of input–output pair is also calculated for nonlinear benchmark process. The proposed method of input–output pair is validated with the conventional method. The proposed control configuration selection is based on closed loop response whereas the conventional method of pairing is based on gain. Thus, using the proposed method of control configuration selection one can design the good nonlinear control.