Open access peer-reviewed chapter

Optimization of Fuzzy Logic Controllers by Particle Swarm Optimization to Increase the Lifetime in Power Electronic Stages

Written By

Pedro Ponce, Luis Arturo Soriano, Arturo Molina and Manuel Garcia

Submitted: February 6th, 2018 Reviewed: May 30th, 2018 Published: December 12th, 2018

DOI: 10.5772/intechopen.79212

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In recent years, brushless direct current motor (BLDCM) applications have been increased due to their advantages as low size, mechanical torque, high-speed range, to mention some. The BLDCM control is required to operate at high frequency, high temperature, large voltage, and quick changes of current; as a result of this kind of operation, the power drive lifetime is affected. The power drives commonly utilized insulated gate bipolar transistors (IGBTs) and metal oxide semiconductor field effect transistors (MOSFETs), which present power losses, on-state losses, and switching losses caused by temperature oscillations. Hence, the power losses are related to the command signals generated by the controller. In this sense, the BLDC motor drive controller design, frequently, does not take into account the power losses and the temperature oscillations, which cause the IGBT lifetime decrease or premature fail. In this chapter, a brushless DC motor drive is designed based on a fuzzy controller tuned with the particle swarm optimization algorithm, where the temperature oscillations and speed set points are considered in order to increase IGBT module lifetime. The validation of the proposed fuzzy-PSO controller is carried out by the co-simulation between LabVIEW™ and Multisim™ and finally analysis and conclusion of the work.


  • power electronics lifetime
  • speed controller
  • fuzzy logic
  • PSO

1. Introduction

In this chapter, a design of a BLDCM speed control based and tuned by particle swarm optimization is presented; this proposal control considers two objectives, the first one is the speed set point and the second one is the power electronic lifetime. The BLDC motor covers a wide range of applications in several fields as the robotic systems, aerospace industry, medical industry, automotive industry, and electronic devices [8, 17, 25, 32]. Their structure of control is integrated by BLDC motor stage, power drive stage, and sensor stage. The power drive is integrated by semiconductors as IGBTs and MOSFETs, these semiconductors frequently work under high thermal stress to reach the mechanical reference of speed, and in some cases, after a certain period of operation, they are damaged due to the generation of command signals by the speed controller [7, 9, 12, 23, 34, 35]. There are several methods to predict and evaluate the lifetime of power electronics devices [34], the manufactures develop these studies as an estimation of certain conditions and operation features, but in some applications, these conditions are not always the same and change according to the control objective, which affects the power electronics lifetime used. For these reason, it is important that the controller design not only considers the mechanical references such as position and velocity in the case of BLDCM, as well as the lifetime of semiconductors [10, 22, 23, 24, 33, 34, 35]. Hence, a great effort for predicting and improving the lifetime in semiconductors has been pushing to develop new control algorithms that help to improve the conditions in the semiconductor [16]. In this chapter, the designed controller uses an optimization process based on an objective function that takes into account the temperature of the power electronic stages in order to increase their lifetime, and tracking motor speed reference [1, 10]. Thus, PSO algorithm has been implemented to optimize the controller proposed as in [13, 18, 21, 27, 30], due to its few parameters that need to be tuned and its easy implementation. Finally, the proposed controller in BLDCM is validated through co-simulation, which helps to combine two or more specialized programs utilizing advanced models and avoiding implementation problems between the control systems and power electronics stage [11, 14, 15].


2. Structure and drive mode of BLDC motor

2.1. Types of BLDCM drives

The BLDC motor drive employs a permanent magnet alternating current; the stator windings are commonly star connection, when voltage source is applied between any two terminals, the current flows between two phases, leaving one of the three without energy, and as a result, only one current at a time needs to be controlled. This kind of operation is known as back electromotive force (EMF) and Figure 1 shows the waveform in the BLDC motor with two phases active.

Figure 1.

Trapezoidal EMF.

According to their physical position, the output is related to 60° or 120° phase shift to each other. To drive the windings, a sequence of commutation is necessary; this kind of operation is commonly called “six-step commutation.” The trapezoidal waveform is due to the rotor revolving in a counterclockwise direction, for example, to phase A, after the 120° rotation to the top conductor of phase.

The motor position must be measured by three Hall effect sensors (A, B, and C) so a voltage is sent to the specific coils to control the speed and position of the brushless motor [3, 25]. A standard circuit to drive BLDCM in Multisim™ program is shown in Figure 2.

Figure 2.

BLDCM drive in Multisim™ for co-simulation.

2.2. States space model

According to [25], the BLDCM can be represented by Eq. (1) where Ris the stator resistance per phase, ias, ibs, and, icsare the stator phase current, and eas, ebs, and ecsare the rotating back-EMF that are produced by the winding flux linkage caused by rotating rotor.


The induced EMF is given by the Eq. (2)


where fasθ, fbs=fasθ2π/3and fcs=fasθ+2π/3are the back-EMF waveform function of phase, respectively. ψmis the maximum value of PM; the flux linkage of each winding as ψm=2NSBm. On the other hand, the dynamic features of BLCDM are expressed in state equations as shown in Eq. (3):


where windings are symmetrical, the self-inductance will be equal, and so as the mutual inductance, Las=Lbs=Lcs=LandLab=Lbc=Lca=M. The electromagnetic torque is given in Eq. (4):


and, the complete model of the electromechanical system is described by Eq. (5):


where Tlis the load torque, Jis the rotor moment of inertia, and Bis the viscous coefficient.


3. Power losses

3.1. Semiconductor losses

Power losses can be classified as on-state losses and switching losses. The IGBT power losses in on-state are calculated by Eq. (6):


and the diode power losses in on-state are calculated by Eq. (7):


These can also be estimated using datasheet information of Figure 3. On the other hand, the IGBT energy losses in turn-on are given by Eq. (8):


and, the energy losses in turn-off are given by Eq. (9):


Figure 3.

TheuCEOandrcrc=Uce/Icvalues of datasheet diagram.

On the other hand, the diode energy losses in turn-on are mostly presented when the reverse-recovery energy occurs, and they are given by:


The switch-off losses in the diode are commonly neglectedEoffD0. In consequence, the switching losses in the IGBT are calculated in Eq. (11) as:


In the case of a diode, they are given as the product of switching energies and the switching frequency Fswas shown in Eq. (12).


Finally, the total losses are calculated by Eq. (13).


Besides, the IGBT and diode switching losses can be estimated from characteristic curve provided by datasheet of manufactures as shown in Figures 3, 4 and 5, respectively [5]. Using the equivalent circuit of Figure 6(a), where Wis a module power loss, Tjis the junction temperature IGBT chip, Tfis the heat sink temperature, Tcis the module case temperature, Tais the ambient temperature, Rthjcis the thermal resistance between case and heat sink, Rthcfis the contact thermal resistance between case and heat sink, and Rthfais the thermal resistance between heat sink and ambient air. The junction temperature Tjcan be calculated using the thermal Eq. (14), according to [1, 10].


Figure 4.

TheuDOandrDrd=Uce/Icvalues of datasheet diagram.

Figure 5.

Switching energy losses as a function of collector current.

Figure 6.

(a) Thermal resistance equivalent circuit, (b) electrothermal model.

Modeling of commutation and conduction losses as well as the temperature profiles on IGBT junction is done by electrothermic networks considering averages on a modulation period as shown in Figure 6(b).


4. Power cycle life

The power cycle life can be calculated from the power cycle capability curve that shows the relation between the temperature change Tjand the number cycles. An example of the temperature changes is shown in Figure 7.

Figure 7.

Pattern diagram flow current ofTjpower cycle and temperature change.

During the Tjpower cycle tests, the junction temperature goes up and down in a short time cycle; as a consequence, the temperature difference between silicon and bonding wire results in thermal stress. The Tjpower cycle lifetime is mainly limited by the aluminum bonding wire joints. Figure 8 shows the power cycle capability curve of the IGBT module to Tjmin=25°Cand to Tjmax=150°Caccording to [5].

Figure 8.

Power cycling lifetime curve.

On the other hand, the cycles before failure (CBF) can be calculated by Eq. (15), according to [28, 29].


where Δ T=PtZth, Pt=Irms2Ron, and Zth=2.3354Fr0.165, and the time before failure (TBF) can be calculate in years by Eq. (16).


where Fris the frequency of the thermal oscillations [5, 29]. Table 2 shows the parameters of IGBTs, which are considered in Multisim co-simulation; these parameters are obtained from datasheet of IGBT 10-0B066PA00Sb-M992F0 [24].


5. Fuzzy logic controller

The fuzzy logic was proposed in [26] as a class of fuzzy sets with a continuum grade of membership; hence, a useful methodology to design fuzzy logic controllers is based on a linguistic phase plane [19, 20] as shown in Figure 9, where the error et, change of error ėt, and the variation of current icare considered as membership functions in the fuzzification stage.


Figure 9.

Linguistic phase plane.

Thus, Eq. (17) is defined as the sum of control error (ec) and error of temperature (et), where ecis defined as the difference of the desired speed edand the real speed er; on the other hand, etis defined as et=etdetr, where etdis the desired temperature and etris the real temperature.

The design of membership functions is according to Mamdani method; the knowledge base can be expressed as if-then statements to design a rules base, which is shown in Table 1. At last, the defuzzification stage gets a crisp value from the rule evaluation stage. Hence, the method of the center of gravity is used to compute the crisp value and is given by Eq. (19).

RulesValuesReference point
7NNNii(os) vi

Table 1.

Fuzzy control rules for Figure 12.

Note: The meaning of symbols is as follows, N: negative, Z: zero, P: positive, e: error, ė: error derivative, ic: output, sp: set point, rt: rise time, os: overshot.

So that, the fuzzy control design is carried out by means of the linguistic plane and the rules presented in Table 1. Thus, the controller with small/big rise time as well as small/big overshoot is possible.


6. Particle swarm optimization

Particle swarm optimization (PSO) was developed by [4]; this method is based on the behavior and movement of bird flocks looking for targets; this algorithm was developed to optimize nonlinear and multidimensional functions as in [13, 18, 27, 30, 31]. PSO algorithm needs to initialize the population in a random manner; each particle has a position xitand velocity vitwith respect to target; then in main loop stage, the xitand vitupdate each iteration; this information is called best local position Pit; on the other hand, between all population, there exists a particle that is more closest with respect to the target and it is called global best gt. Additionally, the position and velocity update are defined by:



  • i=1,2,,N, and Nis the size of population;

  • j=1,2,,D, and Dis the number of dimensions;

  • k=1,2,,iter, and iteris the maximum iteration number;

  • xijkis the position of particle i, dimension jat iteration k;

  • vijkis the velocity of particle i, dimension jat iteration k;

  • Pijkis the local best position of particle i, dimension jat iteration k;

  • gjkis the global best;

  • ωis an inertia factor;

  • Cis an acceleration constant; and

  • r1,r2are the independent random numbers, uniformly distributed in 01.

Thus, the primary objective is to find a minimal global value from the cost function to be minimized as it is shown in the next pseudocode [31].

  1. Step 1.Initialization.

           For each particle of population N,

  1. Initialize the position of each particle.

  2. Initialize Pijk.

  3. Initialize gjk.

  4. Initialize vijk.

  1. Step 2. Repeat until the criterion is satisfied.

           For each particle of population N,

  1. Set random numbers to r1jand r2j.

  2. Update its velocity with Eq. (20).

  3. Update its position with Eq. (21).

  4. If xijk<Pijk, then

    1. Update the best local position.

    2. If Pijk<gjk, then update the best global position gk.

  1. Step 3. Get the best solution gk.


7. Design of fuzzy-PSO controller

The design of controller considers two objectives, the first one reaches the desired motor speed, and the second one is the increase of the semiconductor lifetime. The design of fuzzy-PSO controller to the speed control of BLDCM is based on the diagram shown in Figure 11, where μdis the desired speed and temperature, μtis the temperature sensed, and μcis the speed sensed. Furthermore, one of the leading features is the definition of objective function; this is considered as the sum of error of temperature etand error of speed ec, which is given by Eq. (22).


where etis the difference between the desired temperature and the operating temperature; on the other hand, ecis the difference between the desired speed and the real speed. In optimization process, Eq. (22) is defined as the cost function to be minimized, and each membership functions proposed in Figure 10 are considered as a decision variable; finally, the mechanical capacity of BLDC and thermal capacity of IGBT shown in Table 2 are the constraints of the controller optimization.

Figure 10.

Diagram of fuzzy-PSO control.

Figure 11.

Input-output membership functions wheree: error,ė: error derivative, andic: output.

IGBT 10-0B066PA00Sb-M992F09
TJ, junction temperature80 to 175Nm/A
RJSthermal resistance junction to sink3.50K/W
BLDC motor
Stator inductance0.15mH
Stator resistance0.6Ω
Velocity constant0.03Vs/rad
Torque constant0.03Nm/A
Number of poles0.03
Parameter of IGBT in co-simulation Multisim™
IGBT control threshold0.5V
IGBT on resistance0.1 megΩ
IGBT off resistance10Ω
IGBT forward voltage drop0.7V
Diode on resistance1 mΩ
Diode off resistance10 megΩ
Number of switches in parallel1

Table 2.

Experiment settings.


8. Co-simulation design

The experimental frame is a set of assumptions to obtain the behavior trace and compare it with a real world, which is carried out by co-simulation in order to analyze its dynamic response during a specific period of time [6]. Hence, co-simulation helps to validate how it works under specific assumptions [2, 6]. The problem solution of speed control and lifetime of power electronic components is developed with co-simulation tool of Labview™ and Multisim™, where the BLDCM, the Hall effect sensors, and the six steps are simulated in Multisim™ and the parameter design of the BLDCM, the six IGBT 10-0B066PA00Sb-M992F09 [24], and the six-steps inverter are shown in Table 2.

The proposal control is developed in Labview™ software and its response is shown in Figure 14, and the PID and fuzzy control are developed with control design and simulation module and fuzzy logic toolkit [19]; moreover, PSO algorithm is also developed in Labview™, and their parameters are shown in Table 3.

Figure 12.

BLDCM speed response.

Population size30
Social rate (c1)0.005
Cognitive rate (c2)0.002
Inertia factor (W)0.002

Table 3.

Parameters of PSO.

Finally, the primary purpose of co-simulation is to analyze the complete behavior of the electric drive with the proposed control.


9. Discussion and results

The proposed control considers two control objectives, the first one is to track the speed reference and the second one is to keep the desired temperature to increase the lifetime of the IGBTs. Furthermore, the fuzzy-PSO trade-off was tested with PID and fuzzy controllers in co-simulation program, which were evaluated under 25, 30, 35, 40, 60, 80, and 100°C as a temperature desired, 10 and 5 m/s as the reference speed, respectively. As a result, the PID controller response reaches set point of speed in a short time, but it does not present an improvement in the temperature of semiconductors. The fuzzy logic controller improves the response when the desired temperature values are at 40° and 60° and fuzzy-PSO controller presents the best response in order to accomplish the control objective because they reduce the overshoot of current when it reaches the temperature and reference speed. Figures 13 and 14 show the response of controllers, and Figure 12 shows the final membership function adaptation of fuzzy-PSO controller.

Figure 13.

PID, fuzzy, and fuzzy-PSO controllers under different temperatures.

Figure 14.

Tuning the input and output membership function parameters by means of the PSO.

Table 4 shows the mean square error (MSE) of each controller under different desired temperatures, where the MSE of the fuzzy-PSO response shows good performance. To compare the proposed control response with the traditional estimation, the cycles before failure (CBF) given by Eq. (15) was computed to take into account the maximum temperature Tjmax, the change of temperature, T=TjmaxTf, and the IGBT datasheet.


Table 4.

MSE of controllers.

Table 5 shows the calculation of TBF of the PID, fuzzy, and fuzzy-PSO controllers according to Eq. (16), and Figure 15 shows the behavior of the TBF versus temperature, where the fuzzy-PSO controller reaches a longer lifetime.

TemperatureTBF (in years)TemperatureTBF (in years)

Table 5.

TBF of the controllers.

Figure 15.

The behavior of TBF versus temperature in years.


10. Conclusions

In this chapter, a control design that takes into account the power electronics lifetime stage and the speed set point for BLDCM is presented. The objective function of optimization is integrated with the error of power stage temperature and the error of BLDCM speed. A voltage source inverter with six IGBT to drive the BLDCM is considered as power stage, where the current temperature in the power electronic stage, reference temperature, current motor speed, and reference motor speed are considered in the controller design. The PID controller, fuzzy logic controller, and fuzzy-PSO controller were designed and validated by NI Labview™ and Multisim™ co-simulation software. As a result, the fuzzy-PSO controller obtains a good response that increases the lifetime and reaches the set point desired due to the time that it takes to reach the desired speed increases but it reduces the overshoot of current during the transition time which produces minimal stress and degradation of the power electronic components.


This research is a product of the Project 266632 “Laboratorio Binacional para la Gestión Inteligente de la Sustentabilidad Energética y la Formación Tecnológica” [“Bi-National Laboratory on Smart Sustainable Energy Management and Technology Training”], funded by the CONACYT SENER Fund for Energy Sustainability (Agreement: S0019201401).


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Written By

Pedro Ponce, Luis Arturo Soriano, Arturo Molina and Manuel Garcia

Submitted: February 6th, 2018 Reviewed: May 30th, 2018 Published: December 12th, 2018