Particle Swarm Optimized Fuzzy Controller for Luo Converter

Particle Swarm Optimized Fuzzy Controller for Luo Converter

N. Nachammai

Associate Professor,

Department of Electronics and Instrumentation Engineering Faculty of Engineering and Technology,

Annamalai University Annamalainagar-608002, Tamil Nadu, India

R. Kayalvizhi

Professor,

Department of Electronics and Instrumentation Engineering Faculty of Engineering and Technology,

Annamalai University Annamalainagar-608002, Tamil Nadu, India

Abstract Positive output elementary Luo converter perform the conversion from positive DC input voltage to positive DC output voltage. Since Luo converters are non-linear and time-variant systems, the design of high performance controllers for such converters is a challenging issue. The controller should ensure system stability in any operating condition and good static and dynamic performances in terms of rejection of supply disturbances and load changes. To ensure that the controllers work well in large signal conditions and to enhance their dynamic responses, soft computing techniques such as Fuzzy Logic controller (FLC) and Particle Swarm Optimization based FLC (PSO-FLC) are suggested. In recent years, Fuzzy logic has emerged as an important artificial intelligence tool to characterize and control a system, whose model is not known or ill defined. Fuzzy logic is expressed by means of if-then rules with the human language. In the design of a fuzzy logic controller, the mathematical model is not necessary. However, the rules and the membership functions of a fuzzy logic controller are based on expert experience or knowledge database. To ensure better performance of fuzzy controller, membership functions, control rules, normalizing and de-normalizing parameters are optimized using PSO. The main strength of PSO is its fast convergence than the other global optimization algorithms. To exhibit the effectiveness of proposed algorithm, the performance of the PSO based fuzzy logic controller has been compared with FLC and the necessary results are presented to validate the PSO for control purposes. Comparative study emphasize that the optimized PSO based fuzzy controller provide better performance and superior to the other control strategies because of fast transient response, zero steady state error and good disturbance rejection under variations of line and load and hence output voltage regulation is achieved. Simulation studies have been performed using Matlab- Simulink software.

KeywordsFuzzy Logic Controller, Particle Swarmj Optimization, Luo Converter, Membership Functions

1. INTRODUCTION

   DC-DC converters are electronic devices used to change DC electrical power efficiently from one voltage level to another. These converters are widely used in switched-mode power supplies, adjustable speed drives, uninterruptible power supplies, telecommunication equipment, spacecraft power system etc. Fuzzy logic controller performs the control of nonlinear systems based on designer practical experience. The application of this technique does not require accurate models of the converter and is able to deal with its typical nonlinearities, showing less sensitivity to noise disturbances and parameters variations. In recent years, several heuristic optimization techniques such as Differential Evolution (DE),

   Ant Colony Optimization (ACO) and Genetic Algorithm (GA) were introduced in the field of fuzzy control applications because of their fast computability. Though GA-FLC approach performs well for complex optimization problems, recent research has identified certain problems where variables are highly correlated and GA crossover and mutation operators do not generate individuals with better fitness of offspring as the chromosomes in the population pool. This research work presents an approach to overcome the design problem of GA- FLC by means of PSO-FLC. PSO algorithm has several advantages such as speed of convergence, simplicity of implementation and less susceptibility of being trapped in local optima. PSO has more actual memory ability than the GA, since each particle recalls its best value in previous iteration and the neighbourhood best. As all particles use the information related to the most successful particle in order to improve them, the algorithm is more effective in preserving the variety of the swarm. The population evolves around a subset of the best individuals in PSO, since the poor solutions are discarded and only the good ones are preserved. In this work, two types of controllers are designed namely the Fuzzy controller and PSO-Fuzzy controller. Fuzzy controller parameters were optimized by PSO for regulating the output voltage of Luo converter. Simulation results are compared and it is found that PSO outperforms random search and at the end of the search process, showing better convergence behaviour.

2. POSITIVE OUTPUT ELEMENTARY LUO CONVERTER (POELC)

   Luo converters belong to a series of new DC-DC converters that are developed from the basic converters using the voltage lift technique. Voltage lift technique is a popular method that is applied in electronic circuit design to improve the circuit characteristics. Luo converters overcome the effects of the parasitic elements that limit the voltage conversion ratio. Positive output Luo converter performs the conversion from positive DC input voltage to positive DC output voltage. They work in the first quadrant with large voltage amplification. The elementary Luo converters perform step- down or step-up DC-DC conversion.

   The positive output elementary circuit is shown in Fig. 1. Switch S is a N-channel power MOSFET (NMOS) device. It is driven by a PWM switching signal with repeating frequency and duty ratio . The switching period is = 1/ so that the switch-on period is and the switch-off period is (1 ) . The load is resistive, where = /; and

   are the average output voltage and current. The elementary

   circuit consists of a positive Luo pump S-L1-C-D and a low pass filter L2-C0. The pump inductor L1 transfers the stored energy to capacitor C during the switch-off period and then the energy stored on capacitor C is delivered to load R during the switch-on period. Therefore if the voltage Vc is higher, the output voltage Vo should be higher. When switch S is ON, the source current = 1 + 2 (Fig. 2). Inductor L1 absorbs energy from the source and inductor L2 absorbs energy from the source and capacitor C. Both currents 1 and 2 increase. When switch S is OFF (Fig. 3) source current = 0. Current

   1 flows through the freewheeling diode D to charge capacitor

   C. Inductor L1 transfers its stored energy to capacitor C. Current 2 flows through the (Co-R) circuit and freewheeling diode D to keep itself continuous. Both currents 1 and 2 decrease.When switch S is turned off, current 1 flows through the freewheeling diode D. This current descends in the switch-off period (1 ) . If current 1 does not become zero before switch S is turned on again, this working state is defined as the Continuous Conduction Mode (CCM). If current 1 becomes zero before switch S is turned ON again, the working state is defined as Discontinuous Conduction Mode (DCM). The average output voltage of the converter in Continuous Conduction Mode is

3. FUZZY LOGIC CONTROLLER

   Fuzzy logic is a form of many-valued logic which is derived from fuzzy set theory. In contrast with crisp logic, where binary sets have two-valued logic, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1. Fuzzy logic controller is a control tool for dealing with ncertainty and variability in the plant. The implementation of the proposed controller does not require any specific information about the converter model as well as circuit parameters and works independent of the operating point of the Luo converter.

   =

   (1 )

   (1)

   Fig. 4 Block Diagram of Fuzzy Logic Controller for Luo Converter

   Design of fuzzy logic controllers mainly involves three steps, namely fuzzification, fuzzy rule base and defuzzfication which is shown in Fig.4. Fuzzification is a process in which the inputs are fuzzified between a range of 0 to 1. Rule base is formed by the experts knowledge and depending on the inputs, the rule base generates the corresponding linguistic variable output. This output is defuzzified from 0 to 1 to a global value. The designed FLC has two inputs, error (e) and rate of change of error (ce) and a controller output (du). The number of necessary fuzzy sets and their ranges are designed based upon the experience gained on the process. A Mamdani based

   Fig. 1 Circuit Diagram of Positive Output Elementary Luo Converter

   Fig. 2 Equivalent Circuit During Switch-ON (Mode 1)

   Fig. 3 Equivalent Circuit During Switch-OFF (Mode 2)

   system architecture has been realized. Max-min composition technique and center of gravity method have been used in the inference engine and defuzzification. In the present work, seven triangular fuzzy sets are chosen as shown in Fig. 5 and are defined by the following library of fuzzy set values for the error e, change in error ce and for the change in duty cycle du. NB: Negative Big, NM: Negative Medium, NS: Negative Small, ZE: Zero, PS: Positive Small, PM: Positive Medium, PB: Positive Big. The fuzzy rule base consists of 49 rules which are used to produce change in duty cycle (du) of the MOSFET of the Luo converter

   Fig. 5 Triangular Type Membership Functions for Error, Change in Error and Change in Duty Cycle

   The derivation of the fuzzy control rules is heuristic in nature and based on the following criteria:

   1. When the output of the converter is far from the set point, the change of duty cycle must be large so as to bring the output to the set point quickly.

   2. When the output of the converter is approaching the set point, a small change of duty cycle is necessary.

   3. When the output of the converter is near the set point and is approaching it rapidly, the duty cycle must be kept constant so as to prevent overshoot.

   4. When the set point is reached and the output is still changing, the duty cycle must be changed a little bit to prevent the output from moving away.

   5. When the set point is reached and the output is steady, the duty cycle remains unchanged and when the output is above the set point, the sign of the change of duty cycle must be negative and vice versa.

      According to these criteria, a rule table is derived and is shown in Table 1. The inference mechanism seeks to determine which rules fire to find out which rules are relevant to the current situation. The inference mechanism combines the recommendations of all the rules to come up with a single conclusion.

      TABLE I. RULES FOR MAMDANI-TYPE FUZZY SYSTEM

      ce e	NB	NM	NS	Z	PS	PM	PB
      NB	NB	NB	NB	NB	NM	NS	Z
      NM	NB	NB	NB	NM	NS	Z	PS
      NS	NB	NB	NM	NS	Z	PS	PM
      Z	NB	NM	NS	Z	PS	PM	PB
      PS	NM	NS	Z	PS	PM	PB	PB
      PM	NS	Z	PS	PM	PB	PB	PB
      PB	Z	PS	PM	PB	PB	PB	PB

      Since the inferred output is a linguistic value, a defuzzification operation is performed to obtain a crisp value. In this work, the centre of gravity or centroid method is used for de-fuzzification. As a result the control increment is obtained by the equation.

      ()

      =1

      pbest and corresponding to the experience of neighbouring particles is gbest. The search for the optimal position advances as the velocities and positions of the particles are updated. The fitness of each particle's position and iteration is calculated using a pre defined objective (fitness) function and the velocity of each particle is updated using pbest and gbest, which were previously defined. The velocity of ith particle can be modified by the eqn. 3. The values c1 and c2 are two positive constants represent the social and cognitive accelerations for the pbest and gbest positions, respectively. The flow chart of PSO algorithm is shown in Fig. 6.

      Fig. 6 Flow chart of PSO algorithm

      PSO Algorithm

      Step 1 : Define fitness function.

      Step 2 : Initialize the particles of the population according to the limits. Initialize parameters 1, 2 and itermax.

      Step 3 : Generate the initial population of N particles with random positions and velocities.

      =

      ()

      =1

      (2)

      Step 4: Calculate the fitness and evaluate the fitness values of current particle using the objective function ISE.

      Step 5 Compare the fitness value of each particle with its

      Here is the distance between fuzzy set and the centre.

      ()is area value of fuzzy set.

4. PATICLE SWARM OPTIMIZATION

   Particle Swarm Optimization is a population based stochastic optimization technique, inspired by social behaviour of bird flocking or fish schooling. In PSO the individuals called particles, fly around in a multidimensional search space and change their position with time. During its flight, each particle adjusts its position according to its own experience

   pbest. If the current value is better than pbest, then set pbest value to the current value.

   Step 6 Compare the fitness value of each particle with its gbest. If the current value is better than gbest, then set gbest value to the current value.

   Step 7 The member velocity v of each individual in the population is updated according to the velocity update equation, as given in eqn. 3.

   (+1) = () + 11( ())

   and according to the experience of neighbouring particles. The

   position or value corresponding to its own experiences called

   + 22 ( ()

   ) (3)

   (+1) = () + (+1) (4)

   (+1) is the new velocity of the ith patticle.

   () current velocity of the ith patticle.

   is the inertia weight factor

   1 and 2 are two random numbers between the range (0,1).

   converter but, indeed, increases the computation time. Consequently, for this research work, seven triangular membership functions have been considered for each input variable, seven linguistic sets have been chosen for the output variable of the fuzzy controller structure. The triangular mem- bership function is chosen due to its simplicity. Integral square error (ISE) is used as an objective function. The mathematical equation of the ISE is given by

   1, 2 are learning factors 0 (1 + 2) 4 In this work,

   1 = 2 = 2.

   =

   0

   2 () (5)

   () is the current poition of the th particle.

   Step 8 The position of each individual is modified according to the position updated equation, as given below

   New position = old position + updated velocity

   Step 9 If the number of iterations reaches the maximum, then go to Step 10. Otherwise, go to Step 4

   Step 10 The particle that generates the latest gbest is the solution of the problem.

   Step 11 Stop.

5. PSO BASED FUZZY LOGIC CONTROLLER The parameters representing the linguistic sets, scaling

   gains and fuzzy rules are represented by the optimization variable of the PSO, called particle. It is a vector of real numbers that consists of three parts, the first part is related to the real numbers required to identify the membership functions, the second part is related to the integer numbers required to identify the fuzzy rules and the third part is related to the real numbers to identify the scaling gains. With regards to the first part of the particle identifying the membership functions, a maximum number of seven fuzzy sets has been chosen. Tuning of the membership function can be carried out by shifting right or left and expand or shrink the membership functions in relation to its universe of discourse. As each linguistic variable has been assumed to have a maximum of seven primary terms, two parameters are then required to represent the membership functions of a linguistic variable of the implemented fuzzy controller. Therefore, in order to represent the three linguistic variables, six parameters are needed to characterize the search space of the problem. With regards to the second part of the particle identifying the fuzzy rules, a total of forty-nine fuzzy rules are used. FLC can be optimized by adjusting the scaling gains Ke, Kce and Kdu. Totally 58 parameters are required to design the fuzzy controller and are represented by the particle. PSO stops if any of the following conditions is reached:

   • the maximum generation number exceeds 100,

   • there is no improvement in the objective functions of the non- dominated solutions for 50 consecutive generations.

   The number of the linguistic sets of the proposed controller has been determined by comparing the responses of the Luo converter for different numbers of the fuzzy sets. The fitness function has been compared for four, five and seven fuzzy sets. It has been found that the use of more than seven linguistic sets does not improve the performance of the

   The structure of the fuzzy logic controller with PSO algorithm is shown in Fig. 7. In order to design the optimal fuzzy controller, the PSO algorithm is applied to search globally optimal parameters of the fuzzy logic controller. The performance of the system must be examined in each particle and iteration position during the optimization process. The optimization algorithm is implemented by using MATLAB m-file program and linked with the system simulation program in MATLAB-SIMULINK, to check the system performance in each particle. The PSO produces the fuzzy controller gains of the FLC which give optimal performance of the Luo converter. In this work, the particle of the PSO algorithm includes three parts: the scaling gains for , , and (, and ), the shape of the membership functions (, , , , , ) and the fuzzy inference rules (C1, C2, .C49).

   Fig. 7 Structure of FLC with PSO Algorithm

   Table II lists the parameters of PSO algorithm used in this work Table III lists the fuzzy inference rules with PSO algorithm. Membership functions for inputs and output variables searched by PSO are shown in Fig. 8.

   TABLE II. PARAMETERS OF PSO ALGORITHM

   Parameter	Particle dimension	Swarm size	Number of iterations	1and 2
   Value	58	30	100	2

   TABLE III. OPTIMISED FUZZY RULES

   ce e	NB	NM	NS	Z	PS	PM	PB
   NB	NB	NB	NB	NM	NS	Z	PS
   NM	NB	NM	NM	NM	Z	PS	PM
   NS	NB	NM	NM	NS	Z	PM	PM
   Z	NB	NM	NS	Z	PS	PM	PB
   PS	NB	NM	Z	PS	PM	PB	PB
   PM	NM	NS	Z	PM	PB	PB	PB
   PB	NS	Z	PS	PM	PB	PB	PB

   Fig. 8 Optimized Input and Output Membership Functions of Fuzzy Controller

6. SIMULATION RESULTS AND DISCUSSION Fig. 9 shows the step reponses of Luo converter with FLC

and PSO-FLC. In the present case, the input voltage step is varied from 10 to 12.5 V at 0.02 sec and from 12.5 V to 10 V at 0.04 sec. The time response of the output voltage in a closed-loop system compensated by a PSO fuzzy controller is illustrated in Fig. 10. The changes in the input voltage do not take any variations in the output voltage since the controller adopt the variations in the parameters and continuously track the reference voltage and therefore, the duty cycle of the MOSFET is changed so as to maintain the output voltage. This proves the effectiveness and the robustness of the controller. Table IV list out the circuit parameter of POELC.

Fig. 10 shows the output voltage of the converter with fuzzy controller and PSO-FLC subject to the step change of the line voltage. When the input voltage is increased suddenly from 10 V to 12.5 V, it is observed that the settling time is

3.63 msec and peak overshoot is 35.45% for Fuzzy controller and for PSO-FLC the settling time is 1.81 msec and peak overshoot is 13.63%. When the input voltage is changed from

12.5 V 10 V, the settling time is 4 msec and the peak overshoot is 30.75% for FLC and the settling time is 1.45

msec and the peal overshoot 11.4% for PSO tuned FLC.

Fig. 11 shows the dynamic behavior of the converter system with a 20% step-change in load resistance. The PSO tuned controller takes 1.27 msec settling time with an overshoot of 9% as compared to 3.27 msec and 28.5% in case of FLC tuned controller when the load changes from 10 to 12. The PSO tuned controller takes 1.09 msec settling time with an overshoot of 6.3% whereas FLC takes 1.45 msec and 27.45% when the load decreases from 12 to 10.

The simulation is carried out by varying the system reference voltage where the result for the output voltage is shown in Fig 12. The reference voltage is changed from 20 V to 30 V at moment t = 0.02 sec where it can be seen that the corresponding output voltage has been changed to 30V. Here, the controller adopts the change in reference value, vary the duty cycle of the converter accordingly and produce the reference as the output voltage, the controller approximately does not take any time to vary the output voltage from 20V to 30V.

TABLE IV. CIRCUIT PARAMETERS FOR POELC

Table V shows the performance evaluation of Luo converter in terms of percentage overshoot, rise time and setting time under startup, set point change, change in the input and load.

Fig.9. Step Responses of Luo Converter with FLC and PSO-FLC

Fig. 10 Closed Loop Responses Under 20% Line Disturbances

Fig. 11 Closed Loop Responses Under 25% Load Disturbances

TABLE I. PERFORMANCE COMPARISON OF PSO-FUZZY AND FUZZY CONTROLLERS

Fig. 12 Servo Responses of Luo Converter

CONCLUSION

In this work, Luo converter with fuzzy control system has been modeled and optimized using PSO algorithm. Comparative studies were made with the two proposed controllers for a sudden change in input voltage and load change. The PSO-fuzzy controller gives the better performance and was more robust for disturbances in comparison with the fuzzy controller. Simulated results obtained validate the effectiveness of the proposed PSO-fuzzy control strategy and the controlled converter behaves very well with very less overshoot and settling time. PSO method is an efficient global optimizer for continuous variable problems and it is easily implemented with few parameters to be tuned.

REFERENCES

1. Luo, F.L. (1997), Luo Converters: New DC-DC step-up Converters, Proceedings of IEEE international Symposium on Integrated Circuit-97, Singapore, Vol.2, Jun., pp. 227-230.

2. Luo. F. L. and Hong Ye. , Advanced DC/DC Converters, First edition, CRC Press, LLC, London, 2014.

3. Pierluigi Siano, Costantino Citro, (2014), Designing fuzzy logic controllers for DC-DC converters using multi-objective particle swarm optimization, Electric Power Systems Research, Vol.112, pp 74-83.

4. Ali S. Al-Dmour, (2016), Simulation and Control of DC-DC Converters Using Particle Swarm Optimization Technique, International. Journal of Advanced Scientific and Technical Research, Vol. 5(6), pp 301-323.

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6. Borni A., Abdelkrim T., Zaghba L., Bouchakour A., Lakhdari A., and Zarour L., (2017), Fuzzy logic, PSO based fuzzy logic algorithm and current controls comparative for grid-connected hybrid system, Technologies and Materials for Renewable Energy, Environment and Sustainability, AIP Conference Proceedings.

N.NACHAMMAI received her B.E (Electronics and Instrumentation) from Annamalai University in 1988 and M.Tech (CEDT) from IISC, Bangalore in 1996. She is presently working as an Associate Professor in Department of Electronics and Instrumentation

Engineering, Annamalai University, where she has put in a total service of 24 years. She is presently pursuing PhD in the Department of Electronics and Instrumentation Engineering, Annamalai University. Her areas of interest are modelling, simulation and implementation of optimization techniques for control of power electronic converters.

Dr. R. KAYALVIZHI has obtained B.E (Electronics and Instrumentation), M.E (Power Systems) and PhD in Instrumentation Engineering from Annamalai university in 1984, 1988 and 2007 respectively. She is currently working as a Professor in the Department of

Electronics and Instrumentation Engineering at Annamalai University where she has put in 32 years of service. She produced 5 PhDs and presently guiding 5 PhD scholars. Her research papers 25 has been presented in the International and National conferences. She has 35 publications in National Journals and 30 in International Journals. Her areas of research interest include Power Electronics, Power Systems and Digital Image Processing. She is a life member of Indian society for Technical Education.