DC Buck Converter

ISSN: 2278 – 909X International Journal of Advanced Research in Electronics and Communication Engineering (IJARECE)

Volume 1, Issue 3, September 2012

Fuzzy Sliding Mode Control Method for DC/DC Buck Converter Nanda R Mude#1, Prof. Ashish Sahu#2 Electrical Engineering Department Rungta College of Engineering and Technology, Bhilai

Abstract—This paper proposes a Fuzzy Sliding Mode Control (FSMC) as a control strategy for Buck DC-DC converter. The proposed controller uses a sliding mode control mechanism to improve the performance of a conventional buck converter. The performances of the proposed fuzzy sliding controller are compared to those obtained by a classical sliding mode controller. A simple sliding mode control (SMC) technique for the buck converter that has a fixed switching frequency and zero steady state error. The response of this controller is robust and can be defined directly in the time domain. In addition, fuzzy logic implementation of the proposed SMC is provided. Keywords- DC/DC Buck converter; fuzzy logic controller; sliding mode control; fuzzy sliding Mode Control;

1.

INTRODUCTION

DC-DC converters are nonlinear system in nature due to their switching property. Static and dynamic characteristics of these converters have been widely discussed in the literature. In many industrial applications there is a need for the transformation of a constant dc voltage source to a variable dc voltage source, and like a transformer, the converter can be employed for stepwise increase or reduction of dc source voltage. In this way Buck converter has a wide application in electrical industry and power systems and specifically it can supply the voltage for a direct current consumer. Buck is a one-input and multipleoutput in structure with a non-linear property due to its switching behavior, but at the same time when the switch is on and off its behavior is linear. Therefore, by employing the averaging method, it is possible to exchange a nonlinear system with a linear one. Many of the methods are centered on the isolation of the system variables and PI controller design [1]. Some control methods have defined the subject of control based on pole placement. Manuscript received August 25th , 2012.

Nanda R Mude the pursing ME (Power Electronics) in 2010 from RCET, Bhilai under CSVTU, Bhilai, Durg, India, 9893839430

sliding mode control (SMC) has been investigated as a new control method for DC-to-DC converters. It has the advantages of high robustness, guaranteed first-order response and large signal stability [2]. Despite these advantages, there are a number of problems with sliding mode control. sliding mode like control (SMC) that has good features of sliding mode control and eliminates its problems. Specifically, the proposed controller has a robust first order response that is defined directly in the time domain as with sliding mode control. However, this controller also has fixed switching frequency and provides zero steady state error. This control scheme is developed for the buck converter topology and digital implementation of the controller is considered. It has been noted that fuzzy logic can give a sliding mode like response [3]. This paper also provides an explanation of how this is possible by implementing the proposed sliding mode like control in fuzzy logic. 2.

THE DC–DC BUCK CONVERTER

The Buck converter circuit model is depicted in Fig.1.

Figure 1: Buck Converter

Assist. Prof. Ashish Sahu received M.Tech RCET, Bhilai under CSVTU, Bhilai., India in 2010. He is a Assistant professor in the Department of Electrical Engineering, Rungta College of Enginnering and Technology. Bhilai,

india,9993374419

30 All Rights Reserved © 2012 IJARECE



The function of the circuit is divided into two parts. The first part starts when the switch is turned on at t=0. The input current which is rising passes through L filter inductor, C filter capacitor, and RL load resistance. The second part starts when the switch is turned off at t=t1. Due to the presence of stored energy in the inductor, and the inductor current continues passing from L, C, load and D. The inductor current declines until the second switch switching in the next cycle. In this model, Vo is the system output voltage and Vref is the converter voltage. TABLE – 1 BUCK CONVERTER PARAMETERS Symbol

frequency [9]. Hysteresis can be used to control the switching frequency, but a constant switching frequency can not be guaranteed. However, there is always chattering in the sliding mode when hysteresis is employed. The third disadvantage of sliding mode control is that, in a discretetime implementation, the control action (in this case, ON or OFF of the switch) can only be activated once during each sampling period resulting in a constant control effort over that period. As a result, the system is able to approach the sliding mode but not able to stay on it. Fuzzy control has also been applied to control DC-DC Converters [4]-[6], [7]-[11]. Fuzzy controllers are well suited to nonlinear time-variant systems and do not need an exact mathematical model for the system being controlled.

VALUE 4.

3.

rL

0.7Ω

rd

0.7Ω

rc

1.18 Ω

r1

0.2 Ω

C

1450 µF

L

0.42mH

RL

118Ω

Vdc

50 V

d

0.5

FUZZY LOGIC

In 1965, Zadeh proposed Fuzzy logic; it has been effectively utilized in many field of knowledge to solve such control and optimization problems [12]. Fuzzy logic has been available as a control methodology for over three decades and its application to engineering control systems is well proven. In a sense fuzzy logic is a logical system that is an extension of multi-valued logic although in character it is quite different. It has become popular due to the fact that human reasoning and thought formation is linked very strongly with the ways fuzzy logic is implemented. In power system area, it has been used to stability studies, load frequency control, unit commitment, and to reactive compensation in distribution network and other areas. The most important specifications of fuzzy control method are their fuzzy logical ability in the quality perception of system dynamics and the application of these quality ideas simultaneously for power systems [11]. A simple block diagram of a fuzzy system is shown in Fig.4.

Knowledge Based

SLIDING MODE CONTROL

SMC is a powerful method that can produce a very robust closed-loop system under plant uncertainties and external disturbances, because the sliding mode can be designed entirely independent of these effects. However several disadvantages exist for sliding mode control. First of all, an assumption for sliding mode control is that the control can be switched from one value to another infinitely fast. In practice, it is impossible to change the control infinitely fast because of the time delay for control computations and physical limitations of switching devices. As a result, chattering always occurs in steady state and appears as an oscillation that may excite unmodeled high-frequency dynamics in the system. The second disadvantage is that the sliding mode controller will generate an ON-OFF control for the buck converter that yields a non-constant switching

Defuzzier Interface

Fuzzier interface Fuzzy Logical decision Maker

Fig. 4 Details of a fuzzy controller 31

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Four major units are fuzzification block, a fuzzy knowledge-base block, a fuzzy inference engine and a defuzzification block. The functions of the blocks and working principles of the fuzzy system are briefly summarized [14]. A. Fuzzification The fuzzification block performs the following tasks: • Measures the value of input variables. • Performs a scale mapping that transfers the range of values of input variables into the corresponding universes of discourse. • Performs the function of fuzzification, which converts input data into suitable linguistic values that may be viewed as labels of fuzzy sets. The input signals to FLC are scaled using appropriate scaling factors. These scaled input data are then converted into linguistic variables, which may be viewed as labels of fuzzy sets. Fuzzy sets can be characterized by membership functions. There are many types of membership functions e.g., the bell-shaped, linear function, triangular function, trapezoidal function and exponential function. B. Knowledge-base The knowledge base is comprised of two components namely called fuzzy sets (data base) and fuzzy control rule base. The concepts associated with fuzzy sets are used to characterize fuzzy control rules and fuzzy data manipulation in an FLC. These concepts are subjectively defined and based on experience. So, it should be noted that the correct choice of the membership functions of a term set plays an essential role in the success of an application [14]. The fuzzy rule base consists of a set of linguistic control rules written in the form: IF a set of conditions are satisfied (premise), THEN a set of consequences are inferred The collection of fuzzy control rules that are expressed as fuzzy conditional statements forms the rule base or the rule set of an FLC. In particular, the choice of linguistic variables and their membership function have a strong influence on the linguistic structure of an FLC. Typically, the linguistic variables in an FLC are the state, state error, state error derivative, state error integral, etc. One of the key problems is to find the appropriate fuzzy control rules. In general, there are four models of derivation of fuzzy control rules [14]. • Using the experience and knowledge of an expert. • Modeling the control actions of the operator. • Using a fuzzy model of a process. • Using self-organized fuzzy controllers.

C.

Fuzzy inference engine

The fuzzy engine is the kernel of a fuzzy logic controller, which has capability of simulating human decision making based on fuzzy concepts and of inferring fuzzy control actions using fuzzy implication (fuzzy relation) and the rules of inference in fuzzy logic. This means that the fuzzy inference engine handles rule inference where human experience can easily be injected through linguistic rules.

D. Defuzzification The defuzzification block performs the following functions: 1. Scale mapping, which converts the range of values of output variables into corresponding universes of discourse. 2. Transforms the fuzzy control actions to continuous (crisp) signals, which can be applied to the physical plant.

5.

FUZZY SLIDING MODE CONTROL DESIGN

The proposed controller has a configuration as shown in Fig. 5. In an ordinary fuzzy controller, the input gains g0, gl, output gain h and the rule base are designed based on the in depth knowledge of the converter, and tuned using a trial and error method. In a fuzzy controller using sliding mode algorithm, the input gains g0, gl and the rule table are designed based on the principles of sliding mode control. The only variables that need to be tuned are the output gain h. Therefore, the time required for tuning is greatly reduced for a fuzzy controller using sliding mode algorithm [7]. The integrator in the output side eliminates steady-state error.

Fig 5. The Proposed Controller

The combination of the sliding mode control with the fuzzy logic control aims to improve the robustness and the performances of the controlled nonlinear systems. The proposed fuzzy sliding mode controller forces the derivative of the Lyapunov function to be negative definite. So, the rule base table is established to satisfy the inequality Intuitively, suppose that S > 0 and S˙ > 0, the duty cycle must increase. Also, if S < 0 and S˙ < 0 the duty cycle must decrease. Thus, the surface S and its variation ˙S are the




inputs of the proposed controller. The output signal is the control increment ΔU(k) which is used to update the control law. The control signal is defined as follows: U(k) = ∆U(k) + ∆U(k-1) The proposed Fuzzy sliding mode controller is a zero order Sugeno fuzzy controller which is a special case of Mamdani fuzzy inference system. Only the antecedent part of the Sugeno controller has the ”fuzzyness”, the consequent part is a crisp function. In the Sugeno fuzzy controller, the output is obtained through weighted average of consequents [15]. Trapezoidal and triangular membership functions, denoted by N (Negative), Z (Zero) and P (Positive), were used for both the surface and the surface change.

Fig.7. Output singletons

5.1 RULE TABLE Rule table is designed based on FSMC and is given in Table -2 Ṡ /S

NB

NM

NS

Z

PS

PM

PB

NB

NVB

NVB

NVB

NB

NM

NS

Z

NM

NVB

NVB

NB

NM

NS

Z

PS

NS

NVB

NB

NM

NS

Z

PS

PM

Z

NB

NM

NS

Z

PS

PM

PB

PS

NM

NS

Z

PS

PM

PB

PVB

PM

NS

Z

PS

PM

PB

PVB

PVB

PB

Z

PS

PM

PB

PVB

PVB

PVB

Fig.5. Surface S membership functions

Fig. 6. Surface ds Change membership functions




5.2 TUNING OF OUTPUT GAIN Using simulink based simulation h is designed using trial and error and h = 1.5e-012

6. CONCLUSION we propose a fuzzy sliding mode control for improving the robustness and the dynamical performances of a buck DCDC. The proposed fuzzy controller design has as inputs the sliding surface and its variation. It defines the control signal to satisfy the stability and the attraction condition of the sliding surface. The simulation results show that the proposed controller this controller has been designed for a buck converter and the controller is able to overcomes the chattering problem. Moreover, it is proven that the proposed controller is robust for the case of the desired output currents variation and input voltage variations.

7. ACKNOWLEDGEMENTS We wish to acknowledge the support given by Assistant Prof. Ashish Kumar Sahu , Rungta College of Engineering and Technology, Bhilai for carrying out the present research work department of Electrical Engg. for constant encouragement.

REFERENCES

Fig. 5 Block diagram of the proposed fuzzy sliding mode control Buck Converter

[1] Kostov, K. S., Kyyra, J., Suntio, T., The input impedance of a buck converter, European power Electronics Conf., 2003.




[2] R. Venkataramanan, A. Sabanavic, S . Cuk, "Sliding Mode Control of DC-to-DC Conveners." IECON '85 Conference Proceedings, pp. 251-258, 1985.

[10]. K. Viswanathan, D. Srinivasan, R. Oruganti, “A Universal Fuzzy Controller for A Non-linear Power Electronic Converter,” IEEE International Conference on Fuzzy Systems, 2002, Vol. 1, pp. 46-51.

[3] V.S.C. Raviraj, P.C. Sen, "Comparative Study of Propottional- Integral, Sliding Mode, and Fuuy Logic Controllers for Power Conveners," IEEE Transactions on Industry Applications. vol. 33, no.2, Mar./Apr. 1997.

[11]. L. Guo, J. Y. Hung and R. M. Nelms, “PID controller modifications to improve steady-state performance of digital controllers for buck and boost converters,” IEEE Applied Power Electronics Conference and Exposition, Vol. 1, pp. 381 -388, 2002.

[4]. Tzuu-Hseng S. Li, Yun-Cheng Huang, ―MIMO adaptive fuzzy terminal sliding-mode controller for robotic manipulators”, Journal of Information Sciences, Elsevier Science Inc, Volume 180, Issue. 23, December 2010. [5]. Chao-Lin Kuo, Tzuu-Hseng S. Li, Nai Ren Guo, “Design of a Novel Fuzzy Sliding-Mode Control for Magnetic Ball Levitation System”, Journal of Intelligent and Robotic Systems, Springer, Vol. 42, No. 3, pp. 295-316, 2005. [6]. Hai-Ping Pang, Cheng-Ju Liu, wei Zhang, “Sliding Mode Fuzzy Control with Application to Electrical Servo Drive”, Sixth International Conference on Intelligent Systems Design and Applications (ISDA'06) Volume 1, Jinan, China, October 16-October 18, 2006.

[7]. Chih-Min Lin, Wei-Liang Chin, Chung Li, “Adaptive hierarchical Fuzzy Sliding-Mode Control for a class of Coupling Nonlinear Systems”, International Journal of Contemporary Mathematical sciences, Vol.1, No. 4, pp. 177-204, 2006. International Journal of Artificial Intelligence & Applications (IJAIA), Vol.2, No.2, April 2011 30 [8]. F. Qiao. Q.M. Zhu, A. Winfield, and C. Melhuish, “Fuzzy Sliding mode Control for discrete nonlinear systems’, Transactuions of China Automation Society, Vol. 22, No. 22, June 2003. [9]. M. Smyej, M. Saneba and A. Cheriti, “A Fuzzy Controller for a DC to DC Converter Using a Digital Integrator,” Canadian Conference on Electrical and Computer Engineering, Vol. 1, pp. 7-10, 2000.

[12] Zadeh, L., Fuzzy sets, Information Control 8, 1965. [13] Terano, T., AsaI, K., Sugeno, M., Applied fuzzy systems, Academic Presss Inc., pp.86-93, 1994. [14] Lee, C. C., Fuzzy Logic in Control Systems: Fuzzy Logic Controller- Part I, IEEE Trans. On Syst. Man Cybern., vol. 20, no. 2, pp. 404-418, March/April 1990. [15] M.K. Passino, Fuzzy control, Addison-Wesley. London, 2000.

Nanda R Mude was born in Nagpur, India, She received the Bachelor in Power Electronics Engg. degree from Bapu

Rao Deshmukh Engg College, Wardha (M.S), in Year 2000 and the pursing ME in 2010 from Rungta College of Engg & Tech, Bhilai under Chhattisgarh Swami Technical University, bhilai , in Year, both in Power Electronics engineering.

Ashish Sahu received M.Tech from Rungta College of Engg & Tech, Bhilai under Chhattisgarh Swami Technical University, India in 2010. He is a Assistant professor in the Department of Electrical Engineering, Rungta College of Enginnering and Technology. His research interests include Power System Optimization and Control, voltage security and Stability analysis and ANN, Fuzzy application to power system as well as power electronics problems.
