A NEW STRUCTURE FOR THE FUZZY LOGIC CONTROL IN DC TO DC CONVERTERS

Transcription

1 A NEW STRUCTURE FOR THE FUZZY LOGIC CONTROL IN DC TO DC CONVERTERS JENICA ILEANA CORCAU Division Avionics University of Craiova, Faculty of Electrotechnics Blv. Decebal, nr. 07, Craiova, Dolj ROMANIA ELEONOR STOENESCU University of Craiova, Faculty of Electrotechnics Blv. Decebal, nr. 07, Craiova, Dolj ROMANIA Abstract: - In this paper is presented a new structure for the Fuzzy Logic Controller in dc to dc converters. Fuzzy PI controllers generally give overshoot in the output voltage and have a high initial current when the rise time of the response is reduced. A new structure system is a control system implementing different laws in different regions of the state space divided by a set of boundary manifolds. The control input switches from one control law to another when the state crosses the boundary manifolds. The new structure PI+PD fuzzy controller presented is verified with computer simulations and compared with different types of PID-like Fuzzy Controllers for application(applied to) to dc to dc Buck converters. Key-Words: - fuzzy logic control (FLC), P-like FLC, PI-like FLC, PD-like FLC, PI+PD-like FLC, dc to dc converters. Introduction The modeling and control of the dc to dc converters which contain switches is intriguing from the control point of view because of the unusual properties of the switches in comparison with other circuit elements. The difficulties in the modeling of the switched power electronic circuits are mainly due to the non-linear and time varying nature of the switches []. Therefore, the dynamics of the dc to dc converters are non-linear, and practical converter operation deviates from theoretical prediction because of problems associated with parasitic resistances, stray capacitances and leakage inductances of the components. All these make the design of an optimal compensation circuit for closed loop operation of the converters difficult. Most of the modeling in Power Electronics is intended to convert the non-linear and time varying model to an ideal or non-ideal switch model. Then the state space method is used to solve the state equation for the system [2]. A power electronics system, in general, has a complex non-linear model with a parameter variation problem, and the control needs to be very fast which is crucial to the performance of Power Converters is choice of control methods. With Fuzzy Logic Control, the design concept is totally different. The operation of a Fuzzy Logic Control does not require a precise mathematical modeling of the system non complex computation. This control technique relies on the human capacity to understand the system s behavior which determines how effective linguistic rules of the Fuzzy Controllers, are, and is based on qualitative control rules. In [3] is presented a fuzzy PI control structure which would not always give good performance in the whole control process of the non-linear converters, but in [2] is presented variable structure control (VSC) which provides an effective and robust means of controlling non-linear plants. The fuzzy Logic Controller that has been studied so far: one is the position type Fuzzy Controller which generates the control input (u) from the error (e) and error rate ( ), and the other is the velocity type Fuzzy Logic controller which generates an incremental control input ( u) from the error and error rate. The former is called PD-like FLC and the latter is called PI-like FLC according to the characteristics of the information that they process. It is possible to have a PID like FLC which generates control input (u) from e, and However, a PID-like FLC is very complex requiring three dimensional rule tables and has not been used in practice. ISSN: ISBN:

2 The PI like FLC is, however, known to give poor performance in starting response due to the internal integrating operation. To improve the starting response of an PI-like FLC is not easy, especially to reduce the high starting inductor current, and to retain the good steady state performance at the same time. A new structure for the FLC is presented, which can provide improved performance such as a reduction of the high starting current and an well damped output voltage in Fuzzy Control for dc to dc converters. 2 Types of FLC In this section the family of PID like FLC structures will be discussed in detail and their characteristics are presented. 2. P-like FLC The equation for a conventional P- controller is [2], [8]: () The rule for a P-like FLC is given as: R i : If e i is A i Then u i (k) is C i Where A i (antecedent) and C i (consequent) are fuzzy variables characterized by fuzzy membership functions. The natural language equivalent of the above symbolic description reads as follows: For each sampling time k, if the value of the error has the property of being (linguistic value) then the value of control output has the property of being (linguistic value). For simplicity, the explicit reference to sampling time k will be omitted since such a rule expresses a causal relationship between process state and control output variables which holds for any sampling time k. Thus the final symbolic representation of the above rule is In table is presented a very simple rule table would be obtained. Table The rule base for P-like FLC e PB PM PS Z NS NM NB u NB NM NS Z PS PM PB 2.2 PD-like FLC The equation for a conventional PD- controller is [2], [8]: u = K P e + K D, (2) where K P and K D are the proportional and the differential gain coefficients. Then a PD-like FLC consists of rules, the symbolic description of each rule give as R i : If e i (k) is A i and e i (k) is B i then u i (k) is C i Where A i and BBi (antecedent), C i (consequent) are fuzzy variables characterized by fuzzy membership functions, fuzzy variables characterized by membership functions. In table 2 is presented a rule base table for PD-like FLC. Table 2 The base rule for a PI-like FLC to calculate ( u) and for a PD-like FLC to calculate (u) e\e NB NM NS Z PS PM PB NB PB PB PB PB PM PS Z NM PB PB PB PM PS Z NS NS PB PB PM PS Z NS NM Z PB PM PS Z NS NM NB PS PM PS Z NS NM NB NB PM PS Z NS NM NB NB NB PB Z NS NM NB NB NB NB 2.3 PI-like FLC The equation for a conventional PI-controller is [4], [5] u = K P e + K I, (3) where K P and K I are the proportional and the integral gain coefficients. When we derive (3) we get = K P + K I e (4) The PI-like FLC consists of a rule of the form R i : If e i is A i and e i is B i then u i is C i Where A i and B i (antecedent), C i (consequent), are fuzzy variables characterized by fuzzy membership function. In this case, to obtain the value of the control output variable u(k), the change of control output u(k) is added to u(k-). It is to be stressed here that this addition takes place outside the PI-like FLC, and is not reflected in the rules themselves. This is why PI-like FLC has the similar rule as the PD-like FLC and it is shown in table2. If we translate the equation (4) to a discrete form we get the equation for action value change of the discrete PI controller u(k) = K( e(k) + e(k)) (5) Where u(k)=(u(k)-u(k-))/t, e(k)=(e(k)-e(k-))/t, T is the sampling period, k is the step. From [5] it is obvious that the time constant has a relation to the change in error. Therefore we can modify the equation (5) for a fuzzy PI controller u(k) = ( e(k) + e(k)) (6) In the next step it is necessary to map the rule base to discrete state space e(k), e(k). We define the scale factor M for the universe range M>0. This scale factor sets the universe range for the error and the first difference. We extended the equation (6) and get [5] u(k) = ( e(k) + e(k)). (7) The input or output value is multiplied by a constant which indicates a real range of the universe, figure. ISSN: ISBN:

3 If the universe range is multiplied by a coefficient of 5 before fuzzification, the real range of the universe is [-0,2, 0,2]. For an coefficient of 0, the real range of the universe is [-0, 0]. It s evident that there s no conflict with the commonest and this procedure leads to the significant simplicity of the fuzzy controller design as will be demonstrated [5], [8]. Fig. The membership functions for input and output We apply fuzzification to input variables and after defuzzification we get the equation u(k) = D {F{ e(k) + e(k)}} (8) where F is an operation for fuzzification and D for defuzzification. For u(k) results u(k)= = D{F{ e(k) + e(k)}}( 9) The control signal generated by the fuzzy PI controller in step k is: u(k) = D{F{ e(k) + e(k)}}+u(k-) (0) A realization of the fuzzy PI controller is presented in figure 2. The saturation limit of the action value realizes antiwindup. Fig. 2 The Fuzzy PI controller structure with the normalized universe range with antiwindup 2.4 PID-like FLC The equation for a conventional PID controller is u = K P + K D + K I, () R i : If e i is A i and e i is B i and is C i then u i is D i where A i, B i and C i (antecedent), D i (consequent) are fuzzy variables characterized by fuzzy membership functions. The corresponding rule base is a three dimensional table. For example, when is Positive Big (PB), the two-dimension rule table base derived as follows (Table 3). When is positive medium (PM) the derived two dimension rule table is shown in table 4 [2], [8]. PID-like FLC needs three dimensional rule table to get a final control action. It s number of rule increases as the third power of the number of fuzzy sets (i.e. ). Consequently it requires much more computation time and is thus not used in practice. Table 3 Rule Base for a PID like FLC to calculate u(a) e\ NB NM NS Z PS PM PB e NB PB PM PS Z NS NM NB NM PM PS Z NS NM NB NB NS PS Z NS NM NB NB NB Z Z NS NM NB NB NB NB PS NS NM NB NB NB NB NB PM NM NB NB NB NB NB NB PB NB NB NB NB NB NB NB Table 4 Rule Base for a PID like FLC to calcu late u(b) e\ NB NM NS Z PS PM PB e NB PB PB PM PS Z NS NM NM PB PM PS Z NS NM NB NS PM PS Z NS NM NB NB Z PS Z NS NM NB NB NB PS Z NS NM NB NB NB NB PM NS NM NB NB NB NB NB PB NM NB NB NB NB NB NB From the above analysis it can be noted that all PID controllers have their equivalent variable gain fuzzy PID controllers. Even though the symbolic representation is same, the fuzzy PID gains vary depending of the operating point [6], [7]. The FLC contains a number of sets of parameters that can be altered to modify the controller performance such as: - - the scaling factor for each variable; - - the fuzzy representation the meaning of linguistic value; - - the if-then rules. A non-adaptive FLC is one in which these parameters do not change once the controller is being used on-line. If any of these parameters are altered on-line, the ISSN: ISBN:

4 controller will be called an adaptive FLC. If different types of FLCs are used in the same controlled process according to process over time, a variable structure FLC can be obtained. In figure 3 is presented structure of the fuzzy PD+PI controller with the normalized universe range. This is the type of controller that is utilized in the simulation. Fig. 4 The membership functions for inputs and output In [3] is presented the simulation results of PI-like FLC. For convenience they are shown here again in figure 5. 3 Simulation results The various PID-like fuzzy control algorithms and how they and the variable structure FLC will affect the performance of dc to dc converters control are now investigated by simulations usi ng the package Matlab/Simulink. The parameters of Buck converters are: L=00 H, C=200 F, R 0 =4, =20V [2]. The simulations results are for start up of the Buck converter from the zero initial state. The membership functions in figure 4 are used. The parameters, the denormalization factors,, and, can be found in [2]. In this paper, the simulation results are compared with the results presented in [3]. Simulation results are obtained with a supply voltage change from 20V to 5V and for load resistance change from 4 la 2.5. Fig. 5 Simulation results of fuzzy PI controller Fig. 3 Structure of the fuzzy PI+PD It is should be noted that the integrator in the fuzzy PI controller reduces the steady state error but, fuzzy PI controllers generally give inevitable overshoot in output voltage and high initial inductor current when one tries to reduce the rise time response. This is because of integral saturation. Fuzzy PD controller gives better starting performance but large steady state error. The large steady state error is caused by the lack of integral operation. In order to combine the advantages of fuzzy PI controller with those of fuzzy PD controller, a new structure fuzzy logic control is proposed in this paper, used to create an fuzzy controller as a parallel combination of fuzzy PI and PD controller. In figure 6 is presented the structure of the fuzzy PD+PI controller realized in Matlab/Simulink. The simulation results obtained using PI+PD fuzzy controller are presented in figure 7. We observe in figure 7 that the structure of the fuzzy PD+PI controller gives the desired performance, less overshoot in the output voltage, less initial inductor current, and less steady state error. ISSN: ISBN:

5 Step 0.5 Gain Discrete Filter 2.5 Gain PI Gain2 Discrete Filter Fuzzy Logic Controller with Ruleviewer Scope Vref To Workspace2 PD 6 Constant Vin Iin I0 V0 Subsystem Scope2 Iin To Workspace Scope V0 To Workspace 4 Conclusion In this paper is presented the basic structure of PID-like FLC. The new structure of an PI+PD fuzzy controller is investigated, which can provide improved performance such as reduction of the high starting current and well damped output voltage in fuzzy control for dc to dc Buck converters. 0.5 Gain4 Discrete Filter2 2.5 Gain3 Fuzzy Logic Controller with Ruleviewer Fig. 6 The block scheme realized in Simulink using PI+PD fuzzy controller t[s] References: []. Bor-Ren Lin and Richard G. Hoft. Analysis of Power Converter Control Using Neural Network and Rule-Based Methods". Electric Machines and Power Systems, Vol. 24, No. 7, 996 pp ; [2]. Yigang Shi. Performance improvement of dc-dc converters using Fuzzy Logic Control (FLC). Thesis submitted to the Department of Electrical and Computer Engineering, Canada, 999; [3]. Corcau J., Dinca L. Performance improvement of dc to dc converters using the different slopes of membership functions on fuzzy logic control. ICNPAA- 2008, Mathematical Problems in Engineering Aerospace and Science, June [4]. Corcau J., Stoenescu E., Lungu M. Comparative analysis of classical and fuzzy PI algorithms WSEAS Intern. Conferences, Univ. of Cambridge, February 2008, pg , ISBN , ISSN ; [5]. Pivonka P. Analysis and design of fuzzy PID controller based on classical PID controllers approach, Physica-Verlag, 2000; [6]. Tomescu B. On the use of fuzzy logic to control paralleled dc-dc converters. Dissertation Virginia Polytechnic Institute and State University Blacksburg, Virginia, October, 2000; [7]. Mattavelli, P., Rossetto, L., Spiazzi, G., Tenti, P. General-purpose fuzzy controller for dc/dc converters, APEC, 995; [8]. Edik Arakeljan, Mark Panko, Vasili Usenko. Comparative analysis of classical and fuzzy PID algorithms, Physica-Verlag, t[s] Fig. 7 Simulation results using PI+PD fuzzy controller. a. for supply voltage change from 20V to 5V; b. for load resistance change from 4Ω to 2,5Ω ISSN: ISBN: