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Implementation and design of Fuzzy controller for high performance DC-DC boost converters A. Mansouri, F. Krim Dept of Electronics, Faculty of Technology, University of SETIF1, Algeria. Laboratory of Power Electronics and Industrial Control (LEPCI) [email protected], [email protected] Abstract—This paper discusses the implementation and design of both linear PI and fuzzy controllers for DC-DC boost converters. Design of PI controllers is based on temporal response of closed-loop converters, while fuzzy controllers design is based on heuristic knowledge of boost converters. Linear controller implementation is quite straightforward relying on mathematical models, while fuzzy controller implementation employs one or more artificial intelligences techniques. Comparison between these boost controllers is made in design aspect. Experimental results show that the proposed fuzzy controller system is robust against input voltage and load resistance changing and in respect of start-up transient. Results indicate that fuzzy controller can achieve best control performance concerning faster transient response, steady-state response good stability and accuracy under different operating conditions. Fuzzy controller is more suitable to control boost converters. Key-words—Boost controllers DC-DC converter, Fuzzy, PI I. INTRODUCTION Fuzzy logic has rapidly become one of the most successful of today technologies for developing sophisticated control systems. Fuzzy control is considered one of the most important applications in fuzzy logic which is a technique developed to imitate human behaviour. Fuzzy logic control is one of the intelligent schemes that convert linguistic control strategy based on expert knowledge, human intuition and heuristics into automatic control actions offering a high-level computation. Over past two decades, fuzzy controllers have been successfully developed and used in various applications in power electronic converters as power quality is a serious particular issue in the developing countries [1][5]. Fuzzy logic controllers have recently been implemented as embedded controllers for robotics [6] and have been applied to a broad range in Engineering Sciences [7], [8]. Numerous motor drive problems have been solved using fuzzy principles [9]–[11]. Conventional DC-DC buck, boost, fly-back and cùk (buck-boost) regulators are power electronic systems that convert a fixed DC voltage source into a minimum loss variable voltage by a switching technique using BJT, MOSFET, IGBT transistors or GTO thyristors [12][17]. MOSFET are extremely popular in low power, low voltage and high frequency switching applications (hundreds of kHz).including switching mode small power supplies, solid state DC relays and brushless DC motors. DC converters are used extensively in personal computers, computer peripherals, adapters of consumer electronic devices, and in telecommunication where efficiency, volume and mass constitute important constraint in aerospace, undersea, airborne systems, military equipments. IGBT are extremely popular devices used in medium and high power applications to control DC motors in the converter circuits, in DCAC drives in inverter circuits, in high power supply systems. They can be used for traction motor control in electric automobiles, trolley cars, forklift trucks and mine haulers. Control technique for DC-DC converters must cope with their wide input voltage and load variations to ensure stability under any operating conditions while providing fast transient response, smooth acceleration control and high efficiency. Most used conventional controllers in industrial applications are PI because of their simple structure and good performance in wide range of operating conditions. However, control parameters for design of an optimal compensation circuit for closed loop operation of converters, which ensure proper behavior in any operating conditions, are difficult to obtain because dynamic of DC-DC converters is non-linear, and practical converter operation deviates from theoretical prediction due to problems associated with parasitic resistances, stray capacitances and leakage inductances of the components. Various analysing techniques are adapted as standard instruments for modelling and control of DC-DC converters using state space averaging method [18], but linearization limits their validity to small signal behaviour in operating point before others techniques [19], [20] such as LaplaceTransform and Bode plots can be applied. In recent years, artificial intelligence techniques could be applied such as Artificial Neural Network (ANN) control based on learning to simulate human thinking [21], [22], Fuzzy Logic (FL) control requires linguistic variables to model inaccurate or incomplete knowledge [23][26], Fuzzy Neural Network (FNN) control [27], [28] and their mixture with genetic algorithms (GA) in direct optimization approaches [29]. To test dynamic properties and robustness of intelligent controller under any operating conditions, this paper proposes an adaptive fuzzy inference system (FIS) based controller for DC-DC boost converters. In FIS design, controller is able to regulate the output voltage to a desired value without steady-state oscillations despite change in load resistances or reference voltages, provided fuzzy controller has been designed accurately. For fuzzy control based on artificial intelligences, design concept is totally different from conventional PI controller techniques using a plant model. Then, operation of fuzzy controller does not rely on how accurate model is, but on how effective linguistic rules are, giving better performance in such cases. This makes them more effective in applications where existing models are nonlinear, ill-defined and not reliable enough. Fuzzy control therefore simplifies design of optimal compensation for DC-DC converters. II. PI BOOST CONVERTER CONTROL pulse width modulation (PWM) control signal for DC converters. Continuous mode modelling is naturally very rigorous and well adapted to DC converters operating in PWM. Second order OLTF of buck-boost converter small signal model is given by the following equations (3), (4) for standard state space averaging techniques where D is the nominal duty cycle and D0=1-D: ' V V0 .R.D0 0 Ls Vˆ ( s ) D0 (3) H ( s ) BO 0 2 2 ˆ RLC .s L.s RD0 d ( s) ' Vˆ ( s) V0 .R.D0 (4) G( s) BO 0 2 2 Vref ( s) RLC .s L.s RD0 Major characteristics of typical control systems, which are often used as measures of performance to evaluate systems, are stability, accuracy, and speed of response. Feedback control systems could present defaults so as insufficient steady-state accuracy, bad stability, too high overshoot, and a long settling time. For design of control systems, it is often necessary to introduce controllers to meet a set of specifications witch define the To control CL system, it is necessary to choose overall performance parameters of systems. We will coefficients values of KP and Ki using trial and error implement PI and fuzzy controllers to compare their procedure to meet a set of specifications which define the overall performance because design of control system is performances. Controlled system must respond to the required an attempt. Optimal values of PI controller are: KP = 0.75 Ki = 200 performances by industrial context characterising its transient and steady states: transient state is characterized III. FUZZY CONTROLLER FOR DC-DC CONVERTERS by damping factor (minimal overshoot) and settling time We are interested to replace PI conventional regulator (shorter is within 5% criterion faster response will be). Steady state response is characterised by its static by fuzzy logic controller. For any application, block accuracy and stability. PI regulator parameters will be diagram of fuzzy controller scheme shown in fig.2 of DCimplemented to compensate instability or poor stability, DC converters is composed of five elements computed in insufficient precision, sluggish and large overshoot. PI three steps: Fuzzifier (1), Decision Making based on fuzzy controller which combines two control actions can be logic rules (2), Defuzzifier (3). represented by the following control law: Rules base (1) u (t ) K p .e(t ) K i e(t ).dt e(t) G1 G3 Where e(t) is the output voltage error : e(t ) Vref t V0 t ce(t) Fuzzifier (1) Decision Making (2) Defuzzifier (3) (2) d G2 Proportional gain control KP provides control signal proportional to error. It acts as an amplifier. - If KP is large enough, control signal increases rapidly: overshooting risk and oscillation output increase. - If KP is small, control signal increases slowly: no oscillating risks. Integral action gain Ki reacts slowly to changing error and insures progressive compensation of the reference. While positive error (or negative) subsists, the action u(t) increases (or decreases) until error annulations. Fig. 1 illustrates PI controller boost block diagram to regulate its output voltage V0 and current I0. Vref PI controller up d e PWM + KP + - + u i Ki / s V0 dn _ Boost V0 ; I0 Controller _ Fig .1: PI buck-boost - controller block diagram. _ PI Regulator stabilizes the load output voltage and _ then must eliminate error between reference voltage Vref 8 V0. It provides the duty cycle and measured output voltage d which is compared with- a saw tooth voltage to generate Data base Fig.2: Fuzzy controller scheme. Fuzzifier (1): error e(t) and change of error ce(t) are input physical variables of the fuzzy controller that will be first normalized to an universe of discourse with scaling factors, G1 and G2 gains respectively, for a control action defined by change in duty cycle d scaled by a normalized gain G3 permitting adaptive signals processing. These elements act globally over the control increasing or reducing universe of discourse of control quantities. Fuzzifier module converts these normalized inputs to linguistic codes or sets described by membership factors e, ce, .d. Fuzzifier requires definition of linguistic sets and commonly used membership functions triangular, trapezoidal or bell-shaped depending on the individual application and experience of the process user [30]. These one will be defined over normalized [-1, 1] universe of discourse to affect membership degree to fuzzy input sets (fig.3a), divided into five triangular fuzzy-set levels, and a normalized [0, 1] universe of discourse for the output, partitioned in seven triangular fuzzy-set values (fig.3b) [31]. Decision making (2): Fuzzy controller output d is deduced from the Fuzzifier inputs e and ce using individual contributions of each rule from the rules base to form a decision table for the fuzzy controller. Table 1 represents the inference matrix composed of 25 control rules showing different situations usually obtained from expert knowledge or heuristic (based on judgments of experienced plant operator) and expressed as a set of IfThen rules to obtain a non linear relationship between system states and control action which gives better control action than conventional techniques. For fuzzy control, we can use one of the most used inference mechanism: MAXMIN, MAX-PROD, and SOM-PROD. Defuzzifier (3): Fuzzy logic controller output expressed in linguistic code must be converted to physical or numerical values and scaled to determine the well adapted action of the controller from all contributions. Defuzzifier can either choose one of the most used algorithms: maximum criterion or centre of gravity methods (COG) [32]. COG method is the most popular defuzzification technique and is widely used in actual applications because the easier maximum method is inefficient when the membership function posses many maximums corresponding to maximum abscise of the output value. The weighted average of the membership function or the COG of the area bounded by the membership function curve is computed to be the crispest value of the fuzzy quantity. Error Fuzzy Set Degree of Membership mu(E) NB 1 NS ZE PS PB 0.8 0.6 0.4 0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 Error 0.2 0.4 0.6 0.8 1 Fig.3.a Inputs Membership functions for e and ce. Degree of Membership mu(Delda d) Changing Duty Cycle Fuzzy Set PB 1 PM SS M PB MB BB the error e(k) and the change of error ∆e(k), illustrating clearly the nonlinear characteristics of the proposed fuzzy controller structure. Fig .3.c: Fuzzy control surface. TABLE 1 : FUZZY CONTROL RULES. en en NB NB NS ZE PS PB PB PB PM PS M NS PB PM PS M BP ZE PM PS M BP BM PS PS M BP BM BB PB M BP BM BB BB Five fuzzy levels or sets are chosen and defined by the following library of fuzzy-set values for the error en and change in error en: PS: Positive Small; ZE: Zero Equal; NB: Negative Big; PM: Positive Medium; NS: Negative Small; PB: Positive Big; BP: Big Positive NM: Negative Medium; M: Medium; BM: Big Medium; BB: Big Big. The number of fuzzy levels is not fixed and depends on the input resolution needed in an application. Larger the number of fuzzy levels, higher is the input resolution. Inputs are not quantized in the classical sense that each input is assigned to exactly one level. Triangular functions are used here to reduce complexity in calculations [33]. Hence, the fuzzy representation of quantized values and are the fuzzy sets and the degree to which they belong to each fuzzy set. Inference matrix in table 1 is established by a logic taking into account the system physics. Hence a perfect knowledge of its behaviour to regulate permit establishing fuzzy rules different from conventional methods based on mathematical models. Fuzzy control action can be expressed as follow: 0.8 d = If e is NB and e is NB then d is PB if e is NB and e is PS then d is PS 0.6 Or Or 0.4 Fuzzy control model of boost DC-DC converter 0.2 0 0 0.1 0.2 0.3 0.4 0.5 Delta d 0.6 0.7 0.8 0.9 1 Fig. 3.b Output Membership functions for d. Fig. 3c hereunder represents the normalized output of the proposed fuzzy boost controller structure as a function of ………………………………… . Fig.4 scheme describes block diagram of fuzzy logic control configuration for the DC-DC boost converter. The boost converter is represented by a black box from which only the terminals corresponding to the output voltage V0, DC voltage source Vref and the control duty cycle inputs are shown. The fuzzy controller used to adjust the converter output voltage is the Mamdani implication technique. Inputs of the fuzzy controller are error e and change of error ce. The output of the fuzzy controller is the normalized variation of the duty cycle d, computed in the following three steps for fuzzy adjusting. DC voltage source Vref + - PWM V0 Stage Integrator 1 s Gain G3 Fuzzy controller dk + BOOST Converter Gains G1 ek cek A. Simulation of Fuzzy and PI controlled boost converter - Vref Error + Derivative G2 L= 0.038mH RL=0.47Ω, C=220μH, Load R=50Ω, Vin=30v and V0=50v, PWM switching frequency fs=12 KHz. Regulated DC Output V0 dk Duty cycle Results are given for the simulation of a Boost converter acting in continuous mode. Converter parameters are: 1) Fixed input voltage Vref and load R We fix Vref=50V and load R=50Ω values, to observe system performance parameters: settling time ts, overshoot Dmax in transient state; stability, accuracy in steady state. Fig.5 (a, b, c, d) shows the controlled fuzzy and PI boosts temporal responses of output voltage V0; output current I0, duty cycle d and error E. ek Fig .4 Fuzzy controller boost block diagram. Inputs of the boost fuzzy controller are: 1. Error e(k) (4) which is the difference between sampled reference voltage Vref(k) and converter sampled output voltage V0 (k): th 2. Change of voltage error Ce(k) (5) at the k instant is defined as follow: Ce(k) = e(k) e(k-1) 40 Vout (V) (4) 50 30 Fuzzy V0 PI V0 20 sampling 10 0 0 (5) Output dk of the controller computed, using the preferred COG method, is compared to a wave tooth signal to generate PWM control signal. This signal is generated to control switch in the boost converter appropriately, to adjust the desired level output voltage V0. The three variables e, e, d are normalized so as the scaling factors G1 =80, G2=1/80 and G3 were computed in such a way that normalized inputs e(k) and e(k) are well adapted to the [-1,1] universe of discourse and a normalised one [0, 1] for the output for any operating points, expressed as follow in (6): 0.05 a) 0.1 0.15 Time [s] 0.2 0.3 Fuzzy and PI boost Output voltages Vout . 1 0.8 0.6 0.4 Fuzzy I0 PI I0 0.2 ek= e G1 ; ek = e G2 ; dk =dk G3 0.25 Fuzzy & PI boost Currents IO for fix Vref & R 1.2 Iout (A) e(k) = Vref (k) V0 (k) Fuzzy & PI boost Voltages VO for fix Vref & R 60 (6) 0 0 Output of the fuzzy boost converter is the duty cycle dk at the kTh sampling time determined by adding the previous duty cycle dk-1 to the calculated change in duty cycle dn scaled by G3, defined by (7): 0.05 b) 0.1 0.15 Time [s] 0.2 0.25 0.3 Fuzzy and PI boost Output currents Iout. PI & Fuzzy boost Errors 60 dk =dk-1 + dk G3 50 Where dk is the inferred change of duty cycle by the fuzzy controller kTh sampling time, and G3 is the gain factor of the fuzzy controller. Adjusting G3 can change the effective gain of the controller. In classical control theory, (7) represents an integrating effect of the fuzzy controller output which increases system type and improves steady state error. 40 IV. RESULTS AND DISCUSSION E [V] (7) PI Error Fuzzy Error 30 20 10 0 -10 0 0.05 c) 0.1 0.15 Time (s) 0.2 Fuzzy and PI boost Errors E. 0.25 0.3 Fuzzy & PI boost Duty Cycles d for fix Vref & R 0.5 PI boost Error E for changing R & fix Vref 0.6 0.4 Error E (V) 0.5 d 0.3 Fuzzy duty cycle d PI duty cycle d 0.2 0.4 0.3 0.2 0.1 0.1 0 0 0 0.05 d) 0.1 0.15 Time [s] 0.2 0.25 0.3 -0.1 0 0.05 0.1 Fuzzy and PI boost duty cycles d. c) Fig.6 Fuzzy and PI controlled boost responses for fix Vref and R. 0.2 0.25 0.3 0.25 0.3 PI boost error E. PI boost Duty Cycle d for changing R & fix Vref 0.5 0.4 0.3 d For PI boost controller, fig.5 show that along transient state, overshoot value reaches Dmax=14.8%, system oscillations are quickly dumped and the steady state is reached after ts=22.5ms for a small steady state error EPI=0.5623. Increasing of duty cycle is proportional to output voltage rising and vice versa. 0.15 Time [s] 0.2 0.1 Fig 5 show fuzzy boost controller responses with an overshoot Dmax=3.6 %, reaching very quickly steady state final values in a settling time ts =5ms for a very small steady error EFUZZY= 0.0821<Epi and a duty cycle d= 0.42. 0 0 0.05 0.1 d) 2) Changing load R and fixed voltage Vref 0.15 Time [s] 0.2 PI boost duty cycle d. Fig.6: PI controlled boost for changing R and fix Vref. Fig.6(a, b, c, d) show PI controlled boost system responses of the voltage V0, current I0, error E and duty cycle d for changing R and fix Vref. We first simulate the controlled boost system for a load changing of 30%R, then 60%R at t=0.1s and t=0.2s. PI boost Output Voltage VO for changing R & fix Vref 60 50 Vout (V) 40 1) Robustness tests For robustness tests of the fuzzy boost controller, we study apart the changing influence of load R and reference voltage Vref. We first simulate the system for a fixed reference voltage Vref and a load changing of 30%R, then 60%R at t=0.1s and t=0.2s. After that, we change the reference voltage Vref while the load R is fixed. a) Changing load R and fixed voltage Vref 30 20 10 0 0 B. Simulation of fuzzy controlled boost converter Fig.7(a, b, c, d) show fuzzy controlled system responses of the voltage V0, current I0, error E and duty cycle d for fix Vref and changing R. PI V0 Vref 0.05 0.1 0.15 Time [s] 0.2 0.25 0.3 Fuzzy boost Output Voltage VO for changing R & fix Vref 60 a) PI boost Output voltages V0 and Vref. 50 Fuzzy V0 (V) 3 PI boost Output Current IO for changing R & fix Vref 2.5 Iout (A) 2 1.5 1 40 30 Fuzzy V0 Vref 20 10 0.5 0 0 0.05 0.1 0.15 Time [s] 0.2 0.25 0.3 0 0 0.05 a) b) PI boost Output current I0. 0.1 0.15 Time [s] 0.2 0.25 Fuzzy boost output voltages V0 and Vref. 0.3 Fuzzy boost Output Current IO for changing R & fix Vref Fuzzy boost Voltage VO for changing Vref & fix R 60 2.5 50 2 40 Vout (V) Fuzzy I0(A) 3 1.5 1 Fuzzy V0 Vref 30 20 0.5 10 0 0 0.05 0.1 b) 0.15 Time [s] 0.2 0.25 0.3 0 0 0.15 0.2 0.25 Time [s] Fuzzy boost output Voltage V0 for changing Vref. a) Fuzzy boost output current I0. Fuzzy boost Error E for changing R & fix Vref 50 0.05 0.1 0.3 Fuzzy boost Current IO for changing Vref & fix R 1.2 Fuzzy I0 1 40 Iout (A) Error E (V) 0.8 30 20 0.6 0.4 10 0.2 0 -10 0 0 0 0.05 0.1 c) 0.15 Time [s] 0.2 0.25 0.05 0.1 0.2 0.25 0.3 0.3 b) Fuzzy boost output Current I0 for changing Vref . Fuzzy boost error. Fuzzy boost Error E for changing Vref & fix R 60 0.5 0.15 Time [s] Fuzzy Error E Fuzzy boost Duty Cycle d for changing R & fix Vref 40 Fuzzy E (V) 0.4 d 0.3 20 0.2 0 0.1 -20 0 0 0 0.05 0.1 d) 0.15 Time [s] 0.2 0.25 0.05 0.3 c) Fuzzy boost duty cycle d. 0.1 0.15 Time [s] 0.2 0.25 0.3 Fuzzy boost Error E for changing Vref. Fuzzy boost Duty Cycle d for changing Vref & fix R 0.5 Fuzzy duty cycle d Fig.7 Fuzzy controlled boost responses for changing R and fix Vref . 0.3 d Fig.7 shows that the system output voltage V0 pursues the reference voltage Vref for any load change. We observe a small pick of 1V at t=0.1s and another one of 2V at t=0.2s due to the load value changing with very small errors. 0.4 0.2 0.1 b) Changing voltage Vref and fixed load R Fuzzy controlled system responses for the output voltage V0, output current I0, error E and duty cycle d for changing Vref at t= 0.1s and t = 0.2s for Fixed R, are shown in fig.8(a, b, c, d). 0 0 0.05 d) 0.1 0.15 Time [s] 0.2 0.25 Fuzzy boost duty cycle d for changing Vref. Fig.8 Fuzzy controlled boost for changing Vref and Fix R. 0.3 C. Simulation of PI controlled boost converter Fig.9(a, b, c, d) show PI controlled system responses of the voltage V0, current I0, error E and duty cycle d for changing Vref and fi PI boost Voltage VO for changing Vref & fix R 100 PI V0 Vref 60 D. PI and fuzzy controllers Comparison PI and fuzzy boost controller performance parameters are compared using their responses in fig.10 showing the settling time, overshoot and static error. We use 5% criterion as shown in fig.10 to estimate system speed of response. 40 60 20 50 0 0 0.05 a) 0.1 0.15 Time [s] 0.2 0.25 0.3 PI boost output Voltage V0 for changing Vref. 30 ts=22.5ms ts=5ms Fuzzy Controller PI Controller +5% 65% 20 PI boost Current IO for changing Vref & fix R 2 PI & Fuzzy boost Voltages VO for fix Vref & R 40 Vout [V] Vout,Vref (V) 80 Fig.8 (a, b, c, d) show fuzzy boost controller responses with better tracking compared to PI boost controller illustrated in fig.9 (a, b, c, d). PI Current I0 10 Iout (A) 1.5 0 0 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Time (s) Fig.10 Fuzzy and PI boost output voltages. 0.5 0 0 0.05 b) 0.1 0.15 Time [s] 0.2 0.25 0.3 From fuzzy and PI output voltages of fig.10, we illustrate performance parameters in table.2. PI boost output Current I0 for changing Vref . TABLE.2 PI AND FUZZY PERFORMANCE PARAMETERS. PI boost Error E for changing Vref & fix R 60 Regulators PI Error E PI Fuzzy 40 Settling time Ts (5%) (ms) 22.5 5 Overshoot DMax (%) 14.8 3.6 Mean Error E(V) 0.5623 0.0621 PI E (V) 20 Fig. 10 shows fuzzy output voltage Vo, in steady state, reaching the reference voltage Vref = 50V in a shorter setling time ts (fuzzy) =0.005s for a smaller overshoot Dmax(fuzzy) =3.6% than PI settling time ts(PI)=0.0225s and a PI overshoot Dmax(PI)=14.8% with better accuracy EFuzzy=0.0621<EPI=0.5623. 0 -20 -40 0 0.05 0.1 c) 0.15 Time [s] 0.2 0.25 0.3 V. PI boost Error E for changing Vref. PI boost Duty Cycle d for changing Vref & fix R 1 PI duty cycle d 0.8 d 0.6 0.4 0.2 0 0 0.05 d) 0.1 0.15 Time [s] 0.2 0.25 PI boost duty cycle d for changing Vref. Fig.9 PI controlled boost for changing Vref and Fix R. 0.3 CONCLUSION Various tests have shown that fuzzy regulator is capable of reducing effect of different disturbances such as load changes and reference voltage variations common in industry. Fuzzy regulator yields better dynamic performance than PI especially in transient state concerning speed of response and smooth tracking without overshoot with better steady state accuracy which confirms the overall effectiveness of fuzzy logic method. Unlike conventional PI boost controller, fuzzy controllers are based on artificial intelligence rather than on the plant model ill-defined leading to greater complexities in the design of the control system. For this reason, we have used small signal behaviour for the PI boost controller modelling. Results show that intelligent control systems give better performance parameters in such cases and can provide accurate control over a wide range of operating conditions. They are able to make approximations and intelligent guesses in order to come out with good results under given set of constraints for any type of dc-dc structures. To improve performance, we will combine fuzzy logic with GA or PSO. 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