Design and Simulation of the Auto-Tuning TS-Fuzzy PID Controller for the DC-DC ZETA Converter Lala Bakirova1, Elvin Yusubov2 1 Azerbaijan State Oil and Industry University, Azadliq Ave, Baku, AZ1010, Azerbaijan 2 Azerbaijan State Oil and Industry University, Azadliq Ave, Baku, AZ1142, Azerbaijan Abstract In this paper, an auto-tuning fuzzy logic proportional integral derivative controller (ATFPID) based on a Takagi-Sugeno (TS) model for the DC-DC ZETA converter fed by a photovoltaic module is proposed. Having non-linear properties, ZETA converters with the classic linear proportional integral derivative (PID) controllers and fixed tuning parameters cannot demonstrate robust performance under the input voltage and load resistance variation. To tackle the problem, an adaptive fuzzy controller for each tuning parameter has been designed. The use of a Takagi-Sugeno fuzzy model compared to the famous Mamdani inference system is intended to ease the computational process. Performance analysis of both PID and TS-ATFPID controllers is carried out to evaluate output transient and steady-state responses of the converter using the fuzzy logic toolbox of the MATLAB/SIMULINK software. The results of the simulations demonstrate a significant performance improvement of TS-ATFPID over the conventional PID controller in terms of retaining output reference voltage under various stress levels and minimizing settling and rise time as well as the steady-state error and the overshoot. Keywords 1 Fuzzy logic, PID controller, DC-DC power converter, ZETA converters 1. Introduction In real applications with photovoltaic systems, a ZETA converter connects the photovoltaic module with the load. External factors such as With the rapid increase in demand for solar irradiation and temperatures can have a renewable energy sources, DC-DC converters significant negative impact on the output have found considerable interest in a wide variety performance of the module, a problem of which of applications, ranging from consumer can easily be tackled with the help of ZETA electronics to photovoltaic systems (PV) [1, 2]. converters. Advancements in the control A ZETA converter is a special type of DC-DC techniques of these converters are intended to converter which is similar to a single-ended improve the overall operational efficiency of the primary inductor converter (SEPIC). One of the converters. major similarities of these two converters is the Traditional linear proportional integral non-inverted output voltage polarity, which is not derivative (PID) converters can be used to control the case in the popular buck-boost topology [3]. the output of ZETA converters by changing the Another similarity is the ability of both regulators duty cycle applied to the switching element of the to output voltages with input voltages above or converter. However, optimal tuning of PID gains below the output voltage. However, in can be a challenging task, a problem of which can comparison with the SEPIC, a ZETA converter is based on a buck configuration [4]. ISIT 2021: II International Scientific and Practical Conference «Intellectual Systems and Information Technologies», September 13–19, 2021, Odesa, Ukraine EMAIL: lala_bekirova@mail.ru (A. 1); elvinyusifov05@gmail.com (A. 2); ORCID: 0000-0003-0584-7916 (A. 1); 0000-0001-6199-9266 (A. 2) ©️ 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) be eliminated by introducing a fuzzy logic also observed, as time passes. The capacitor, C1 controller for each PID parameter to be tuned. commences charging to the output voltage The main aim of the work is to design and In the second mode, MOSFET is switched off. simulate an adaptive fuzzy tuned PID controller Since the polarity changes, the diode, D goes to for the ZETA converter to address tuning the forward-biasing mode, in which electrical problems associated with the PID controllers and current can easily flow through it. Since, the achieve increased robustness to the input and load current flows the diode, the inductor, L2 starts to disturbances. A Sugeno type inference system be in parallel with the output capacitor, 𝐶𝑜𝑢𝑡 . The must be chosen for the fuzzy PID controller to capacitor, C1 discharges through the inductor, L1. alleviate the computational process as well as The simulation parameters of the designed their ability to work with linear control methods. Zeta converter is presented in Table 1. A pulse-width modulation (PWM) based 2. System modeling control mechanism is employed through the switching element of the converter, which is a MOSFET in our case, to regulate the output A ZETA converter and PID, TS-ATFPID voltage of the ZETA converter. controllers for the converter must be designed and simulated since the design and simulation of the Table 1 controllers are crucial to assess their respective ZETA simulation parameters output performances and show superiority of the TS-ATFPID controllers. Parameters Nominal value Supply voltage (E) 24 Volts 2.1. ZETA converter modeling Input voltage variation 16-20 Volts Input voltage variation 20-24 Volts The Simulink model of the ZETA converter Capacitance (C1, 𝐶𝑜𝑢𝑡 ) 19 mF operating in continuous conduction mode (CCM) Inductors (L1, L2) 4 mH is illustrated in Fig.1. In CCM mode, the inductor Loads 35Ω/15Ω current never falls to zero, compared to the Output reference 50 Volts discontinuous conduction mode (DCM). A simple model of the ZETA converter involves two 2.2. PID controller inductors (L1, L2), two capacitors (C1, C2), a diode (D), a metal oxide semiconductor field- To evaluate the improvements in the effect transistor (M). operational performance of the TS-ATFPID, a PID controller must be designed. PID controllers dominate the industry and are also considerably used in power electronics for the control circuit of the converters, due to their robustness, simple configuration, applicability in low-cost products. Being composed of three simple proportional, integral and derivative terms, PID controllers have the following general mathematical representation: 𝑑𝑒(𝑡) (1) u(t)=𝐾𝑝 e(t)+ 𝐾𝑖 ∫ 𝑒(𝑡)𝑑𝑡+𝐾𝑑 𝑑𝑡 In the formula (1), u(t), e(t), K p , K i , K d are the Figure 1: Simulink model of the ZETA converter control signal, error, proportional coefficient, integral coefficient, derivative coefficient, The converter operates on two modes; respectively. In the first mode, MOSFET is switched on. A Simulink model of the PID controller is The diode, D starts to be in its reverse-biasing shown in Fig.2. mode, which involves the block of electrical A PID controller receives the error which is the current through it. The voltage across the difference between the reference voltage (𝑉𝑟𝑒𝑓 ) inductor, L1 becomes equal to the supply voltage and actual output voltage (𝑉𝑎𝑐𝑡𝑢𝑎𝑙 ) and performs and the linear increase of the inductor current is the relevant mathematical operations in a parallel configuration [5]. Each term of a PID controller reduces. Possible steady-state errors can be plays an important role in improving the output restricted to a tolerance level by introducing the response of the system. integral term. The derivative term is considered The proportional term is intended to increase anticipatory which operates on the rate of change the speed of output response thereby decreasing of the error. rise time. However, as the error decreases, the effectiveness of the proportional term also Figure 2: Simulink model of PID controller Each coefficient of the relevant terms To design fuzzy controllers, the number of determines the strength of the terms, which inputs must be selected and the conversion of requires to be optimally tuned.. The most popular these crisp input values to their corresponding traditional tuning method is the use of the Ziegler fuzzy values with a certain range is needed. An - Nichols method [6, 7]. increase in the number of inputs expands the fuzzy In the design process of the PID controller, the rule base, which increases processing power. Ziegler-Nichols method with the combination of The error e(t) and the change in the error ∆e(t) trial-error methods has been employed. To are selected as inputs for the fuzzy logic PID implement this technique, first, all coefficients controller. For each input corresponding, 7 except for the proportional parameter is set to 0, membership functions of Gaussian type are after which the value of the proportional chosen. coefficient is increased until the system becomes The input space for e(t) and ∆e(t) is defined to unstable. The value of the proportional gain at the be in the interval of [-1,1] and [-0.001, 0.001], unstable state is recorded as 𝐾𝑚𝑎𝑥 . The oscillation respectively and demonstrated in Fig.3 and Fig. 4. frequency of the system is denoted as 𝑓0. The next stage involves the calculation process of the parameters. Proportional, integral, derivative parameters can be calculated as 0.6𝐾𝑚𝑎𝑥 , 2𝑓0, 𝐾𝑚𝑎𝑥 ∕ 𝑓0 , respectively. Adopting this method, the coefficients of the PID controller are calculated as 𝐾𝑝 =0.032, 𝐾𝑖 =0.65 and 𝐾𝑑 =0.18. 2.3. Fuzzy-PID controller As is seen in the design process of the PID controller, one of the challenging tasks is the optimal tuning of the parameters. However, this problem can be tackled with the help of fuzzy logic controllers. Figure 3: Membership functions for the error (NM), negative small (NS), zero (ZO), positive small (PS), positive medium (PM), positive big (PB). A Takagi-Sugeno type inference system is preferred and chosen over the popular Mamdani model to ease the computational burden as well as ensuring compatibility with adaptive methods [8, 9]. The linguistic variables for output space are very small (VS), medium-small (MS), small (S), medium (M), big (B), medium-big (MB), very big (VB), each one of them corresponds to a specific Figure 4: Membership for the change in error linear function with the coefficients (a, b, c) being VS=[0.12 0.012 0], MS=[0.34 0.034 0], S=[0.45 0.044 0], M=[0.455 0.046 0], B=[0.76 0.037 0], The change in error 𝑒(𝑡) is determined by MB=[0.83 0.047 0], VB=[0.93 0.047 0]. subtracting the previous output value of the error The rules of the presented TS type fuzzy logic 𝑒(𝑡 − 1) from the actual value (3). controller has the following mathematical e(t)= 𝑉𝑟𝑒𝑓 − 𝑉𝑎𝑐𝑡𝑢𝑎𝑙 , (2) common form: ∆e(t)= 𝑒(𝑡) − 𝑒(𝑡 − 1). (3) If input_1 is 𝑒 and input_2 is ∆e then output is The linguistic variables for the input are 𝑎𝑒 + 𝑏∆e + 𝑐 (4) selected as negative big (NB), negative medium Table 2 The fuzzy logic rule-table for 𝑲𝒑, 𝑲𝒊 , 𝑲𝒅 e\∆e NB NM NS Z PS PM PB NB VB/ VS /B VB/ VS /B MB/ VS /M MB/MS/M B/MS/M M/M/VB M/M/VB NM VB/ VS /S VB/ VS /S MB/MS/S B/MS/S B/S/M M/M/S S/M/MB NS MB/MS/ VS MB/MS/ VS MB/S/MS B/S/S M/M/M S/B/B S/B/MB Z MB/MS/ VS MB/S/MS B/S/S M/M/S S/B/M MS/B/B M/MB/MB PS B/S/ VS B/S/MS M/M/S S/B/S S/B/M MS/MB/B MS/MB/B PM B/M/MS M/M/S S/B/S MS/MB/S MS/MB/M MS/VB/B VS /VB/B PB M/M/B M/M/M MS/B/M MS/MB/M MS/VB/M VS /VB/VB VS /VB/VB The fuzzy rule base is illustrated in Table 2. output responses are analyzed in terms of rise and The designed TS-ATFPID controller is depicted settling time as well as the steady-state error and in Fig.5. overshoot. The reference output voltage is selected to be 50 Volts (V). 3. Simulation Results In the first stage, output responses for the load resistance of 35Ω and 15Ω are plotted with the supply voltage of 24V and the reference voltage The performance of the controllers are tested of 50V in Fig.6 and Fig.7, respectively. under load and input variations and their relevant Figure 5: TS-ATFPIF controller for ZETA In the second stage, the input voltage is varied from 20V to 24V and from 16V to 20V with the frequency of 200Hz and their relevant responses are shown in Fig.8 and Fig.9. Obtained numerical values are presented in Table 3 and Table 4. Figure 8: Output response (35Ω with 20-24V supply with 200Hz) Figure 6: Output response (35Ω with 24V supply) Figure 9: Output response (35Ω with 16-20V supply with 200Hz) Table 3 Performance of controllers to load different load resistance BILEVEL LOAD ATFPID PID MEASUREMENTS Figure 7: Output response (15Ω with 24V supply) Rise time (ms) 28.262 84.608 15 Ω Settling time(ms) 28.860 85.934 Overshoot (%) 0.358 0.502 Steady-State error (V) 0.064 0.095 Rise time (ms) 27.427 74.967 Settling time (ms) 27.838 80.236 35 Ω Overshoot (%) 0.347 0.506 Steady-State error(V) 0.029 0.075 [4] Deepak, R. K. Pachauri and Y. K. Chauhan, Table 4 "Modeling and simulation analysis of PV fed Performance of controllers to input variation Cuk, Sepic, Zeta and Luo DC-DC converter," Input BILEVEL 2016 IEEE 1st International Conference on ATFPID PID variation MEASUREMENTS Power Electronics, Intelligent Control and Rise time (ms) 32.081 77.759 Energy Systems (ICPEICES), 2016, pp. 1-6, 20-24V 35 Ω Settling time(ms) 32.360 78.234 doi: 10.1109/ICPEICES.2016.7853596. 200 Hz Overshoot (%) 0.388 0.505 [5] R. S. M. Sadigh, "Optimizing PID Controller Steady-State error (V) 0.065 0.092 Rise time (ms) 39.065 90.192 Coefficients Using Fractional Order Based 16-20V 35 Ω Settling time(ms) 40.125 90.895 on Intelligent Optimization Algorithms for Overshoot (%) 0.407 0.508 Quadcopter," 2018 6th RSI International 200 Hz Steady-State error (V) 0.068 0.071 Conference on Robotics and Mechatronics (IcRoM), 2018, pp. 146-151, doi: 4. Conclusions 10.1109/ICRoM.2018.8657616. [6] C. A. Aung, Y. V. Hote, G. Pillai and S. Jain, An auto-tuning Takagi-Sugeno type fuzzy "PID Controller Design for Solar Tracker via logic PID (TS-ATFPID) controller for ZETA Modified Ziegler Nichols Rules," 2020 2nd converters has been proposed in this paper. The International Conference on Smart Power & PID and TS-ATFPID controllers have been Internet Energy Systems (SPIES), 2020, pp. designed and simulated to assess their 531-536, doi: comparative performance. The simulations of the 10.1109/SPIES48661.2020.9243009. PID and TS-ATFPID controllers (TS-ATFPID [7] C. A. Aung, Y. V. Hote, G. Pillai and S. Jain, and PID) are performed under load variations and "PID Controller Design for Solar Tracker via supply voltage disturbances. 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