Robust Sliding Mode Controller Design for Boost Converter Applications

This paper presents detailed steps to design an effective, robust sliding mode controller for boost converter applications. Before that, the paper models a boost converter circuit during a continuous conduction mode (CCM) operation, obtains the related dynamic equations and explains the variation effects of the circuit parameters on the converter performance. The design steps of the proposed controller are illustrated, and the robustness of the controller is demonstrated in terms of maintaining output voltage stability under input voltage variations and load fluctuations. On the other hand, this paper shows a fast and accurate dynamic response of the load voltage during different reference voltages. Simulation results are collected, analyzed, and demonstrated the robustness and correctness of the proposed controller design.

Boost converter; Converter modeling; Simulation; Sliding mode control

At the same time, it deserves to be mentioned that many research studies proposed a successful design to suppress the chattering demerit in the controlling input voltage to the SM controller (Huayang et al., 2023; Xin, Huashan, and Wenke, 2021; Mobayen et al., 2021; Amirzubir et al., 2016).

This paper models a DC-DC boost converter and demonstrates a detailed sliding mode controller design suitable for controlling the boost converter. The study started by modeling the converter, obtaining the dynamic equations, explaining the design steps of the desired SMC, and then evaluating the converter performance by analyzing the collected Simulink simulation results. The remainder of this paper is as follows: modeling a DC-DC boost converter and driving the related dynamic equations shown in Section 2, detailed design steps and equations of a sliding mode controller explained in Section 3. Simulating the proposed SMC with a DC-DC boost converter and collecting and analyzing the collected simulation results are all demonstrated in Section 4. Section 5 summarizes the conclusion of this study. 

Modelling of DC-DC Boost Converter

A boost converter or a step-up converter works on having a regulated output load voltage of a level greater than the input voltage level. This converter has been implemented by adding an LC low-pass filter to a basic converter circuit (Farzin, 2021; Attia, 2020a; 2020b; Daniel and Hart, 2011; Rashid, 2001). Figure 1 shows the circuit of the DC-DC boost converter. In this converter, the diode will be reverse-biased when the switch is ON, whereas the diode is directing the inductor current during the OFF state of the switch.

  Figure 2(a) shows the equivalent converter circuit when the switch is ON and the diode is reverse biased, whereas Figure 2 (b) shows the equivalent converter circuit when the switch is OFF and the diode is forward biased.

When the switch is ON (close), the source voltage across the inductor is shown in Equation 1, whereas Equation 2 demonstrates the inductor current derivative. 

    The behavior of the current derivative is linear and positive during the switch closing, Equation 3 demonstrates this current derivative during this period. Equation 4 shows the variation in inductor current with respect to the duty ratio D.

When the switch is open, the diode becomes forward-biased to provide a path for inductor current, which cannot change instantaneously. By assuming constant output voltage  the voltage across the inductor is shown in Equation 5, and based on that the inductor current during opening the switch is demonstrated by Equation 6.

Figure 1 DC-DC boost converter circuit

Figure 2 DC-DC boost converter; (a) Converter circuit when the switch is ON, (b) Converter circuit when the switch is OFF

  Equation 7 shows the inductor current derivative during the switch OFF (open), whereas Equation 8 shows the inductor current change with respect to duty ratio D.

During steady-state operation, the net change in inductor current for each one switching period is zero as demonstrated Equation 9, and it can demonstrated after variables replacement as shown in Equation 10. Based on that Equation 11 shows the converter output voltage.

Or,

From Equation 11, the boost converter produces an output voltage that is greater than or equal to the input voltage based on the instantaneous value of the Duty cycle (D).

The instantaneous value of the inductor current variation  equal to the summation of By considering the duty cycle (DT) is (u) for the switch ON time, (T-DT) is (1-u) for the switch OFF time, the dynamic equation of can be written as shown in Equation 12, and can be rearrange as shown in Equation 13.

When the switch is OFF (open), the inductor current equals to the summation of the capacitor and the resistor current as shown in Equation 14.  Based on that Equation 15 demonstrates the capacitor current, and it can be written by considering the capacitor voltage derivative multiplying by the capacitance value as shown in Equation 16. Equation 17 shows the expression of the capacitor derivative by moving the capacitance to the right side.  

Equations (13) and (17) represent the dynamic equations of the inductor current and output voltage of the DC-DC boost converter, respectively.

Design of Sliding Mode Controller

       The function of the Sliding Mode (SM) controller is to decide the switching state u of the converter switch (Tahri, Tahri, and Flazi, 2014; Saad et al., 2011; Guldemir, 2011; Guldemir, 2005; Trushev et al., 2005). The sliding surface S of the boost converter can be represented by the summation of error in the output voltage as shown in Equation 18, which is the difference between the reference voltage and actual output voltage which is the change of the error of the output voltage dx₁/dt as demonstrated in Equation 19.

Replace in Equation 19 yields sliding surface in circuit parameters form as shown in Equation 20, and Equation 21. 

Or,  

Sliding mode control depends on the objective of the slide mode S, and the derivative of the surface to be zero value as indicated in Equation 22.

So can be determined by doing derivative to the surface  as shown in Equation 23.

Replacing Equation 13 and Equation 17 in Equation 23 yields Equation 24 which demonstrates the derivative of 

The general structure of the controlling state u includes two components as shown in Equation 25: equivalent controlling component and the nonlinear component  (Tahri, Tahri, and Flazi, 2014; Saad et al., 2011; Guldemir, 2011);

Equaling to zero yields the equivalent cntrol of switching ON state u_eq as demonstrated in Equation 26.

The nonlinear component can be defined as shown in Equation 30.

Figure 3 demonstrates the DC-DC boost converter circuit controlled by the designed sliding mode controller through the Pulse Width Modulation PWM technique to generate the drive pulses.

Simulation with Results Analysis

Simulation of the boost converter is done using MATLAB®/Simulink® version 2015b after selecting a fixed switching frequency of 15 kHz. Many practical research studies have been focused on using a low switching frequency starting from 1.2 kHz in power converter applications to have an effective power electronic system with low switching losses (Busacca et al. 2022; Rohten et al. 2021; Ye, Malysz, and Emadi, 2015; Abrishamifar, Ahmad, and Mohamadian, 2012). Table 1 shows the simulated converter parameters, which were selected by considering the work of (Abouchabana et al., 2021; Attia, 2020a; Attia, 2020b). Table 1 also demonstrates the range of simulated input voltage, reference voltage, connected load, and converter parameters, which are determined through the relationships of (Sreedhar and Basavaraju, 2018). 

Figure 3 Block diagram of the proposed Sliding Mode Controller SMC for DC-DC boost converter

Table 1 Parameters for testing the SMC-based converter

Figure 4 shows the MATLAB/Simulink simulation of the proposed converter controlled by the designed sliding mode controller, whereas Figure 4(b) shows the details of the calculated SMC parameters.

Figure 4 MATLAB/Simulink simulation of proposed system, (a) The SM controller with DC-DC boost converter, (b) Simulation of the designed SM controller with the calculated parameters

Figure 5 illustrates the robustness and accuracy of the controller under a fixed source voltage of 20 Volts, focusing on load voltage regulation. The load voltage is maintained at 30 V while the load varies from 24for the initial 0.5 seconds of simulation to 12 for the subsequent 0.5 seconds, covering the entire simulation time of 1 second. Figure 5(b) shows a zoom-in of the starting transient response, in which the increments in load current and load voltage are clearly noticeable at each step of sampling time 0.5with soft starting without any overshoot in the load voltage and load current. Figure 5(c) shows a zoom-in view of the system response during a steady period, in which measuring a short period approximately equals 67(14.9 kHz), whereas measuring a long period approximately equals 133(7.5 kHz). Figure 5(d) shows a zoom-in view of the system response during the same steady period, in which measuring a long period approximately equals 133 µsec (7.5 kHz). In other words, the sliding mode controller controls the switching frequency of the PWM drive pulses based on the status of the sliding surface and, consequently, the instantaneous level of the duty cycle.  

Figure 5 Load voltage and current when load resistor 24  then 12  (a) Results of 1 sec simulation period, (b) Zoom in during the transient period, (c) Zoom in during steady period with time measuring of the high switching frequency range, (d) Zoom in during steady period with time measuring of the low switching frequency 

      Figure 6 illustrates the controller response at various reference voltages. The simulation initiates with a reference voltage of 30 Volts for the first quarter of the 1-second simulation period. Subsequently, reference voltages of 35 Volts, 40 Volts, and 35 Volts are applied for the remaining three-quarters of the simulation period. As depicted in Figure 6, the load voltage accurately tracks the reference voltage. Figure 7 demonstrates the controller's effectiveness and response during the variation of input source voltage.

Figure 6 Load voltage and current at different V_ref (30 V, 35 V, 40 V, 35 V) when load resistor 12 

Figure 7 Load voltage and current at different Vs (24 V, 15 V) when load resistor 12 

The paper has presented a comprehensive demonstration of the detailed steps involved in designing a sliding mode controller for DC-DC boost converters. Initially, the paper covered the modeling of the converter circuit during continuous conduction mode (CCM) operation. Subsequently, the paper outlines the design steps of a robust SM controller to decide the instantaneous value of the controlling state involving the effects of equivalent controlling components and nonlinear components. Simulation results have been collected and analyzed using MATLAB/Simulink software. The study's findings and analysis underscore the effectiveness and robustness of the designed controller, particularly in coping with variations in source voltage and connected loads. Furthermore, it is demonstrated that the controller adeptly tracks the instantaneous reference voltage.

    The author expresses gratitude for the financial support received from the Office of Research & Community Service at the American University of Ras Al Khaimah, UAE, https://aurak.ac.ae/en/academics/office-of-research-community-service/.

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