Sliding Mode Variable Structure Control of Boost Circuit with Dynamic Error Correction

Abstract: Based on the sliding mode equivalent control, considering the non-ideal switching conditions in actual control and the physical constraints of the actual control quantity, a simple new sliding mode variable structure control algorithm suitable for the continuous conduction mode (CCM) of the Boost circuit is proposed. The control algorithm dynamically corrects the sliding mode error according to the switching duty cycle, which will help to approximately ensure that the system moves along the switching surface, and can reduce the system steady-state error, so as to achieve the purpose of weakening high-frequency jitter. The starting process of the Boost circuit and the disturbance change of the steady-state system are simulated respectively, and the results are consistent with the theoretical analysis. The control scheme proposed in this paper can reduce the system overshoot, shorten the transition process time, improve the dynamic quality of the system, and effectively solve the high-frequency jitter problem in the sliding mode control. The control system has good robustness.

Keywords: Sliding mode variable structure control Equivalent control method Boost transformation Jitter

Slide－ mode Control Scheme for Boost Converter

Abstract:A novel control scheme is presented by using sliding－ mode control for boost converter operating in continuous conduction mode(CCM).Although the non－ ideal switching condition and physical constraint of the control are considered on the base of equivalent control, the scheme is still simple. By modifying the sliding－ mode errors in each switching period, the steady－ state errors and chattering can be substantially reduced. Simulation results confirm the theoretical analysis and show the improvement of the converter's start－ up behavior and low sensitivity to external perturbation. Keywords:Sliding－ mode control Equivalent control Boost converter Chattering

1 Introduction

For the control of nonlinear systems, the sliding mode variable structure control method has attracted more and more attention [1-2]. Since the 1980s, power electronics experts have begun to use this method in the control of DC/DC switching converters [3-10]. The sliding mode variable structure control method has many advantages, such as good system stability, strong robustness (Robustness, indicating the ability to resist parameter changes and disturbances), good dynamic quality, and easy control. However, the sliding mode variable structure control will have high-frequency jitter when it is physically implemented. In addition, the control law obtained by the equivalent control method has a stable sliding mode error. In order to achieve the sliding mode as much as possible, the selection of the sliding mode control coefficient is very strict [3-7].

In order to overcome these shortcomings of sliding mode control, people have tried various methods to achieve the purpose of eliminating steady-state errors. For example, reference [8] uses a time-varying switching surface equation; reference [9] cleverly applies the traditional PID control mode to the switching surface equation and obtains a sliding surface equation that contains only one variable, the output voltage error, and a linear combination of the proportional, differential and integral to achieve the purpose of controlling the output voltage; reference [10] uses a compensation network to correct the equivalent control, that is, the new equivalent control has taken into account the influence of the compensation network. So far, there has been no report on a control scheme that considers weakening high-frequency jitter when implementing a sliding mode variable structure control scheme for a DC/DC switching converter. From a theoretical analysis, the introduction of a variable structure reaching law [11] will simplify the determination of control and help improve the quality of the system. However, in actual control, how to use the variable structure reaching law to implement variable structure control and achieve the purpose of weakening or even eliminating jitter has rarely been used or involved.

In view of this, this paper proposes a control scheme for the Boost circuit working in CCM mode, which can dynamically correct the sliding mode error, thereby dynamically compensating the size of the control quantity, reducing the steady-state error, weakening the high-frequency jitter, and achieving some good control quality of the system.

Sliding Mode Variable Structure Control of 2Boost Circuit

The boost circuit is shown in Figure 1. The purpose of control is to stabilize the system state at the desired value Xd (operating point) by controlling the duty cycle of the active switching device.

2.1 Control Algorithm

The state equation of the circuit when the boost circuit works in CCM mode

Figure 1 Boost converter

Equivalent control is to achieve ideal sliding mode motion under ideal switching conditions. However, in actual control, due to non-ideal switching factors such as the inertia of the switching device and the switching delay, the sliding mode motion will not move on the switching surface of S=0, but move within its neighborhood Δ.

In other words, the introduction of Δu is to correct the sliding mode error caused by non-ideal switching due to non-ideal factors of the actual system. Substituting into equation (3), it is obvious that when Δu≠0, then ≠0. In order to meet the sliding mode arrival condition and improve the dynamic quality of the system, the system arrival condition s.<0 is guaranteed by selecting an appropriate form, so that the system tends to the switching surface in some way to form a sliding mode. Here, by introducing the reaching law〖 11〗

Therefore, in principle, the sliding mode variable structure control law of the Boost circuit working in CCM mode is equivalent to the duty cycle in the circuit from a physical point of view. That is, the actual size will be limited by the physical nature of the converter itself, ∈(0,1).

2.2 Selection of K1 and K2 coefficients

It can be seen from formula (10) that the size of Δu is related to the coefficients of K1 and K2. Theoretically, as long as K1 and K2 are not less than zero, the sliding mode will be stable. However, if the value of K1 is too large, the speed at which the system reaches the switching surface will be very large, which may easily cause a large degree of jitter in the system; if the value of K1 is too small, the control transition process will be long. Therefore, the control transition process and the quality of dynamic quality are more determined by the coefficient K1, and the linear term -K2S can only mitigate the speed of the system rushing to the switching surface to a certain extent. It is hoped that the speed of the system approaching the switching surface can be automatically determined according to the size of the s distance from the switching surface s=0 determined by the system state. Therefore, the coefficients K1 and K2 are determined in the following way.

Where T is the switching duty cycle of the Boost converter.

Here we emphasize taking different K1(m) values ​​at different times.

To ensure K1(m)>0, the value range of K2 is: 0≤K2≤fS(15)

2.3 Physical constraints in actual control

For the Boost circuit, we use the duty cycle as the control variable, which must be limited by the physical properties of the Boost circuit itself. When the size of the control variable exceeds the range of (0, 1), we must constrain the size of the control variable in the control scheme. The DC analysis of the Boost circuit shows that its duty cycle is inversely proportional to the size of its DC solution I and U. In order to improve the response speed of the control, here we also use dynamic changes in the size of the constrained control variable.

That is, the size of the constraint control quantity decays according to the switch duty cycle.

In summary, we get the sliding mode variable structure control law of the mth working cycle when the Boost circuit works in CCM mode:

The component parameters are: L=6mH, C=45μF, R=30Ω, Ug=37.5V, fS=10kHz, and the open-loop duty cycle D is 0.25. The DC analysis results are: U=50V, I=2.2A. The expected stable operating point is: Xd=[2.250〗T. The control parameters are: KC=[-1501]T, K2=800. The starting process of the Boost circuit and the situation where its steady-state system has disturbance changes are simulated and studied respectively.

Figure 2 shows the starting transient process of the Boost circuit under different control laws, and Figure 3 is the phase plane diagram of the starting process, where "0" is the position of the desired working point Xd. It can be clearly seen from the figure that when the equivalent control of formula (6) is used as the actual sliding mode control law (curve 3), the system will have obvious steady-state errors, and the system will not tend to the switching surface in the end, nor will it move to the desired working point (dashed line in Figure 3). The control algorithm using formula (17) can solve this problem well (curve 1 and solid line in Figure 3), and effectively solve the high-frequency jitter problem in sliding mode control. If the control parameter in the control algorithm of formula (17) is a constant and the linear term - K2S is ignored, that is, when the control algorithm for dynamically correcting the sliding mode error is not used, the dynamic response time will be very long and the value of K1 will be very large. For example, when K1=10000, the starting transient process is shown in curve 2 in Figure 2.

Figures 4 and 5 are transient characteristic curves considering system disturbances. In Figure 4, the disturbance of the input voltage of the system in the first stage suddenly decreases by 50% from the normal voltage, and in the second stage the disturbance of the input voltage suddenly increases by 10% from the normal voltage. In Figure 5, the disturbance of the load of the system in the first stage suddenly increases by 100% from the normal load, and in the second stage the disturbance of the load suddenly decreases by 50% from the normal voltage. As can be seen from the figure, no matter how the system disturbance changes, the stability of the system can still be guaranteed, and the control system has good robustness.

Figure 2 Comparison of startup transient processes under different control

Figure 3 Phase plane diagram of the starting process

Figure 4 Input voltage disturbance transient process

Figure 5 Load disturbance transient process

4 Conclusion

When implementing sliding mode variable structure control, non-ideal switching conditions in actual control and physical constraints of actual control quantities must be considered. The sliding mode variable structure control algorithm proposed in this paper is simple. The simulation results show that the control scheme of this paper can reduce system overshoot, shorten the transition process time, improve the dynamic quality of the system, and effectively solve the high-frequency jitter problem in sliding mode control. In steady state, even if the system input voltage or output load has a large disturbance, the stability of the system can still be guaranteed, and the control system has good robustness.