Abstract
Sliding Mode Control (SMC) is a robust control strategy that is insensitive to system uncertainties and external disturbances. It is widely used in designing controllers, observers and differentiators. However, the inevitable chattering problem affects the SMC applications in real-life engineering. This paper presents an improved SMC algorithm based on discrete second-order time optimal control (TOC). The proposed algorithm adopts a simple method to calculate the distance from the state variable to the sliding surface, and it can adjust the linear or nonlinear control law according to the calculated distance. On the other hand, the control law deviation in the two-step reachable region is corrected. The improved control algorithm shortens the convergence time and reduces the chattering problem of the system. It is applied to the design of magnetic suspension controllers. This allows the system to achieve a fast, accurate and stable suspension target when the system has external disturbances and internal parameter perturbations.
Highlights
Sliding mode control (SMC) is a robust control approach
This paper presents an improved sliding mode control algorithm based on time optimal control (TOC)
The algorithm is improved on the basis of time optimal control synthesis function for the second-order discrete system, which defines the distance from the state variable to sliding surface clearly, and corrects the deviation of control law inside and outside the two-step reachable region
Summary
Sliding mode control (SMC) is a robust control approach. It establishes a control strategy with non-smooth characteristics to enable state variables to effectively reach the vicinity of the sliding surface and move along the sliding surface to the desired control point. In literature [8], an optimized constant rate reaching law is proposed With this method, the linear combination of state variables is used to define the distance from the state variable to the sliding surface, and adjusts the approaching rate according to the distance, which can shorten convergence time and reduce the chattering of the system. Terminal sliding mode control (TSMC) can make the system tracking error converge to zero in finite time This feature effectively solves the chattering problem caused by the overly high controller gain in the discrete system under the limited sampling frequency. In order to solve the problem of large sliding mode control error caused by unknown disturbances and unknown state variables, JianXin Xu and Khalid Abidi designed a new VOLUME 8, 2020 integral-type sliding surface for arbitrary output reference tracking control. Literature [15] proposed an approach that divides the phase plane into linear and nonlinear regions to control respective, which effectively solves the problem of the systems disturbances and chattering
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