Effective Disturbance Compensation Method Under Control Saturation in Discrete-Time Sliding Mode Control

Abstract

This article presents a novel method of dealing with disturbances and control saturation in the framework of discrete-time sliding mode control (DSMC). A DSMC with decoupled disturbance compensator (DDC) was developed for SMC to recover the loss of stability in the discrete-time domain. However, windup phenomena occur in both the switching function and the disturbance estimate when control saturation occurs, and the method cannot guarantee stability. The article develops a new method for maintaining stability under both disturbances and control saturation by incorporating a novel auxiliary state into the DSMC with DDC method. The auxiliary state prevents the windup phenomena, and the developed new method preserves the asymptotic convergence property of the disturbance estimation error dynamics and the stability of the sliding mode dynamics. Also, the error states are stable under bounded disturbances and control saturation. Simulations and experiments are performed on a commonly used industrial servo system to demonstrate the effectiveness of the proposed method. Index Terms-Discrete-time systems, sliding mode control (SMC), servosystems. I. INTRODUCTIONS LIDING mode control (SMC) is a special kind of variable structure control and is one of the most successful approaches in general control systems with bounded and matched disturbances. SMC drives the state variables to a predesigned sliding surface in a finite time and then keeps them on the sliding surface in the presence of the bounded disturbance. Therefore,

Finite-Time Dynamic Tracking Control of Parallel Robots with Uncertainties and Input Saturation

“…The smooth hyperbolic tangent function was adopted in [ 18 , 19 , 20 ] to approximate the saturation function in the actual saturation control input, thus eliminating the sharp corner in the saturation function. In [ 21 , 22 , 23 ], SMC was used as the master controller with other assistive technology to deal with the uncertainties and input saturation in system. Recently, a strategy to cope with the input saturation problem by constructing an auxiliary system can be found in [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 ].…”

“…The basic principle is to take the input saturation error as the input of the designed auxiliary system, and the control law is then designed based on the state variables of the auxiliary system. However, it should be noted that in the above-mentioned literature [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 ], the tracking errors can only be convergent to a neighborhood of the origin asymptotically, which is very different from finite-time convergence to the origin.…”

Disturbance estimator-based switching function for discrete-time sliding mode control systems with control saturation

“…The unwanted CS may result in serious control deterioration and even instability of the controlled system. Only few research studies (Corradini et al, 2014;Han et al, 2020;Xiong et al, 2019) are concerned about the DSMC design with CS. To prevent the windup phenomena, Corradini et al (2014) presented a control strategy on the basis of a nonlinear sliding surface with the assumption that all states are measurable.…”

“…To prevent the windup phenomena, Corradini et al (2014) presented a control strategy on the basis of a nonlinear sliding surface with the assumption that all states are measurable. Han et al (2020) figured out a new DSMC with decoupled disturbance compensator by integrating a designed auxiliary state. Xiong et al (2019) studied the optimal event-triggered DSMC for saturated nonlinear systems.…”

Multi-hierarchy interaction control of a redundant robot using impedance learning

“…In [37], a high-order disturbance observer was used for a mobile wheeled inverted pendulum by using optimal gain matrices. The disturbance observers combining with sliding mode control were also designed for discrete-time systems [38,39]. Inspired by the idea of DOB, in this paper, an adaptive DOB is further developed to compensate for the disturbances caused by system uncertainties and external forces during the motion of the robot.…”