Quadratic Integral Sliding Mode Control for Nonlinear Harmonic Gear Drive Systems with Mismatched Uncertainties

Abstract

For a class of nonlinear harmonic gear drive systems with mismatched uncertainties, a novel robust control method is presented on the basis of quadratic integral sliding mode surface, and the closed-loop system has satisfying performance and strong robustness against mismatched uncertainties and nonlinear disturbances. Considering time-varying nonlinear torques and parameters variations which are caused by nonlinear frictions and backlash, a nonlinear harmonic gear drive system mathematic model is established and the effect of nonlinear parts is compensated during control system design. It is proven that the quadratic integral sliding mode surface can be reached in finite time and the closed-loop system is asymptotic stable robustly. The simulation studies are carried out in comparison with traditional linear sliding mode control and integral sliding mode control, verifying the effectiveness of the proposed method.

Continuous sliding mode control for uncertain linear time-invariant systems with matched and unmatched uncertainties using the Lyapunov-function integral sliding mode

“…Zhang (2015) proposed an ISM controller design based on the quadratic integral sliding mode (QISM) for SISO systems with unmatched disturbance. Ding and Xiao (2018) adopted the QISM method to control the nonlinear harmonic gear drive systems. These studies demonstrated that the ISM method has the potential to reject unmatched uncertainty or disturbance if the appropriate format of the ISM is selected.…”

Pre-compensation Strategy for Tracking Error and Contour Error by Using Friction and Cross-Coupled Control

“…Therefore, it is necessary to analyze the tracking error in detail and design advanced control strategies to compensate for it. In the process of precision machining, internal factors such as servo delay, friction, thrust fluctuation, and vibration, as well as external factors like assembly, wear, and temperature, can all influence tracking error [10][11]. This paper focuses on internal friction disturbance, analyzes its influence on tracking error, and establishes an estimation model and control strategy.…”

Erratum to “Quadratic Integral Sliding Mode Control for Nonlinear Harmonic Gear Drive Systems with Mismatched Uncertainties”

“…In the article titled "Quadratic Integral Sliding Mode Control for Nonlinear Harmonic Gear Drive Systems with Mismatched Uncertainties" [1], an additional reference should have been cited, which is included in the text below, as reference 19 [2]. Accordingly, the sentence referring to Equation (18) in Section 3, "Quadratic Integral Sliding Mode Design," should read as follows:…”