Sub-Optimal Second-Order Sliding Mode Controller Parameters’ Selection for a Positioning System with a Synchronous Reluctance Motor

Abstract

This paper discusses nonlinear controller structure design for a synchronous reluctance motor (SynRM). The SynRM is represented with a nonlinear dynamic model. All presented nonlinearities of the SynRM are respected in the controller design procedure. A nonlinear controller policy is used for a SynRM positing system. The nonlinear controller design is based on the chattering alleviation technique for the super-twisted algorithm (STA). The alleviation technique assumes the presence of a fast parasitic dynamic, or fast, actuator. Based on the motor structure, the STA controller is designed only for the mechanical subsystem, where the electrical part presents the parasitic dynamic, and is taken in to account in the chattering suppression procedure. Chattering rejection is based on the STA describing function and harmonic balance equation. The approach allows determination of fast oscillation parameters, such as amplitude and frequency of oscillation. The conditions for the controller parameters’ selection are derived with regard to the given oscillation parameters. The derived conditions cover the stability analysis for the STA controller, as well as the stability condition for current controllers and chattering amplitude minimization. The result is confirmed with an example.

The Advanced Control Approach based on SMC Design for the High-Fidelity Haptic Power Lever of a Small Hybrid Electric Aircraft

“…The sliding mode control (SMC) design approach may be utilized to improve robustness in feedback control considerably [89]. Thus, we can find numerous applications of sliding mode control in many areas, such as: control of a parallel robotic manipulator with uncertain dynamics [90], bilateral control of a hydraulic manipulator [91], control of a therapeutic exoskeleton [76], an electronically controlled power steering system [92], steer-by-wire systems [47], an automotive electronic throttle [93], robust speed control of PMSM [94], position control of a synchronous reluctance motor [95], a PEM fuel cell power system [96], etc. The basic SMC is characterized by a variable structure system and switching of the control input variable [97].…”