Robust High Order Sliding Mode Control of Permanent Magnet Synchronous Motors

Abstract

Nonlinear system control has been widely concern of the research. At present, the nonlinear system decoupling control and static feedback linearization that based on the theory of differential geometry brought the research getting rid of limitation for local linearization and small scale motion. However, differential geometry control must depend on precise mathematical model. As a matter of fact, the control system usually is with parameters uncertainties and output disturbance. Considering sliding mode variable structure control with good robust, which was not sensitive for parameters perturbation and external disturbance, the combination idea of nonlinear system and sliding mode controls was obtained by reference to the large number of documents. Thus, it not only can improve system robustness but solve the difficulties problem of nonlinear sliding mode surface structure. As known to all, traditional sliding mode had a defect that is chattering phenomenon. A plenty of research papers focus on elimination/avoidance chattering by using different methods. By comparing, the chapter is concerned with novel design method for high order sliding mode control, which can eliminate chattering fundamentally. Especially, the approach and realization of nonlinear system high order sliding mode control is presented. High order sliding mode technique is the latest study. This chapter from the theory analysis to the simulation and experiment deeply study high order sliding mode control principle and its applications. The arbitrary order sliding mode controller is employed, whose relative degree can equal any values instead of one. In addition, the control systems design is very often to differentiate the variables. Through the derivation of sliding mode, the expression of sliding mode differential value is obtained. At the same time, the differentiator for arbitrary sliding mode is given to avoiding complex numerical calculation. It not only remains the precision of variables differential value, but also obtains the robustness. Due to its inherent advantages, the permanent magnet synchronous motor (PMSM) deserves attention and is the most used drive in machine tool servos and modern speed control applications. For improving performance, this chapter will apply nonlinear high order sliding mode research achievement to MIMO permanent magnet synchronous motor. It changes the coupling nonlinear PMSM to single input single output (SISO) linear