Adaptive variable gain linear active disturbance rejection control parameter optimization in magnetic levitation

Abstract

The magnetic levitation ball system is characterized by strong nonlinearity, multiple disturbances, and intrinsic instability, which has long been a thorny problem in the field of control engineering. The magnetic levitation system can be continuously and stably levitated, even in a complex environment. In this thesis, the model of the magnetic levitation ball system is firstly constructed according to the kinetic theory and simplified according to the actual situation. After that, a linear active disturbance rejection control (LADRC) controller for the magnetic levitation ball system is designed. Considering that there are many parameters in the LADRC controller and it is difficult to obtain the optimal control effect by manual tuning, an adaptive variable gain LADRC algorithm is proposed to optimize the control strategy of LADRC parameters. An adaptive iterative algorithm is used to adaptively adjust the bandwidth of the linear extended state observer (LESO) in LADRC, and the convergence of the algorithm is demonstrated by using the Lyapunov function. To solve the problem that the proportional and differential gains of the LADRC controller can only be adjusted unidirectionally and simultaneously, this paper proposes an error variable gain algorithm. The aim is to realize the non-unidirectional and more detailed adjustment of the controller parameters, and it is rigorously analyzed and demonstrated through simulation and experiment. The results show that the proposed algorithm is better than proportional–integral–derivative (PID), sliding mode control (SMC), and LADRC in terms of dynamic performance, steady-state performance, and anti-interference.