Adaptive backstepping control for permanent magnet linear motors against uncertainties and disturbances

Abstract

In practical operation, the system parameters of a permanent magnet linear motor are affected by unknown factors, including nonlinear friction, sudden load changes, thrust fluctuations, and so on. Therefore, a controller designed for fixed parameters often cannot produce satisfactory results. To solve this problem, a novel design method for permanent magnet linear motor systems based on backstepping is proposed in this article. The proposed control scheme does not require the values or range of changes of the system parameters in advance but constructs an update law to perform online parameter estimation. A difficulty encountered in controller design and stability analysis is the estimation of the unknown coefficient of a single-variable state, which can be considered as a virtual input. In this article, the estimated virtual control coefficient is introduced into the coordinate transformation to construct a novel coordinate transformation. However, introducing the estimated coefficient into the virtual control makes the derivative of the Lyapunov function used in the stability analysis more complex. This novel nonlinear dynamic term can be precisely cancelled by changing the update law of the coefficient. Finally, simulations are performed to assess the performance of the proposed control scheme against that of a traditional proportional–integral–derivative controller, and the simulation results show that the proposed control law can effectively improve the system performance.

Experimental Validation of Different Control Techniques Applied to a Five-Phase Open-End Winding Induction Motor

“…Stability characteristics: Pole compensation is used for the RFOC technique and Lyapunov stability is used for the BSC strategy in the stability study. Both techniques exhibit steady performance, with BSC showing quicker convergence compared to other techniques such as those presented previously in [2,[30][31][32].…”

“…The fundamental goal of the BSC approach is to convert the equivalent closed-loop system into stable subsystems with order equal one [31,32], which are placed in cascade by the Lyapunov function, which guarantees the stability of each synthesis step [2]. In this paper, the proposed backstepping technique is presented in Figure 5 and it is divided into two steps:…”

“…Simple control strategies are proposed to be implemented on an industrial motor control hardware system with a low computation load e in comparison with the previous works (e.g., those presented in [2,5,23,[29][30][31][32][33][34][35][36]).…”

Research on the Dynamic Characteristics of a Dual Linear-Motor Differential-Drive Micro-Feed Servo System

“…Many research achievements have been made on the influence of nonlinear friction on micro-feed systems [13][14][15][16][17][18]. Luna L [13] introduced a delay-based nonlinear controller aimed at position control of linear ultrasonic motors, which is termed the cascade nonlinear proportional integral retarded control law, to achieve high precision and fast response in spite of the effects of inner disturbances, hysteresis, and friction phenomena.…”

“…Li YR [16] presented an asymmetric friction model and an indirect integral method (IIM), the asymmetric friction model is able to capture the nonlinear position drifting phenomenon. Yang QY [17] proposed a novel design method for permanent magnet linear motor systems based on backstepping, in order to solve the influence of unknown factors on the system parameters of a permanent magnet linear motor including nonlinear friction, sudden load changes, thrust fluctuations, and so on. In order to avoid discontinuities, the nonlinear friction of the motor, which includes static, coulomb, and viscous terms, is considered a smooth function.…”