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.

In order to improve the efficiency of human–robot interaction (HRI), it is necessary to carry out research on precise control of the manipulator. In this paper, an adaptive non-singular fast terminal sliding mode control scheme is proposed for robot manipulators to solve the trajectory tracking problem with model uncertainty and external disturbances. At first, a novel non-singular fast terminal sliding mode surface is proposed, and by introducing an auxiliary function, the singularity problem caused by the inverse of the error-related matrix could be avoided in the controller design process. Then, the controller is developed by using Lyapunov synthesis. A robust adaptive strategy is used to deal with lumped uncertainty, with an adaptive update law designed to compensate for the upper bound of lumped uncertainty whose upper bound is prior unknown. Finally, a two-link robot manipulators as a simulation example is given to illustrate the effectiveness of the proposed scheme. Compared with other similar algorithms, the proposed adaptive non-singular fast terminal sliding mode control scheme has higher efficiency and smaller computational complexity for the reason that no piecewise continuous function is needed to be constructed during the controller design.