Barrier Lyapunov function-based adaptive prescribed performance control of the PMSM used in robots with full-state and input constraints

The permanent magnet synchronous motor is extensively used in robots due to its superior performances. However, robots mostly operate in unstructured and dynamically changing environments. Therefore, it is urgent and challenging to achieve high-performance control with high security and reliability. This paper investigates an accelerated adaptive fuzzy neural prescribed performance controller for the PMSM to solve chaotic oscillations, prescribed output performance constraint, full-state constraints, input constraints, uncertain time delays, and unknown external disturbances. First, for ensuring the permanent magnet synchronous motor with higher security, faster response speed, and lower tracking error simultaneously, a novel unified prescribed performance log-type barrier Lyapunov function is proposed to handle both prescribed output performance constraint and full-state constraints. Subsequently, a continuous differentiable constraint function-based model is introduced for solving input constraints nonlinearity. The Lyapunov–Krasovskii functions are utilized to compensate the uncertain time delays. Besides, a type-2 sequential fuzzy neural network is exploited to approximate unknown nonlinearities and unknown gain. For the “explosion of complexity” associated with backstepping, a tracking differentiator is integrated into this controller. Furthermore, a speed function is introduced in the backstepping technique for accelerated convergence. On the basis of above works, the accelerated adaptive backstepping controller is achieved. And the presented controller can ensure that all the closed-loop signals are ultimate boundedness, and all state variables are restricted in the prespecified regions and the permanent magnet synchronous motor successfully escapes from chaotic oscillations. Finally, the simulation results verify the effectiveness of the proposed controller.

Full-Order Sliding Mode Bounded Control for Euler-Lagrange Systems with External Disturbances

This paper researches two finite-time bounded control methods for Euler-Lagrange systems exposed to external disturbances. A novel full-order terminal sliding mode surface that is convenient for solving the input constraints is designed based on the characters of the hyperbolic tangent function. By using the designed full-order terminal sliding mode surface, the finite-time controller with input constraints can deal with external disturbances with the exactly known upper bound. Further, an adaptive finite-time bounded controller is designed to deal with the external disturbances with the upper bound that cannot be accurately known. Finally, the finite-time stability of the system is proved by using Lyapunov theory and numerical simulations.