Data-driven model-free adaptive fractional-order sliding mode control for the SMA actuator with prescribed performance

In this paper, a novel data-driven model-free adaptive fractional-order sliding mode controller with prescribed performance is proposed for the shape memory alloy (SMA) actuator. Due to the strong asymmetric saturated hysteresis nonlinear characteristics of the SMA actuators, it is not easy to establish an accurate model and develop an effective controller. Therefore, we present a controller without using the model of the SMA actuators. In other words, the proposed controller depends merely on the input/output (I/O) data of the SMA actuators. To obtain the reasonable compensation for hysteresis, enhance the noise robustness of the controller, and reduce the chattering, a fractional-order sliding mode controller with memory characteristics is employed to improve the performance of the controller. In addition, the prescribed performance control (PPC) strategy is introduced in our work to guarantee the tracking errors converge to a sufficiently small boundary and the convergence rate is not less than a predetermined value which are significant and considerable in practical engineering applications of the SMA actuator. Finally, experiments are carried out, and results reveal the effectiveness and success of the proposed controller. Comparisons with the classical Proportional Integral Differential (PID), model-free adaptive control (MFAC), and model-free adaptive sliding mode control (MFAC-SMC) are also performed.

Prescribed Performance Tracking Control for High-Order Uncertain Nonlinear Systems

This paper considers the prescribed performance tracking control for high-order uncertain nonlinear systems. For any initial system condition, a state feedback control is designed, which guarantees the prescribed tracking performance and the boundedness of closed-loop signals. The proposed controller can be implemented without using any approximation techniques for estimating unknown nonlinearities. In this respect, a significant advantage of this article is that the explosion of complexity is avoided, which is raised by backstepping-like approaches that are typically employed to the control of uncertain nonlinear systems, and a low-complexity controller is achieved. Moreover, contrary to the existing results in existing literature, the restrictions on powers of high-order nonlinear systems are relaxed to make the considered problem having stronger theoretical and practical values. The effectiveness of the proposed scheme is verified by some simulation results.

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.

Variable Gain Prescribed Performance Control for Dynamic Positioning of Ships with Positioning Error Constraints

In this paper, a variable gain prescribed performance control law is proposed for dynamic positioning (DP) of ships with positioning error constraints, input saturation and unknown external disturbances. The error performance index functions are designed to preset the prescribed performance bounds and the error mapping functions are constructed to incorporate the prescribed performance bounds into the DP control design. The variable gain technique is used to limit the output amplitude of the control law to avoid input saturation of the system by dynamically adjusting the control gain of the DP control law according to the positioning errors, and the error mapping function replaces the positioning error as a recursive sliding-mode surface to realize the prescribed performance control of the system and guarantee the stability of the closed-loop system with variable control gains. It has been proved that the proposed DP control law can make the uniformly ultimately boundedness of all signals in the DP closed-loop control system. The numerical simulation results illustrate that the proposed control law can make the ship’s position and heading maintain at the desired value with positioning error constraints, enhance the non-fragility of the DP control law to the perturbation of system’s parameters and improve the system’s rejection ability to external disturbances.