Optimal Fixed‐Time ADRC for a 2‐DOF Pneumatic Motion Simulation Platform With Time‐Varying Disturbances

ABSTRACT This paper presents a novel optimal fixed‐time active disturbance rejection control (OFTADRC) method to guarantee both fixed‐time stability and optimality for a 2‐degree‐of‐freedom (2‐DOF) pneumatic motion simulation platform actuated by pneumatic artificial muscles (PAMs) with time‐varying disturbances. To improve control performance, the time‐varying disturbances are estimated by an optimal fixed‐time extended state observer (OFTESO) and compensated in an optimal fixed‐time controller (OFTC). Sufficient conditions for error feedback laws achieving optimality and stabilizing the system in fixed time are established using a modified fixed‐time stability criterion. Based on the criterion, the optimal error feedback laws of OFTADRC are obtained by solving Hamilton‐Jacobi‐Bellman (HJB) equations to minimize given performance measures. By designing performance measures and introducing a Lyapunov function into the HJB function, exponential terms of system errors in the HJB equations are eliminated to reduce the computational difficulty of solving the HJB equations. The desired tracking accuracy and speed can be achieved by adjusting the weights in the performance measures. The effectiveness of the proposed method is illustrated by simulation and experimental results.