Fixed-Time Adaptive Optimal Parameter Estimation Subject to Dead-Zone and Control of Servo Systems

A fixed-time adaptive optimal parameter estimation (FxT-AOPE) scheme is proposed to address the difficulties in estimating dead zone parameters and slow convergence speed of tracking errors in permanent magnet synchronous motor systems. First, the continuous piecewise linear neural network is used to model the nonlinear dead zone dynamics. Second, an auxiliary filter is constructed to extract estimation errors, and this filter is used to drive an adaptive law with time-varying gain, minimizing the cost function of estimation errors and achieving adaptive optimal parameter estimation (AOPE). Then, the AOPE method is introduced into the fixed-time non-singular terminal sliding mode control (FxT-NTSMC) of the permanent magnet synchronous motor system, and the FxT-AOPE strategy is proposed to ensure the fixed time convergence of estimation error and tracking error. The stability of the closed-loop system is analyzed using Lyapunov stability theory. Finally, the feasibility of the proposed control strategy is verified through comparative simulations and experiments.