The direct nonlinear PID adaptive control for a class of nonlinear time-delay systems

The minimized nonlinear incremental model, the noise estimator, the nonlinear error-increment PID control law, and the parameter adaptive recursive predicting algorithm are presented for a class of nonlinear time-delayed discrete-time systems based on dynamic approximate nonlinearization model. They realize the direct nonlinear PID adaptive control for nonlinear systems with time-delays. The simulation results prove the correctness and effectiveness of the proposed algorithm.