A STABLE ON-LINE SELF-TUNING OPTIMAL PID CONTROLLER FOR A CLASS OF UNKNOWN SYSTEMS

In this paper, a novel self-tuning method of optimal PID control laws is proposed for both continuous-time systems and discrete-time systems. The controlled plant is assumed to be unknown except the system order (or system delay) and the direction of transmitting control input. Through the minimiza-tion of PID gains subject to the Lyapunov stability based reaching condition, the tuning of the three PID control gains is transformed to solve the inequality constraint optimization problem. An unknown SISO nonlinear system subject to a unit step input, and the tracking control problem of the piezoelectric ac-tuator (PZA) with unknown dynamics are simulated. The simulation results show that the excellent tracking performance can be achieved