Adaptive PID controller for stable/unstable linear and non-linear systems

Proposes and analyzes a direct adaptive proportional-integral-derivative (APID) control scheme for off-line and online tuning of PID parameters. The tuning algorithm determines a set of PID parameters by minimizing an error function. The theory of adaptive interaction is used to design the APID control law. Two versions of the tuning algorithm are presented: the Frechet and approximation methods. These algorithms are applied to linear and nonlinear plants. Lyapunov stability theory is used to proof the stability of the approximation method. The analysis of the convergence properties and system performance are conducted by using computer simulations and several known adaptation concepts. The approximation method does not require the knowledge of the plant to be controlled; therefore, the control scheme becomes robust to plant changes.