Backstepping-based adaptive PID control

This paper addresses analysis and design issues in adaptive PID control for linear second-order minimal phase processes using the backstepping algorithm. The first step consists in adding an integral action to the basic backstepping algorithm to obtain a zero static error.. An integrator is therefore added to the plant model and is then slid back to the controller equation at the end of the design. The control law is made adaptive without using a certainty-equivalence design and is robustified even more with nonlinear damping. The resulting adaptive PID control is u_ce+u_dyn+u_nld, where u_ce is what would be the output of the adaptive PID if a certainty-equivalence-based design were used, u_dyn compensates for the adaptation dynamics and u_nld is a nonlinear damping term added to increase the robustness by bounding the errors, even when the adaptation is off. The resulting PID controller is hence more robust and presents better transients than the basic certainty-equivalence PID version. An example compares the proposed PID to a certainty-equivalence PID