Robust gain-scheduled controller for linear parameter varying systems

Proportional-integral-derivative (PID) controller is the most widely used in industry due to its simplicity and performance characteristics. However, a number of processes with time-variant or nonlinear characteristics are difficult to be handled with a conventional PID controller. To address this problem, an enhanced PID controller exhibiting improved performance than the conventional linear fixed-gain PID controller is proposed. The algorithms proposed use a gainscheduling technique, and integrates robustness and explicit input-output constraint-handling capabilities in the controller design. Nonlinear processes are modeled as a linear parameter varying (LPV) system. The gain-scheduled P controller is designed by off-line solving robust optimal control problem in order to construct a sequence of state feedback gains. The associated sequence of nested invariant sets is used to define the corresponding operating region of each state feedback gain computed. At each control iteration, the smallest invariant set containing the current state measured is determined, a corresponding feedback gain is then implemented to the process. Further, an interpolation algorithm is proposed to improve control performances. The feedback gain implemented to the process is determined by maximizing its norm subjected to a set of constraints associated with the current invariant set. Stability of a closed loop behaviour can be guaranteed. Simulation example of a spherical level tank is used to illustrate the applicability of the algorithms proposed. Comparison between our algorithms and a conventional PI controller tuned by existing technique is performed. The simulation results showed that the proposed algorithms can stabilize the system while satisfying input-output constraints, and provide a better control performance than the conventional PI controller. Interpolation algorithm can improve control performance while on-line computation is still tractable.