Smith predictor PID-based robust adaptive gain-scheduled control for a class of fractional order LPV systems with time delays

In this paper, a novel robust gain scheduled adaptive control design is proposed for a class of fractional order linear parameter varying (LPV) systems with time-varying delay. The control design is based on a set of predefined PID controllers with an adaptive switching law. The considered class of fractional second-order-like systems with delay is able to represent a wide range of industrial and practical processes. The controller structure includes a Smith predictor, whereas the switching law is based only on the models' outputs. The main contribution of this paper is the generalization of the gain scheduling adaptive control strategy to delayed fractional order LPV systems using a set of fractional order PID regulators. Stability analysis of the proposed controller is performed. A numerical implementation example on a piece of a sewer system illustrates the efficiency of its efficiency and robustness.