Gain-scheduled Smith proportional–integral derivative controllers for linear parameter varying first-order plus time-varying delay systems

Practical control problems often deal with parameter-varying uncertain systems that can be described by a first-order-plus-delay (FOPD) model. In this paper, a new approach to design gain-scheduled robust linear parameter varying (LPV) propotional–intergral derivative controllers with pole placement constraints through linear matrix inequalities (LMI) regions is proposed. The controller structure includes a Smith Predictor (SP) to deal with the delays. System parameter variations are measured online and used to schedule the controller and the SP. Although the known part of the delay is compensated with the ‘delay scheduling’ SP, the proposed approach allows to consider uncertainty in the delay estimation. This uncertainty is taken into account in the controller design as an unstructured dynamic uncertainty. Finally, two applications are used to assess the proposed methodology: a simulated artificial example and a simulated physical system based on an open canal system used for irrigation purposes. Both applications are represented by FOPD models with large and variable delays as well as parameters that depend on the operating conditions.