Observer based anti‐windup compensator with functional state feedback for time delay controllers—design and case study application

Abstract

Abstract Observer‐based anti‐windup compensator technique is proposed for controllers with time delays in the structure. Taking into consideration the functional character of such controllers and their infinite dimensionality, the feedback is designed as functional. For this purpose, the Ackermann formula is applied to form the functional observer feedback within the scheme involving the control‐action saturation and utilising the back‐calculation principle. It is demonstrated that for the considered controller form and anti‐windup compensator structure, the functional feedback results as causal and turns the design task to finite spectrum assignment. Nevertheless, due to the involved saturation, the feedback parameter tuning remains a nonlinear optimisation task. However, it is shown that via tuning the loop by assigning a multiple root, the optimisation problem is well feasible and can be done, e.g. by minimising an integral squared error criterion. The proposed design technique is step by step demonstrated on control of a benchmark model of heating system with substantial delays in the states, with distinct hereditary dynamics and with saturation at the system control‐input.