Optimal analytical cascade control for FOPDT systems

Abstract

This paper proposes a novel control strategy based on optimal Linear Quadratic Regulator (LQR) design applied to cascade systems with stable, integrative, and unstable First Order plus Dead-Time (FOPDT) outer loop models. The secondary (inner) and primary (outer) loop controller designs are performed using the Simplified Filtered Smith Predictor (SFSP). The optimal analytical design is derived from a novel strategy where the pole of the internal loop is placed so that the LQR criterion can be achieved with a simple tuning of the external loop. In contrast to related work, the secondary controller is designed using an SFSP control structure to nominally achieve optimal LQR performance and accelerated rejection of disturbances acting on the inner-loop process. To illustrate the usefulness of the proposed design, we evaluated the strategy in different scenarios, showing the optimality and performance of the analytical design.