Design of PI Controller for a Class of Discrete Cascade Control Systems

Abstract

This paper mainly studies the modeling, stability analysis and proportional-integral (PI) controller design for a class of discrete-time cascade control systems (CCSs). In the existing CCSs for solving gain of the controller, the controller mostly adopts the proportional (P) controller, but the most commonly used controller in industrial production is PI controller. Based on the actual demand in industry and in order to obtain a better control effect, the design problem of primary and secondary controllers in a class of discrete cascade control is considered, in which the primary controller adopts a PI controller and the secondary controller adopts a P controller. On this basis, the model of cascade control system (CCS) is established. Then, we can create a new Lyapunov functional, the sufficient conditions for the stability of the system is given. Then, the collaborative design method of primary PI controller and secondary P controller is given by using linear matrix inequality (LMI) technique. Finally, a simulation example of a main steam temperature with CCS structure is given to demonstrate the effectiveness of the method. The PI controller is better than the existing P controller, this method has not only the rapidity of P control, but also the ability of integral control to eliminate steady-state errors. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> — The inspiration of this paper comes from the adjustment of plant controller parameters. The PI controller is the most widely used controller in the existing industrial production, but the adjustment of proportional and integral parameters of the controller is a very troublesome thing. In order to obtain a better controller parameters, a professional engineer may spend a whole day to adjust the parameters. This paper can design the solution of the primary and secondary controller parameters to stabilize the CCS at the same time by LMI technique, which can greatly reduce the work of adjusting the controller parameters. Through simulation, we can know that this method can make the system stable, which shows this method is feasible.