Design of PI-P Controllers for a Class of Nonlinear Discrete Cascade Control Systems

To address the parameter coordination and system integration issues in nonlinear discrete-time cascade control systems, this paper proposes, for the first time, a novel collaborative PI-P controller design method. First, an augmented state-space model for the PI-P controller is introduced, where the integral term is embedded into the state variables. Then, stability conditions are derived using Lyapunov stability theory, which are formulated as linear matrix inequality (LMI) constraints, enabling the simultaneous design of both primary and secondary controllers. The method is validated through simulations on a steam temperature control system. The results demonstrate that the proposed method outperforms conventional methods, achieving a faster response, reduced overshoot, and enhanced robustness. Moreover, the proposed method shows strong disturbance rejection capability and improved overall dynamic performance, further confirming its effectiveness and potential for application in nonlinear discrete-time cascade control systems.