A Robustness Study of Process Control Loops Designed Using Exact Linearization

Exact linearization is widely used in the control of nonlinear systems. This method necessitates a thorough understanding of the system's model structure as well as the precise values of the system parameters. However, when the real parameters of the controlled process differ from the nominal values used for the exact linearization, the system may fail to remain linear, and its dynamic characteristics, such as gains and time constants, may not align with expectations. This discrepancy can lead to performance degradation or instability in the control system. In response, this paper introduces a simple yet effective procedure that begins with a parameter grid-based characterization of the uncertain nonlinear system, followed by the design of linearizing feedback using nominal parameters. The approach is further enhanced by the design of an H∞ controller, which is robust to parameter uncertainties. The method's effectiveness is demonstrated through examples, including first-order systems and the nonlinear Van der Pol oscillator. Furthermore, the procedure is applied to SCARA-type robotic arms, illustrating the advancements in robotics and the integration of artificial intelligence algorithms for improved control performance in practical applications. The proposed approach not only addresses the challenges of parameter uncertainties but also provides a systematic framework for designing controllers that ensure stable and reliable performance across a range of real-world conditions.