Robustness Margins by PID Control: Towards an Explainable Theory

Description

For well over a century, PID control stood out as the most favored method for its unparallel simplicity, ease of implementation and cost-effectiveness. For a technology so mature and successful, what can be new and worthy of attention? Surprisingly, even in a post-modern and information-centric era of present time, PID control continues to demonstrate its sustained power, serving an awe-inspiring testimony to its incredible vitality and overwhelming acceptance by industrial control and automation communities. This dominance of PID control is unlikely to be changed in the near future due to the long existing industrial control infrastructure. Despite its omnipresent utilities, however, PID control is also limited. The fact that PID controllers rely exclusively on empirical, trial-and-error tuning makes it not readily adaptable, and in fact poorly equipped for coping with the increased complexity of today's and future complex engineering systems, thus calling for reexamination and further development of the PID method. Toward this need, we seek to develop systematically an explainable PID control theory, for which we target system robustness-arguably the most important goal in feedback control-as pilot problems. The project is focused on the maximal gain and phase margins attainable by PID control, two key measures of robustness. The project also seeks extensions of PID control to multi-agent systems, investigating the robustness of PID feedback protocols for consensus control. Four synergistic tasks are proposed, consisting of (1) developing analytical and computational methods for quantifying the maximal gain/phase margins achievable by PID control; (2) characterizing the gain/phase margins and performance tradeoffs with PID controllers; (3) developing PID gain/phase consensus margins for multi-agent systems; and (4) validating the theoretical development by simulation and experimental implementation. Being at the core of the PID control design and implementation, and of an explainable PID control theory, these objectives, from both model-based design and model-free tuning perspectives, hold the key for the broader applications of PID control to increasingly more complex, uncertain, and more performance-driven networked industrial control systems, while still retaining its essential simplicity and leveraging on the existing industrial control infrastructure. Built on the PI’s prior successes and ongoing work on PID control and multi-agent systems, a coherent technical approach has been carved out, which consists of realistic solution strategies that are believed to be both theoretically significant and practically feasible, answering to some of the key challenges for future applications of the PID control method.