Optimal error governor for PID controllers

Abstract

Error Governor (EG) deals with the problem of dynamically modifying the feedback error driving a controller having bounded control signals, for preventing controller or actuators saturation, avoiding integrator and/or slow dynamics windup and preserving the nominal linear controller behaviour. In this paper, an optimisation-based EG scheme is proposed for discrete-time Proportional–Integral–Derivative (PID) controllers driving Single-Input Single-Output (SISO) plants. The PID controller is considered in state-space form, and this formulation is used to pose the EG problem as a constrained quadratic program (QP). Because the QP problem is subject to inequality constraints related to controller saturation, in order to use the proposed scheme in real-world applications, it should be necessary to consider appropriate algorithms for efficiently solving the optimisation problem. An efficient way to efficiently compute the solution of the EG problem is presented, reducing the computational effort required to solve the EG QP for using the proposed scheme in real control loops with high sampling rate. An analysis of control performance and computational burden is provided, comparing in simulation studies the optimal EG scheme performance with respect to control results provided by saturated PID with and without anti-windup action.

Keywords:

• Error governor
• PID
• anti-windup
• SISO

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Notes on contributors

Luca Cavanini

Luca Cavanini received the Ph.D. degree in automation, information and management engineering from Università Politecnica delle Marche, Ancona, Italy, in 2018. He works as Technical Consultant at Industrial Systems and Control Ltd. His activity includes model predictive control, autonomous mobile robotics and artificial intelligence and machine learning techniques for control systems.

Francesco Ferracuti

Francesco Ferracuti received the Ph.D. degree in automation, information and management engineering from Università Politecnica delle Marche, Ancona, Italy, in 2014. He is a research at Università Politecnica delle Marche. His research interests include model-based and data-driven fault diagnosis, system identification, signal processing and their applications in industry.

Andrea Monteriù

Andrea Monteriù received the Ph.D. degree in Artificial Intelligence Systems from Università Politecnica delle Marche, Italy, in 2006. He is associate professor at Università Politecnica delle Marche. His research interests mainly focus on the areas of fault diagnosis, fault tolerant control, periodic systems, nonlinear dynamics and control, applied in different fields including aerospace, marine, robotic and artificial intelligent systems.