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Optimal Fault Tolerant Error Governor for PID Controllers

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  • Control Theory and Applications
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Abstract

The Error Governor (EG) paradigm considers the issue of dynamically changing the error which drives a feedback controller featured by bounded control action magnitude to prevent the actuators’ saturation and to avoid the slow wind-up effects due to integrator or slow dynamics. Fault Tolerant (FT) policies are control methods permitting to mitigate the effect of faults occurring on driven actuators by modifying the structure of the controller which provides the reference signal for such actuators. In this paper, a FT policy based on an optimal EG approach is proposed. The policy, termed Fault-Tolerant Error Governor (FT-EG), permits to introduce a FT action in a closed-loop system driven by PID controllers neglecting changes in the controller structure and, further, the wind-up issue given by nominal actuator saturation. The FT-EG is based on the solution of a constrained optimization problem and a computationally efficient version of the algorithm is presented. An analysis of control performance and the computational burden is provided, comparing in simulation studies the optimal FT-EG scheme performance with respect to control results provided by the baseline EG policy and saturated PID controller in the fault-free and the faulty scenario.

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Abbreviations

ē :

Governed error

ū :

Saturated input

ū m, ū M :

Saturation bounds

δ :

Controller derivative filtering term

\(\mathbb{U}\) :

Control input admissible set

\({\cal C}\) :

Controller

\({\cal P}\) :

Plant

\({\cal S}\) :

Saturation function

ρ :

QP problem time-varying parameters vector

A c, B c, C c, D c :

Controller state-space matrices

A p, B p, C p :

Plant state-space matrices

e :

Feedback error

H, h, G, W, w :

QP problem matrices

\(K_k^f\) :

Fault coefficient

K p, K i, K d :

Controller gains

T s :

Controller sampling time

x, u, y :

Plant state, input and output

z :

QP problem optimisation variable

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Author information

Authors and Affiliations

  1. Industrial Systems and Control Ltd, Culzean House, 36 Renfield Street, Glasgow, G2 1LU, UK

    Luca Cavanini

  2. Department of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche, Ancona, 60131, Italy

    Francesco Ferracuti, Sauro Longhi & Andrea Monteriù

Authors
  1. Luca Cavanini
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  2. Francesco Ferracuti
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  3. Sauro Longhi
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  4. Andrea Monteriù
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Corresponding author

Correspondence to Andrea Monteriù.

Additional information

Luca Cavanini received his Ph.D. degree in automation, information and management engineering from Università Politecnica delle Marche, Ancona, Italy, in 2018. He works as a 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 received his 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, signal processing, statistical pattern recognition, and machine learning and their applications in industry.

Sauro Longhi holds the position of Full Professor in Robot Technologies at Università Politecnica delle Marche. His main research interests include modelling, identification and control of linear and non linear systems, control of mobile robots, service robots for assistive applications supporting mobility and cognitive actions, home and building automation, and automatic fault detection and isolation.

Andrea Monteriù received his M.Sc. degree in electronic engineering and a Ph.D. degree in artificial intelligence systems from Università Politecnica delle Marche, Italy, in 2003 and 2006, respectively. Currently, he is an associate professor at Università Politecnica delle Marche. His research interests mainly focus on the areas of fault diagnosis and fault tolerant control applied on robotic, and unmanned and artificial intelligent systems.

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Cavanini, L., Ferracuti, F., Longhi, S. et al. Optimal Fault Tolerant Error Governor for PID Controllers. Int. J. Control Autom. Syst. 20, 1814–1826 (2022). https://doi.org/10.1007/s12555-020-0544-0

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  • DOI: https://doi.org/10.1007/s12555-020-0544-0

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