<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In control practices, problems of parametric or time-varying uncertainties must be dealt with. Robust control based on norm theory and convex and non-convex optimization algorithms is a powerful tool to solve these problems in theory, but it is employed rarely in applications. In most engineering cases, Proportional-Integration-Derivative (PID) control is still the most popular method for its easy-to-tune and controllable properties. The control method proposed in this paper integrates the PID control into robust control formulation as a robust Structured Static Output Feedback (SSOF) problem of Linear-Parameter-Varying (LPV) systems, which can be converted into a Parameter Dependent Bilinear-Matrix-Inequality (PDBMI) optimization problem. A convex-concave decomposition based method is given to solve the proposed PDBMI problem. The proposed solution has a simple structure in PID form and can guarantee stability and robustness of the system being controlled in the whole operation range with less conservativeness than existing solution.</p></abstract>

In control practices, problems of parametric or time-varying uncertainties must be dealt with. Robust control based on norm theory and convex and non-convex optimization algorithms is a powerful tool to solve these problems in theory, but it is employed rarely in applications. In most engineering cases, Proportional-Integration-Derivative (PID) control is still the most popular method for its easy-to-tune and controllable properties. The control method proposed in this paper integrates the PID control into robust control formulation as a robust Structured Static Output Feedback (SSOF) problem of Linear-Parameter-Varying (LPV) systems, which can be converted into a Parameter Dependent Bilinear-Matrix-Inequality (PDBMI) optimization problem. A convex-concave decomposition based method is given to solve the proposed PDBMI problem. The proposed solution has a simple structure in PID form and can guarantee stability and robustness of the system being controlled in the whole operation range with less conservativeness than existing solution.

Robust Gain-Scheduled PID Control: A Parameter Dependent BMI Solution

Department of Electronic and Computer Engineering

Hong Kong University of Science and Technology

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Robust Gain-Scheduled PID Control: A Parameter Dependent BMI Solution"}

In control practices, problems of parametric or time-varying uncertainties must be dealt with. Robust control based on norm theory and convex and non-convex...

Robust Gain-Scheduled PID Control: A Parameter Dependent BMI Solution

Published Online: Mar 27, 2020

Page range: 156 - 167

Received: Dec 30, 2019

Accepted: Feb 25, 2020

DOI: https://doi.org/10.2478/cait-2020-0011

Keywords
Robust control, gain scheduling, Proportional-Integration-Derivative (PID) control, Bilinear-Matrix-Inequality (BMI), Linear-Matrix-Inequality (LMI), Linear-Parameter-Varying (LPV) system

© 2020 Pengyuan Shao et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Robust Gain-Scheduled PID Control: A Parameter Dependent BMI Solution

Published Online: Mar 27, 2020

Page range: 156 - 167

Received: Dec 30, 2019

Accepted: Feb 25, 2020

DOI: https://doi.org/10.2478/cait-2020-0011

KeywordsRobust control, gain scheduling, Proportional-Integration-Derivative (PID) control, Bilinear-Matrix-Inequality (BMI), Linear-Matrix-Inequality (LMI), Linear-Parameter-Varying (LPV) system

© 2020 Pengyuan Shao et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Robust control, gain scheduling, Proportional-Integration-Derivative (PID) control, Bilinear-Matrix-Inequality (BMI), Linear-Matrix-Inequality (LMI), Linear-Parameter-Varying (LPV) system