An Introduction on Robust Control

About the Presenter

Hassan Bevrani received a Ph.D. degree in electrical engineering from Osaka University in 2004. He is a full professor and the Program Leader of the Micro/Smart Grids Research Center (SMGRC) at the University of Kurdistan. Over the years, he has worked with Osaka University, Kumamoto University, Kyushu Institute of Technology, Doshisha University, Nagoya University (Japan), Queensland University of Technology (Australia), Centrale Lille (France), and Technical University of Berlin (Germany). He is the author of 8 international books, 15 book chapters, and more than 400 journal/conference papers. He has been the guest editor of 4 volumes of Elsevier Energy Procedia and Energy Reports journals. His current research interests include Robust control theory and applications, Smart grid operation and control, Power system stability, Microgrid dynamics and control, and Intelligent/robust control applications in the power electric industry.

 

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In control theory, Robust Control contains a class of approaches that are used to controllers synthesis in the presence of uncertainties and disturbances. Therefore, robust control methods aim to achieve robust stability and/or robust performance in an uncertain environment including bounded modeling errors, parameters perturbation, and unmodeled dynamics. Although the early bases required tools go back to more than 80 years ago, the main start point of the theory of robust control took shape in the 1980s and 1990s. In contrast with an adaptive/intelligent control policy, a robust control policy is static, rather than adapting to measurements of variations, the structure of the controller is usually fixed, and it is designed to work assuming that certain parameters/variables will be unknown but bounded.

Historically and from the closed-loop transfer function perspective, a high open-loop gain, which its principle was already well understood by Bode and Black in 1927, leads to substantial disturbance rejection in the face of system parameter uncertainty. Thus, high-gain feedback is a simple example of a robust control method; because it allows simplified models of operational amplifiers and emitter-degenerated bipolar transistors to be used in a variety of different settings. But the major obstacle to achieving high loop gains is the need to maintain system closed-loop stability. Loop shaping may provide a solution to fix this challenge.

Some of the modern examples of robust control techniques are Hꚙ, structured singular value (μ), sliding mode control (SMC), robust LQG, quantitative feedback theory (QFT), and Kharitonov’s theorem. The control laws given by many robust control methodologies such as Hꚙ, H2, mixed H2/Hꚙ, and μ may be represented by high order transfer functions required to accomplish desired performance and stable robust closed-loop operation, simultaneously. Therefore, order reduction after the controller design process may be required.

In the first lecture, a short introduction on Robust Control with basic definitions, concepts, main differences with other control theorems, and a brief history are discussed. Therefore, this lecture will be useful for everyone who does not have a clear vision of Robust Control theory.