Two-Degree-of-Freedom Robust Controller Design Approach for Fuzzy Parametric Uncertain Systems using Particle Swarm Optimization

ABSTRACT

In this proposed work, a two-degree-of-freedom robust controller design approach for fuzzy parametric uncertain systems to ensure both the robust stability and performance is proposed. A fuzzy parametric uncertain system is a linear time-invariant uncertain system with fuzzy coefficients. Using nearest approximation, these fuzzy coefficients are approximated into crisp sets called intervals to get an interval system. In the proposed approach, the robust stability is determined by utilizing the newly developed stability conditions of interval systems. Consequently, these stability conditions are used to derive a set of inequalities in terms of controller parameters and these inequalities are solved to obtain a robust stabilizing controller with the help of particle swarm optimization for an unstable fuzzy parametric uncertain system. Finally, the required system performance is achieved by synthesizing a pre-filter using the frequency-domain method. The proposed method has the advantage of having less computational complexity and easy implementation on a digital computer. The viability of the proposed approach is illustrated through a numerical example of its successful implementation. The efficacy of the proposed approach is also evaluated against the available method in the literature and the simulation results were successfully implemented for robust stability and performance of fuzzy parametric uncertain systems.

KEYWORDS:

• Fuzzy parametric uncertain system
• Kharitonov's theorem
• Particle swarm optimization
• Pre-filter
• Robust controller
• Two-degree-of-freedom design

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Srinivasa Rao Danaboyina

Srinivasa Rao Danaboyina received his BTech degree in electrical and electronics engineering from J.N.T.U College of Engineering, Kakinada in 1993 and his MTech degree in electrical machines and industrial drives from NIT Wangal, in 2003. Presently, he is pursuing his PhD degree at J.N.T University Kakinada. His area of interest includes model order reduction, controller design, electrical machines, and power electronics.

E-mail: [email protected]

Siva Kumar Mangipudi

Siva Kumar Mangipudi was born in Amalapuram, Andhra Pradesh, India, in 1971. He received the bachelor's degree in electrical and electronics engineering from JNTU College of Engineering, Kakinada and the ME and PhD degrees in control systems from Andhra University College of Engineering, Visakhapatnam, in 2002 and 2010, respectively. His research interests include model order reduction, interval system analysis, and design of PI/PID controllers for interval systems, sliding mode control, and soft computing techniques. Presently, he is working as professor and H.O.D of electrical engineering department, Gudlavalleru Engineering College, Andhra Pradesh, India. He received best paper awards in several national conferences held in India.

Ramalinga Raju Manyala

Ramalinga Raju Manyala graduated in 1986 from JNTU, received the Master's degree in 1989 from REC, Warangal, and the PhD degree in 2004 from JNT University, India. Presently, he is working as professor and director for Admissions, University College of Engineering Kakinada, JNTUK. He has presented many research papers in various national and international conferences and journals. His research interests include energy management, conservation and auditing, distributed generation, and IT applications in power utility companies.

E-mail: [email protected]