A set of decentralized PID controllers for an n – link robot manipulator

• Published in: Sadhana (Bangalore) Vol. 37; no. 3; pp. 405 - 423
• Main Authors: LEENA, G, RAY, G
• Format: Journal Article
• Language: English
• Published: India Springer-Verlag 01-06-2012
• Subjects: Controllers; Decentralized; Engineering; Manipulators; Mathematical models; Proportional integral derivative; Robot arms; Robots; Theorems; robot manipulator; tracking error; interconnected system; decentralized controller; Kharitnov theorem; linear matrix inequality
• ISSN: 0256-2499; 0973-7677
• DOI: 10.1007/s12046-012-0082-4

A class of stabilizing decentralized proportional integral derivative (PID) controllers for an
n
-link robot manipulator system is proposed. The range of decentralized PID controller parameters for an
n
-link robot manipulator is obtained using Kharitonov theorem and stability boundary equations. Basically, the proposed design technique is based on the gain-phase margin tester and Kharitonov’s theorem that synthesizes a set of PID controllers for the linear model while nonlinear interaction terms involve in system dynamics are treated as zero. The stability analysis of the composite system with the designed set of decentralized PID controllers is investigated by incorporating bounding parameters of interconnection terms in LMI formulation. From the range of controller gains obtained by the proposed method, a genetic algorithm is adopted to get an optimal controller gains so that the tracking error is minimum. Simulation results are shown to demonstrate the applicability of the proposed control scheme for solution of fixed as well as time-varying trajectory tracking control problems.