In today’s scenario, nonlinear self-sustaining oscillations otherwise called as limit cycles are one of the most important entity that limits the performance of most of the physical systems in the world. It is a formidable task to suppress the limit cycles for 2x2 systems with memory type nonlinearity in particular. Backlash is one of the nonlinearities commonly occurring in physical systems that limit the performance of speed and position control in robotics, automation industry and other occasions. The feasibility of suppression of such nonlinear self-oscillations has been explored by using pole placement technique. The novelty of the work lies with the investigation in case of the memory type non-linearity like backlash especially which is an inherent Characteristic of a Governor used for usual load frequency control of an inter-connected power system and elsewhere. Suppression of Limit Cycle using pole placement is adopted either arbitrary or optimal selection using Riccati Equation through State Feed Back. The Governing equation is d/dt [X(t)]=(A BK)X: which facilitates the determination of feedback gain matrix K for closed loop Poles/ Eigen values placement where the limit cycles are suppressed/eliminated in the general multivariable systems. The analysis is based on harmonic linearization using graphical method which has been substantiated by digital simulation / use of SIMULINK Tool Box and the same have been illustrated through example. The Poles / Eigen values are determined for Limit Cycling Systems with Memory type nonlinearities whose describing functions (harmonic linearization) are complex functions of X and ω. Hence, it is felt necessary to develop a graphical technique using harmonic balance method. The poles of such systems are placed suitably so that the systems do not exhibit limit cycles. There is ample scope of extension of the present work for prediction of limit cycles and it’s suppression in 3 X 3 or higher dimensional systems.
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