Research on Stabilizing and Eliminating Limit Cycles in 3D Nonlinear Systems Characterized by Hysteresis

The work proposes a systematic and innovative graphical technique that practices computer graphics in the prediction of limit cycles (LC) in 3×3 multivariable systems with memory-type nonlinearities. If the system in an autonomous state exhibits LC, the present work investigates the quenching of LC using the method of signal stabilization with high-frequency signals random/deterministic. State feedback combined with pole placement techniques is a key strategy for suppression of LC oscillations. The feedback gain K is determined either through arbitrary selection of poles, subject to controllability conditions, or optimally, using the Riccati equation. The complexity involved in formulating the problem with memory-type nonlinearities is reduced considerably using the harmonic linearization. The complexity is further reduced if the system considered shows the LC primarily at a single frequency. The proposed methods are illustrated using examples and validation, done by digital simulation and by using SIMULINK Toolbox of MATLAB software.