Investigation of Limit Cycles and Signal Stabilization by Deterministic and Gaussian Random Signals Based on Deadbeat Approach in 3×3 Nonlinear Systems with Memory Nonlinearities

The hierarchy of technological development in design procedure for control systems, classical (based on the trial and error method), modern & postmodern (based on the pole placement method using state feedback with either arbitrary or optimal selection of feedback gain matrix K), and the latest current design address the uncertainty that uses the stochastic systems that, in turn, deal with random signals. This study begins by predicting limit cycles (LC) in 3×3 nonlinear systems operating under autonomous conditions. Subsequently the work investigates the quenching of limit cycling oscillations by signal stabilization using deterministic/Gaussian random signals. It is observed that the process of signal stabilization takes some time to reach a steady state and that with some ripples/steady state error. To overcome these setbacks and to achieve transient-free signals with no steady state error/ripples and faster response, signal stabilization supported by a deadbeat response has been attempted. The results thus obtained from computer simulation, either by a developed program using MATLAB code or by using SIMULINK Toolbox, are fabulous and unexpectedly good, as desired.