Prediction of limit cycle oscillations in piecewise linear systems

The exact mathematical model of most of mechanical and/or electrical systems involves the piecewise linear system, which consists of linear parts along with piecewise nonlinearities. Piecewise linear systems can possess a periodic solution called a limit-cycle oscillation (LCO), which can seriously undermine the system performance depending on the amplitude and the frequency of the LCO. Therefore, how to analyze LCO and its parameters of piecewise linear systems is one of the primary concerns for the control and system engineers of the system. This thesis work presents a novel framework to predict and analyze LCO of piecewise linear systems. On top of the well-known piecewise linear analysis we apply the Floquet theory to identify LCO parameters and determine the stability of the LCO. The introduction of Floquet theory to piecewise linear systems is allowed through transforming piecewise nonlinearities to corresponding equivalent analytic functions. In addition, the establishment of switching equation provides another necessary condition to predict LCO parameters. We take an example of a realistic flight control system to demonstrate the effectiveness and efficiency of our framework.Ph.D