Prediction of limit cycle oscillations in piecewise linear systems with multiple piecewise nonlinearities

Mathematical modelings of many electric and mechanical systems involve piecewise linear system. Piecewise linear system can possess a periodic solution called a limit-cycle oscillation (LCO), which can seriously undermine the system performance. Therefore, how to analyze LCO and its parameters in piecewise linear systems is one of the primary concerns for the control and system engineers. This work presents a novel framework to predict and analyze LCO of piecewise linear systems, focused on systems with multiple piecewise nonlinearities. On top of the well-known piecewise linear analysis, the Floquet theory is applied 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. An example of a realistic flight control system is taken to demonstrate the effectiveness and efficiency of authors' framework.