The frequency response method is a powerful tool for the analysis and design of linear control systems. It is based on describing a linear system by a complex-valued function, the frequency-response, instead of a differential equation.
For some nonlinear systems, an extended version of the frequency response method , called describing function method, can be used to approximately analyse and predict nonlinear behavior. The main use is for the prediction of limit cycles in nonlinear system, as for example described in this PhD thesis. Often, limit cycles tend to cause poor control accuracy and the constant oscillation can cause wear or mechanical failure of the control system hardware.
The basic assumptions for describing function analysis are:
- there is only a single nonlinear component
- the nonlinear component is time invariant.
- the nonlinearity is odd
- higher-frequency harmonics could be neglected