Closed loop response of nonlinear systems by a functional transformation approach

A graphical technique is presented for determining the closed loop response of nonlinear control systems driven by sinusoidal inputs. The nonlinear portion of the system is represented by its conventional describing function, which may be frequency dependent as well as amplitude dependent. The linear portion of the system is represented by its complex frequency response function G(j\omega) . A transparent overlay is used to mechanize a functional transformation similar to that performed by a Nichols chart, allowing rapid determination of the system output for sinusoidal inputs. The accuracy of the method is limited by the accuracy of the describing function approximation. In addition to offering a rapid solution to what has been regarded as a time consuming problem, the method gives the designer sufficient insight into the behavior of the system to allow the intelligent choice of compensating networks to improve system performance. A numerical example is used as a vehicle for discussion of compensation, and experimental results are presented to verify the analysis.