Synthesis of Nonlinear Controllers with Rate Feedback via Sinusoidal-Input Describing Function Methods

In this paper, we report on recent advances in the design of fully nonlinear controllers for amplitude-sensitive nonlinear plants using sinusoidal-input describing function methods. This work includes the development of a new nonlinear controller synthesis approach that includes derivative action in an inner-loop feedback path (nonlinear rate feedback), and its application to a motor + load model with torque saturation and stiction. This approach is capable of treaing nonlinear systems of a very general nature, with no restrictions as to system order, number of nonlinearities, configuration, or nonlinearity type; additionally, the techniques can be generalized for the design of nonlinear controllers of different structures. The end result is a closed-loop nonlinear control system that is relatively insensitive to reference-input amplitude.