Synthesis of Linear PID Controllers for Nonlinear Multivariable Systems

We report on a new, systematic approach to the synthesis of linear multivariable controllers for use with multiple-input/multiple-output (MIMO) nonlinear systems. The approach is based on describing function models of the system followed by numerical optimization in the frequency domain. The end result is a closed-loop feedback system which is insensitive to the amplitude level of the excitation signal, and which approximates a set of user-defined performance criteria with minimum mean square error. We demonstrate the procedure by solving an example problem.