ABSTRACT
Presented in this paper is a frequency domain design methodology for a linear, uncertain, SISO system for maximizing the size of a persistent bounded disturbance in the presence of a hard time domain constraints on system states, output and control input, and bandwidth limits on the controller. It is assumed that the plant dynamics can be represented by a combination of parametric uncertainty in the low frequencies and unstructured uncertainty in the high frequencies. Parametric uncertainty in the low frequencies and certain frequency domain “equivalents” of the time domain constraints manifest as upper and lower bounds on the nominal loop transfer function in the complex plane. The high frequency unmodeled dynamics impose a robust stability constraint which manifests as a close contour in the complex plane which cannot be penetrated by the nominal loop transfer function. Once the pointwise frequency domain bounds on the nominal loop transfer function obtained a suitable loop transfer function is shaped to satisfy those bounds. The size of the maximum step disturbance that can be tolerated by the closed loop system is estimated by solving a min-max problem prior to designing the control loop and its true value is determined by a special computation once the nominal loop transfer function is designed. Also given is an estimate of the maximum size of persistent bounded disturbance that can be tolerated by the nominal closed loop. Two examples illustrating the methodology are also included.
