Minimization of sensitivity with stability constraints in linear control systems

This paper presents a method for minimizing the sensitivity to parameter variations in linear control systems under the constraint that the system has a desired degree of relative stability. In the proposed procedure, an integral is established as an index of sensitivity. The integral is then minimized in the parameter plane wherein all the roots of the characteristic equation are placed in evidence. This enables the transient response requirements to be incorporated in the minimization of the sensitivity index, and thus the sensitivity and the system response characteristics can be considered simultaneously in control system design. The method is illustrated by examples.