The Optimal Mix of Structure Redesign and Active Dynamic Controllers

For a given plant, this paper begins with the assumption that a controller is given which yields desired closed-loop properties. Both the controller and the original plant are redesigned so as to yield the same original closed-loop properties with a minimal active control effort. The initial linear controller before plant redesign is not restricted; it could be static or dynamic. We call this the optimal mix problem since we optimally mix parameter changes of the plant with parameter changes of the controller. The problem requires matching the entire plant matrix of the original system (before and after redesign). The problem is reduced to a standard mathematical quadratic program. Hence globally optimal answer is obtained in a finite number of steps. The applicability of the optimal mix theory to a general mechanical system is demonstrated by numerical examples of a spring-mass-damper system.