Control design for time-delay systems based on quasi-direct pole placement

A novel method for the determination of controller parameters in a broad class of linear control systems affected by time-delays is presented. This method is based on an appropriate shaping of the spectrum of the closed-loop system. Its application follows two steps. First, a number of rightmost poles, smaller than the number of controller parameters, are directly assigned. This leads to constraints on the controller parameters. By using algebraic techniques a complete parametrization of all controllers satisfying these constraints is obtained. In the second step, the remaining degrees of freedom in the parameter space are used to shift the remaining part of the system spectrum as far to the left as possible. This corresponds to an optimization problem involving a nonsmooth, non-convex objective function. An extensive real-plant example is presented to demonstrate the effectiveness and applicability of the procedure.