Convex integrated design (CID) method and its application to the design of a linear positioning system

In this paper, a methodology is presented to solve an integrated mechanical structure and control system design problem, with a set of n prespecified closed-loop performance specifications. Utilizing the convex integrated design (CID) method proposed here, the transfer matrix of the closed-loop system is first determined such that the set of n conflicting closed-loop performance specifications is simultaneously satisfied. However, the mechanical structure parameters and the control system gain parameter choices that comprise the closed-loop system transfer matrix are not uniquely determined. While arbitrary choices of these parameters could be made, the authors propose an approach to determine these design parameters by solving an equality-constrained optimization problem. The merit functions to the optimization problem are the closed-loop performance criteria. With this approach, the mechanical structure parameters, the controller structure and the control gains, are simultaneously determined and the closed-loop system performance is further improved beyond that required by the set of n closed-loop performance specifications. This method is demonstrated with a four-specification linear positioning system design. Experimental results verify the effectiveness of this method.