Control System Design Using Optimization Solvers for Achieving Time-Domain and Frequency-Domain Performances Simultaneously

The objective of this paper is to give a controller design method using optimization solvers for achieving desired time-domain and frequency-domain performances simultaneously in discretetime systems. The time-domain performance is described by constraint conditions for overshoots, undershoots, rising times and so on. The frequency-domain performance is described by an H-infinity norm condition for robust stability. The proposed design method reduces the controller design problem for achieving these performances to a nonconvex nonlinear optimization problem. Although the obtained problem is not convex, the optimization solvers of Matlab can yield a local optimal solution which satisfies the constraint conditions for achieving the performances, which is demonstrated by a numerical example.