LQ and H2 Tuning of Fixed-Structure Controller for Continuous Time Invariant System with H∞ Constraints

The problem of fixed-order and fixed-structure controller tuning has been known for more than half a century and is a one of the classic problems of the control theory. Great number of papers and several monographs are devoted to this problem (e.g., Rotach et al., 1984; Datta, 1998; Datta et al., 2000; Astrom & Hagglund, 2006). Analytic methods based on information on structure and form of plant mathematical model play the main role among the methods for solving this problem. These include: • tuning methods based on single-stage solution of controller parameters synthesis problem (Rotach et al., 1984; Astrom & Hagglund, 2006); • automatic tuning methods based on application of relay feedback (Rotach et al., 1984; Datta, 1998; Datta et al., 2000; Hjalmarsson, 2002; Astrom & Hagglund, 2006); • methods based on indirect adaptive control, or implicit reference model (internal model control) (Petrov & Rutkovskiy, 1965; Datta, 1998; Datta et al., 2000; Astrom & Hagglund, 2006). For recent two decades, many papers devoted to application of powerful 2 H and ∞ H optimization tools to design and tuning problems for fixed-structure controllers have been presented (McFarlane & Glover, 1992; Zhou et al., 1996; Balandin & Kogan, 2007). Moreover, the concepts of robust design have brought to a new view of known controller tuning methods. In (McFarlane & Glover, 1992), a practically effective solution for fixed-order controller tuning problem was obtained. It is based on shaping frequency responses of open control loop by means of preand post-filters (loop shaping) in conjunction with minimizing ∞ H norm of closed-loop system. The main advantage of this approach consists in that the resulting controller is not only stabilizing, but possesses assured performance characteristics in conditions of uncertainty. The method has been successfully applied for synthesis of PID (Proportional-Intagrating-Derivative) controller for SISO (Single-Input Single-Output) plant, as well as multiloop PID controller for MIMO (Multi-Input Multi-Output) plant. The controller tuning problem is close to the plant identification problem that implies using of constrained and unconstrained optimization technique for finding optimal controller tuning algorithms in model matching problem (Poznyak, 1991) and, in particular, in internal model