A Unified Framework for Mixed Continuous/Discrete-time H_inf-Control

Doctoral thesis, 2003

This thesis presents a unified and general state-space framework for mixed continuous/discrete-time H_inf-controller design. H_inf-design considers robust and optimal control of multivariable systems. A versatile unified notation for signals and systems in continuous and discrete time is introduced, providing a means to show a very close relationship between the continuous-time and discrete-time solutions. In fact they are two different interpretations of the general result. The solution is mainly Riccati equation based, and in the periodic case, the continuous-time state evolution over the period is achieved from a discretised (or "lifted") system model. Typical applications are control of continuous-time or discrete-time (periodic) systems, as well as (multirate) sampled-data control, including mixed continuous and sampled-data measurements. Especially the sampled-data application with a hold-circuit at controller output implies significant simplifications in the solutions, and this is presented to its full extent. The results are also applied to the loop-shaping situation, where no so called ?-iteration is needed. The controller order becomes with these methods the same as that of the augmented plant, and this is often unacceptably high. A parametric numeric optimisation approach for achieving a lower order controller is presented by means of bilinear matrix inequalities. To achieve good robustness and performance for the closed loop, it is necessary to use appropriate weight functions in the augmented plant. For this choice, a versatile genetic algorithm is used, based on fair evaluation criteria for the closed loop. Simulation results are presented for two example plants throughout the thesis, one SISO-plant and a MIMO model of a jet engine.