H∞-Optimierung abgetasteter Regelsysteme

If a System contains both continuous-time and discrete-time parts, known methods for its optimization can only treat its continuous-time behaviour in a very indirect manner. In this paper a new method is presented which allows straightforward optimization of such systems. The methodrelies on using an approximation of the original system (with arbitrarily small error) by a purely discrete-time, periodic system. By a reordering of variables which does not affect the performance index, the periodic system can be described with a time-invariant transfer function, and the optimization problem solved with the use of conventional H∞ optimization, employing well known methods and commercially available software. The optimization method presented is used to derive a new technique for discretization of a continuous-time controller. Stability of the resulting closed-loop can be guaranteed. A second application is a scheme for the direct design of a discrete-time controller given a continuous-time H∞ perforrnance index. Both applications of the rnethod illustrate how the continuous-time behaviour of such mixed (i.e. continuous-time and discrete-time) systems can be optimized.