TABLE OF CONTENTS In this chapter the design methodology for a discrete-time control system with two-time-scale motions is extended for the purpose of sampled-data control system design. This is done by taking into account the particularities of the model of a series connection of a ZOH and a continuous-time system on the condition of high sampling rate. We derive an approximate discrete-time model for a nonlinear time-varying system preceded by a ZOH. The model takes the form of a difference equation having a small parameter, where the parameter depends on the sampling period. Both SISO and MIMO sampled-data control systems are treated.
As a preliminary, let us consider the asymptotic properties of a pulse transfer function for a series connection of a ZOH and a continuous-time linear system with high sampling rate. We will show that the approximate model of the sampled-data system is a difference equation with a small parameter that depends on the sampling period. Hence, the previous discrete-time control system design methodology can be extended to sampled-data control systems.
Let G( s) be a rational, strictly proper, continuous-time transfer function
| (12.1) |  |
with relative degree ? = n - m > 0, where a n ? 0 and b m ? 0.
The roots of the polynomial
lie in the stable half-plane Re s < 0 or, in other words, the internal stability requirement is satisfied for the system given by...
