Control of Hybrid Systems

The following sections are included:

• Introduction

• The Definition of the Z-Transform

• Some Examples

• Properties of the Z-Transform

• Sampled-data Systems

• The Sample-and-Hold Element

• The Delta Function and its Laplace Transform

• The Ideal Sampler

• The Zero-Order Hold

• Calculating the Pulse Transfer Function

• Using MATLAB to Perform the Calculations

• The Transfer Function of a Discrete-Time System

• Adding a Digital Compensator

• Stability of Discrete-Time Systems

• A Condition for Stability

• The Frequency Response

• A Bit about Aliasing

• The Behavior of the System in the Steady-State

• The Bilinear Transform

• The Behavior of the Bilinear Transform as T → 0

• Digital Compensators

• When Is There No Pulse Transfer Function?

• An Introduction to the Modified Z-Transform

• Exercises