Department of Electrical and Computer Engineering

ECE411S – Real-time Computer Control

LAB 1

Sampled-Data Systems Are Different

1 Purpose

The purpose of this experiment is to familiarize you with some differences in the behaviour

of sampled-data systems compared to purely continuous time systems or purely discrete time

systems. We use Matlab as the analysis tool.

2 Introduction

You have used Matlab in previous control courses to analyze linear time-invariant continuous

time systems. The operation of sample and hold brings in discrete time system operations.

Aspects related to control design will be discussed in depth in the lectures and course notes.

Here we explore some interesting aspects of sampled-data systems not present in their purely

continuous time or discrete time counterparts.

3 Experiment

3.1 Aliasing

Aliasing occurs when continuous signals are sampled. Here we illustrate this phenomenon using

the frequency response of a continuous time system.

1. Consider a continuous time transfer function

G(s) = 1

s

2 + 0.8s + 1

Using the Matlab bode.m file, determine and plot the magnitude of the frequency response

of G(s) over the frequency range

0 6

.

2. Let us first determine the effects of sampling on the frequency response. This means we

want to determine the frequency response of the system given by the cascade of G(s) and

the sampling operator S. We can proceed as follows:

(i) Choose the input u(t) to be the Dirac delta function. The output y(t) is then the

impulse response g(t). For simplicity, set T = 1 and sample the output at t = kT, k ≥

0. This produces the sequence g(kT), k ≥ 0. Denote its z-transform by G(z). Then

1

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