Description
LAB 1 Sampled Data Systems Are Different
Real-time Computer Control
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
