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Control and instrumentation Simulation, identification and control of discrete time

Control and instrumentation Simulation, identification and control of discrete time
systems
Intended Learning Outcomes:
– Solve discrete time identification and control problems using Matlab software.
– Produce a scientific report.
Introduction
This individual coursework on the simulation, identification and control of discrete
time systems consists of three main sections:
• In section 1 (or question 1), the aim is to link the continuous and discrete time
control systems for a simple integrated first order system, in the time domain
and in the frequency domain. Continuous and discrete time commands of
Matlab’s control system toolbox (Most of which are learnt during tutorials)
will be used. The analytic analysis of the discrete time system will be
complemented by the conventional Graphic analysis methods for discrete time
control systems.
• In section 2, a second order model will be developed and Matlab will be used
to simulate the uncontrolled discrete time system. A discrete time PID
controller will then be designed and simulated.
• In section 3, the least squares system identification method will be used to
determine the parameters of a discrete time second order system and extract
the parameters of the original second order continuous time system. This will
be done using an array of input/output measurements.
Question 1: Discretisation effects on stability [40 marks]
A system has the following open loop transfer function (use k=1 in 1.a ):
Input u
ZOH
k
s(s + 2)
Output y
a)
i. Comment on the stability of the system in the continuous time domain.
Use Matlab to plot the response of the system to a unit step input (k=1).
ii. Calculate the open loop transfer function of this system in the Z-domain.
(10 marks)
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