State-space control

SYSTEMS MODELLING ASSIGNMENT – PART 2
1. INTRODUCTION
1.] Background
This assignment follows on from assignment 1. which you completed in Block 1. As before, it
relates to the DC Motor Control Trainer (DCMCT), which will be used for practical
application of the techniques we have Ieamed in Block 3. It is going to be controlled by
computer as a ‘l-Iardwarc-in-thc-Loop’ simulation.
1.2 Objective
The objectives of this lab are to:
Develop and validate a DC motor model through first principles modelling and
experimental tests
Design and implement a controller to achieve desired performance specifications.
The coursework is split into three parts: a system modelling assignment, a controller design
assignment, and a lab report detailing the practical experimentation.
This assignment covers the controller design part of the coursework. The objective is to
design a controller for the system.
1.3 DC Motor Modelling
In Assignment 1, a model 01. the hardware was produced. In addition to this hardware, there
are some components and calibration factors which were not modelled. The overall system is
described by the transfer function:
(0(5) _ 193
2 l1)
r(s) 0.015 + 8s +193
2. PIKE-LABORATORY COURSEWORK ASSIGNMENT 2: CONTROLLER DESIGN
Write a short document which addresses the following points.
a) Express the model in equation (I) in state space format [Hints this was covered in Block
I. and in Nise Chapter 3.5]. Determine the poles of the open loop system. Compare
your answer to the poles you found in Assignment 1, and comment on the dynamics of
the system.
b) Design a state feedback controller for the system, so that the closed loop model responds
to a step input with no more than 5% overshoot and a settling time of 0.25s.
c) What are the states in physical terms (Le. displacement, voltage)? Are they the same
states used in the model you developed in Assignment 1? llow would you obtain the
other states?

: