EEET2109 CONTROL SYSTEMS Lab 1: Simulation LINEAR CONTROL SYSTEMS: CASE STUDY - DC MOTOR SPEED CONTROL

Aim
1. To develop a Laplace domain modelling of linear systems with a DC motor example
2. To examine the open-loop response of linear systems with a DC motor example
3. To implement and simulate closed loop control action for linear systems with a DC motor
example
4. To examine dynamic response of control systems
1 Theoretical Concepts: Modelling linear systems
The Laplace transform of a time domain signal y(t) is defined as:
( )  ( ) ( ) 

−
==
0
tyesYty dt st L
(1)
where s is the Laplace variable and is closely related to the quantity frequency. When applied to a
differential operation we obtain the results:
( ) sY ( ) ( ) ys 0
dt
dy t
−=






L
(2)
( ) ( ) ( ) ( )
dt
dy sYs sy
dt
tyd 0
0
2
2
2
−−=








L
(3)
where
y( ) 0
and
( )
dt
dy 0
are the initial values for the time signal y(t) and its’ derivative.
Consider a general expression for a second order differential equation involving the time signal y(t)
when driven with the signal x(t):
( ) ( )
cy( ) ( )txt
dt
dy t
b
dt
tyd
a =++
2
2
(4)
Taking the Laplace transform gives:
( ) ( ) ( ) b  sY ( ) ( ) ys cY( ) ( )sXs
dt
dy sYsa sy =+−+





−− 0
0
0
2
(5)
The transfer function that relates the output signal Y(s) to the input X(s) in the Laplace domain is
given by:
( )
( )sX bsas c
sY
++
=
2
1
(6)
where
y ( ) 0
is assumed to be zero. Equations (4) and (6) are equivalent representations