[PID] Control Systems Simulation using Matlab and Simulink.pdf

UNIVERSITY OF CALIFORNIA AT BERKELEY
Department of Mechanical Engineering
ME134 Automatic Control Systems
Spring 2002
Report Due: Tuesday, February 26 One report per group is required.
Control Systems Simulation
Using Matlab and Simulink
1 Introduction
In ME134, we will make extensive use of Matlab and Simulink in order to design, analyze and
simulate the response of control systems.
2 Control of Second Order System
We will simulate the open loop and closed loop step response of the dynamic system described by
the state and output equations
d
x = −. 1 x + . 1 x (1)
dt 1 1 2
d
x = −. 2 x + . 1 u
dt 2 2
y = x 1
(2)
and transfer function
. 01
G ( s )= (3)
s 2 + . 3 s + . 02
Y ( s )= G ( s ) U ( s )
Here u is the input, y is the output, and x 1 and x 2 are the two states of the system.
The two tank fluid system shown in Fig. 1 can be modeled by the above state and output
equations and/or transfer function.
Open loop unit-step response
Consider the open loop unit-step input response of this system. The unit-step input is given by
u ( t )= µ ( t ), were


0if t< 0
µ ( t ):=
1if t ≥ 0
1
Figure 1: fluid system
Load the simulink file tank . Using simulink, modify the system to the obtain the open
loop unit-step input response of this system. Plot the open loop response on a plot.
Continuous Time (.) closed l