PID TUNING OF A HYDRAULIC CONTROL SYSTEM
YED TEPE UNIVERSITY
DEPARTMENT OF MECHANICAL ENGINEERING
1
YEDITEPE UNIVERSITY
MECHANICAL ENGINEERING LABORATORY
PID Tuning of a Hydraulic Control System
1. Objective
To be able to set a PID controller using the Zi
ME 352
System Dynamics and Control
Homework #5
Due: Mon 19.04.2010
[1]. Determine the type of the following unity-feedback systems for which the forward-path transfer functions
are given.
K
(1 + s )(1 + 10 s )(1 + 20 s )
10( s + 1)
(b) G ( s ) =
s ( s + 5
ME 352
Modeling and Control of Dynamic Systems
Homework #1 Solutions
1. (a) Force equations:
2
f (t ) = M 1
d y1
+ B1
2
dt
dy1 dy2 + K y y
( 1 2)
dt dt
dy1
+ B3
dt
2
dy1 dy2 + K y y + M d y2 + B dy 2
( 1 2 )= 2 2
2
dt
dt
dt dt
B3
Rearrange the equ
ME 352
System Dynamics and Control
Homework #8 Solutions
Solutions given for the following ID
250705005
x = 5
a=5
y = 0
b=6
z = 5
[1]. The closed-loop transfer function is
Gc ( s ) =
G ( s)
a
5
5
=
=
Gc ( j) =
1 + G ( s ) s + a + b s + 11
j + 11
(a) For
ME 352
System Dynamics and Control
Homework #5 Solutions
Solutions given for the following ID
250705005
x = 5
a=5
y = 0
b=6
z = 5
[1]. Unit-step response is obtained, on the s-shaped response curve R and L values are calculated.
Homework #5 - PID Tuning
ME 352
System Dynamics and Control
Homework #7 Solutions
Solutions given for the following ID
250705005
x = 5
a=5
y = 0
b=6
z = 5
[1]. The closed-loop transfer function is
Gc ( s ) =
G ( s)
a
5
5
=
=
Gc ( j) =
1 + G ( s ) s + a + b s + 11
j + 11
For the
ME 352
System Dynamics and Control
Homework #1
Due: Mon 25.02.2013
This is a personalized homework assignment. You will need to complete the following steps to construct
your own blockdiagrams.
In your student ID number, obtain digits x, y, and z:
2x07050
ME 352
System Dynamics and Control
Homework #1
Due:
Friday 02.03.2012, 5 PM
[1]. For the car suspension system discussed in class (two mass car suspension system quarter car model),
(a) Plot the position of the car and the wheel after the car hits a unit
ME 352
System Dynamics and Control
Homework #3
Due: Friday 06.04.2012, 5:00 pm.
[1]. Find the free response and the forced (step) response of the following models (i.e., solve the differential
equations by using the Laplace transform). If the solution is
ME 352
System Dynamics and Control
Homework #2
Due:
Monday 19.03.2011, 5:00 pm.
1. A solid block of thermal capacity Cth is being heated with an electric resistance heater. The input voltage
Vin(t) is provided to the heater, and the electrical resistance
ME 352
System Dynamics and Control
Homework #6
Due: Friday 18.05.2012, 5:00 pm.
Consider a unit feedback control system. The plant has a transfer function of
G (s) =
Y (s)
U (s)
=
s+9
s ( s + 5 )( s + 18 )( s + 20 )
and the controller transfer function is
ME 352
System Dynamics and Control
Homework #7
Due: Friday 25.05.2012, 5:00 pm.
This is a personalized homework assignment. You will need to complete the following steps to construct
your own personalized questions.
In your student ID number, collect digi
ME 352
System Dynamics and Control
Homework #4
Due: Thursday 19.04.2012, 4:00 pm.
[1]. For each pair of second-order system time domain specifications below, find the corresponding region
for the poles in the s-plane.
(a) Overshoot < 10%, 2% settling time
ME 352
System Dynamics and Control
Lab #1 Spring 2011
Dr. Koray K. afak
1-DOF ROBOT ARM CLOSED-LOOP CONTROL
The purpose of this computer lab experiment is to model a 1 degree-of-freedom robot arm
using Simulink and try to follow a desired position traject
ME 352
System Dynamics and Control
Homework #8
Due: Friday 20.05.2011
This is a personalized homework assignment. You will need to complete the following steps to construct
your own personalized questions.
In your student ID number, collect digits x, y, a
ME 352
System Dynamics and Control
Homework #4 Solutions
1.
1
Y ( s)
K
n2
s ( s + 6)
=
=2
=2
1
R(s) 1 + K
s + 6 s + K s + 2n s + n2
s ( s + 6)
K
n = K
=
6
2n
=
M p = e
K=
9
2
3
K
1 2
0.08 0.6266
22.92 0 < K 22.92
2.
K
35
Y ( s)
35 K
35 K
( s + a ) ( s
ME 352
System Dynamics and Control
Homework #2 Solutions
1.
2.
Differential equations:
L( y ) =
d L( y ) i ( t )
e( t ) = Ri ( t ) +
L
y
= Ri( t ) + i ( t )
dL( y ) dy ( t )
dt
dy
2
My ( t ) = Mg
Ki ( t )
y (t )
Eeq
dyeq
R
Thus, ieq =
dt
=0
dt
di ( t )
ME 352
Modeling and Control of Dynamic Systems
Homework #2
Due: Tuesday 09.03.2010
[1]. Figure 1(a) shows the setup of the temperature control of an air-flow system. The hot water reservoir
supplies the water that flows into the heat exchanger for heating
ME 352
Modeling and Control of Dynamic Systems
Homework #4
Due: Tue 06.04.2010
1. For the unity feedback system shown below, specify the gain K of the proportional controller so
that the output y(t) has an overshoot of no more than 10% in response to a un
ME 352
Modeling and Control of Dynamic Systems
Homework #4 Solutions
1.
1
2
Y ( s)
K
n
s ( s + 4)
=
=2
=2
2
1
R(s) 1 + K
s + 4 s + K s + 2 n s + n
s ( s + 4)
K
n = K
=
4
2n
=
M p = e
K=
4
2
2
K
1 2
0.1 0.591
11.45 0 < K 11.45
2.
K
25
Y ( s)
25 K
25 K
=
ME 352
System Dynamics and Control
Homework #3 Solutions
1.
4s
(a) G ( s ) =
(s
2
+4
)
1
+
s+2
4
(b) G ( s ) =
2
s + 4s + 8
2.
(a) Taking the Laplace transform of the differential equation, we get
1
2
( s + 5s + 4 ) F ( s ) =
f (t ) =
1
e
4 t
6
s+ 2
1 2t
ME 352
System Dynamics and Control
Homework #6
Due: Monday 10.05.2010
[1]. The forward-path transfer functions of unity-feedback control systems are given in the following.
K ( s + 3)
s ( s + 4s + 4)( s + 5)( s + 6)
K
(b) G ( s) =
s ( s + 2)(s + 4)( s + 1
ME 352
System Dynamics and Control
Homework #7
Due: Thursday 20.05.2010
[1]. Sketch the Bode diagrams of the forward-path transfer functions given in the following. Find the gain margin,
gain-crossover frequency, phase margin and phase-crossover frequency
ME 352
Modeling and Control of Dynamic Systems
Homework #1
Due: Friday 26.2.2009
[1]. Write the equations of motion for the linear translational systems shown in Figure 1. Define the state
variables as follows:
(a) x1 = y 2 , x 2 = dy 2 / dt , x3 = y1 , x
ME352
System Dynamics and Control
Lab #1 Servo Control of a Linear Axis
Supplemental Document (19.02.2010)
In addition to the laboratory manual, please derive equations of motion and find a transfer
function of the servo control system. Choose the car pos