-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
DEPARTMENT OF ENGINEERING MECHANICS
CONTROL LABORATORY
LAPORAN MAKMAL/LABORATORY REPORT
Kod M/Pelajaran/ Subject Code
ENGINEERING LABORATORY VI BDA 37101
Kod & Tajuk Ujikaji/ Code & Title of Experiment
Kod Kursus/ Course Code
Seksyen /Section
Kumpulan/Group No. K.P / I.C No. Nama Pelajar/Name of
Student
No. Matrik
Lecturer/Instructor/Tutors Name
1. 2.
Nama Ahli Kumpulan/ Group Members
No. Matrik Penilaian / Assesment
1. Teori / Theory 10 %
2. Keputusan / Results 15 %
3. Pemerhatian /Observation 20 %
4. Pengiraan / Calculation 10 %
5. Perbincangan / Discussions 25 %
Tarikh Ujikaji / Date of Experiment
Kesimpulan / Conclusion 15 %
Tarikh Hantar / Date of Submission
Rujukan / References 5 %
JUMLAH / TOTAL 100%
COP DITERIMA/APPROVED STAMP
ULASAN PEMERIKSA/COMMENTS
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
2
COURSE INFORMATION
COURSE TITLE: ENGINEERING LABORATORY VI (BDA 37101) TOPIC 1: PV
POSITION CONTROL (INVERTED PENDULUM SYSTEM) 1. INTRODUCTION
The IP02 consist of a precisely machined solid aluminium cart
driven by a high quality DC Motor equipped with a planetary
gearbox. The cart slides along a stainless steel shaft using linear
bearings. The cart is driven via rack and pinion mechanism. In the
case of IP02, the cart position is sensed by a ten-turn
potentiometer. This cart is also equipped with rotary joint with
ball bearings to which a free turning erected rod can be attached
and it can acts as an inverted pendulum.
2. OBJECTIVES The objective of this experiment is to control the
position of IP02 linear motion servo plant. At the end of the
session, student should know the following;
i) To simulate with a Simulink the IP02 model and to close the
servo loop by implementing a Proportional-plus-Velocity (PV)
position controller.
ii) To change, during the simulation, the two gains, Kp and Kv,
of the PV controller and observe the effect on the position
response.
iii) To implement with Wincon the previously designed PV
position controller in order to command your IP02 servo plant.
iv) To run the simulation simultaneously at every sampling
period in order to compare the actual and simulated response.
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
3
3. LEARNING OUTCOMES At the end of this experiment, students
should be able to understand the modeling of the IP02 control
system plant, simulate the system and control it using PV
controller scheme by simulation and in real time mode. 4.
THEORY
The IP02 plant system input is the commanded voltage to the DC
Motor. Since we want to control the carts position, the plant
output is selected to be the carts linear position on the rack as
in Figure 1;
Figure 1: The IP01 / IP02 Plant Input and Output
Thus the open loop transfer function for the IP02 system which
is called G(s), can be written as; Head could be defined as :
)()()(sV
sxsGm
.(1)
Where mV : Motor voltage x : Carts position
The mathematical modeling of the IP02 servo plant will provide
the above mentioned open loop transfer function, which in turns
will be used to design an appropriate controller. The simplified
mathematical modeling is given in Equation 2 below. Complete
derivation of the transfer function of the IP02 servo plant is
given in Reference [1].
srRBKKKsMrR
KKrsG
mpmeqmtmGGmpm
tmGGmp
)()( 222
(2)
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
4
Where
mpr : motor pinion radius M : Total mass of the carts system
(i.e moving parts)
G : Planetary gearbox efficiency mK : back electro-motive force
(EMF) constant
GK : Planetary gearbox gear ratio eqB : equivalent viscous
damping coefficient
m : motor efficiency mR : motor armature resistance
tK : motor torque constant 4.1 POSITION CONTROLLER DESIGN The PV
controller design in this laboratory for the IP02 servo plant is
based on corrective terms actions done by this controller. The PV
controller scheme introduces two corrective terms ; one is
proportional (by pK ) to the position error and the other is
proportional (by VK ) to the velocity (or the derivative of the
actual position) of the plant. Equation 3 below expresses the PV
control law, where dx is the reference signal (i.e the desired
position to track).
dt
tdxKtxtxKtV Vdpm )()( ..(3)
Figure 2 below depicts the block diagram of the PV control
scheme as it will be implemented in this lab session.
Figure 2: Block diagram of the PV Control scheme
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
5
4.1 ADDITIONAL THEORY
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
6
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
7
5. EQUIPMENTS To setup this experiment, the following hardware
and software are required:
i. Power Module: Quanser UPM 1503/2405, or equivalent. ii. Data
Acquisition Board: Quanser MultiQ PCI / MQ3, or equivalent. iii.
Linear Motion Servo Plant: Quanser IP02. iv. Real-Time Control
Software:The WinCon-Simulink-RTX configuration,
as detailed in the Reference [5], or equivalent. v. PC equipped
with licensed MATLAB Simulink connected to item (i), (ii),
(iii) and (iv).
For a complete and detailed description of the main components
comprising this setup, please refer to the manuals corresponding to
available configuration. 6. PROCEDURES 6.1 CONTROLLER DESIGN
SPECIFICATIONS
In the present laboratory (i.e. the pre-lab and in-lab
sessions), student will design and implement a control strategy
based on the Proportional-Velocity (PV) control scheme, in order
for the IP02 closed-loop system to satisfy the following
performance requirements (which are time-domain
specifications):
i. The Percent Overshoot (i.e. PO) should be less than 10% (PO
10 %), i.e. = 0.59
ii. The time to first peak (tp) should be 150 ms, i.e ; tp =
0.15 s From these specifications, the corresponding gains for
proportional (Kp) and velocity (Kv) controller are as follows ; Kp
= 274.62 V/m Kv = 5.53 Vs/m 6.2 IP02 CONFIGURATION This experiment
is designed for an IP02 cart without the extra weight on it.
However, once a working controller has been tested, the additional
mass can be mounted on top the cart in order to see its effect on
the response of the system. As an extension to the lab, the first
PV controller design could be modified in order to account for the
additional weight. In this lab, it requires student to design a
Proportional-plus-Velocity (PV) controller to control the position
of IP02 cart with the performance specifications as stated in
Section 6.0
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
8
6.3 CHECK WIRING AND CONNECTION The first task upon entering the
lab is to ensure that the complete system is wired as fully
describe in Reference [2]. You should be familiar with the complete
wiring and connections of the IP02 system during the preparatory
session described in Reference [1]. If still unsure of the wiring,
please ask for assistance from the Teaching Assistant assigned to
the lab. When you are confident with your connections, you can
power up the UPM. You are now ready to begin the lab. 6.4 PART 1:
SIMULATION OF THE SERVO PLANT WITH PV
CONTROLLER Start-up Matlab and follow the steps described below:
Step1. In Simulink, open a model called s_position_pv_ip01_2.mdl.
This
diagram should be similar to the one shown in Fig.3. It includes
a subsystem containing IP02 modeled plant, as well as the PV
controller two feedback loops. In order to be conveniently changed
on-the-fly, the two controller gains Kp and Kv are both set by
slider gains. Check that the signal generator block properties are
properly set to output a square wave signal, of amplitude 1 and of
frequency 2/3 Hz.
Step 2. Before begin, student must run the Matlab script called
setup_lab_ip01_2_position_pv.m.This file initializes all the IP02
system parameters and configuration variables used by the Simulink
diagrams.
Step 3. Ensure that the Simulink simulation mode is set to
Normal. Click on Simulation |Start from the Simulink menu bar, and
bring up the Position Response (m) scope. As student monitor the
position response, adjust Kqqp and Kv using the slider gains, as
depicted in Fig.4 and Fig.5. Try a variety of combinations, and
note the effects of varying each gain (one at a time) on the system
response. Also bring up the Position Error (m) as well as the Vm
(V): Control Signal scopes.
Step 4. To specifically include in the laComplete the Table 1
which describe the changes in the system response, characteristics
tp and PO with respect to changes in Kp and Kv. *Note: Hold one
gain constant while changing the other within the preset range.
Provide at least 3 suitable plots of the response described in
Table 1.
Step 5. Now that student is familiar with the effects of each
one of the two controller gains, enter in the designed Kp and Kv as
provided in Section 3.0 to meet the system requirements.
*Note: the values should fall within the slider limits. Step 6.
After running the simulation with the gains set to their
calculated
values, complete the Observation questions on Section 8.0.
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
9
Step 7 If the simulated response is as expected, you can move to
the next part
in order to implementa real time controller. If your response is
close to meeting the set requirements, try fine- tuning the
controller gains to achieve the desired response. If the system
response is far from the specifications, then re-iterate your
design process and recalculate your controller gains Kp and Kv.
Figure 3 Simulink Diagram used for the simulation of the PV
control system
Figure 4: Slider gain for Kp Figure 5: Slider gain for Kv 6.5
PART 2: REAL TIME IMPLEMENTATION OF THE PV
CONTROLLER
After having designed the PV Controller, calculated its two
gains satisfying the desired time requirements, and checked the
position response of the obtained closed loop system through
simulation, students are now ready to implement the designed
controller in real time and observe its effect on the actual IP02
Plant.
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
10
Step 1: Open only one of the following Simulink models:
q_position_pv_mqpci_ip02.mdl. The student should obtain a
similar diagram as shown in Figure 6. The model has two parallel
and independents control loops: one runs a pure simulations of PV
controller connected to the same plant model as the one developed
in the previous lab experiment on the simulation part. The other
loop directly interfaces with the hardware and runs the actual IP02
plant.Open both subsystems to familiarize with their composing
blocks and take note the I/O connections. Check that the model
manual switch for the position set point generation correctly
selects the signal coming from the signal generator block, called
Square Wave. Also check that the signal generator block properties
are properly set to output a square wave signal, of amplitude 1 and
of frequency 2/3 Hz. Moreover, the sampling time should be set to
1ms.
Step2: Before compiling the diagram and running it in real time
with WinCon,
student must enter the previously designed values of Kp and Kv
in the MATLAB Workspace. To assign Kp and Kv, type their value in
the MATLAB command window. Now students are ready to build the real
time code corresponding to the diagram by using the Wincon | Build
option from the Simulink menu bar. This command will generate the
real time code and will be compiled to the Wincon server. Manually
move the IP02 Cart to the middle of the track and make sure that it
is free to move on both sides. To start the real time controller,
click on the START/STOP button of the Wincon server window. The
cart should be tracking the desired setpoint.
Step3: Open the sink Meas.(0) and Sim.(2) Resp. in a Wincon
scope. Students
can now be able to monitor on-line, as the cart moves, the
actual position as it tracks the predefined reference input and
compare it to the simulation result produced by IP02 model. Click
on the scope button of the Wincon server to open the scope and
choose the display that students want to open (e.g Meas.(1) and
Sim.(2) resp.) from the selection list.
Step4: Once the results are in agreement with the desired design
requirements
and the response looks similar to the one displayed in Figure 7,
students can move and begin writing report for this experiment.
Remember there is no such things as a perfect model, and that the
calculated controller gains Kp and Kv, were based on a theoretical
and ideal plant model.
Step5: However, in order to perfectly meet the chosen design
requirements of
the closed loop system, any controller design will usually
involve some-form of fine tuning. At this point student should be
manually fine-tuning the Kp and Kv based on the previous
experimental observations in order to ensure the response matches
perfectly the system requirements.
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
11
Figure 6: Diagram used for the Real-Time Implementation of the
PV Controller
Figure 7: Actual and Simulated Position Responses to a Square
Wave Set point
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
12
7. RESULTS
a. Complete the Table 1 which describe the changes in the system
response, characteristics tp and PO with respect to changes in Kp
and Kv
Table 1: Variation of resulting response due to variety of
combinations of Kp and
Kv. Kp (V/m) =
Kp (V/m)= Kp (V/m)=
Kv (Vs/m) tp (s)
PO (%)
Kv (Vs/m) tp (s)
PO (%)
Kv (Vs/m) tp (s)
PO (%)
Kv (Vs/m) =
Kv (Vs/m)= Kv (Vs/m) =
Kp (V/m) tp (s)
PO (%)
Kp (V/m) tp (s)
PO (%)
Kp (V/m) tp (s)
PO (%)
b. Show the calculation.(if any) c. Provide at least 3 suitable
plots of the response described in Table 1 for
Part 1 of this experiment. d. Provide at least 3 best plots of
the response as in Figure 7 for Part 2 of this
experiment
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
13
7.1 CALCULATION
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
14
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
15
8. OBSERVATIONS 8.1 PART 1 : SIMULATION OF THE SERVO PLANT WITH
PV
CONTROLLER
After running the simulation with the gains set to their
calculated values, specify in your lab reports the following
observations;
i) In simulation mode, does the system response looks like what
you had
expected? ii) Do they match the design requirements?
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
16
8.2 PART 2 : REAL TIME IMPLEMENTATION OF THE PV
CONTROLLER i) How does the IP02 carts actual position compare to
the simulated
response? ii) Is there any discrepancy in the results? If so,
find some of the possible
reasons.
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
17
9. DISCUSSIONS 9.1 PART 1: SIMULATION OF THE SERVO PLANT WITH
PV
CONTROLLER i) Based on the simplified dynamic modeling of the
IP02 servo plant, derive
a block diagram to represent such a transfer function as in
equation 10. Represents it in the form of basic mechanical and
electrical equations that is being used to determine G(s). The
resulting block diagram should have an overall closed loop transfer
as in Equation 2.
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
18
ii) Finally, using the IP02 model parameter values listed in
Reference [2],
evaluate the IP02s open loop transfer function, G(s) that is
supplied in this experiment. Determine the plants pole(s), zero(s)
and DC gain
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
19
9.2 PART 2 : REAL TIME IMPLEMENTATION OF THE PV
CONTROLLER i) From the plot of the actual cart position, measure
the final system peak
time and percent overshoot. Are the values in agreement with the
design specifications? You must calculate for each of the plot.
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
20
ii) During the course of this experiment, were there any
problems or
limitations encountered? If so, what were they and how were you
be able to overcome them?
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
21
iii) Most controllers of this form also introduce integral
action into the system
(PID). Do you see any benefits to introducing an integral gain
in this experiment?
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
22
10. CONCLUSION Deduce conclusions from the experiment. Please
comment on your experimental work in terms of achievement, problems
faced throughout the experiment and suggest recommendation for
improvements.
-
UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and
Manufacturing Engineering
__________________________________________________________________
BDA37101-Edition III/2011
23
11. REFERENCES