PID controller
Author: Santoso P Sugondo
d1129
Introduction (Pendahuluan):
Control engineering theory (sistem Pengaturan)
is an interdisciplinary branch of engineering and applied
mathematics, that deals with the behavior or characteristics of
physical dynamical systems.
The system dynamics is presented as a mathematical model in
order to be able to analyze, modify or compensate the system
The desired output of a system is called the reference. When one
or more output variables of a system need to follow a certain
reference over time, a controller manipulates the inputs to a
system to obtain the desired effect on the output of the system.
– a theory that deals with influencing the behavior of dynamical
systems
– This control theory which is an interdisciplinary subfield of
science, originated in engineering and mathematics, and then
evolved into use by the social sciences, like psychology, sociology
and criminology.
PID control and associated controller types
•
Module overview.
Proportional-integral-derivative (PID) control constitutes the proceeding
to a solution by trial and error (heuristic) approach to controller design that
has found wide acceptance in industrial applications. This type of
controller family is introduced and its behaviour discussed in detail. A
comparison of the controller members of this family using performance
responses is displayed to demonstrate the differences in their control
behaviour using the Matlab program .
•
Module objectives.
When you have completed this module you should be able to:
– Understand PID-type controllers.
– Tune PID-type controllers using Matlab program
– Learn more of tuning to do fine Tune PID-type controllers using the Ziegler
and Nichols as industrial practical method.
•
Module prerequisites.
– Transfer function, performance output characteristics .
Plant is controlled system (adalah bagian yang akan
dikendalikan), whereas controller is main part of the system
used to control characteristics system.
Fungsi kontroler sangat penting karena:
•Kontroler menyediakan sinyal pengendali ke plant (bag. Yg akan
dikendalikan).
•Kontroler didesain untuk mengendalikan perilaku sistem secara
keseluruhan
PID controller
It is known that The PID controller is probably the most-used feedback
control design. "PID" means Proportional-Integral-Derivative, referring to
the three terms
operating on the error signal to produce a control signal. If u(t) is the control
signal sent to the system, y(t) is the measured output and r(t) is the desired
output, and tracking error e(t) = r(t) − y(t), a PID controller has the general
form
The desired closed loop dynamics is obtained by adjusting the three
parameters KP, KI and KD, often iteratively by "tuning" and without specific
knowledge of a plant model. Stability can often be ensured using only the
proportional term. The integral term permits the rejection of a step
disturbance (often a striking specification in process control). The derivative
term is used to provide damping or shaping of the response. PID controllers
are the most well established class of control systems: however, they cannot
be used in several more complicated cases, especially if MIMO systems are
considered.
Applying Laplace transformation results in the transformed PID controller
equation
with the PID controller transfer function
Step Response
2
1.8
Kp=300
1.4
1.2
Amplitude
Ki=0
1.6
1
0.8
Kd=0
0.6
0.4
0.2
0
0
5
kp=300 , ki=0 ,kd=0
10
w aktu
15
(sec)
Diagram
blok motor
kecepatan
konstan
1
( s  12 s  25)
2
Diagram
blok motor
posisi
1
s ( s  12 s  25)
2
Step Response
1.8
1.6
1.4
Kp=200
Kd=0
Amplitude
Ki=0
1.2
1
0.8
0.6
0.4
0.2
0
0
5
10
kp=200 , ki=0 ,kd=0
20
15
w aktu
(sec)
25
Step Response
1.5
Kp=100
Ki=0
Amplitude
1
0.5
Kd=0
0
0
5
10
kp=100 , ki=0 ,kd=0
w aktu
15
(sec)
Step Response
1.4
1.2
Kp=70
Kd=0
Amplitude
Ki=0
1
0.8
0.6
0.4
0.2
0
0
5
kp=70 , ki=0 ,kd=0
10
w aktu
(sec)
15
Step Response
1.4
1.2
Kp=50
Amplitude
1
Ki=0
0.8
0.6
0.4
0.2
Kd=0
0
0
5
10
kp=50 , ki=0 ,kd=0
w aktu
15
(sec)
Step Response
1.4
Kp=40
1.2
1
Kd=0
Amplitude
Ki=0
0.8
0.6
0.4
0.2
0
0
5
kp=40 , ki=0 ,kd=0
10
w aktu
(sec)
15
Step Response
1.4
1.2
Kp=40
Amplitude
1
Ki=0
0.8
0.6
0.4
0.2
Kd=0
0
0
5
10
kp=40 , ki=0 ,kd=0
w aktu
15
(sec)
Step Response
1.4
1.2
Kp=30
Ki=0
Kd=0
Amplitude
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
kp=30 , ki=0 ,kd=0
5
6
w aktu
7
(sec)
8
9
Step Res pons e
1.4
1.2
Kp=30
Amplitude
1
Ki=0.1
0.8
0.6
0.4
0.2
Kd=0
0
0
5
10
kp=30 , ki=0.1 ,kd=0
w aktu
15
(s ec )
Step Res pons e
1.4
Kp=20
1.2
Amplitude
1
Ki=0
0.8
0.6
0.4
0.2
Kd=0
0
0
5
10
kp=20 , ki=0 ,kd=0
w aktu
15
(s ec )
Step Res pons e
1
0.9
0.8
0.7
0.6
Amplitude
Kp=2
0.5
0.4
Ki=0
0.3
0.2
0.1
Kd=0
0
0
20
40
kp=2 , ki=0 ,kd=0
60
80
w aktu
(s ec )
100
120
Step Res pons e
1.4
1.2
1
Ki=0.1
Amplitude
Kp=45
0.8
0.6
0.4
Kd=2
0.2
0
0
5
kp=45 , ki=0.1 ,kd=2
10
w aktu
15
(s ec )
Evaluasi materi :
I.
self test
Jika nilai penguatan proporsional Kp dinaikkan maka akan
berpengaruh pada karakteristik transient berupa:
pilih salah satu
a.Rise time akan .....
lambat
b.Overshoot menjadi
Mengecil
Membesar
cepat
lambat
kecil
besar
c.Settling time akan ...
d.Steady state eror menjadi ...
cepat
Anda salah pilih
return
Pilihan anda tepat
return
pilih salah satu
II. Menaikkan nilai KD derivative controller
berarti:
1. Steady state error mengalami perubahan besar
2.overshoot akan meningkat
3.settling time meningkat
4.rise time hampir tidak berubah
B
S
B
S
B
S
B
S
III. Menurunkan nilai KI integral controller berarti:pilih salah satu
1. Steady state error dapat dieliminasi
B
S
2.overshoot akan meningkat
B
S
3.settling time meningkat
B
S
B
S
4.rise time tidak berubah
Kesimpulan:
Langkah mencari response yg diinginkan dg kontroler
PID:
1. cari response sistem lup terbuka dan tentukan apa/ bagian mana
yang dapat dilakukan perbaikan(improve)
2. tambahkan proporsional control untuk memperbaiki kinerja
rise Time
3. tambahkan derivative control untuk memperbaiki kinerja
karakteristik output overshoot
4. tambahkan integral control untuk mengeliminasi steady
state error
5. setel masing2 KP , KI dan KD (fine tuning) agar diperoleh
karakteristik output yang anda inginkan
Terminologi/Glossary:
•
•
•
•
•
•
•
•
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Steady state error
Rise Time
Over shoot
Settling time
Peak overshoot
Proportional controller
Integral controller
Derivative controller
On / off controller
Steady state error:
nilai kesalahan keadaan tunak (saat t  ta berhingga)
Rise Time
waktu untuk mencapai 90% dari nilai steady state
Over shoot
response transient sistem yang diatas/ melewati nilai steady state
Settling time
waktu saat nilai penetapan yaitu nilai dengan deviasi+ 2,5% didaerah
steady state
Peak overshoot
response puncak transient sistem yang diatas/ melewati nilai steady
state
Proportional controller
kontroler dengan response memperkuat (amplify)sinyal error menjadi
outputnya
Integral controller
kontroler dengan response melakukan integrasi sinyal error menjadi
outputnya
Derivative controller
kontroler dengan response melakukan diferensiasi sinyal error untuk
dijadikan menjadi outputnya
On / off controller
kontroler dengan response menghidupkan atau mematikan plant
berdasarkan sinyal yang diterima
References:
1.
Ogata, Katsuhiko. (1997),3rd edition, Modern Control Engineering. 3. Prentice
Hall Int. London. ISBN: 0-13-227307-1
2.
Kuo ,Benjamin C. (1989),Fourth edition, Automatic Control Systems. 4.
Prentice Hall India. New Delhi. ISBN:-087692-338-4
3.
Distefano, Stuberud. (1995),2nd edtion,. Feedback control system. 2.
McGraw-Hill. New York. , ISBN: 0070170525
4.
Visioli Antonio,(2006). Practical PID Control (Advances in industrial control),
Springer-Verlag , London, ISBN : 9781846285851
5.
6.
7.
8.
9.
http://en.wikipedia.org/wiki/PID_controller
http://www.omega.com/temperature/z/pdf/z115-117.pdf
http://www.engin.umich.edu/group/ctm/model/model.html
http://www.theorem.net/theorem/lewis1.html
http://everything2.com/title/history+of+automatic+control