Performance analysis of an inverted
pendulum stabilization using PID type
controllers
Journal Name:
- Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi
Key Words:
Keywords (Original Language):
| Author Name | University of Author |
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Abstract (2. Language):
Inverted pendulum is one of the most popular
benchmarks used in the field of control engineering.
In addition to being an educational system used to
teach the bases of control theory, it is a good
mechanism to test design methods developed by
researchers. Since, the inverted pendulum has an
unstable and non-linear structure it is a very
interesting system and is frequently handled in
control engineering studies. The inverted pendulum
system has one input, namely the force, and two
outputs, namely the pendulum angle and position of
the cart. Thus, the inverted pendulum is a wellknown
example of single-input multiple-output
(SIMO) system.
In this paper, stabilization of an inverted pendulum
on a cart while the cart is tracking a desired
trajectory has been studied. PID controllers, tuning
parameters of which are obtained by using pole
placement method, are used in a SIMO design
approach to control both the pendulum angle and
the cart position. Performance analysis of the PID
controllers to control the cart-inverted pendulum
system has been given based on both computer
simulation and real-time implementation results.
In this study, a cart-pendulum setup produced by
Feedback Instruments was used for real time
implementation. The cart-pendulum setup has a cart
and two pendulum arms attached to it. As the
structure of the cart pendulum setup is very complex,
obtaining the system mathematical model by using
physical equations was not considered as a suitable
approach. Examining the studies in the literature
about identification of the cart-pendulum systems, it
has been seen that the cart-pendulum setup handled
in this paper was also used in another study by Yuce
and Tan (2013). The transfer functions for pendulum
angle and cart position obtained by them were
assayed with the many collected input-output data
from cart-pendulum setup. It was observed that
these transfer functions have good matching
percentage to real system and so, these transfer
functions were used for the cart-pendulum model.
In this work, PID controllers are used for holding
the pendulum in the upright unstable position while
the cart is tracking a desired trajectory. The design
procedure is as follows: Firstly, according to the
pendulum angle and cart position transfer functions,
two PID controllers were designed for closed-loop
control of the pendulum angle and the cart position
separately. Then, these two PID controllers were
combined in a SIMO design approach. Taking into
account the physical characteristics of the cartpendulum
setup, the result is that the closed loop
systems created by using PID controllers must be
over damped for both pendulum angle and cart
position.
In the simulation study, the first angle value of the
pendulum was chosen as Θ = 0.25 rad. A sine wave
with an amplitude of 0.3 m and a frequency of 0.025
Hz was selected as the desired trajectory for the
cart. Simulation results were given for both
pendulum angle and cart position of the SIMO
control system. In the simulation study, the effect of
changing PID tuning parameters was also shown.
In the real-time implementation study, the system
control begins after the pendulum enters a specific
region. The boundaries of this region are taken as Θ
=∓0.25 rad. By using the system software that
comes with the cart-pendulum setup, the pendulum
was ensured to reach this region from down vertical
position (Θ = π rad). Similar to the simulation study,
a sine wave with amplitude of 0.3 m and a frequency
of 0.025 Hz was selected as the desired trajectory of
the cart. Again, results were provided for both
pendulum angle and cart position of the SIMO
control system in real-time, as in simulation results.
The effect of varying PID tuning parameters was
also supplied in the real-time implementation. It was
observed from both the simulations and real time
implementations that small changes in PID tuning
parameters has very little effect on the closed loop
control of cart-pendulum system.
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Abstract (Original Language):
Bu çalışmada, bir ters sarkaç sisteminin PID denetleyiciler kullanılarak stabilizasyonu amaçlanmıştır. Ters
sarkaç, kontrol mühendisliği ve robotik alanlarında kullanılan temel ölçütlerden biridir. Sistem iyi bilinen
bir tek giriş-çok çıkışlı (single-input multiple-output, SIMO) sistem örneğidir. Çalışmada, PID denetleyiciler
kullanılarak bir arabaya bağlı sarkacın, araba istenilen bir yörüngeyi takip ederken, yukarı pozisyonda
dengede kalması sağlanmıştır. Araba-sarkaç sistemini kontrol etmek için kullanılan PID denetleyicilerin
ayar parametreleri, kutup yerleştirme metodu kullanılarak elde edilmiştir. Tasarlanan kontrol sistemine ait
hem bilgisayar simülasyonu hem de gerçek zamanlı uygulama sonuçları sarkaç açısı ve araba pozisyonu için
ayrı ayrı verilmiştir. PID denetleyiciler kullanılarak yapılan araba-sarkaç sisteminin kontrolüne ait
performans analizi yapılmıştır.
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