Robust Control of Inverted Pendulum using Fuzzy
Logic Controller
Sandeep . TripathiHimanshu Pandayand Prerna Gaur
Absact-Robust Control has been used in various applications
to improve the performance of the system. The Inverted
pendulum (also called "Cart-Pole system) is a classical example
of nonlinear and unstable control system. In This paper we
present different design techniques of controller for stabilizing
the inverted pendulum (cart system) problem and there
comparative analysis of performance and reliability which is
done through simulation on MATLab-Simulink. Robust control
(H) in association with fuzzy produce better response as
compared to fuzzy controller.
Ind Terms-Inverted Pendulum, H, Fuzzy Logic, Robust
Control
I. INTRODUCTION
A two dimensional Inverted Pendulum consists of a eely
hinged rod over a dynamic platform that can be driven by
either belt-motor system or by cart system. has inherently
two states i.e. stable and the unstable. The stable state is
undesirable state and the pendulum is downward oriented. In
unstable state pendulum orient sictly upward and hence,
requires a counter force to stay align to this position because
disturbance will shiſts the rod away om equilibrium. This
problem has been addressed by testing and implementation of
under-actuated mechaonical system and conolling of
inherently open loop unstable with highly non-linear dynamics
like robotics [1-3] and space rocket guidance systems.
Process model is that component of control system which
manipulates the inputs to get the desired output, however due
to unexpected disturbances, its output deviates. So, in order to
sense and recti these random deviations dynamically
feedback with conoller to make it a close-loop system has
been proposed.
Initially upright position of the pendulum has been assumed
due to disturbance uncompensated model of the system has
tendency to move downward towards the stability. Our
proposed Controller will y to compensate this disturbance
and maintain its upward state. Numerous controlling
techniques are available, ranging om conventional conoller,
artificial intelligence conollers [4]-[6] to recent robust
controllers [7]-[13] .
Sandeep . Tripathi is with Netaji Subhas Institute Of Technology, New
Delhi INDIA
Himanshu Panday is with
'
Galgotia College of Engineering &Techno]ogy, Gr.
Noida INDIA
978-1-4673-5630-513/$3l.00 ©20 13 IEEE
In our design, Matlab/Simulink platform used for observing
such compensating conoller. The inverted pendulum problem
is the classical problem of the conol system. It is a highly
non linear system. Such type of conol problem needs very
precise and robust conol. The overshoot and the error, both
play crucial role in the stability of Inverted
Pendulum (lP). The objective of the present work is to get the
optimized and robust performance of a nonlinear system with
the help of Robust (Hꝏ) conoller using Fuzzy Logic
Algorithm.
II. MATHEMATICAL ANALYSIS
In order to analyses the conol system, mathematical model is
established to predict the behavior before utilizing it into a real
system. In this process, we rationalize differential and
algebraic equations obtained om conservational laws and its
characteristics to obtain ansfer nction of the process.
We have taken mathematical model of [1] for our work. The
separate Free Body Diagram of the cart and pendulum as
shown in figure 2.1 is used to obtain its mathematical model.
Figure 2.1 Free Body Diagram of the System
By applying Newton's 2nd law of motion to the cart system
and assuming the (nonlinear) coulomb iction applied to the
linear cart is assumed to be neglected. The force on the linear
cart due to the pendulum's action has also been neglected in
the presently developed model, the following dynamic
equation in horizontal and vertical direction are:
a) Horizontal direction: Summing the forces in the Free
Body Diagram of the cart in the horizontal direction, we get
the following equation of motion:
=F-bx-N
................................... (2.1)
The force exerted in the horizontal direction due to the
moment on the pendulum is determined as follows:
d
2
N =m-
2
(x+lsinB)
dt
................................... (2.2)