09-05-2012, 04:34 PM
Inverted Pendulum
[attachment=21712]
INTRODUCTION
Remember when you were a child and you tried to balance a broom-stick on your index
finger or the palm of your hand? You had to constantly adjust the position of your hand
to keep the object upright. An INVERTED PENDULUM does basically the same thing.
However, it is limited in that it only moves in one dimension, while your hand could move
up, down, sideways, etc.
Just like the broom-stick, an Inverted Pendulum is an inherently unstable system. Force
must be properly applied to keep the system intact. To achieve this, proper control
theory is required. The Inverted Pendulum is essential in the evaluating and comparing
of various control theories.
The inverted pendulum (IP) is among the most difficult systems to control in the field of
control engineering. Due to its importance in the field of control engineering, it has been
a task of choice to be assigned to Control Engineering students to analyze its model and
propose a linear compensator according to the PID control law. Being an unstable
system, Inverted Pendulum is very common control problem being assigned to a student
of Control System Engineering (from Bachelor to Postgraduate level), to control it's
dynamics.
The reasons for selecting the IP as the system are:
· It is the most easily available system (in most academia) for laboratory usage.
· It is a nonlinear system, which can be treated to be linear, without much error, for
quite a wide range of variation.
· Provides a good practice for prospective control engineers.
The various stages of the work for accomplishing the task of controlling the Inverted
Pendulum are as follows:
· Modeling the IP and linearizing the model for the operating range.
· Analyzing the uncompensated closed loop response with the help of a root locus
plot.
· Designing the PID controller and simulating it in MATLAB for proper tuning and
verification.
· Analyzing the compensated closed loop response of the system.
· Implementing the controller on the physical IP model.
i
APPLICATIONS OF INVERTED PENDULUM
Among the some considerable applications of inverted pendulum (IP) are:
SIMULATION OF DYNAMICS OF A ROBOTIC ARM
The Inverted Pendulum problem resembles the control systems that exist in robotic
arms. The dynamics of Inverted Pendulum simulates the dynamics of robotic arm in the
condition when the center of pressure lies below the centre of gravity for the arm so that
the system is also unstable. Robotic arm behaves very much like Inverted Pendulum
under this condition.
MODEL OF A HUMAN STANDING STILL
The ability to maintain stability while standing straight is of great importance for the daily
activities of people. The central nervous system (CNS) registers the pose and changes
in the pose of the human body, and activates muscles in order to maintain balance.
The inverted pendulum is widely accepted as an adequate model of a human standing
still (quiet standing).
An inverted pendulum (assuming no attached springs) is unstable, and it is hence
obvious that feedback of the state of the pendulum is needed to stabilize the pendulum.
Two models for the CNS feedback control are generally considered:
Time invariant, linear feedback control;
Linear feedback outside a threshold. No sensory feedback within the threshold.
There are certain passive mechanisms, such as stiffness in muscles and supportive
tissue, which may be modeled as a spring and damper.
[attachment=21712]
INTRODUCTION
Remember when you were a child and you tried to balance a broom-stick on your index
finger or the palm of your hand? You had to constantly adjust the position of your hand
to keep the object upright. An INVERTED PENDULUM does basically the same thing.
However, it is limited in that it only moves in one dimension, while your hand could move
up, down, sideways, etc.
Just like the broom-stick, an Inverted Pendulum is an inherently unstable system. Force
must be properly applied to keep the system intact. To achieve this, proper control
theory is required. The Inverted Pendulum is essential in the evaluating and comparing
of various control theories.
The inverted pendulum (IP) is among the most difficult systems to control in the field of
control engineering. Due to its importance in the field of control engineering, it has been
a task of choice to be assigned to Control Engineering students to analyze its model and
propose a linear compensator according to the PID control law. Being an unstable
system, Inverted Pendulum is very common control problem being assigned to a student
of Control System Engineering (from Bachelor to Postgraduate level), to control it's
dynamics.
The reasons for selecting the IP as the system are:
· It is the most easily available system (in most academia) for laboratory usage.
· It is a nonlinear system, which can be treated to be linear, without much error, for
quite a wide range of variation.
· Provides a good practice for prospective control engineers.
The various stages of the work for accomplishing the task of controlling the Inverted
Pendulum are as follows:
· Modeling the IP and linearizing the model for the operating range.
· Analyzing the uncompensated closed loop response with the help of a root locus
plot.
· Designing the PID controller and simulating it in MATLAB for proper tuning and
verification.
· Analyzing the compensated closed loop response of the system.
· Implementing the controller on the physical IP model.
i
APPLICATIONS OF INVERTED PENDULUM
Among the some considerable applications of inverted pendulum (IP) are:
SIMULATION OF DYNAMICS OF A ROBOTIC ARM
The Inverted Pendulum problem resembles the control systems that exist in robotic
arms. The dynamics of Inverted Pendulum simulates the dynamics of robotic arm in the
condition when the center of pressure lies below the centre of gravity for the arm so that
the system is also unstable. Robotic arm behaves very much like Inverted Pendulum
under this condition.
MODEL OF A HUMAN STANDING STILL
The ability to maintain stability while standing straight is of great importance for the daily
activities of people. The central nervous system (CNS) registers the pose and changes
in the pose of the human body, and activates muscles in order to maintain balance.
The inverted pendulum is widely accepted as an adequate model of a human standing
still (quiet standing).
An inverted pendulum (assuming no attached springs) is unstable, and it is hence
obvious that feedback of the state of the pendulum is needed to stabilize the pendulum.
Two models for the CNS feedback control are generally considered:
Time invariant, linear feedback control;
Linear feedback outside a threshold. No sensory feedback within the threshold.
There are certain passive mechanisms, such as stiffness in muscles and supportive
tissue, which may be modeled as a spring and damper.