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8/6/2019 FYP Mid Ppt ed

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THE INVERTED PENDULUM

Created By

Safia RafiqWaseem Nazak

Zubair Anwar Wada

BEE(Electronics) - 8


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CONTENTS:

1. Overview

2. Control or Balancing

3.Tools and technique

4. Designing the Compensator

5. Out puts

6. References


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OVERVIEW:

An inverted pendulum (also called a cart and pole) consists of a thin rod whichhas its mass above its pivot point and attached at the bottom to a mobile cart

that can move horizontally. Unlike a normal pendulum which is stable when

hanging downwards, an inverted pendulum is inherently unstable. Inverted

pendulums must be actively balanced to remain erect.

The objective of our project is to balance an inverted pendulum, using PID

Controller.


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Control or Balancing

The inverted pendulum is a classic problem in dynamics and control theory andis widely used as a benchmark for testing control algorithms (PIDcontrollers, neural networks, fuzzy control, genetic algorithms, etc).

There are many ways to balance an inverted pendulum, we are using PID

Controller.


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Analog controllers can be of the following forms:

1. PI( Proportional integral)

2. PD(Proportional derivative)

3. PID(Proportional integral derivative)

PI PD PID


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Block Diagram of Compensated System


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What is PID Controller ?

A proportionalintegralderivative controller (PID controller) is ageneric control loop feedback mechanism.

A PID controller calculates an "error" value as the difference between ameasured process variable and a desired set point. The controllerattempts to minimize the error by adjusting the process control inputs.

The PID controller calculation (algorithm) involves three separateconstant parameters, and is accordingly sometimes called three-termcontrol: the proportional, the integral and derivative values, denoted P,I, and D.


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BLOCK DIAGRAM OF PID:


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Software used

We have used the following software:

1. MatLab: for plotting the root-locus and designing the compensator2. MultiSim: for the circuit


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Mathematical Model

A transfer function is a mathematical representation of the relation between

the input and output of a system.

The transfer function of the system (motor + cart & pendulum), was foundout, by calculations, to be:

This transfer function is used to plot the root-locus and to design thecompensator.


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Root-Locus

The compensator is designed using Root-Locus method.

The Root-Locus plot of the uncompensated system (motor + cart andpendulum) is:

Since there is a real pole in the right-half plane, the system is unstable.


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Compensator designPoles and Zeros are placed, so that all the roots are in the left-half plane ofthe axes, which indicates that the system is stable.


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The circuit for the PID Controller which is used in the project is:


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Continuing work

So far, the designing of the circuit is complete. We are developing the

hardware, which is expected to reach completion soon.

After it is developed, the circuit will be tested to balance the pendulum.

Once the pendulum is balanced, we will go a step further to balance theDouble Inverted Pendulum.


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References1. Design of Feedback Control Systems by Stefani, Shahian, Savant and

Hostetter, Fourth Edition

2. http://lims.mech.northwestern.edu/~design/mechatronics/2004/Team11/index.html

3. Inverted Pendulum: Analysis, Design and Implementation. IIEE Visionaries,Document version 1.0

4. http://en.wikipedia.org/wiki/Inverted_pendulum

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