FYP Mid Ppt ed
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Transcript of 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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8/6/2019 FYP Mid Ppt ed
3/19
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