PRT100Y1 Lecture Notes - Lecture 4: Pid Controller, Rise Time, Matlab

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School
Department
Course
MIDDLE EAST TECHNICAL UNIVERSITY
ELECTRICAL AND ELECTRONICS
ENGINEERING DEPARTMENT
EE402- DISCRETE TIME CONTROL SYSTEMS
RECITATION 4 REPORT
P, PD, PI, PID CONTROLLERS
Group Members:
Sena TEMEL
Semih YAĞLI
Semih GÖREN
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Table of Contents
Title
Page
Introduction
2
Aim of the Recitation
2
P Controller
3
P-I Controller
3
P-D Controller
3
P-I-D Controller
4
Simulations and Results to Find the Constraints on Loop Tuning
4
Loop Tuning
6
Manual Tuning Method
10
Ziegler-Nichols Method
10
Cohen-Coon Tuning Method
12
Transient Responses of P, PD, PI and PID controllers
14
Transient Response of P Controller
14
Transient Response of P-D Controller
24
Transient Response of P-I Controller
27
Transient Response of P-I-D Controller
30
Digital P-I-D Control
33
PID Controller Design for Controlling DC Motor Speed in the Project
38
The Block Diagram of the DC Motor Speed Control Loop
39
PID Parameters
40
The Design Requirements of the System
40
The Schematic of the DC Motor
40
The Parameters of the DC Motor
41
The open loop transfer function of the DC motor
41
s*-domain to z-domain with ZOH (only plant-DC motor)
45
The Step Response of the System with PID Controller
48
PID Controller Design for Controlling DC Motor Position in the Project
48
The Design Requirements of the System
50
The Transfer Function of the DC Motor with Zero Order Hold
53
Conclusions
57
Appendix
58
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Introduction:
This report is written to analyze the recitation that was presented on 02.04.2013. The
recitation was presented by Sena TEMEL, Semih YAĞLI and Semih REN. It was mainly
about P, P-D, P-I and P-I-D controllers, their digital versus continuous time realizations and
their characteristics including sampling period effects on the response of digital ones.
Moreover, position and velocity form of P-I-D control was modeled on the ‘Gate’ project.
Apart from these topics, P-I-D tuning methods such as manual tuning, Ziegler-Nichols tuning,
Cohen-Coon tuning and MATLAB tuning method were discussed. Transient performances of
P, P-D, P-I and P-I-D controllers were explained in detail. Modeling a discrete time P-I-D
controller to control a continuous time plant was explained over a MATLAB code introducing
the effect of sampling time and the choice of s*-domain to z-domain transformation method
on MATLAB. It was explained how to remove poles that cause instability in discrete time by
adding a new pole. Finally, it was shown how one could control the speed and position of the
vehicle using discrete time P-I-D controller on the ‘Gate’ project.
Aim of the Recitation:
Aim of the recitation was to introduce the concept of Discrete Time P-I-D controllers and how
they can be implemented on real life projects.
It was first intended to explain the usage of continuous time P-I-D controllers. In the first part
of the recitation, it was aimed to show the how P, P-I, P-I-D controllers change the steady
state response of the closed loop systems. Moreover, the methods to tune P-I-D controllers
were introduced. It was meant to show that how hard it could get to properly tune a P-I-D
controller. Secondly, it was intended to show how P, P-D, P-I, and P-I-D controllers affect the
transient response of the closed loop system. It was meant to show how one can gain a feature
but lose the other. Thirdly, it was intended to show how one should estimate the dynamics of
the continuous time plant and use proper sampling time for discrete time P-I-D controller. It
was also meant to show how changing transformation method may cause different pole
locations on the z-plane. Lastly, it was intended to show how one could control the velocity
and the position of the vehicle of the ‘Gate’ project by implementing a discrete time P-I-D
controller in that project.
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