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1 15EI303L- CONTROL SYSTEMS ENGINEERING LABORATORY Department of Electronics and Instrumentation Engineering Faculty of Engineering and Technology Department of Electronics and Instrumentation Engineering SRM University, SRM Nagar Kattankulathur 603203 Kancheepuram District Tamil Nadu

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Page 1: 15EI303L- CONTROL SYSTEMS ENGINEERING LABORATORY · 1 15EI303L-CONTROL SYSTEMS ENGINEERING LABORATORY Department of Electronics and Instrumentation Engineering Faculty of Engineering

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15EI303L- CONTROL SYSTEMS

ENGINEERING LABORATORY

Department of Electronics and Instrumentation

Engineering

Faculty of Engineering and Technology

Department of Electronics and Instrumentation Engineering

SRM University, SRM Nagar

Kattankulathur – 603203

Kancheepuram District

Tamil Nadu

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CONTENTS

S.No. CONTENTS Page No.

1 Mark Assessment details 3

2 General Instructions for Laboratory classes 4

3 Syllabus 5

4 Introduction to the laboratory 6

5 List of Experiments

5.1 Step, ramp and impulse response 7 5.2 Identification of damping in second order 13 5.3 Time domain analysis 20 5.4 Stability analysis using routh- hurwitz method 24 5.5 Stability analysis of linear system using various graphical methods 27 5.6 Frequency response analysis using bode plot 30

5.7 Frequency response analysis using polar plot 33

5.8 Design of PID Controller for first order and second order systems 36

5.9 Design of PID Controller for speed control of DC Motor System. 41

5.10 Design of PID Based controller for Twin Rotor Multi Input Multi Output

System 45

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1. MARK ASSESSMENT DETAILS

ALLOTMENT OF MARKS:

Internal assessment = 60 marks

Practical examination = 40 marks

----------------------

Total = 100 marks

----------------------

INTERNAL ASSESSMENT (60 MARKS)

Split up of internal marks

Record 5 marks

Model exam 10 marks

Quiz/Viva 5 marks

Experiments 40 marks

Total 60 marks

PRACTICAL EXAMINATION (40 MARKS)

Split up of practical examination marks

Aim and

Procedure 25 marks

Circuit

Diagram 30 marks

Tabulation 30 marks

Result 05 marks

Viva voce 10 marks

Total 100 marks

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2. GENERAL INSTRUCTIONS FOR LABORATORY CLASSES

1. Enter the Lab with CLOSED TOE SHOES.

2. Students should wear lab coat.

3. The HAIR should be protected, let it not be loose.

4. TOOLS, APPARATUS and COMPONENT sets are to be returned before

leaving the lab.

5. HEADINGS and DETAILS should be neatly written

i. Aim of the experiment

ii. Apparatus / Tools / Instruments

required

iii. Theory

iv. Procedure / Algorithm /

Program

v. Model Calculations/ Design

calculations

vi. Block Diagram / Flow charts/

Circuit diagram

vii. Tabulations/ Waveforms/ Graph

viii. Result / discussions .

6. Experiment number and date should be written in the appropriate place.

7. After completing the experiment, the answer to pre lab viva-voce questions should

be neatly written in the workbook.

8. Be REGULAR, SYSTEMATIC, PATIENT, AND STEADY.

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3. SYLLABUS

15EI303L Control Systems Engineering Laboratory L T P C

0 0 2 1

Co-requisite: 15EI303

Prerequisite: NIL

Data Book /

Codes/Standards NIL

Course Category P PROFESSIONAL CORE CONTROL ENGINEERING

Course designed by Department of Electronics and Instrumentation Engineering

Approval 32nd Academic Council Meeting held on 23rd July, 2016

PURPOSE To apply the concepts of control system and design and verify using software tools

INSTRUCTIONAL OBJECTIVES STUDENT OUTCOMES

At the end of the course, student will be able to

1. Analyze the first and second order systems using time domain

analysis. a b

2. Analyze the first and second order systems using frequency domain

analysis. a b

3. Design PID controller a b c e k

4. Design and Implement PID controller for any applications. a b c e k

Sl. No. Description of experiments Contact

hours

C-D-

I-O IOs Reference

1.

a) Step, ramp and Impulse response of first order systems.

b) Step, ramp and Impulse response of second order

systems.

3 C,I 1 1

2. Identification of damping in second order systems. 3 C,I 1 1

3. Time domain analysis for second order systems 3 C,I 1 1

4. Stability analysis of linear systems using Routh-Hurwitz

method 3 C,I 1 1

5. Stability analysis of linear systems using Root Locus. 3 C,I 1 1

6. Frequency response analysis using Bode Plot. 3 C,I 2 1

7. Frequency response analysis using Polar Plot 3 C,I 2 1

8. Design of PID Controller for first order and second order

systems. 3 C,D,I,O 3 1

9. Design of PID Controller for speed control of DC Motor

System. 3 C,D,I,O 3 2

10. Design of PID Based controller for Twin Rotor Multi Input

Multi Output System. 3 C,D,I,O 3 3

Total contact hours 30

LEARNING RESOURCES

Sl.

No. REFERENCES

1. LAB manual

2. Guoshinghuang, “PC – based PID speed control in DC Motor”, IEEE, ISBN-978-1-4244-1723-0,2008.

3. “Control of Twin Rotor MIMO System (TRMS) Using PID Controller”, International Journal of Advance

Engineering and Research Development, ISSN:2348-6406, 2015.

Course nature Practical

Assessment Method (Weightage 100%)

In-

semester

Assessment

tool Experiments Record

MCQ/Quiz/Viva

Voce

Model

examination Total

Weightage 40% 5% 5% 10% 60%

End semester examination Weightage : 40%

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INTRODUCTION TO THE LABORATORY

BACKGROUND

Industrial applications of intelligent methods covering a large area from paper and

metallurgical industries to biotechnology and also electronics production and

telecommunications. Applications consist of soft sensors, advanced control and

diagnostics (lime kiln, pulp cooking, bleaching, TMP-refiner, paper machine, blast furnace,

converter plant, continuous casting, solar power plant, waste water processes, bioprocesses,

fluidised bed granulator), electronics production (testing, diagnostics, process analysis and

simulation), rotary drying (pilot-scale process, measurements, and control test bench,

distributed simulation over the web).

DESCRIPTION

Control Engineering Laboratory takes care of teaching at the graduate level in basics

of control and instrumentation, modeling, simulation, and optimization, intelligent methods,

applications in paper, metallurgical and biotechnical processes. For research students,

intelligent methods (fuzzy logic, neural networks, genetic algorithms, expert systems) are the

main area.

CURRENT EQUIPMENT: This lab is currently equipped with 22 systems. 19 systems with HP Compaq and 2

with IBM, 1 with LENOVA with LCD display monitor, optical ps2 mouse and keyboard,

CPU with Pentium processor, 2GB RAM, 150 GB hard disk, Windows XP sp2 operating

system, MATLAB and other application software’s.

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Exercise Number: 1

Title of the Experiment: STEP, RAMP AND IMPULSE RESPONSE

Date of the Exercise:

OBJECTIVE (AIM) OF THE EXPERIMENT

To obtain step, ramp, impulse response of first and second order system.

FACILITIES REQUIRED AND PROCEDURE

a) FACILITIES REQUIRED TO DO THE EXPERIMENT:

S.NO APPARATUS QUANTITY

1. Matlab software 1

2. Computer 1

3.

Control system

tool box 1

b) THEORY: Transfer function: It is the laplace of the output divided by the laplace of the input of

a system.

Step-The response of a system (with all initial conditions equal to zero at t= 0-, i.e,

zero state response) to the unit step input is called the unit step response.

Ramp : The ramp function is a unary real function whose graph is shaped like a graph.

c) PROCEDURE:

Enter the program in the editor window. If the program is typed in command window,

the functions should be typed without semi-colon.

Enter the values in the numerator & denominator depending on order of the system.

The syntax used to get transfer function is tf.

The syntax used for impulse is impulse.

Finally save the program and run it.

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DESIGN PROCEDURE/ DESIGN CALCULATIONS:

Step and Impulse Function

A=input(‘enter numerator’);

B=input(‘enter denominator’);

h = tf(A,B);

step(h);

impulse(h);

subplot(2,1,1),plot(step(h));

subplot(2,1,2),plot(impulse(h));

Ramp Function

t = -1:0.1:1;

x1= t>0;

u = (t.*x1);

lsim(h,u,t);

STEP RESPONSE:

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IMPULSE RESPONSE:

RAMP RESPONSE:

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FIRST ORDER

STEP RESPONSE

IMPULSE RESPONSE:

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RAMP RESPONSE:

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Pre lab questions:

1. What is meant by order of a system?

The highest power of the s term in the denominator of the transfer function of the

system is called the order of the system.

2. What is a transfer function?

It is the laplace of the output divided by the laplace of the input of the system.

Post lab questions:

1. What is step response of a system?

The response of a system (with all initial conditions equal to zero at t=0- i.e zero

state response) to the unit step input is called the step response.

2. What is a ramp function? The ramp function is a unary real function whose graph is shaped like a ramp.

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Exercise Number: 2

Title of the Experiment: IDENTIFICATION OF DAMPING IN SECOND ORDER

SYSTEM.

Date of the Exercise:

OBJECTIVE (AIM) OF THE EXPERIMENT:

To study and identify the damping in second order system using MATLAB.

FACILITIES REQUIRED:

MATLAB software

PROCEDURE:

1. Open MATLAB software. 2. Type “SIMULINK” in the command window or just go to the simulink library bar. A new

box will open where we can get the output of different responses using block diagrams. 3. In the ‘New Model’ window, add input response, transfer function, scope and workspace. 4. Run the simulink and double click on the scope block. 5. Take the output graph.

THEORY:

The general second order transfer function is G(s) = 𝜔𝑛

2

𝑠2+2𝜁𝜔𝑛𝑠+𝜔𝑛2

Where,

ζ=Damping coefficient

𝝎𝒏=natural frequency

There are 4 conditions of 𝜻:

1) When ζ=0, Undamped

2) When 0< 𝜁 < 1, Underdamped

3) When ζ=1, Critically Damped

4) When 𝜻 > 𝟏,Over Damped

As the ζ value is varied, the output graph is varied for the various inputs given be it

step, ramp or impulse.

For ‘Undamped’ system, the graph is of continuous wave w.r.t. critical line. The

amplitude differs for different 𝝎 values. If it is high, amplitude is high and vice versa.

For ‘Under Damped’ system, the graph is also a continuous wave but the amplitude

decreases with time and it finally merges with the critical line passing through 1.

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For ‘Critically Damped’ system, the wave increases gradually and gets in straight line

with the value of 1. This indicates the perfect damping required in a system which is

controllable.

For ‘Over Damped’ system, the wave always remains below or critical line for any𝝎

value.

The graph always remains the same for the damping conditions. Just the nature of

waves changes w.r.t. to the

Critically damped system is the commonly used and effective.

With varying 𝝎 values, the amplitude changes. They don’t make any significant

changes. The important factor is ζ.

We can check the damping by using any values in the place of 𝝎&ζ.

CIRCUIT DIAGRAM / MODEL GRAPH:

Undamped Condition (step) G(s)=100

𝒔𝟐+𝟏𝟎𝟎

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Undamped Condition (ramp) G(s)=𝟏𝟎𝟎

𝒔𝟐+𝟏𝟎𝟎

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Under Damped (step) G(s)=𝟏𝟎𝟎

𝒔𝟐+𝟐𝒔+𝟏𝟎𝟎

Under Damped (ramp) G(s)=𝟏𝟎𝟎

𝒔𝟐+𝟐𝒔+𝟏𝟎𝟎

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Critically Damped (step) G(s)=𝟏𝟎𝟎

𝒔𝟐+𝟐𝟎𝒔+𝟏𝟎𝟎

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Critically Damped (ramp) ) G(s)=𝟏𝟎𝟎

𝒔𝟐+𝟐𝟎𝒔+𝟏𝟎𝟎

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RESULT:

Thus the importance of Damping Coefficient ζwas studied with its various conditions and for

various 𝝎values for various inputs.

PRE LAB QUESTIONS:

1) What is steady state error?

2) What is target value?

POST LAB QUESTIONS:

1) What do you mean by order of a system?

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Exercise Number: 3

Title of the Experiment: TIME DOMAIN ANALYSIS

Date of the Exercise: 28/07/2017

OBJECTIVE (AIM) OF THE EXPERIMENT

To Analyze the Time Domain specifications of Under damped second order system.

FACILITIES REQUIRED AND PROCEDURE:

FACILITIES REQUIRED TO DO THE EXPERIMENT

Matlab software

A) THEORY:

We can analyze the time domain of the second order under damped system. Peak value,

Rise time, overshoot, settling time and steady point.

The system has some in-built tolerance; therefore, the settling time is achieved when the

wave signal enters this tolerance range. But in some ζ conditions, the wave isn’t actually

merging with reference line but is in continuous wave motion but since it has entered the

tolerance range, it is considered as settled.

B) PROCEDURE:

Open MATLAB software.

Go to ‘New Script’ option which opens the editor window.

Write the generic code for second order transfer function which is :

Num=[25];

Den=[1,2,25];

Y=tf(num,den);

Stepplot(y)

By giving ζ value between 0 and 1 we can have underdamped transfer function.

Changing the numerator and denominator values as per our requirement, we can

generate graphs.

We can measure peak value, overshoot, rise time etc in the graph itself.

C) PROGRAM /COMMAND :

1. num= [10000];

2. den =[1,20,10000];

3. y= tf(num,den);

4. stepplot(y)

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D) CIRCUIT DIAGRAM / MODEL GRAPH:

1)

2)

3)

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1) Here, ζ=0.1 and 𝜔 = 5

Peak amplitude = 1.53 Rise Time = 0.241 seconds

Overshoot = 52.7 % Settling time = 3.92 seconds

2) Here, ζ=0.05 and 𝜔 = 10

Peak amplitude = 1.85 Rise Time = 0.108 seconds

Overshoot = 0.314 % Settling time = 7.6 seconds

3) Here, ζ=0.1 and 𝜔 = 100

Peak amplitude = 1.73 Rise time = 0.013 seconds

Overshoot = 72.9% Settling time = 0.384 seconds

INFERENCE:

Through the above graphs we understand that if the 𝜁 value is varied in between 0 and

1, the no. of waves may increase or decrease depending on 𝜔 value.

If 𝜔 is taken of very high value, then rise time as well as settling time decreases. And

if it is taken low then, the rise time and settling time are of mediocre range.

If the ζ value is very much decreased then high overshooting takes place and it takes

time to settle, i.e., high peak value is attained.

In some cases we may see that settling time is achieved much before the peak value is

attained. It is because that the ζ value is very close to achieve critical damping

condition.

RESULT:

Thus the time domain of second order underdamped system is analyzed for various ζ

and 𝜔 values. The graphs for the same are also plotted with step response.

PRELAB QUESTIONS:

1) Define peak time and rise time?

2) What is settling time? Give example.

POSTLAB QUESTIONS:

1) What is Frequency Response?

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Exercise Number: 4

Title of the Experiment: STABILITY ANALYSIS USING ROUTH- HURWITZ METHOD

Date of the Exercise:

AIM OF THE EXPERIMENT:

To determine the stability of a system using Routh Hurwitz method.

FACILITIES REQUIRED:

MATLAB software.

Computer.

THEORY:

The theory of network synthesis states that any pole of the system lies on the right hand side

of the origin of the s plane, it makes the system unstable. On the basis of this condition A.

Hurwitz and E.J.Routh started investigating the necessary and sufficient conditions of

stability of a system. We will discuss two criteria for stability of the system. A first criterion

is given by A. Hurwitz and this criterion is also known as Hurwitz Criterion for

stability or Routh Hurwitz Stability Criterion. With the help of characteristic equation, we will

make a number of Hurwitz determinants in order to find out the stability of the system. We

define characteristic equation of the system as:

where n determinants for nth order characteristic equation.

PROCEDURE:

Enter the program in the editor window.

Execute the program.

Enter the coefficients of characteristic equation in the command window.

Finally save the program and run it.

The Routh matrix is obtained in the command window.

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Program:

clear clc %% firstly it is required to get first two row of routh matrix e=input('enter the coefficients of characteristic equation: '); disp('------------------------------------------------------------------------- ') l=length(e); m=mod(l,2); if m==0 a=rand(1,(l/2)); b=rand(1,(l/2)); for i=1:(l/2) a(i)=e((2*i)-1); b(i)=e(2*i); end else e1=[e 0]; a=rand(1,((l+1)/2)); b=[rand(1,((l-1)/2)),0]; for i=1:((l+1)/2) a(i)=e1((2*i)-1); b(i)=e1(2*i); end end %% now we genrate the remaining rows of routh matrix l1=length(a); c=zeros(l,l1); c(1,:)=a; c(2,:)=b; for m=3:l for n=1:l1-1 c(m,n)=-(1/c(m-1,1))*det([c((m-2),1) c((m-2),(n+1));c((m-1),1) c((m-1),(n+1))]); end end disp('the routh matrix:') disp(c) %% now we check the stablity of system if c(:,1)>0 disp('System is Stable') else disp('System is Unstable'); end

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OUTPUT:

enter the coefficients of characteristic equation: [1 1 3 1 6]

-------------------------------------------------------------------------

the routh matrix:

1 3 6

1 1 0

2 6 0

-2 0 0

6 0 0

System is Unstable

PRE LAB QUESTIONS:

1. What is meant by the stabitity of a system?

2. How to determine stability of a system?

POST LAB QUESTIONS:

1. Define the Routh Hurwitz rule.

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Exercise Number: 5

Title of the Experiment: STABILITY ANALYSIS OF LINEAR SYSTEM USING ROOT LOCUS

Date of the Exercise:

OBJECTIVE (AIM) OF THE EXPERIMENT

• To analyze the stability of the system by using Root locus,

FACILITIES REQUIRED AND PROCEDURE

• FACILITIES REQUIRED TO DO THE EXPERIMENT:

S.NO APPARATUS QUANTITY

1.

2.

Personal Computer

Matlab Software

1

1

• ROOT LOCUS

• THEORY: The root locus technique is a powerful tool for adjusting the location of closed

loop poles to achieve the desired system performance by varying one or more system

parameters. The path taken by the roots of the characteristics equation when open

loop gain K is varied from 0 to ∞ are called root loci.

• PROCEDURE:

1. Enter the command window of the MATLAB.

2. Create a new M – file by selecting File – New – M – File.

3. Type and save the program.

4. Execute the program by either pressing F5 or Debug – Run.

5. View the results.

6. Analyze the stability of the system for various values of gain.

DESIGN PROCEDURE/ DESIGN CALCULATIONS:

Problem:

The open loop transfer function of a unity feedback system G(s)=K/s (s2 +8s+17)

Draw the root locus using MATLAB Software. (Assume K=1).

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Matlab Program:

% Root locus of the transfer function G(s)=1/(S^3+8S^2+17S)

num=[1];

den=[1 8 17 0];

figure(1);

rlocus(num,den);

Title('Root Locus for the transfer function G(s)=1/(S^3+8S^2+17S)')

grid;

Matlab Output:

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Pre lab questions:

• Define stability of the system.

• What are the disadvantages of RH criterion?

• How many roots are in the left half of s plane for the equation s3 - 4s2 + s + 6 ?

Post lab questions:

• Discuss the effects of adding poles and zeros in a closed loop system.

• The transfer function of an unity feedback system is G(s) = k/s(s+2). Find the

centroid and breakaway point.

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Exercise Number: 6

Title of the Experiment: FREQUENCY RESPONSE ANALYSIS USING BODE PLOT

Date of the Exercise:

OBJECTIVE (AIM) OF THE EXPERIMENT

To analyze the stability of the given linear system using Bode plot .

FACILITIES REQUIRED AND PROCEDURE

• FACILITIES REQUIRED TO DO THE EXPERIMENT:

S.NO APPARATUS QUANTITY

1.

2.

Personal Computer

Matlab Software

1

1

• BODE PLOT :

THEORY: The bode plot is a frequency response plot of the transfer function of a system.

A bode plot consists of two graphs. One is plot of the magnitude of a sinusoidal

transfer function versus log ω . The other is plot of the phase angle of a sinusoidal

transfer function versus logω .The main advantage of the bode plot is that

multiplication of magnitude can be converted into addition. Also a simple method for

sketching an approximate log magnitude curve is available.

DESIGN PROCEDURE/ DESIGN CALCULATIONS:

Problem:

• The open loop transfer function of a unity feedback system G(s)=K/s(s2 +2s+3)

Draw the Bode Plot. Find (i)Gain Margin (ii)Phase Margin (iii)Gain cross over

frequency (iv)Phase cross over frequency (v) Resonant Peak (vi)Resonant

Frequency (vii)Bandwidth and Check the same results using MATLAB

Software. (Assume K=1)

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Matlab Program:

%Draw the Bode Plot for the given transfer functionG(S)=1/S(S2+2S+3) %Find (i)Gain

Margin (ii) Phase Margin (iii) Gain Cross over Frequency %(iv) Phase Cross over Frequency

(v)Resonant Peak (vi)Resonant %Frequency (vii)Bandwidth

num=[1 ];

den=[1 2 3 0];

w=logspace(-1,3,100);

figure(1);

bode(num,den,w);

title('Bode Plot for the given transfer function G(s)=1/s(s^2+2s+3)')

grid;

[Gm Pm Wcg Wcp] =margin(num,den);

Gain_Margin_dB=20*log10(Gm)

Phase_Margin=Pm

Gaincrossover_Frequency=Wcp

Phasecrossover_Frequency=Wcg

[M P w]=bode(num,den);

[Mp i]=max(M);

Resonant_PeakdB=20*log10(Mp)

Wp=w(i);

Resonant_Frequency=Wp

for i=1:1:length(M);

if M(i)<=1/(sqrt(2));

Bandwidth=w(i)

break;

end;

end;

Matlab Output:

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Gain_Margin_dB =15.5630

Phase_Margin = 76.8410

Gaincrossover_Frequency = 0.3374rad/sec

Phasecrossover_Frequency= 1.7321 rad/sec

Resonant_PeakdB = 10.4672

Resonant_Frequency = 0.1000 rad/sec

Bandwidth = 0.5356

Pre lab questions:

• Define frequency response analysis.

• What is Gain margin and phase margin?

Post lab questions:

• What are theadvantages and disadvantages of Bode plot?

• How can you analyse the stability of the system with Bode plot?

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Exercise Number: 7

Title of the Experiment: FREQUENCY RESPONSE ANALYSIS USING POLAR PLOT

Date of the Exercise:

OBJECTIVE (AIM) OF THE EXPERIMENT

• To analyze the stability of the given linear system using polar plot.

FACILITIES REQUIRED AND PROCEDURE

• FACILITIES REQUIRED TO DO THE EXPERIMENT:

S.NO APPARATUS QUANTITY

1.

2.

Personal Computer

Matlab Software

1

1

• POLAR PLOT :

THEORY: The Polar plot provides a simple test for stability of a closed- loop control

system by examining the open-loop system. Stability of the closed-loop control system

may be determined directly by computing the poles of the closed-loop transfer function.

The Polar Criteria can tell us things about the frequency characteristics of the system.

A Polar plot is used in automatic control and signal processing for assessing the stability

of a system with feedback. It is represented by a graph in polar coordinates in which the

gain and phase of a frequency response are plotted. The plot of these phasor quantities

shows the phase as the angle and the magnitude as the distance from the origin. This

plot combines the two types of Bode plot — magnitude and phase — on a single graph

with frequencry as a parameter along the curve.

DESIGN PROCEDURE/ DESIGN CALCULATIONS:

Problem:

• The open loop transfer function of a unity feedback system G(s)=K/s(s2 +2s+3)

Draw the Polar Plot. Find (i)Gain Margin (ii)Phase Margin (iii)Gain cross over

frequency (iv)Phase cross over frequency and Check the same results using

MATLAB Software. (Assume K=1)

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Matlab Program:

%Polar Plot for the Transfer Function G(s)=1/(s+1)^3

num=[1];

den=[1 3 3 1];

figure(1);

polar (num,den)

Title('Polar Plot for the Transfer Function G(s)=1/(s+1)^3')

[Gm,Pm,Wcg,Wcp] = margin(num,den)

grid;

[Gm,Pm,Wcg,Wcp] = margin(num,den);

Gain_Margin = Gm

Phase_Margin = Pm

PhaseCrossover_Frequency = Wcg

GainCrossover_Frequency = Wc

Matlab Output:

Gain_Margin = 8.0011

Phase_Margin = -180

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PhaseCrossover_Frequency = 1.7322 rad/sec

GainCrossover_Frequency = 0 rad/sec

Pre lab questions:

• What is contour?

• Define the type number and order of the system.

Post lab questions:

• Explain the conditions for stable system in Polar plot.

• State Polar stability criterion.

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Exercise Number:8

Title of the Experiment: Design of PID Controller for first order and second order systems

Date of the Exercise:

OBJECTIVE OF THE EXPERIMENT

To design a PID controller for the following first order and second order system,

1. 𝐺(𝑠) =3.6

(𝑠+10)

2. 𝐺(𝑠) =5

𝑠2+6𝑠+5

Your design should satisfy the following specifications:

i) Percentage overshoot < 15%.

ii) Rise time < 100 msec.

iii) Settling time < 500 msec.

iv)Zero steady-state error to a step.

FACILITIES REQUIRED AND PROCEDURE

d) FACILITIES REQUIRED TO DO THE EXPERIMENT:

S.NO APPARATUS SPECIFICATION QUANTITY

1. PC - 1 2. MATLAB Any version Package

e) THEORY:

Most PID controllers are adjusted on-site and many different types of tuning rules

have been proposed in different literatures. Using these tuning rules, delicate and fine tuning

of PID controllers can be made on-site. Also, automatic tuning methods have been developed

and some of the PID controllers may possess on-line automatic tuning capabilities. Modified

forms of PID control, such as I-PD control and two-degrees-of- freedom PID control, are

currently in use in industry

f) PROCEDURE:

Implement the understanding of effects of Proportional, Integral and Derivative Gains

over the system response.

g) DESIGN PROCEDURE/ DESIGN CALCULATIONS:

Trial and Error basis

If needed use the cascaded controllers like PID with another PID or any other

combinations in series.

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e) BLOCK DIAGRAM:

f) DESIGN PARAMETERS OF PID CONTROLLERS: FIRST ORDER SYSTEM: Kp = Ki = Kd = SECOND ORDER SYSTEM: Kp = Ki =

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Kd = g) MODEL OUTPUT RESPONSE:

Figure 1: First order uncontrolled open loop response

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Figure 2: First order controlled closed loop response

Figure 3: Second order uncontrolled open loop response

Figure 4: Second order controlled closed loop response

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Pre lab questions:

2. What is conventional controller?

2. What is the effect of P, I and D on output response of a system?

Post lab questions:

3. List the advantages of PID over PI controller. 4. What is the effect of addition of poles and zeros to a system?

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Exercise Number: 9

Title of the Experiment: Design of PID Controller for speed control of DC Motor System.

Date of the Exercise:

OBJECTIVE OF THE EXPERIMENT

To design a PID controller for the speed control of DC Motor Control System represented by the following transfer function,

ɵ(s) = (Kt /Ra B)

Va(s) s[(1+sTa)(1+sTm) + (KbKt/RaB)]

Where kt=0.01

J=0.01

B=1

Kf=1

Kb=1

Ra=1

La=0.5

And

La = Ta Electrical time constant

Ra

J = Tm Mechanical time constant

B

Your design should satisfy the following specifications:

i) Percentage overshoot < 12%.

ii) Rise time < 80 msec.

iii) Settling time < 300 msec.

iv)Zero steady-state error to a step.

FACILITIES REQUIRED AND PROCEDURE

a) FACILITIES REQUIRED TO DO THE EXPERIMENT:

S.NO APPARATUS SPECIFICATION QUANTITY

1. PC - 1 2. MATLAB Any version Package

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b) THEORY:

Most PID controllers are adjusted on-site and many different types of tuning rules

have been proposed in different literatures. Using these tuning rules, delicate and fine tuning

of PID controllers can be made on-site. Also, automatic tuning methods have been developed

and some of the PID controllers may possess on-line automatic tuning capabilities. Modified

forms of PID control, such as I-PD control and two-degrees-of- freedom PID control, are

currently in use in industry

c) PROCEDURE:

Implement the understanding of effects of Proportional, Integral and Derivative Gains

over the system response.

d) DESIGN PROCEDURE/ DESIGN CALCULATIONS:

Trial and Error basis

If needed use the cascaded controllers like PID with another PID or any other

combinations in series.

e) BLOCK DIAGRAM:

f) DESIGN PARAMETERS OF PID CONTROLLERS: Kp = Ki = Kd =

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g) MODEL OUTPUT RESPONSE:

Figure 1: DC Motor uncontrolled open loop response

Figure 2: DC Motor controlled closed loop response

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Pre lab questions:

1. What is cascaded controller?

2. What causes instability in system considering the Pole-zero form of a system?

Post lab questions:

3. Discuss the effect of PD controller on system

performance. 4. Summarize the P – Controller and its characteristics.

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Exercise Number: 10

Title of the Experiment: Design of PID Based controller for Twin Rotor Multi Input Multi

Output System.

Date of the Exercise:

OBJECTIVE OF THE EXPERIMENT

To design a PID Based controller for orientation control of Twin Rotor Multi Input Multi Output System represented by the following transfer function,

𝐺(𝑠) =3.6

𝑠3 + 6𝑠2 + 5𝑠

Your design should satisfy the following specifications:

i) Percentage overshoot <20%.

ii) Rise time <120 msec.

iii) Settling time < 600 msec.

iv)Zero steady-state error to a step.

FACILITIES REQUIRED AND PROCEDURE

a) FACILITIES REQUIRED TO DO THE EXPERIMENT:

S.NO APPARATUS SPECIFICATION QUANTITY

1. PC - 1 2. MATLAB Any version Package

b) THEORY:

Most PID controllers are adjusted on-site and many different types of tuning rules

have been proposed in different literatures. Using these tuning rules, delicate and fine tuning

of PID controllers can be made on-site. Also, automatic tuning methods have been developed

and some of the PID controllers may possess on-line automatic tuning capabilities. Modified

forms of PID control, such as I-PD control and two-degrees-of- freedom PID control, are

currently in use in industry

c) PROCEDURE:

Implement the understanding of effects of Proportional, Integral and Derivative Gains

over the system response.

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45

d) DESIGN PROCEDURE/ DESIGN CALCULATIONS:

Trial and Error basis

If needed use the cascaded controllers like PID with another PID or any other

combinations in series.

e) BLOCK DIAGRAM:

f) DESIGN PARAMETERS OF PID CONTROLLERS: Kp = Ki = Kd =

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46

g) MODEL OUTPUT RESPONSE:

Figure 1: TRMS uncontrolled open loop response

Figure 2: TRMS controlled closed loop response

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Pre-lab questions:

1. What is TRMS?

2. State the purpose of TRMS.

Post lab questions:

3. Discuss the effect of PI controller on system

performance. 4. Discuss the effect of adding zero to open loop transfer function of a system.