This document introduces control system concepts and how they can be analyzed using MATLAB. It discusses open and closed loop systems, Laplace transforms, state variable approaches, and MATLAB commands to analyze systems. Examples are provided on determining transfer functions, computing step and frequency responses, plotting root loci and Bode diagrams, and performing time and frequency domain analyses. Block diagrams can be reduced and overall transfer functions obtained through series and parallel combinations.

1. INTRODUCTION TO
CONTROL SYSTEM
CONCEPTS IN MATALAB

2. CONTENTS
• Introduction to control system concepts
• MATLAB for Control Engineering
• Tutorial problems

3. MATLAB Functions
• Control system solutions can be found by
using MATLAB functions/commands.
• Transfer functions from polynomial coefficents
can be obtained
• Transfer functions can be determined for
complex control system
• Pole-zero mapping
• Time response for given input
• Plot on root locus and Nyquist plots etc

4. INTRODUCTION TO CONTROL SYSTEM
CONCEPTS
• Open loop system
• Closed loop system
• Laplace transform approach (Frequency –
domain approach)
• State variable approach (Time-domain
approach)

5. INTRODUCTION TO CONTROL SYSTEM
CONCEPTS
Differential
equatons
(Time Domain)
Algebraic equations
(Frequency domain)

6. Differential equations
(Time Domain)
Algebraic equations
(Frequency domain)

7. MATLAB COMMANDS
COMMAND DESCRIPTION
tf(num,den) Computes transfer function with
numerator(num) and denominator(den)
tfdata Returns the numerator(S) and
denominator(S) of the transfer function
Step Computes unit step response of a system
dstep Computes unit step response of a discrete
system
series Finds transfer function of blocks
connected in series
parallel Finds transfer function of blocks
connected in parallel
Pzmap (sys) Plots the pole –zero map of the LTI model
system
ltiview LTI Viewer (time and frequency response
analysis)

8. ss Creates state –space (SS) models
tf2ss Converts transfer function to state
variable form
ss2tf Converts state variable form to transfer
function form
residue Computes partial fraction expansion from
polynomial coefficents
roots Finds the roots of a polynomial
rlocus Computes the root locus of given transfer
function
bode Generates the bode plot
margin Calculates gain and phase margin, gain
cross over and phase cross over
frequency
nyquist Computes nyquist plot

9. CONTROL SYSTEM APPLICATIONS
Example: 1
G1=tf([1 2 3],[1 2 3 4])
bode(G1);
Example: 2
G1=tf([1 2 3],[1 2 3 4])
G2=tf([2 6 8] ,[4 6 7 8])
G3=G1*G2;

10. [num,den]=tfdata (G3,'V')
Example:3 (A) (Laplace and Inverse Laplace Transform)
syms s t;
a=sin(t);
b=laplace(a);
disp(b);
disp(ilaplace(b));

11. Example:3(B) (Laplace and Inverse Laplace
Transform)
syms t
ft = 3*exp(-2*t);
Fs=laplace(ft);
Fs=3/(s+2)
Example:3(C)
f(t)= e-2t [1-cos(t)].

12. Example:3(D) (Laplace and Inverse Laplace
Transform)
F(s)= s2+2s+3/s3+6s2+12s+8
syms s t
Fs = (s^2+2*s +3)/(s^3+6*s^2 + 12*s+8)
Fs = (s^2+2*s +3)/(s^3+6*s^2 + 12*s+8);
ft=ilaplace(Fs)
Example:3(E) ( find inverse laplace transform)
F(s)= 1/ s(s+2)

13. • Example:3(F)
s+6/s3+4s2+3s
n = [1 6];
d = [1 4 3 0];
[r, p, k] = residue( n,d)
Find partial fraction (S3 +8s+6)/(s3 +4s2+3s+1)

14. CONTROL ANALYSIS RESPONSES
Example4: (Step Response)
G=tf([1 7 24 24],[1 10 35 50 24]);
step(G,10);
G2=2*G;
Step(G,G2,20);

15. Example:5 (Root locus)
num=[1 4 8];
den=[1 18 120.3 357.5 478.5 306];
G=tf(num,den);
rlocus(G);

16. Exampl:6 (Bode plot)
s=tf('s');
G=(s+8)/(s+(s^2+0.2*s+4)*(s+1)*(s+3));
bode(G);
[gm pm wgc wpc]=margin(G)
Bodemag(G); – For magnitude plot
nyquist(G); - For nyquist plot
nichols(G);

17. PLOTTING OPTIONS
a=[1 2 3];
b=[4 5 6];
plot(a,b,'k' ,2*a,2*b,'b:');
grid;
xlabel('X-axis');
ylabel('y-axis');
title('title');

18. legend('plot(i)' , 'plot(ii)');
text(6,10,'f(x)=x^2','color' , 'r');
Example:7 (Block diagram reduction)
Find the overall transfer function and pole zero
map for the given block

19. %print TF1
n1=[1];
d1=[1 1];
disp('TF1 is: ' );
printsys(n1 ,d1)
%print TF2
n2=[1 2];
d2=[0 1];
disp('TF2 is: ');
printsys(n2,d2)

20. %print TF3
n3=[1 0];
d3=[1 0 2];
disp('TF3 is: ');
printsys(n3,d3)
%print TF4
n4=(1);
d4=(1);
disp('TF4 is; ');
printsys(n4,d4)

21. %obtain TF5 from parallel combination of TF1
and TF2
[n5, d5]=parallel (n1,d1,n2,d2);
disp('TF5 is: ');
printsys(n5,d5)
%obtain TF6 from feedback loop of TF3 and TF4
[n6,d6]=feedback(n3,d3,n4,d4);
disp('TF6 is: ');
printsys(n6,d6)

22. %overall transfer function is obtained by series
connection of TF5 and TF6
[n7,d7]=series(n5,d5,n6,d6);
disp('overall Transfer function is; ');
printsys(n7,d7);
%obtain pole zero map from TF7
sys1=tf(n7,d7);
pzmap(sys1)