PROGRAM – 1 : Underdamped System

num=[0 0 49];den=[1 2 49];g=tf(num,den)t=0.0:0.005:6;step(g,t)figure 2;PZMAP(g)

Transfer function:

49--------------s^2 + 2 s + 49

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PROGRAM – 2 : Undamped System

num=[0 0 20];den=[1 0 20];g=tf(num,den)t=0.0:0.005:6;step(g,t)figure (2);PZMAP(g)

Transfer function:

20--------------s^2 + 20

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PROGRAM – 3 : Overdamped System

num=[0 0 20];den=[1 10 20];g=tf(num,den)t=0.0:0.005:6;step(g,t)figure(2);PZMAP(g)

Transfer function:

20------------------s^2 + 10 s + 20

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PROGRAM – 4 : Critically Damped System

num=[0 0 81];den=[1 18 81];g=tf(num,den)t=0.0:0.005:6;step(g,t)figure(2);PZMAP(g)

Transfer function:

81------------------s^2 + 18 s + 81

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STEADY STATE ERROR & STEADY STATE ERROR COEFFICIENTSMATLAB PROGRAM:

num=[0 0 250];den=[1 214 40];a=tf(num,den)kp=dcgain(a)ess1=1/(1+kp)num1=conv([0 1 0],num);b=tf(num1,den)kv=dcgain(b)ess2=1/kvnum2=conv([1 0 0],num);c=tf(num2,den)ka=dcgain(c)ess3=1/ka

Output:

Transfer function:

250----------------s^2 + 214 s + 40

kp =

6.2500

ess1 =

0.1379

Transfer function:

250 s----------------s^2 + 214 s + 40

kv =

0

Warning: Divide by zero.

> In ssc at 9

ess2 =

Inf

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Transfer function:

250 s^2----------------s^2 + 214 s + 40

ka =

0

Warning: Divide by zero.

> In ssc at 13

ess3 =

Inf

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P type Controller

Diagram:

Output:

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PD type controller

Diagram:

Output:

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PI type Controller

Diagram:

Output:

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PID type controller

Diagram:

Output:

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ROOT LOCUS

num=[0 0 0 4];den=[1 2 2 4];a=tf(num,den)rlocus(a)

-5 -4 -3 -2 -1 0 1 2-4

-3

-2

-1

0

1

2

3

40.140.30.440.580.72

0.84

0.92

0.98

0.140.30.440.580.72

0.84

0.92

0.98

12345

Root Locus

Real Axis

Imag

inar

y A

xis

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BODE PLOT

num=[0 0 10 100];den=[0.1 0.7 1 0];a=tf(num,den)bode(a)

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LEAD UNCOMPENSATED

PROGRAM:

num=[0 0 12];den=[1 1 0];g=tf(num,den)bode(g)

TRANSFER FUNCTION :

12-------s^2 + s

BODE PLOT :

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LAG UNCOMPENSATED

PROGRAM:

num=[0 0 0 5];den=[0.25 1.25 1 0];g=tf(num,den)bode(g)

TRANSFER FUNCTION :

5--------------------------------0.25 s^3 + 1.25 s^2 + s

BODE PLOT :

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