# Addition of poles and zeros to the forward path transfer function

## Effect of addition of pole and zero to forward path transfer function

### Aim:

Study and plot unit step response of addition of pole and zero to the forward path transfer function for a unity feedback system. Plot the response for four different values of poles and zeros. Comment on the effect of addition of poles and zeros to forward path transfer function of a system.

### Theory:

Addition of pole to forward path transfer function:

The forward path transfer function of general second order system is given by,

Addition of pole to forward path transfer function:

When we add a pole, the transfer function becomes,

MATLAB PROGRAM:

addition of pole to forward path transfer function 1
addition of pole to forward path transfer function 1

Conclusion:

Effect of addition of pole to forward path transfer function:

1)Â Â Â Â Â  Unit step response of closed loop system when Wn=10, zeta=0.5, P=[1,5,10,20]. These responses show that addition of pole to forward path transfer function generally has the effect of increasing maximum overshoot of closed loop system.

2)Â Â Â Â Â  As the pole moves closer to the origin in s plane, the maximum overshoot increases.

3)Â Â Â Â Â  These responses also show that added pole increases rise time of step response.

Addition of zero to forward path transfer function:

The forward path transfer function of general second order system is given by,

Addition of zero to forward path transfer function:

When we add a zero the forward path transfer function becomes,

MATLAB PROGRAM:

addition of zero to forward path transfer function 1
addition of zero to forward path transfer function 1

Conclusion:

Effect of addition of zero to forward path transfer function:

1)Â Â Â Â Â  Addition of forward path zeros to left hand side of s plane increases speed of output response but a large overshoot may result if the zero is sufficiently lose to 0.

2)Â Â Â Â Â  The order of system does not increase with addition of zero to forward path transfer function.

3)Â Â Â Â Â  The zero in right half of s plane retards the system and produces an overshoot. The percentage overshoot decreases as the zero moves along positive real axis towards infinity. Again system oscillates for a large time.