# Effects of addition of poles and zeros to closed loop transfer function

## Effect of addition of pole and zero to closed loop transfer function

### Aim:

Study and plot unit step response of addition of pole and zero to the closed loop 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 closed loop transfer function of a system.

### Theory:

#### Addition of pole to closed loop transfer function:

The closed loop transfer function of general second order system is given by,

Addition of pole to closed loop transfer function:

When we add a pole, the transfer function becomes,

### MATLAB PROGRAM:

addition of pole to closed loop transfer function

addition of pole to closed loop transfer function

Effect of addition of pole to closed loop transfer function:

1)      As the pole moves towards the origin in s plane, the rise time increases and the maximum overshoot decreases, as far as the overshoot is concerned, adding a pole to the closed loop transfer function has just the opposite effect to that of adding a pole to forward path transfer function as discussed in the last article.

2)      The addition of left half pole tends to slow down the system response.

3)      The effect of addition of pole becomes more pronounced as pole location drifts away from imaginary axis.

4)      Addition of right half pole will make overall system response to be an unstable one.

### Addition of zero to closed loop transfer function:

Suppose a zero at s=-z is added to closed loop transfer function, then the resultant transfer function becomes,

### MATLAB PROGRAM:

addition of zero to closed loop transfer function 1

addition of zero to closed loop transfer function 1

### Conclusion:

Effect of addition of zero to closed loop transfer function

1)      Makes the system overall response faster.

2)      Rise time, peak time, decreases but overshoot increases.

3)      Addition of right half zeros means system response slower and system exhibits inverse response. Such systems are said to be non-minimum phase systems.

Minimum phase system: The system which doesn’t have zeros in right half of s plane is said to be minimum phase system.

Non-minimum phase system: If a transfer function has poles or zeros in right half of s plane then the system shows the non-minimum phase behavior.