Practical Implications of Zeros of a transfer function

[knji]

- Zeros on the left hand side of the jw axis indicates that the system is minimum phase.

- Zeros on the right hand side of the jw axis indicates that the system is non-minimum phase.

- Zeros on the jw axis indicates that the system is 'marginally' minimum phase. The magnitude and frequency response of such a system indicates a phase shift of 2*pi rad between the input and output while the magnitude of the input/output response is 0db for a major part of the frequency range.

My Questions are as follows:

1. What is a transfer function without zeros at all referred to?

2. If the relative degree of a linear system is the difference between its poles and zeros, a transfer function without zeros has its relative degree = number of poles.
What does this mean in terms of the practical response of the system?

3. Is it preferable to have a system with left hand zeros or no zeros in terms of its transient response? Looking at the bode plots, no zeros seem to support a wide frequency response. However, at a certain frequency, the input is dramatically attenuated and the phase shift is undefined!

4. The zeros of a transfer function dictates wether its zero dynamics is stable. Zeros of a transfer function coincide with the roots of its zero dynamics. Does this mean that a system without zeros has no zero dynamics and therefore is advantageous when designing a controller?

Thanks,

Klaus

 

[sreid]

First, if you find Root Locus plots abstract and baffeling, join the club. As a practical design tool state space computer simulation has superceeded Root Locus plots. Having said that;

1)I do not know of any special name for a no zeros transfer function.

2)All pole transfer functions are quite common. The more poles in the transfer function, the greater the phase shift with frequency. A zero (phase lead) may be added in the controller to either improve the phase margin (better damping of the step response) or a phase lead may absolutely be required to have a stable system at all.

3) The controlled plant may have a zero and that is not necessarly good or bad. As stated before, a zero in the controller may be required to either damp the response or to stabalize the system.

4) Don't know.

 

[knji]

Thank You.