Contents
Do zeros determine stability?
The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs.
Does addition of zero increases the stability?
2. Addition of zero increases the stability. Explanation: Zero is defined as the root of the numerator of the transfer function and addition of zeroes increases the stability as the speed of response increases.
Is the transfer function stable?
Transfer function stability is solely determined by its denominator. The roots of a denominator are called poles. Poles located in the left half-plane are stable while poles located in the right half-plane are not stable.
How do zeros affect overshoot?
Adding a LHP zero to the transfer function makes the step response faster (decreases the rise time and the peak time) and increases the overshoot. Adding a RHP zero to the transfer function makes the step response slower, and can make the response undershoot.
That is not the case with a non-minimum-phase system. If one inverts a non-minimum-phase system, the result will have poles in the unstable region and will be unstable. Zeros are very import for the system behavior. They influence the stability and the transient behavior of the system.
Why are zeros important in a closed loop system?
In order for the closed loop system to be stable, the poles have to be located in the left half plane. The zeros have no importance, since the stability of a linear system is solely determined by the position of the poles. When designing a closed loop system (i.e. a circuit), this is usually done by analyzing the open loop system.
Why are zeros with positive real parts bad?
1)zeros with positive real part give a negative phase contribution, reducing the phase margin (which is bad) thus limits the performance of the system. 2)Time delay in the system can also be approximated as a zero with positive real part (see first order Pade approximation 1 ), similar effect as previous point.
Where do zeros and Poles have to be in a minimum phase?
So both zeros and poles have to be in the left half s -plane or inside the unit circle in the z -plane for the system to be both stable and minimum phase. And a minimum-phase system can be inverted (which causes swapping of poles and zeros) and will continue to be stable.