What happens if there is pole zero cancellation in a system?

The problem is that when an added zero does not exactly cancel the corresponding unstable pole (which is always the case in real life), a part of the root locus will be trapped in the right-half plane. This causes the closed-loop response to be unstable.

How do you tell if a system is stable based on its poles?

When the poles of the closed-loop transfer function of a given system are located in the right-half of the S-plane (RHP), the system becomes unstable. When the poles of the system are located in the left-half plane (LHP) and the system is not improper, the system is shown to be stable.

Can you have more zeros than poles?

The effects of zeros and poles of a system combine and when the system has more finite zeros than poles then the overall effect is an anticipative one, and the system is not causal. When a system has more poles than finite zeros (i.e. the transfer function of the system is strictly proper) then the system is causal.

What is pole and zero of a system?

Poles and Zeros of a transfer function are the frequencies for which the value of the denominator and numerator of transfer function becomes zero respectively. The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs.

What happens if there are no zeros?

Without zero there would be: No algebra, no arithmetic, no decimal, no accounts, no physical quantity to measure, no boundary between negative and positive numbers and most importantly- no computers!

Is a pole at 0 unstable?

If the pole is at S=0 (existing on the origin) the response will be the unit step function (this is characteristic of integrators). Therefore, if S=0 is the transfer function, the system is marginally stable.

Is a zero pole stable?

A system with a pole at the origin is also marginally stable but in this case there will be no oscillation in the response as the imaginary part is also zero (jw = 0 means w = 0 rad/sec).

What is a non causal system?

A non-causal system is just opposite to that of causal system. If a system depends upon the future values of the input at any instant of the time then the system is said to be non-causal system.

What is improper system?

An improper system cannot be causal and stable. If the order of the numerator is greater than the order of the denominator, you’ll always have at least one pole at infinity. Consequently, not all poles are in the left half-plane (or inside the unit circle in the case of discrete-time systems).

What are the Poles and zeros of a differential equation?

The poles and zeros are properties of the transfer function, and therefore of the differentialequation describing the input-output system dynamics. Together with the gain constant Ktheycompletely characterize the differential equation, and provide a complete description of the system.

What is the difference between z-plane zeros and Poles?

Zeros are easy: if system has a zero at $z_0$, that means a signal defined by $z_0$ on a z-plane will pass through a feedback loop and sum with itself strictly out-of-phase resulting in zero output. Poles are a bit trickier: if system has a pole at $z_0$, that means a system will generate this signal than it’s disturbed and moving freely.

Why Poles and zeros are used in IIR?

Second, poles and zeros are used to describe an IIR system, i.e. a system with a feedback. Zeros are easy: if system has a zero at z 0, that means a signal defined by z 0 on a z-plane will pass through a feedback loop and sum with itself strictly out-of-phase resulting in zero output.

What are the Poles and zeros of the transfer function?

The poles and zeros are properties of the transfer function, and therefore of the differential equation describing the input-output system dynamics. Together with the gain constantKthey completelycharacterizethedifferentialequation, andprovideacompletedescriptionofthesystem. Example