What is the role of zero in transfer function?

Zeros are frequencies at which the response magnitude becomes zero. Poles determine the transient response of the system, while the zero determines the speed of response to be more general. Zeros become important when there are delays, or non-minimum phase.

Why do we assume zero initial conditions in transfer function?

We take initial condition zero so as to make RHS of transfer function independent of input. Hence while we take the Laplace transform of that function this facilitate us to put those residual term of (0–) and (0+) intentionally to be zero.

What is transfer function of a control system?

The transfer function of a control system is defined as the ratio of the Laplace transform of the output variable to Laplace transform of the input variable assuming all initial conditions to be zero. It is also defined as the Laplace transform of the impulse response.

What happens when a zero is added to the open loop transfer function of the system?

When zeros are added to a transfer function the stability improves i.e. the root locus shifts to the left in s-plane. Imagine an open loop transfer function with three poles and no zeros with gain constant K. The angle of asymptotes for this system would be 60°, 180°, 300°.

Can a transfer function have more zeros than poles?

Mathematically you may have more zeros than poles. But if you do then the magnitude of the transfer function diverges to infinity at high frequency. This is why this is not possible in any transfer function that represents any true physical system.

What does zero initial conditions mean?

Zero initial conditions mean that the system is rest and no energy is stored in any components of the circuit. Generally, zero indicates linear system i.e. if there is no input then there should be zero output.

What does assume zero initial conditions mean?

Zero initial condition means that all capacitors have zero initial voltage and all inductors have zero initial current, so no energy is stored in the circuit. In that way, the behaviour of the circuit depends uniquely on the inputs.