Steady-State Error in Feedback Control System

The steady-state error is the deviation between the desired output and the actual output of a control system when the system reaches a stable state. It is a measure of the system's ability to track the reference input accurately.

Types of Systems

In control system theory, systems are classified into different types based on the number of integrators present in the open-loop transfer function. The type of the system can be determined by counting the number of integrators and poles at the origin in the transfer function.

The types of systems are as follows:
- Type-0 system: No integrators or poles at the origin
- Type-1 system: One integrator or pole at the origin
- Type-2 system: Two integrators or poles at the origin
- Type-3 system: Three integrators or poles at the origin
- and so on...

Acceleration Input

An acceleration input refers to a unit step input applied to the system. It represents a sudden change in the input signal, causing the system to respond with a ramp output.

Explanation of Answer

The given question states that the steady-state error of a feedback control system with an acceleration input becomes finite. It means that the steady-state error does not tend to zero and remains at a non-zero value.

Reasoning:

When a system with an acceleration input is analyzed, it can be observed that the steady-state error is inversely proportional to the number of integrators or poles at the origin in the system.

- A type-0 system (no integrators) will have a finite steady-state error with an acceleration input.
- A type-1 system (one integrator) will have a steady-state error that tends to zero with an acceleration input.
- A type-2 system (two integrators) will have a steady-state error that tends to zero faster than a type-1 system with an acceleration input.

By this reasoning, we can conclude that the steady-state error of a feedback control system with an acceleration input becomes finite in a type-2 system.