In control systems engineering, the steady-state error depends on input type and loop gain; it is generally decreased by increasing the (appropriate) system gain rather than being independent of input or tied to transient behavior.

Introduction / Context:
Steady-state error (ess) measures how far the output remains from the desired input after transients die out. It is a key performance metric for tracking tasks under standard test inputs (step, ramp, parabolic). Engineers tune gains and choose controller structures (e.g., adding integral action) to reduce ess while balancing stability and robustness.

Given Data / Assumptions:

• The plant and controller form a feedback loop.
• We consider classical results for standard inputs and system “type.”
• Gain adjustments affect error constants and therefore ess.

Concept / Approach:
For unity feedback, ess depends on input type (step, ramp, etc.) and system type (number of pure integrators in the loop). Increasing proportional or integral gain typically increases position/velocity error constants, thereby reducing ess for the corresponding input classes. However, excessive gain can harm stability and overshoot; thus gains must be tuned. It is not a function of transient response per se, though controller choices influence both transient and steady-state behaviors.

Step-by-Step Solution:
Relate ess to error constants (Kp, Kv, Ka) and input type.Note that higher appropriate gain increases these constants, reducing ess.Check statements: independence from input is false; tying ess to transients is incorrect; “zero for all inputs to type 1 systems” is false (type 1 has zero step error but nonzero ramp error).Select “decreased by increasing gain.”

Verification / Alternative check:
Consider a type 0 system tracking a step: ess = 1/(1+Kp). Raising Kp decreases ess toward 0, verifying the effect of gain on steady-state error.

Why Other Options Are Wrong:
Independent of input: incorrect; input class matters.Function of transient response: transient metrics (e.g., overshoot) differ from steady-state error.Zero for all inputs to type 1 systems: only step input is zero; ramp is finite, parabolic diverges.None of the above: invalid because gain can reduce ess.

Common Pitfalls:
Cranking up gain without checking phase margin; ignoring actuator limits; forgetting that integral action changes system type and can eliminate step error but may slow settling or induce oscillations.

Final Answer:
Decreased by increasing gain