Integral square error (ISE): If the error voltage is denoted as e(t), how is the integral square error defined in control system performance analysis?

Introduction / Context:
Integral performance indices are widely used in control systems to quantify error over time. One of the most common measures is the Integral Square Error (ISE), which penalizes large deviations more heavily than small ones by squaring the error before integration.

Given Data / Assumptions:

• Error signal: e(t).
• Performance index being evaluated: Integral Square Error.

Concept / Approach:

The ISE is defined as the integral of the square of the error over the entire time domain. By squaring, both positive and negative errors contribute positively, and larger errors are penalized quadratically.

Step-by-Step Solution:

Verification / Alternative check:

ISE is one of several criteria: others include Integral Absolute Error (IAE = ∫ |e(t)| dt) and Integral Time Squared Error (ITSE = ∫ t*e^2(t) dt). Among these, ISE is specifically the square of the error integrated, confirming the answer.

Why Other Options Are Wrong:

• Integral of e(t) dt: would allow positive and negative errors to cancel out.
• Integral of |e(t)| dt: corresponds to IAE, not ISE.
• Integral of (de/dt)^2 dt: not a standard performance measure.
• None of the above: incorrect since a valid definition exists.

Common Pitfalls:

• Confusing ISE with IAE.
• Forgetting that squaring magnifies larger errors disproportionately.

Final Answer:

Integral of e^2(t) dt.