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ITSE

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

ITSE is an integral performance metric that weights squared control error by elapsed time.

ITSE (integral time squared error) evaluates a control response by integrating time multiplied by squared error: ITSE = ∫ t e(t)² dt. The time factor penalizes errors that persist, while squaring emphasizes larger deviations. In PID tuning, this makes later errors especially costly and can favor responses with slower rise times but more oscillation. section 8.7

PID step-response evaluation

For a unit-step response, calculate error as the difference between the desired output and actual output, square the sampled error, multiply by time, and approximate the integral numerically with the trapezoidal rule. A genetic algorithm can then minimize this value while searching for Kp, Ki, and Kd. section 8.7

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Defines the formula and shows numerical implementation, without deriving the metric or analyzing its optimization behavior formally.
Examples
Uses a heater step response and Python objective-function code to demonstrate evaluation during PID tuning.
What it assumes
Assumes understanding of control error, step responses, and PID parameters while defining the metric in context.
What you can do after
Apply ITSE through numerical integration as an objective for genetic-algorithm PID tuning.
How it connects
Links time-weighted error to PID tuning, step response, ITAE, IAE, and ISE.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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Related concepts

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