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Integral gain

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

An integral gain is a PID parameter that scales the response to accumulated error over time.

Integral gain (Ki) is the PID parameter that scales the controller’s response to error accumulated over time. Increasing Ki decreases steady-state error significantly, but can also increase overshoot and settling time. section 8.7

Use integral gain as one component of PID tuning:

  • Represent Ki alongside proportional gain (Kp) and derivative gain (Kd) in the PID transfer function. section 8.7

Optimizing Ki with a genetic algorithm

A PID tuning problem treats Kp, Ki, and Kd as three variables, searches values from 0 to 100, and scores each candidate using a response-based objective. A genetic algorithm then searches 50 candidates across 60 generations before plotting and inspecting the resulting step response.

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

How deep it goes
Defines Ki, compares its response effects, and applies it within transfer-function and genetic-algorithm tuning code.
Examples
Demonstrates Ki in HVAC-style closed-loop control, PID transfer functions, genetic-algorithm search, and step-response diagnostics.
What it assumes
Assumes familiarity with PID parameters, closed-loop control, transfer functions, and step-response measures.
What you can do after
Evaluate and tune Ki through Python control-system simulations and response metrics.
How it connects
Connects integral gain with PID controllers, proportional gain, derivative gain, transfer functions, and step responses.
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