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Derivative gain

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

A derivative gain is a PID parameter that scales the response to the rate of change of error.

Derivative gain (Kd) is the PID parameter that scales the controller’s response to the rate of change of error. In a closed-loop system, it helps reduce overshoot and settling time while producing only a small change in rise time and steady-state error. section 8.7

Use derivative gain when tuning a PID response:

  • Increase or optimize Kd to reduce overshoot and settling time. section 8.7
  • Treat Kd as one of three coupled parameters with proportional gain and integral gain. section 8.7
  • Evaluate candidate values through the system’s step response and measures such as overshoot, rise time, settling time, and steady-state value. section 8.7

Genetic-algorithm tuning

A Python tuning problem represents Kp, Ki, and Kd as three variables, evaluates each candidate through a transfer function, and uses a genetic algorithm to minimize a response criterion. The resulting parameters are tested by plotting the step response and calling control.step_info(T). section 8.7

Table 8.6 Effects of adding PID controller parameters on the system’s response (view table figure)

Parameter

Rise time

Overshoot

Settling time

Steady-state error

Kp

Decreases

Increases

Small change

Decreases

Ki

Decreases

Increases

Increases

Decreases significantly

Kd

Small change

Decreases

Decreases

Small change

Compare how Kp, Ki, and Kd change rise time, overshoot, settling time, and steady-state error. section 8.7

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

How deep it goes
Defines Kd, compares its response effects, and applies it within transfer-function optimization code.
Examples
Uses HVAC and heater step-response systems, transfer-function code, response plots, and control.step_info output.
What it assumes
Assumes PID parameters, closed-loop control, transfer functions, and step-response measures.
What you can do after
Apply it via Python control and genetic-algorithm tooling to optimize and inspect PID parameters.
How it connects
Connects derivative gain to proportional gain, integral gain, PID control, transfer functions, genetic algorithms, and step response.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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