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Proportional gain

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

A proportional gain is a PID parameter that scales the controller response to the current error.

Proportional gain (Kp) is the PID parameter that scales the controller’s response to the current error. Increasing Kp generally decreases rise time and steady-state error, but increases overshoot. section 8.7

In a closed-loop system, Kp appears alongside integral gain and derivative gain in the PID transfer function. Its effect is practical rather than isolated: tuning Kp changes the system’s step response and must be judged against competing response characteristics. section 8.7

HVAC temperature control

For a heater responding to the difference between actual and desired temperature, proportional action produces a control response based on that error. A step response can then reveal rise time, overshoot, settling time, and steady-state error while Kp is varied or optimized with the other PID parameters. 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 alter 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 Kp through the PID transfer function and response effects, but stops short of a standalone manual tuning procedure.
Examples
Uses HVAC temperature control, a heater step response, response metrics, and Python-based PID parameter optimization.
What you can do after
Evaluate how changing Kp affects rise time, overshoot, settling time, and steady-state error.
How it connects
Connects proportional gain with PID control, integral gain, derivative gain, transfer functions, closed-loop systems, and step response.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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