Understand proportional, integral and derivative control through the signals inside a real closed loop.
u(t)=Kpe(t)+Ki∫e(t)dt+Kddtde(t)
A PID controller repeatedly compares a desired setpoint with a measured process value. It combines the present error, accumulated error and rate of change into a command for the actuator.
01
The feedback loop
The controller is only one part of the system. The actuator applies its command to a plant, a sensor measures the result, and that measurement returns to the controller. Delay, saturation, noise and sample time all change what tuning can achieve.
SIGNAL VIEW 01
P, I and D leave different fingerprints
The same unit error creates an immediate proportional push, a growing integral contribution, and a short derivative pulse.
ProportionalIntegralDerivative
READ THE PLOTP reacts now · I remembers · D anticipates movement
02
Three different jobs
Proportional action supplies immediate correction. Integral action removes persistent offset. Derivative action adds damping by reacting to movement, but it must be filtered because measurements are never perfectly clean.
RESPONSE VIEW 02
Three tunings, three recognizable shapes
Low gains are calm but slow, a balanced loop settles quickly, and an aggressive loop trades speed for overshoot and ringing.
SetpointToo softBalancedAggressive
READ THE PLOTThe fastest rise is not automatically the best loop
03
A tuning is a trade-off
A faster rise is not automatically better. A useful tuning balances tracking, disturbance rejection, overshoot, actuator effort, robustness and measurement sensitivity for the actual plant.
LOOP VIEW 03
The controller acts before the plant catches up
After a setpoint step, controller output moves first. The process value follows the plant dynamics while the error closes toward zero.
SetpointController outputProcess valueError
READ THE PLOTRead controller output and process value together