Control

Computer Organization & Embedded System — Real-Time Operating and Control System, NEC licence examination syllabus (Nepal Engineering Council).

Control: from ON-OFF to PID

The three-term controller behind almost every real control system.

ON-OFF control: simplest form — output is either fully on or fully off based on a threshold (e.g., a basic home thermostat). Causes oscillation around the setpoint.

PID Controller

From cruise control in a car to the temperature stability in a 3D printer's hotend, this exact formula is quietly running underneath.

Output = Kp·e(t) + Ki·∫e(t)dt + Kd·(de/dt) e(t) = error = setpoint − measured value

🎛️ The Three Terms

P (Proportional)Reacts to the CURRENT error — bigger error, bigger correction. Alone, it usually leaves a steady-state error.

I (Integral)Reacts to ACCUMULATED past error — eliminates steady-state error over time, but can cause overshoot if too aggressive.

D (Derivative)Reacts to how FAST the error is changing — helps dampen oscillation and predict overshoot before it happens.

💡 One-liner exam favourite: "What does each PID term correct for?" → P=present error, I=accumulated past error, D=predicted future error (rate of change).

Why proportional control alone is never enough

The chapter says P alone "usually leaves a steady-state error". That is true, and the reason is worth seeing because it explains the whole controller.

A proportional controller produces output only while there is error. If the error reached zero the output would be zero too — and with no output, nothing holds the system at the setpoint, so it drifts back. The controller therefore settles at whatever error is large enough to generate the output the system needs.

Setpoint = 10, simple system, proportional control only: Kp = 1 settles at 5.00 error 5.000 Kp = 10 settles at 9.09 error 0.909 Kp = 100 settles at 9.90 error 0.099 More gain shrinks the error but NEVER removes it. Zero error would mean zero output, and zero output cannot sustain the setpoint.

💡 So the integral term is not a refinement, it is a necessity. I accumulates error over time, so even a tiny persistent error keeps growing its contribution until the output is enough to close the gap entirely — producing a non-zero output at zero error, which P mathematically cannot do.

What each term costs

🎛️ The trade-off in each gain

Raise KpFaster response and smaller steady-state error — but too high and the system overshoots and oscillates.

Raise KiRemoves steady-state error — but the accumulated history makes the system sluggish to reverse, and can cause integral windup when the output is saturated.

Raise KdDamps overshoot by reacting to the RATE of change, effectively anticipating — but it amplifies measurement noise, since noise has a large derivative.

Integral windup is the failure worth naming. If the output is already at maximum and the error persists, the integral term keeps accumulating even though more output is impossible. When the error finally reverses, that accumulated total must be unwound before the controller responds at all — producing a large overshoot long after the disturbance ended.

💡 Why ON-OFF control oscillates is the same reasoning in miniature: with only two output levels there is no setting that exactly balances the system, so it must alternate around the setpoint rather than settle on it. A PID controller's continuous output is what makes settling possible.

Syllabus points

Controller basics; ON-OFF control
PID controller (P, I, D actions)

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