Feedback Control Fundamentals

Feedback control compares what a system is doing with what it should do, then commands the actuator to reduce the error. It is the reason a servo reaches position, a heater holds temperature, and a robot balances disturbances.

Learning Objectives

By the end of this lesson, you should be able to define setpoint, feedback, error, actuator, plant, disturbance, stability, steady-state error, overshoot, and bandwidth.

Closed-Loop Blocks

flowchart LR SP["Setpoint"] --> SUM["Compare"] --> C["Controller"] --> A["Actuator"] --> P["Plant"] --> Y["Output"] Y --> S["Sensor"] --> SUM D["Disturbance"] --> P

The controller acts on error:

$$
e(t)=r(t)-y(t)
$$

where r(t) is the setpoint and y(t) is the measured output.

Open Loop vs Closed Loop

Open-loop control commands an actuator without measuring the result. Closed-loop control measures the result and corrects errors. Closed loop improves accuracy and disturbance rejection, but it can oscillate if the controller is too aggressive or the sensor is delayed.

Time Response Terms

Term	Meaning
Rise time	how quickly output approaches target
Overshoot	how far output exceeds target
Settling time	time to remain within a tolerance band
Steady-state error	final difference after transients
Bandwidth	frequency range the loop can follow
Stability margin	tolerance before oscillation

Sensor and Actuator Limits

Control quality is limited by hardware. Deadband, backlash, saturation, quantization, sample delay, friction, and noise all affect the loop. A perfect equation cannot fix a poor sensor location or an undersized actuator.

Practical Design Rules

Measure the variable you actually need to control.
Sample fast enough for the plant dynamics.
Keep actuator commands within safe limits.
Add limits and fault states before tuning aggressively.
Plot setpoint, feedback, error, and actuator command during tests.

Common Mistakes

Tuning by feel without recording response data.
Ignoring delay and filtering phase lag.
Letting the controller command impossible actuator output.
Measuring the wrong point in the mechanism.
Assuming closed loop automatically means safe.

Summary

Feedback control reduces error by measuring output and correcting actuator command. Stability and performance depend on the controller, sensor, actuator, plant dynamics, sampling, delay, and mechanical realities.

Mind Map

mindmap root((Feedback Control)) Core concept Compare setpoint and output Error drives actuator Disturbance rejected Formulas Error equals reference minus output Bandwidth limits tracking Saturation clips command Applications Servo position Temperature Speed control Robotics Design rules Measure controlled variable Sample fast enough Limit actuator Record response Practical checks Overshoot Settling time Steady error Noise and delay Common mistakes Too much gain Wrong sensor point No saturation handling Tuning without plots