🎯 Feedback & Control Systems

Open-Loop vs. Closed-Loop Control

Open-loop control: The controller issues commands without checking whether the desired outcome was achieved. Example: a washing machine timer — it runs for a set time regardless of how clean the clothes are.

Closed-loop (feedback) control: The controller measures the output, compares it to the desired setpoint, and adjusts its command based on the error. Example: a thermostat — it keeps measuring temperature and turning the heater on/off to maintain the setpoint.

PID Controller

The most widely used feedback controller is the PID controller. It computes a control signal from three terms:

• Proportional (P): Output is proportional to the current error. Large Kp = fast response but may oscillate.
• Integral (I): Output is proportional to the accumulated error over time. Eliminates steady-state error.
• Derivative (D): Output is proportional to the rate of change of error. Reduces overshoot and improves stability.

u(t) = Kp·e(t) + Ki·∫e(t)dt + Kd·de/dt

Performance Metrics

• Rise time: Time to go from 10% to 90% of the setpoint
• Overshoot: Maximum amount the output exceeds the setpoint (expressed as %)
• Settling time: Time until output stays within ±2% of setpoint
• Steady-state error: Difference between setpoint and final value