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Control Systems: Feedback Loops
Thermostats, Cruise Control, and Error Signals
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Control systems are used to make machines and processes behave in a desired way. They appear in cruise control, room thermostats, robot arms, aircraft autopilots, and factory automation. The main idea is to compare what you want with what is actually happening, then use that difference to make corrections. This matters because real systems face disturbances, delays, and changing conditions.
A feedback loop connects sensors, controllers, and actuators so the system can continuously adjust itself. In a closed loop, the output is measured and fed back to the controller, which reduces error between the setpoint and the measured value. Engineers often model these systems with block diagrams, transfer functions, and time response graphs. Good control design balances accuracy, speed, stability, and robustness rather than maximizing only one feature.
Key Facts
- Error signal: e(t) = r(t) - y(t), where r(t) is the setpoint and y(t) is the output.
- Open-loop systems do not use output feedback, while closed-loop systems use feedback to correct error.
- For a proportional controller, control effort is u(t) = Kp e(t).
- For a PID controller, u(t) = Kp e(t) + Ki integral of e(t) dt + Kd de(t)/dt.
- A common closed-loop transfer function is T(s) = G(s) / (1 + G(s)H(s)).
- Key performance measures include rise time, settling time, overshoot, steady-state error, and stability.
Vocabulary
- Setpoint
- The setpoint is the desired target value that the control system tries to achieve.
- Feedback
- Feedback is information about the actual output that is sent back to the controller for comparison.
- Controller
- A controller is the part of the system that decides how to adjust the input based on the error.
- Actuator
- An actuator is a device that converts the controller signal into physical action, such as motion or force.
- Stability
- Stability means the system response stays bounded and eventually settles instead of growing without limit.
Common Mistakes to Avoid
- Confusing open-loop and closed-loop control, which is wrong because only closed-loop systems measure the output and use it to reduce error.
- Assuming more gain always improves performance, which is wrong because excessive gain can cause oscillation, overshoot, or instability.
- Ignoring sensor dynamics or delay, which is wrong because real feedback signals are not instant and can strongly affect stability and response speed.
- Treating zero steady-state error as the only design goal, which is wrong because a system can be accurate in the end but still be too slow or too unstable during the response.
Practice Questions
- 1 A temperature controller has setpoint r = 75 degrees C and measured output y = 68 degrees C. Find the error e = r - y. If Kp = 4, find the proportional control effort u = Kp e.
- 2 A unity-feedback system has forward transfer function G(s) = 8. Use T(s) = G(s) / (1 + G(s)H(s)) with H(s) = 1 to find the closed-loop gain.
- 3 A robot arm reaches its target quickly but oscillates around the final position for several seconds. Explain whether this suggests a stability or tuning problem, and describe one controller change that could reduce the oscillation.