Unit
- Open-loop control: The system operates without feedback, relying on a predefined sequence. The controller sends a signal to the actuator based on input, but does not monitor the output. Examples include traffic light timers and simple washing machine cycles. Accuracy depends entirely on calibration and absence of disturbances.
- Closed-loop control: Feedback from the output is compared to the reference input, generating an error signal that drives the controller. This self-correcting mechanism compensates for disturbances and model inaccuracies. Common in thermostats, cruise control, and industrial robotics.
- Transfer function representation: In the Laplace domain, open-loop systems are represented by a single forward path transfer function G(s). Closed-loop systems include a feedback path H(s), yielding the overall transfer function G(s) / (1 + G(s)H(s)). This compact form enables stability analysis.
- Sensitivity and robustness: Closed-loop systems reduce sensitivity to parameter variations and external disturbances. For example, if a motor's gain changes with temperature, the feedback loop adjusts the control signal to maintain desired output.
- Steady-state accuracy: Closed-loop systems can achieve near-zero steady-state error for certain input types, especially with integral action. Open-loop systems drift over time and require recalibration.
- Stability trade-off: Closing the loop introduces the possibility of instability if the feedback adds too much phase lag or gain. The design must balance performance with a stability margin.
- Actuator and sensor dynamics: Both open and closed-loop systems rely on actuators (motors, valves) and sensors (encoders, thermocouples). Delays or nonlinearities in these components affect overall performance.
- Practical example: A simple toaster uses open-loop timing; a modern oven uses a closed-loop thermostat with a proportional controller to maintain temperature within a band.
- Disturbance rejection: Closed-loop systems actively reject external disturbances by comparing actual output to the reference and adjusting the control signal accordingly. For example, in a speed controller, if a load torque suddenly increases, the feedback loop detects the speed drop, computes the error, and increases motor current to restore the setpoint. Open-loop systems lack this corrective action and will deviate permanently.
- Transient response shaping: Feedback allows designers to shape the system's transient response by tuning controller gains. Increasing proportional gain reduces rise time but may increase overshoot. Derivative action dampens oscillations, while integral action eliminates steady-state error. Engineers use root locus or frequency response methods to balance these conflicting requirements.
- Bandwidth and speed of response: Closed-loop control can extend the system's bandwidth beyond the open-loop plant, enabling faster tracking of command changes. However, higher bandwidth also amplifies sensor noise and may excite structural resonances. Designers must select a bandwidth that achieves adequate speed while maintaining stability and noise rejection.
- Noise amplification in feedback: A notable disadvantage of closed-loop systems is that sensor noise enters the controller and can propagate to the actuator. High controller gains amplify this noise, causing erratic actuator movements or chatter. Low-pass filters are commonly added to smooth the measurement, but they introduce phase lag that reduces phase margin and can lead to instability.
Code Example
MATLAB
% Open-loop transfer function
G = tf(1, [1 10 20])
% Closed-loop with unity feedback
T = feedback(G, 1)
% Step response comparison
step(G, 'b--', T, 'r-', 5)
legend('Open-loop', 'Closed-loop')
grid onThe code defines a second-order open-loop system and then closes the loop with unity feedback. The step response plot shows that the closed-loop system reaches steady state faster and with reduced overshoot compared to the open-loop system.
Quick Revision
- Open-loop control lacks feedback; closed-loop uses error correction.
- Closed-loop systems reduce sensitivity to disturbances and parameter changes.
- Transfer functions model both configurations using block diagrams.
- Closed-loop systems can become unstable; proper design ensures adequate margins.