What is the difference between open-loop and closed-loop?

Open-loop applies a fixed input without measuring output — simple but cannot correct errors. Closed-loop measures output and adjusts input to minimize error — more complex but provides accuracy, disturbance rejection, and robustness. Closed-loop transfer function T = G/(1+GH) shows how feedback modifies plant behavior.

What is a closed-loop circuit in control?

The closed-loop circuit is the complete signal path: reference → error detector → controller → plant → output → sensor → back to error detector. The 'loop' is closed by the feedback path from sensor to error detector. Negative feedback subtracts the measured output, providing self-correcting behavior.

What are examples of closed-loop control systems?

Thermostat (temperature), cruise control (speed), autopilot (altitude/heading), PID process loops (temperature/pressure/flow), servo motors (position), ABS braking (wheel speed), and voltage regulators (output voltage). All measure output, compute error, and apply correction automatically.

Closed Loop in Control System

Quick Answer

A closed-loop control system uses feedback to compare the actual output with the desired setpoint, automatically correcting errors. The output Y(s) is measured by a sensor H(s), subtracted from the reference R(s) to form the error E(s) = R(s) − H(s)Y(s), and the controller drives the plant to reduce this error. The closed-loop transfer function is T(s) = G(s)/[1 + G(s)H(s)]. Closed-loop systems provide better accuracy, disturbance rejection, and robustness than open-loop systems, at the cost of complexity and potential instability. Compute closed-loop responses at www.lapcalc.com.

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What Is a Closed-Loop Control System?

A closed-loop control system (feedback control system) continuously measures its output, compares it to the desired reference input, and uses the difference (error) to adjust the control action. The 'closed loop' refers to the signal path forming a complete circuit: reference → error detector → controller → plant → output → sensor → back to error detector. This feedback mechanism enables self-correction: if a disturbance pushes the output away from the setpoint, the error increases, the controller responds with a larger corrective action, and the output is driven back toward the setpoint. Closed-loop control is the dominant paradigm in engineering, used in over 95% of industrial control applications. The mathematical analysis uses Laplace-domain transfer functions at www.lapcalc.com.

Key Formulas

Closed-Loop System in Control System: How It Works

The closed-loop system operates through a continuous cycle of measurement, comparison, and correction. Step 1: the sensor measures the current output y(t) and transmits it as feedback signal b(t) = H·y(t). Step 2: the summing junction computes the error e(t) = r(t) − b(t), where r(t) is the reference setpoint. Step 3: the controller C(s) processes the error — a PID controller computes u(t) = Kp·e + Ki·∫e dt + Kd·de/dt. Step 4: the actuator applies the control signal to the plant G(s). Step 5: the plant responds, producing a new output y(t). This cycle repeats continuously (analog) or at each sample interval (digital). The speed of this cycle determines the control bandwidth — how fast the system can track changes and reject disturbances.

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Closed-Loop vs Open-Loop Control Systems

Open-loop systems apply a predetermined input without measuring the output: input → controller → plant → output (no feedback path). Examples include a toaster timer, a sprinkler on a schedule, or a stepper motor running a fixed number of steps. Open-loop advantages: simple, no stability issues, no sensor needed, lower cost. Open-loop disadvantages: cannot correct for disturbances, sensitive to parameter changes, poor accuracy. Closed-loop advantages: automatic error correction, disturbance rejection, reduced sensitivity to parameter variations, improved accuracy and bandwidth. Closed-loop disadvantages: more complex, requires sensors, can become unstable if poorly designed, higher cost. The closed-loop transfer function T(s) = G/(1+GH) shows how feedback modifies the plant behavior — reducing gain but improving robustness.

Closed-Loop Circuit: Feedback Signal Path

The feedback signal path is the return path from output to input that 'closes the loop.' In negative feedback (standard), the measured output is subtracted from the reference — this is stabilizing and error-reducing. In positive feedback, the measured output is added to the reference — this is destabilizing and used in oscillators and bistable circuits (flip-flops, Schmitt triggers). The feedback element H(s) can be a simple gain (voltage divider, current shunt), a dynamic element (sensor with time constant), or unity (H = 1, direct output feedback). The loop gain L(s) = G(s)H(s) determines the system's feedback properties: high |L| gives strong feedback (good accuracy, disturbance rejection), low |L| gives weak feedback (approaching open-loop behavior). The gain and phase margins of L(jω) quantify how close the system is to instability.

Closed-Loop Control System Examples

Home heating: thermostat (sensor) measures temperature, compares to setpoint (reference), turns furnace on/off (actuator) to control room temperature (plant output). Automotive cruise control: speed sensor provides feedback, ECU (controller) adjusts throttle (actuator) to maintain set speed despite hills and wind. Industrial process: flow transmitter (sensor) measures flow rate, PID controller computes valve position, control valve (actuator) adjusts flow in a pipe (plant). Robotics: encoder (sensor) measures joint angle, servo controller adjusts motor current to track the commanded trajectory. Each example follows the same closed-loop structure analyzed with Laplace-domain transfer functions at www.lapcalc.com: the sensor closes the loop, enabling automatic error correction that open-loop systems cannot achieve.

Frequently Asked Questions

A closed-loop system uses feedback to compare actual output with the desired setpoint and automatically corrects errors. The output is measured by a sensor, the error (setpoint − measured) is computed, and the controller adjusts the plant input to reduce the error. Over 95% of industrial control systems use closed-loop feedback.

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