Open loop and closed loop: why feedback?
A controller compares what you wanted with what happened, then acts on the difference.
Identify the target, measured output, error, controller, and physical limit in one feedback loop.
A motor slows when its load changes. To hold a target speed, we need a way to react to what the motor actually does.
First, picture it
Imagine riding a bicycle uphill. If you keep pushing the pedals in exactly the same way, you slow down. If you watch your speed and push harder when it falls, you are using feedback: you measure the result and change your action.
Build the idea step by step
The plant is the physical system we want to control, such as a motor. A sensor measures its output, such as speed. The controller subtracts that measurement from the target to find the error. It uses the error to choose an input, such as voltage. This returning measurement closes the loop. In our motor example, a positive error means the motor is too slow, so a positive proportional gain asks for more voltage.
Read the equations
Error is target minus measured output. A positive error asks the controller to increase the output.
A proportional controller asks for input in proportion to error; the actuator may deliver less if it reaches a limit.
What the symbols mean
- target speed, in radians per second
- measured speed, in radians per second
- speed error, in radians per second
- proportional gain, in volts per radian per second
- time, in seconds
- requested voltage before the actuator limit
The requested voltage and the applied voltage can differ. A motor driver cannot exceed its voltage limit. We use a motor whose speed increases with positive voltage; the correct feedback sign depends on the device.
Both outputs can be displayed. Only the lower path uses measured speed to calculate voltage. The diagram assumes unity measurement feedback and omits load and noise paths for clarity.
A load slows a speed loop
Set the target to 10 radians per second. The sensor reports 8.
With a gain of 2 volts per radian per second, the controller requests 4 volts.
If the actuator can supply only 3 volts, the applied input is 3 volts. Error can remain until the load or limit changes.
More detail and model assumptions
What closes a loop?
In open-loop operation, the command does not depend on the measured output. You might hold a voltage or follow a precomputed schedule. The device can still have a sensor and display a graph: measurement alone does not close the loop. Ask whether that measurement changes the next command.
In a closed loop, the measured output returns to the controller. For unity negative feedback, e=r−y and the controller uses e to calculate its command. A load that slows a motor can therefore change its voltage without a person turning a knob. This is a structural difference, not a promise that every feedback design performs well.
A voltage that worked before the load
For the nominal motor, set the derivatives of current and speed to zero. Mechanical balance gives i=(bω+τL)/Kt; electrical balance gives V=Ri+Keω. Substituting the lab parameters produces V=0.07ω+40τL, with V in volts, ω in rad/s and τL in N·m. With no load, 7 V supports 100 rad/s at equilibrium.
Now apply a persistent 0.04 N·m load at 4 s. A held 7 V supports only (7−40×0.04)/0.07≈77.14 rad/s. Recovering 100 rad/s needs 8.6 V. The guided feedback preset can deliver that voltage within the ±12 V limit; its integrator supplies the lasting correction. These numbers belong to this model and load, not every motor.
Keep reference, disturbance and measurement separate
The reference r states your goal. The physical speed y and its sensor reading need not be identical when noise is present. A shaft load enters the mechanical equation, while measurement noise changes what the controller thinks it saw. The open-loop exercise still plots a target and an error, but neither signal changes its manual voltage.
Compare the two modes from the same starting state, with the same motor, target and load event. Their startup traces can differ because the commands differ. To study load rejection, inspect the voltage and speed around 4 s and afterward, rather than explaining every difference by feedback alone.
Feedback needs authority and a suitable design
If the required voltage exceeds 12 V, feedback cannot supply it. A badly chosen gain, sensor delay or noise may also worsen the response. Open-loop operation can be useful when a repeatable model and known conditions meet the specification; feedforward can anticipate known changes and be combined with feedback. Decide from requirements and uncertainty, not from a label.
An open-loop transfer function is an analysis object
You can operate a closed-loop controller while analyzing the loop transfer L(s)=C(s)P(s). Under linear, unity negative-feedback assumptions and zero initial conditions, Y=P C(R−Y), so Y/R=PC/(1+PC). Bode and Nyquist use L to study the effect of closing the loop. An 'open-loop plot' does not mean the running motor has its feedback switched off.
Connect the example to the lab
Raise the motor's load torque. Open-loop voltage stays fixed and speed falls; a speed controller sees a positive error and increases voltage, until its limit is reached.
Compare open-loop and closed-loop operationMake a prediction before moving a control.
- PREDICTWhen the 4 s load arrives, which voltage reacts to the speed error?
- CHANGE ONE THINGOpen the open/closed-loop guide. Pin the closed-loop run, then switch only to Open loop at 7 V.
- OBSERVECompare speed and applied voltage after 4 s. Then change the target in open loop and check whether voltage changes.
- EXPLAINExplain why one run recovers, identify the required voltage, and state what a 12 V limit can prevent.
Feedback does not erase physical limits. A saturated actuator cannot provide the extra effort the controller asks for.
Check your understanding+
If a load suddenly slows a motor, what changes first in a speed-feedback loop?
The measured output falls; the error grows, then the controller increases its command.Why the next lesson follows
To predict how voltage changes speed, we need a model of the motor's electrical and mechanical parts.