Open Loop

An open-loop system acts on a command without measuring the result. Learn how it works, its gain and calibration, why disturbances and parameter changes cause errors, and when open loop is the right choice.

In an open-loop system the controller sends a command based only on the input — a timer, a setting or a lookup table — and never checks what actually happened. A toaster heats for a set time regardless of how brown the bread gets; a stepper motor moves a set number of steps without confirming position.

Open loop is simple, cheap and can't go unstable through feedback, but it is only as accurate as its calibration and blind to disturbances.

An analogy

Open loop is like throwing a ball at a target with your eyes closed after one practice throw: fine if nothing changes, wrong the moment the wind picks up.

Structure

Reference → controller → actuator → plant → output. No sensor feeds the output back. Examples: traffic lights on fixed timers, a washing machine's programme, a microwave's timer, a fan's speed switch.

Sensitivity to changes

Because the controller assumes a model, any change in the plant appears fully in the output: a 10 % gain drop gives a 10 % output error (sensitivity = 1). Unmeasured disturbances (load torque, ambient temperature) also pass straight through.

When open loop is right

Use open loop when the plant is well known and stable, disturbances are small, feedback sensors are expensive or impossible, or accuracy needs are modest. Stepper-motor positioning, feed-forward in drives and inkjet dosing all rely on it.

Feed-forward: open loop done well

High-performance systems combine a feed-forward path (an inverse model computing the command needed for a known reference or a measured disturbance) with feedback for residual errors. Feed-forward gives speed without destabilising the loop; feedback supplies accuracy.

Formulas

• Open-loop output: y = G · C · r + d
• Calibration: C = 1 / G_nominal → y = (G_actual / G_nominal) · r
• Relative error from gain drift: Δy / y = ΔG / G (sensitivity = 1)

Worked example: Motor speed by calibration

Given: Nominal gain 100 rpm/V; Desired speed 1500 rpm; Actual gain under load drops to 90 rpm/V

Find: Command voltage and actual speed.

• Command = 1500/100 = 15 V
• Actual = 15 × 90 = 1350 rpm
• Error = 150 rpm = 10 %

Answer: 15 V gives 1350 rpm — a 10 % error with no way to correct it

Worked example: Toaster timing

Given: Timer set for 2 min; Bread starts frozen instead of room temperature

Find: What happens?

• Energy delivered is fixed by time, not by browning
• Frozen bread needs more energy → under-toasted
• The controller never senses the result

Answer: Under-toasted — a disturbance the open loop can't see

Common mistakes

• Wrong: Expecting an open-loop system to reject disturbances. — Right: Only feedback (or measured-disturbance feed-forward) can compensate disturbances.
• Wrong: Calling a system closed loop because it has a sensor. — Right: The sensor must feed back into the control action for the loop to be closed.

Applications

• Stepper-motor positioning: 3D printers move by counting steps — open loop that works because load torque stays within the motor's capability.
• Irrigation timers: Sprinklers run for fixed times; soil-moisture feedback turns them into closed-loop systems.
• Feed-forward in drives: Motor drives add inertia and friction feed-forward terms so the feedback loop only corrects small residuals.

Key takeaways

• Open loop acts without measuring the output.
• Output error equals the plant model error (sensitivity = 1).
• Cheap and inherently stable for stable plants, but blind to disturbances.
• Best used as feed-forward alongside feedback.

Going further

• Inverse-model feed-forward limits: A perfect inverse is impossible if the plant has delay or right-half-plane zeros; the feed-forward filter must be causal and stable, which bounds achievable tracking speed.
• Iterative learning control: For repetitive tasks, ILC updates the open-loop command trial by trial using the previous error, approaching perfect tracking of a repeated trajectory.
• Open-loop stability: Open loop can't be destabilised by feedback, but an open-loop-unstable plant (a balancing robot, an inverted pendulum) can only be operated with feedback.