Closed-loop control

Summary¶

A closed-loop control system measures its own output, compares it to a desired value, and uses the difference to correct its input — continuously. An open-loop system applies a fixed input and accepts whatever output results. Drone flight control is impossible without closed-loop feedback: a human pilot cannot execute the thousands of corrections per second needed to keep a multirotor stable. The flight controller closes the loop using gyroscope measurements, running the sense-compare-correct cycle at 8,000 times per second. Without sensors to close the loop, the controller is blind and the drone falls.

Concept¶

The sense-compare-correct cycle¶

Every closed-loop controller follows the same cycle:

1. Sense — measure the current state of the system
2. Compare — find the difference between current state and desired state (the error)
3. Correct — apply a corrective output proportional to the error
4. Repeat

The faster this cycle runs, the more responsive and stable the system. A thermostat runs the cycle every few minutes — acceptable for temperature control, which changes slowly. A drone runs the cycle 8,000 times per second — necessary for attitude control, where disturbances (wind gusts, motor transients) happen in milliseconds.

Why open-loop control fails for multirotors¶

An open-loop multirotor would require the pilot to manually calculate and command each motor's speed every instant. Four motors, each at variable speed, with coupled effects on all three axes simultaneously. Even at 10 corrections per second — the maximum achievable by a human — the drone would be uncontrollable: disturbances would accumulate between corrections until the drone flipped.

Closed-loop control removes this problem. The flight controller measures the actual attitude 8,000 times per second and applies corrections at the same rate. No human involvement required between pilot stick inputs.

What closes the loop¶

The gyroscope is the sensor that closes the loop for attitude control. It measures the actual rotation rate on all three axes — roll rate, pitch rate, yaw rate — and delivers this to the flight controller every 125 µs. The flight controller compares this to the commanded rotation rate (from pilot sticks) and computes the necessary motor corrections.

The accelerometer closes the loop for the level/attitude estimate. The GPS closes the loop for position. Each additional sensor adds another closed loop at a higher level of the control hierarchy. → See [[sensors-fc]].

Sensor dependencies and failure modes¶

The dependency chain is the safety-critical knowledge every operator needs:

• Lose gyroscope: attitude control fails, drone is uncontrollable
• Lose accelerometer: attitude hold fails, GPS modes fail, pilot falls back to rate mode
• Lose GPS: position hold fails, RTH unavailable, pilot falls back to attitude mode
• Lose RC link: failsafe activates (usually RTH if GPS available, or disarm)

A pilot who understands the dependency chain responds correctly to failures. A pilot who does not may fight the wrong problem.

Reference¶

Control hierarchy in Betaflight / ArduPilot¶

Each outer loop feeds setpoints to the inner loop. Failure of an outer-loop sensor drops the control to the next inner level.

Loop rates¶

The inner loop runs the fastest because attitude dynamics are the fastest to diverge. GPS position changes slowly — 10 Hz is adequate.

Procedure¶

Rationale¶

Why this article precedes the PID articles¶

The PID articles describe specific implementations of closed-loop control. This article establishes the concept — what a closed loop is, why it is necessary, and how sensors make it work. A student who reads this article first will understand why the P, I, and D terms exist before encountering the mathematical details of each.

Connections¶

requires: - six-degrees-of-freedom related: - pid-proportional-term - pid-integral-term - pid-derivative-term leads_to: - pid-proportional-term