System Identification (SysID)

Executive Summary

System Identification (SysID) is an engineering method to build a mathematical model of a physical system by stimulating it with known inputs and measuring the output.

ArduPilot's System ID Mode injects a "Chirp" signal (sweeping frequency sine wave) into the control loops. By analyzing the vehicle's response (Gyro/Accel) compared to the input (Chirp), we can generate Bode Plots to determine the system's bandwidth, phase margin, and optimal PID gains.

Theory & Concepts

1. The Chirp Signal

The "Chirp" is a sinusoidal signal that sweeps from a low frequency to a high frequency over a set duration.

• Start Frequency (f_start): Low frequency to test steady-state response.
• Stop Frequency (f_stop): High frequency (typically 20-40Hz) to test high-speed dynamics and noise rejection.
• Amplitude: The magnitude of the disturbance. It must be large enough to overcome friction/stiction but small enough to prevent the drone from flipping over.

2. Frequency Response Analysis (Bode Plot)

The data from the Chirp is used to generate a Bode Plot, which shows the system's gain and phase lag across the frequency spectrum.

• Gain Margin: How much gain can be added before the system becomes unstable.
• Phase Margin: How much delay (lag) the system can tolerate.
• Bandwidth: The frequency where the system can no longer track the input.

Codebase Investigation

1. The Mode Logic: ModeSystemId::run()

Located in ArduCopter/mode_systemid.cpp.

• It generates the waveform:

  waveform_sample = chirp_input.update(waveform_time - SYSTEM_ID_DELAY, waveform_magnitude);
  

• It adds this sample to the target based on SID_AXIS. For example, if SID_AXIS = 7 (Rate Roll):

  attitude_control->rate_bf_roll_sysid(radians(waveform_sample));
  

2. Logging

Crucially, SysID logs high-rate data specifically for analysis tools.

• SIDD Log Message: Contains Time, Input Value, Current Frequency, and Gyro/Accel response.
• PID Logs: The standard PID logs are also critical for verifying tracking.

Source Code Reference

• Mode Implementation: ArduCopter/mode_systemid.cpp
• Chirp Generator: libraries/AP_Math/control.cpp (See Chirp class).

Practical Guide: Running a SysID Flight

1. Safety First

• Space: You need a large, open area. The drone will drift during the test.
• AltHold: SysID usually runs in a mode similar to Althold. You control throttle; the computer controls attitude (with the chirp overlaid).

2. Configuration

• SID_AXIS: Start with 0 (None) to get to the field. Set to 1 (Input Roll) or 2 (Input Pitch) for initial tuning.
• SID_MAGNITUDE: Start small. 5 degrees for angle, 50 deg/s for rate.
• SID_F_START / SID_F_STOP: 0.5Hz to 20Hz is standard for large quads.

3. The Procedure

1. Take off in Loiter/AltHold.
2. Switch to System ID Mode.
3. Wait. The drone will pause (Fade In), then start oscillating.
4. Do not touch the sticks unless it drifts too far. Correcting the drift ruins the data (adds external inputs).
5. Wait for the chirp to finish (Fade Out).
6. Land and analyze the logs.