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Chapter 6

Autopilot Design

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Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 6: Slide 1

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Architecture

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Outline

  • Different Options for Autopilot Design
    • Successive Loop Closure
    • Total Energy Control
    • LQR Control

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 6: Slide 3

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Successive Loop Closure

Open-loop system

Closed-loop system

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SLC: Inner Loop Closed

At frequencies below inner-loop bandwidth, approximate CLTF as 1,

then design middle loop

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SLC: Two Loops Closed

At frequencies below

middle-loop bandwidth,

approximate CLTF as 1,

then design outer loop

Key idea: Each successive loop must be lower in bandwidth� --- typically by a factor of 10 or more

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Lateral-directional Autopilot

Yaw Damper

Roll Control

Course Control

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Roll Autopilot

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Roll Autopilot

  • The book suggests using an integrator on roll in the roll loop to correct for any steady-state error due to disturbances

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  • Our current suggestion is to not have an integrator on inner loops, including the roll loop

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    • Integrators add delay and instability -> not a good idea for inner-most loops

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    • An integrator will be used on the course loop to correct for steady-state errors

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Lateral-directional Autopilot

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Course Hold Loop

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TF Zero Affects Response

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Course Hold Loop

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Yaw Damper

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Lateral Autopilot - Summary

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Lateral Autopilot – In Flight Tuning

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Longitudinal Flight Regimes

Take-off zone

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Altitude Hold Using Commanded Pitch

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Pitch Attitude Hold

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Altitude Hold Using Commanded Pitch

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Altitude from Pitch – Simplified

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Altitude from Pitch Gain Calculations

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Airspeed Hold Using Throttle

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Airspeed from Throttle Gain Calculations

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Longitudinal Autopilot - Summary

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Longitudinal Autopilot – In Flight Tuning

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Python Implementation

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Wrap Function

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PID Loop Implementation

PID continuous time

Taking Laplace transform…

Use bandwidth-limited differentiator to reduce noise

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 6: Slide 29

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PID Loop Implementation

Tustin’s rule or trapezoidal rule:

Integrator:

Differentiator:

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Integrator Anti-wind-up

control before anti-wind-up update

control after anti-wind-up update

is anti-wind-up update

subtracting top two equations

Let

value of control after saturation is applied

solving…

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PID Implementation (Python)

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PID Implementation (Matlab)

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Yaw Damper Implementation

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Yaw Damper Implementation

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Yaw Damper Implementation

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Yaw Damper Implementation Alternative

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Simulation Project

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Outline

  • Successive Loop Closure
  • Total Energy Control
  • LQR Control

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Total Energy Control

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Total Energy Control

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Total Energy Control

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Total Energy Control

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Total Energy Control

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Total Energy Control

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Total Energy Control

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Total Energy Control

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Step in Altitude, Constant Airspeed

Total Energy Control

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Step in Airspeed, Constant Altitude

Total Energy Control

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Step in Altitude and Airspeed

Total Energy Control

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  • Observations
    • TECS seems to work better than successive loop closure.
    • Removes needs for different flight modes.
    • Nonlinear TECS seems to better, but the Ardupilot controller works very well.

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Total Energy Control

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Outline

  • Successive Loop Closure
  • Total Energy Control
  • LQR Control

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LQR Control

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LQR Control

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LQR Control

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LQR Control

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LQR Control

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LQR Control

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LQR Control

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LQR Control

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LQR Control

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Python Code

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 6: Slide 62