LINEAR CONTROL SYSTEMS: QUADROTOR MOTOR FAILURE RECOVERY
Coordinate systems
Non-linear and linearized quadcopter dynamics for six position and orientation states
LQR performance without motor failure
LQR and MRAC performance with 50% thrust failure in one motor
LQR and MRAC performance with 70% thrust failure in one motor. Note that while LQR fails, MRAC recovers easily
Objectives:
- Design a baseline LQR controller to fly the quadrotor without any motor failure.
- Design a MRAC to fly the quadrotor with sudden 50% lost of thrust in one motor.
Time Frame:
Two weeks
Skills Demonstrated:
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Control systems
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Python programming
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Webots simulation software
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UAV dynamics
Design:
For a linear control systems course, applied understanding of adaptive control theory to augment a LQR-based MPC controller and test its effectiveness in the event of a single quadrotor motor experiencing a 50% and higher loss of thrust. In the Webots simulation, used a DJITM Mavic 2 Pro drone. For the system dynamics, first assumed the quadcopter to be a rigid body and operating at low speeds. Then, since the quadcopter operates close to the hover position, I was able to apply the small angle approximation and also neglect higher-order terms to linearize the system. In the linearized dynamics, the change in U1 represents the collective thrust, and U2, U3, and U4 are the roll, pitch, and yaw input torques. Applying this model into an LQR controller with baseline feedback gains works sufficiently well until the presence of model uncertainty is introduced, such as when a motor fails. Then, it becomes clear that an adaptive controller is required to stabilize the drone.
Results:
Determined an adaptive control input to the MRAC to effectively augment a baseline LQR controller. The LQR controller could recover with up to 67% loss of thrust in one motor, while the MRAC was able to recover for up to 78% loss of thrust in one motor.
Simulation of controllers with 70% thrust failure in one motor occurring after seven seconds. MRAC performance is on the left and LQR performance is on the right