# Thrust Control Loop Design for Electric-Powered UAV

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## Abstract

This paper describes a process of designing a thrust control loop for an electric-powered fixed-wing unmanned aerial vehicle equipped with a propeller and a motor. In particular, the modeling method of the thrust system for thrust control is described in detail and the propeller thrust and torque force are modeled using blade element theory. A relation between current and torque of the motor is obtained using an experimental setup. Another relation between current, voltage and angular velocity is also obtained. The electric motor and the propeller dynamics are combined to model the thrust dynamics. The associated trim and linearization equations are derived. Then, the thrust dynamics are coupled with the flight dynamics to allow a proper design for the thrust loop in the flight control. The proposed method is validated by an application to a testbed UAV through simulations and flight test.

## Keywords

Electric-powered aircraft Thrust modeling Thrust control Unmanned aerial vehicle## List of Symbols

- \(\alpha \)
Angle of attack [rad]

- \(\beta \)
Propeller twist angle [rad]

- \(D_\mathrm{prop} \)
Propeller diameter [m]

- \(\mathrm{{d}}L\)
Propeller elemental lift [N]

- \(\mathrm{{d}}D\)
Propeller elemental drag [N]

*i*Current [A]

- \(i_0 \)
No-load current [A]

- \(I_\mathrm{rotor} \)
Rotor inertia

- \(I_\mathrm{prop} \)
Propeller inertia

*J*Advance ratio [-]

- \(K_V \)
Velocity constant [(rad/s)/V]

- \(K_\mathrm{bemf} \)
Back electromotive force constant [V/(rad/s)]

- \(K_\mathrm{Q} \)
Torque constant [N m/A]

- \(k_\mathrm{T} \)
Thrust coefficient [-]

- \(k_\mathrm{Q} \)
Torque coefficient [-]

- \(a_\mathrm{T} \)
Second order coefficient of approximated thrust coefficient

- \(b_\mathrm{T} \)
First order coefficient of approximated thrust coefficient

- \(c_\mathrm{T} \)
Zero order coefficient of approximated thrust coefficient

- \(a_\mathrm{Q} \)
Second order coefficient of approximated torque coefficient

- \(b_\mathrm{Q} \)
First order coefficient of approximated torque coefficient

- \(c_\mathrm{Q} \)
Zero order coefficient of approximated torque coefficient

*L*Inductance

*n*Revolution per second [RPS]

*P*Power

- \(Q_\mathrm{motor} \)
Motor torque [N m]

- \(Q_\mathrm{prop} \)
Propeller torque [N m]

- \(R_\mathrm{motor} \)
Estimated motor resistance [Ohm]

- \(R_\Omega \)
Measured motor resistance [Ohm]

- \(\rho \)
Air density [\({m^{3}}/{kg}\) ]

- \(T_\mathrm{prop} \)
Propeller thrust [N]

- \(\upsilon \)
Viscous friction coefficient [N\(\cdot \)m/(rad/s)]

- \(V_\infty \)
Forward air speed [m/s]

- \(\omega \)
Angular velocity [rad/s]

- \(\omega _\mathrm{prop} \)
Propeller angular velocity [rad/s]

- \(\beta _\mathrm{gear} \)
Gear ratio

- \(V_{in} \)
Input voltage [V]

- \(\omega _{co} \)
Crossover frequency [rad/s]

- \(\mathrm{PM}\)
Phase margin [\(^{\circ }\)]

- \(\mathrm{GM}\)
Gain margin [-]

- \(\theta \)
Pitch angle [rad]

## Notes

### Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (KRF) funded by the Ministry of Education (NRF-2015R1D1A1A01060574).

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