Systems and methods for open-loop control of a brushless motor

1. A method comprising:

receiving data representing a target rotational position of an output shaft of a brushless motor configured to control a rotational position of the output shaft with continuous resolution;

determining a plurality of control signals corresponding to the target rotational position of the output shaft, wherein determining the plurality of control signals comprises:

determining a magnitude and a polarity of a control signal of the plurality of control signals based on an equation K[sin(θ+φ)]=V, wherein K represents a constant, θ represents a rotational position of the output shaft with respect to a reference rotational position of the output shaft, φ represents a phase constant, and V represents the magnitude and the polarity of the control signal; and

determining a pulse width of a control signal of the plurality of control signals and a state of a bridge circuit, wherein the pulse width of the control signal determines a magnitude of a voltage across a winding of the brushless motor and the state of the bridge circuit determines a polarity of the voltage across the winding of the brushless motor;

rotating the output shaft of the brushless motor to the target rotational position by applying the plurality of control signals to the brushless motor without using a feedback signal from a sensor indicating an actual rotational position of the output shaft; and

holding the output shaft at the target rotational position by applying a second set of control signals.

2. The method of claim 1 , wherein determining the plurality of control signals further comprises:

determining a magnitude and a polarity of a second control signal of the plurality of control signals based on an equation K[sin(θ−120°)]=V B , wherein V B represents the magnitude and the polarity of the second control signal; and

determining a magnitude and a polarity of a third control signal of the plurality of control signals based on an equation K[sin(θ−240°)]=V C , wherein V C represents the magnitude and the polarity of the third control signal.

3. The method of claim 1 , wherein determining the plurality of control signals comprises:

determining a pulse width of a second control signal of the plurality of control signals and a state of a second bridge circuit, wherein the pulse width of the second control signal determines a magnitude of a voltage across a second winding of the brushless motor and the state of the second bridge circuit determines a polarity of the voltage across the second winding of the brushless motor; and

determining a pulse width of a third control signal of the plurality of control signals and a state of a third bridge circuit, wherein the pulse width of the third control signal determines a magnitude of a voltage across a third winding of the brushless motor and the state of the third bridge circuit determines a polarity of the voltage across the third winding of the brushless motor.

4. A system comprising:

a brushless motor comprising an output shaft; and

a control module configured to (i) determine a plurality of control signals corresponding to a target rotational position of the output shaft, wherein the control module is configured to determine (a) a magnitude and a polarity of a control signal of the plurality of control signals based on an equation K[sin(θ+φ)]=V, wherein K represents a constant, θ represents a rotational position of the output shaft with respect to a reference rotational position of the output shaft, φ represents a phase constant, and V represents the magnitude and the polarity of the control signal and (b) a pulse width of a control signal of the plurality of control signals and a state of a bridge circuit, wherein the pulse width of the control signal determines a magnitude of a voltage across a winding of the brushless motor and the state of the bridge circuit determines a polarity of the voltage across the winding of the brushless motor, (ii) rotate the output shaft to the target rotational position by applying the plurality of control signals to the brushless motor without using a feedback signal from a sensor indicating an actual rotational position of the output shaft, and (iii) hold the output shaft at the target rotational position by applying a second set of control signals.

5. The system of claim 4 , wherein the brushless motor is configured to change at least one of (i) a position of a control surface of an aircraft via the output shaft, (ii) a position of a control surface of a boat via the output shaft, or (iii) a steering position of a car via the output shaft.

6. The system of claim 5 , wherein the control surface is coupled to the output shaft via a direct drive mechanism.

7. The system of claim 4 , further comprising:

an inertial measurement unit (IMU) configured to provide the control module with data representing at least one of (i) an acceleration of an aircraft, (ii) a roll, pitch, or yaw of the aircraft, and (iii) a rate of change in the roll, pitch, or yaw of the aircraft.

8. The system of claim 4 , wherein the bridge circuit is electrically coupled to a winding of the brushless motor and is configured to change a time-average voltage across the winding.

9. A system comprising:

an inertial measurement unit configured to measure an attitude of an aircraft, wherein the aircraft comprises a brushless motor configured to rotate an output shaft to move a control surface of the aircraft; and

control circuitry configured to:

receive data representing a desired attitude of the aircraft;

determine a plurality of control signals corresponding to a target rotational position of the output shaft, wherein determining the plurality of control signals comprises determining a pulse width of a control signal of the plurality of control signals and a state of a bridge circuit, wherein the pulse width of the control signal determines a magnitude of a voltage across a winding of the brushless motor and the state of the bridge circuit determines a polarity of the voltage across the winding of the brushless motor;

rotate the output shaft to the target rotational position by applying the plurality of control signals to the brushless motor without using a feedback signal from a sensor indicating an actual rotational position of the output shaft, and thereby cause the attitude of the aircraft to converge toward the desired attitude;

hold the output shaft at the target rotational position by applying a second set of control signals;

determine an attitude error between the measured attitude of the aircraft and the desired attitude of the aircraft;

calculate a position error between the target rotational position of the output shaft and an actual rotational position of the output shaft based on the attitude error; and

rotate the output shaft toward the target rotational position based on the position error.