Figure 2 Figure 1 as the vehicle moves laterally against the direction of the swing. To counter this tendency to swing and to assure stationary and level flight, the vehicle control system is required to dampen the oscillation by controlling the motors (See Figure 4) to oppose any unwanted swinging motion. The Laplace-domain root locus of a simple rate-damping scheme is shown in Figure 1. With rate damping, the naturally- unstable “pendulum” poles can stabilized with a damping ratio of approximately Rate-damping alone does not guarantee robustness to outside disturbance. Proportional and integral feedback, such as shown in the block diagram in Figure 2, allow the vehicle to reject external forces and closely follow the feed-forward control. The notch filter block in Figure 2 has the effect of attracting the two dominant poles closer to the real line and increasing the stability of the system. The simulated response of the system to an external disturbance is shown in Figure 3. With only rate damping, the vehicle would settle at the disturbance trim condition shown in the dashed blue line. With proportional and integral feedback, the vehicle is able to reject the external disturbance and settle back to the stable state in approximately 2 seconds. Control System for AirSTWing Quadrotor A BSTRACT As research into systems of multiple autonomous robots has increased in recent years, interest has grown in airborne robots. This project explores the feasibility of designing a control system for an indoor semi-autonomous quadrotor air vehicle that will serve as a flexible experimental platform. A UTHORS Roman Geykhman (EE '07) Noah Robbin (EE '07) A DVISOR Prof. Daniel Lee (ESE) S PECIAL T HANKS Jim Keller (GRASP) Alex Rattner (MEAM '09) Prof. Vijay Kumar (MEAM) Prof. Jorge Santiago (ESE) D EMO T IMES 10:00 AM 11:00 AM 1:00 PM 2:00 PM 3:00 PM D EMO L OCATION GRASP Laboratory Room L457, 4th Floor, Levine Hall ESE 442 Senior Design Group #14 +x +y Motor 1 Motor 3 Motor 2 Motor 4 Figure 4 The quadrotor configuration consists of two perpendicular sets of propellers, one rotating clockwise (Motors 3 and 4), the other counterclockwise (Motors 1 and 2). In equilibrium, all of the propellers spin at the same velocity, providing uniform thrust about the center vehicle’s of gravity, resulting in zero torque about the vehicle's x- and y-axes. Perturbations from this equilibrium will cause the vehicle to tilt, and to gradually accelerate in the direction of that tilt. Rotations can be executed by lowering the speed on one set of co-rotating propellers (i.e. 1 and 2) while raising the speed on the other set. This results in a net torque about the z-axis as the faster set of propellers encounters more rotational resistance from the air in one direction than the slower set does in the other. In order to achieve a stationary hover it is necessary to control the quadrotor's propellers in such a way that the vehicle will remain level in equilibrium and will be able to recover quickly from external disturbances or sudden maneuvers. The vehicle's dynamics can be modeled by a swinging pendulum. Perturbation of this hovering pendulum will cause a 1 Hz oscillation. With only “open-loop” control, this swinging mode will continue undamped, resulting in uncontrolled behavior +z Ө x Ө y Actuator Dynamics The off-the-shelf brushless electric motors and controllers used for the construction of the test vehicle are designed to operate model airplanes. As such, their dynamic response is not ideal for the rapid actuation required to keep a quadrotor stable. As seen in Figure 4, the step-input response of the motor-propeller combination can be approximately modelled as a single-pole system. A software compensator is implemented inside the PC control loop in order to reduce the propeller settling time to less than ½ second in order to reduce phase loss in the system’s feedback loop. The effect of the propeller dynamics is shown in the root locus plot in Figure 1. Theory of Quadrotor Operation and Stability Excitation To PIC ADC 4 x 50 Hz PWM RS 232 Serial* The vehicle's microcontroller is responsible for collecting data from the onboard sensors and relaying it to the ground computer via an RS- 232 tether.* The ground computer runs the main control loop that computes appropriate control signals for the individual propellers and sends them via the link back to the microcontroller, which sends pulse width modulated (PWM) speed signals directly to the motors. *Serial tether may be replaced with RS-232 to wireless adapter for remote operation Voltage Monitoring to ADC Approx 5A / Motor System Architecture Thunderpower TP4600-4SXL 4.6 A-Hr Battery Onboard PIC24 Microcontroller PC Software Control Loop Spectron SP5000 Dual Axis Inclinometer Castle Creations Phoenix-25 Brushless Motor Controllers HiMax HA2025 Brushless Motors Figure 3