Transcript Control System for AirSTWing Quadrotor

Control System for AirSTWing Quadrotor
Theory of Quadrotor Operation and Stability
ABSTRACT
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.
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
+x
+z
Motor 1
Motor 3
Өx
+y
Өy
Motor 4
Motor 2
AUTHORS
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 naturallyunstable “pendulum” poles can stabilized with a damping ratio of
approximately 0.25.
Roman Geykhman (EE '07)
Noah Robbin (EE '07)
System Architecture
ADVISOR
Prof. Daniel Lee (ESE)
Jim Keller (GRASP)
Alex Rattner (MEAM '09)
Prof. Vijay Kumar (MEAM)
Prof. Jorge Santiago (ESE)
DEMO TIMES
10:00 AM
11:00 AM
1:00 PM
2:00 PM
3:00 PM
DEMO LOCATION
GRASP Laboratory
Room L457, 4th Floor,
Levine Hall
ESE 442 Senior Design
Group #14
Spectron SP5000
Dual Axis Inclinometer
To PIC ADC
Onboard PIC24
Microcontroller
Castle Creations Phoenix-25
Brushless Motor Controllers
HiMax HA2025 Brushless Motors
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.
RS 232 Serial*
4 x 50 Hz PWM
Approx 5A / Motor
Thunderpower TP4600-4SXL
4.6 A-Hr Battery
Voltage Monitoring to ADC
SPECIAL THANKS
Excitation
Figure 1
PC Software
Control Loop
The vehicle's microcontroller is responsible for
collecting data from the onboard sensors and
relaying it to the ground computer via an RS232 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
Figure 2
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.
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.
Figure 4
Figure 3