Control System for AirSTWing Quadrotor

1
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. AUTHORS Roman
Geykhman (EE '07) Noah Robbin (EE
'07) ADVISOR Prof. Daniel Lee (ESE) SPECIAL
THANKS Jim Keller (GRASP) Alex Rattner (MEAM
'09) Prof. Vijay Kumar (MEAM) Prof. Jorge
Santiago (ESE) DEMO TIMES 1000 AM
1100 AM 100 PM 200 PM
300 PM DEMO LOCATION GRASP Laboratory Room
L457, 4th Floor, Levine Hall ESE 442 Senior
Design Group 14
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 0.25.
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.
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 vehicles 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
y
?y
Figure 1
Motor 4
Motor 2
System Architecture


RS 232 Serial
Excitation

To PIC ADC
Figure 2
Spectron SP5000 Dual Axis Inclinometer
PC Software Control Loop
Onboard PIC24 Microcontroller

4 x 50 Hz PWM
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
Castle Creations Phoenix-25 Brushless Motor
Controllers HiMax HA2025 Brushless Motors
Voltage Monitoring to ADC

Approx 5A / Motor
Thunderpower TP4600-4SXL 4.6 A-Hr Battery
Figure 4
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 systems feedback loop. The
effect of the propeller dynamics is shown in the
root locus plot in Figure 1.
Figure 3