List of Figures
1.1 Examples of quadrotor implementations found in the literature. . . . . . . . . 3
1.2 Examples of commercially available quadrotors. . . . . . . . . . . . . . . . . . 4
2.1 Quadrotor’s body-fixed and inertial coordinate systems. . . . . . . . . . . . . 5
2.2 Basic electric model of a brushed DC motor. . . . . . . . . . . . . . . . . . . 7
2.3 Basic rotations in the body-fixed frame. . . . . . . . . . . . . . . . . . . . . . 10
2.4 Simplified block diagram of the quadrotor’s dynamics. . . . . . . . . . . . . . 11
3.1 Quadrotor’s airframe and inertial identification scheme. . . . . . . . . . . . . 13
3.2 Setup for rotor torque identification experiment. . . . . . . . . . . . . . . . . 14
3.3 Rotor torque identification result. . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.4 Rotor steady-state experiment in channel u → ω. . . . . . . . . . . . . . . . . 15
3.5 Step input response u → ω experiment. . . . . . . . . . . . . . . . . . . . . . 16
3.6 Validation test for rotor dynamics identification. . . . . . . . . . . . . . . . . 17
3.7 Results of thrust identification experiment. . . . . . . . . . . . . . . . . . . . 17
3.8 Simulink model for non-linear rotor simulation. . . . . . . . . . . . . . . . . . 18
3.9 Time responses of full 2
nd
and simplified 1
st
-order rotor models. . . . . . . . . 19
5.1 LQG composed of continuous-time Kalman Filter and LQ control. . . . . . . 26
5.2 Effect of noises on the LQ-controlled non-linear quadrotor model. . . . . . . . 27
5.3 Kalman filtering results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6.1 Quadrotor’s airframe G
i,j
(s) and total H
i,j
(s) MIMO system. . . . . . . . . . 29
6.2 Proposed nested classical PID control architecture. . . . . . . . . . . . . . . . 30
6.3 Tuning of climb rate controller K
w
(s). . . . . . . . . . . . . . . . . . . . . . . 31
6.4 Step response around linearization point with PID control. . . . . . . . . . . 32
6.5 Step response further from linearization point with PID control. . . . . . . . 33
6.6 Flight trajectory and heading reference tracking with PID control and noisy
~
Ω sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
6.7 State-feedback LQ control structure for the quadrotor. . . . . . . . . . . . . . 36
6.8 LQ control performance on quadrotor’s linearized model. . . . . . . . . . . . . 37
6.9 LQ control performance on quadrotor’s non-linear model. . . . . . . . . . . . 37
6.10 Instability of LQ controller tuning for general maneuver and with noisy
~
Ω
sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6.11 Good performance of LQ controller for isolated yaw maneuver. . . . . . . . . 38
6.12 Attempt of nested LQ implementation for the quadrotor. . . . . . . . . . . . 39
6.13 S/K S/T mixed-sensitivity control design configuration for reference tracking. 40
6.14 Instability on PID closed-loop system induced by payload coupling. . . . . . . 41
6.15 Weighting filters for tuning of mixed-sensitivity H
∞
controller. . . . . . . . . 42
6.16 System performance with mixed-sensitivity H
∞
control for I
0
x
= I
0
y
= 4 I
x
0
. . 43
6.17 Improvement in mixed-sensitivity H
∞
control performance with W
2
. . . . . . 43
6.18 Instability in PID-controlled non-linear system induced by I
0
G
= 3.1I
G
nom
. . . 45
xiii