1. Qball-X4 Simulator
Seang Cau
February 16, 2011

2. Introduction Simulator is run under MatLAB and rendered using Quarc.
Simulates the behavioral properties of the Quanser Qball-X4.

3. Quanser Qball-X4
Visualization is transfer information to the 3D renderer
Figure 1: Visualization
Figure 2: Qball Simulator

4. Purpose To understand the physics of the Qball
To understand the capabilities of the Qball
To utilize the simulator as a preliminary study for integration of sensors

5. Qball-X4 Model x, y, and z axis are defined as positions in a 3D space
Roll, pitch, and yaw are defined as the angles of rotation about the x, y, and z axis respectively.
X, Y, and Z are the global workspace axes

6. Actuator Dynamics
Thrust is generated by each propeller using the first-order system
Where u is the PWM input, w is the actuator bandwidth and K is the positive gain
A state variable, v, will be used to represent the actuator dynamics

7. Qball-X4 3D Simulator Consists of two part for each axis
Position Controllers
Model
Constants are specified in Qball_X4_parameters.m

8. Yaw Yaw is a constant in the simulator
It controls the orientation of the QBall
Figure 3: Yaw Black Box
Figure 4: Yaw Controller/Model

9. Yaw Controller & Model Ky = 4 N*m Jy = 0.032
Torque = Ky * u where u is the PWM input
Figure 5: Yaw Controller
Figure 6: Yaw Model

10. Height K = 120 N w (omega) = 15 rad/s M = 1.4 kg
Figure 7: Height Controller/Model

11. Height Controller
Navigates the height based on previous value and target value.
Figure 8: Height Controller

12. Height Model The dynamic model of height can be written as
Height is affected by thrust, pitch, and roll
Figure 9: Height Model

13. XY Model Thrust affects the x and y axis of the Qball
Assuming yaw angle is zero, dynamics of motion in X and Y axes can be written as
Figure 10: XY Model

14. X axis X controller affects the pitch angle
Figure 11: X Controller/Model

15. X Controller
Figure 12: X Controller

16. Pitch Controller/Model
Figure 13: Pitch Controller/Model

17. Pitch Controller & Model
Figure 14: Pitch Controller
Figure 15: Pitch Model

18. Y axis Y Controller affects the roll angle
Figure 16: Y Controller/Model

19. Y Controller
Figure 17: Y Controller

20. Roll Controller/Model
Figure 18: Roll Controller/Model

21. Roll Controller & Model
Figure 19: Roll Controller
Figure 20: Roll Model

22. Summary
Qball X4 model uses absolute coordinate system in the xy and height control
Converts the xy and height commands into Pitch and Roll commands
Yaw is kept constant at an assumed zero

23. Conclusion
Useful to understand how the integration of sensor input will occur
Will be unable to mimick the Qball in actual conditions due to assumptions