Qball-X4 Simulator Seang Cau February 16, 2011

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

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

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

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

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

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

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

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

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

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

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

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

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

X Controller Figure 12: X Controller

Pitch Controller/Model Figure 13: Pitch Controller/Model

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

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

Y Controller Figure 17: Y Controller

Roll Controller/Model Figure 18: Roll Controller/Model

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

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

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