The object-tracking system shown in Fig. 1 consists of a computer-controlled tilt table on which a...

 

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The object-tracking system shown in Fig. 1 consists of a computer-controlled tilt table on which a camera is mounted. The table, mounted on a mechanical bearing to the base frame, can be rotated by appropriately controlling a pair of electromagnets (EMS) in the magnetic field of permanent magnets (PMs). In Fig. 1, the angle of the tilt table is measured in the counter-clockwise direction from the horizontal axis. When no current flows through the EMs, the table is maintained horizontally by the repulsive forces of the PMs. Fig. 2 illustrates the electromechanical system, R and L are the electrical resistance and inductance of the EM, while the back EMF is negligible. The EMS exert a torque T = a(0)i on the tilt table when is current i flows through the EM. J is the combined moment of inertia of the table/camera about the rotation axis, and has negligible friction at the bearing. The combined gravitational and repulsive PM forces exert a torque T(0) on the tilt table, and can be modeled as a non-linear spring. Fig. 3 shows the experimentally obtained data of T() and a(0). Bearing Tilt table PM EN PM Camera Object R PM V EM PM Base frame aff Cont Figure 1. Vision-based object tracking system (Nm) I Figure 2. Equivalent electromechanical system 0.05 0.04 0.03 0.02 0.09r 0.085 0.08 0.075 0.01 0 (N-m/A) 0.07 0.01 0065 D -0.0122 0.06 -0.02 0.055 -0.03 0.05 -0.04 0.046 -0.05 0.045 -15 -10 8 5 10 15 -15 -10 -5 5 10 15 Table angle (deg) Table angle (deg) Figure 3. Experimental data (a) Derive the dynamic equations for the electromechanical system. Obtain a linearized approximation about an equilibrium where the input voltage V = 0. (b) Determine the transfer function G(s)=- e(s) V(s) The object-tracking system shown in Fig. 1 consists of a computer-controlled tilt table on which a camera is mounted. The table, mounted on a mechanical bearing to the base frame, can be rotated by appropriately controlling a pair of electromagnets (EMS) in the magnetic field of permanent magnets (PMs). In Fig. 1, the angle of the tilt table is measured in the counter-clockwise direction from the horizontal axis. When no current flows through the EMs, the table is maintained horizontally by the repulsive forces of the PMs. Fig. 2 illustrates the electromechanical system, R and L are the electrical resistance and inductance of the EM, while the back EMF is negligible. The EMS exert a torque T = a(0)i on the tilt table when is current i flows through the EM. J is the combined moment of inertia of the table/camera about the rotation axis, and has negligible friction at the bearing. The combined gravitational and repulsive PM forces exert a torque T(0) on the tilt table, and can be modeled as a non-linear spring. Fig. 3 shows the experimentally obtained data of T() and a(0). Bearing Tilt table PM EN PM Camera Object R PM V EM PM Base frame aff Cont Figure 1. Vision-based object tracking system (Nm) I Figure 2. Equivalent electromechanical system 0.05 0.04 0.03 0.02 0.09r 0.085 0.08 0.075 0.01 0 (N-m/A) 0.07 0.01 0065 D -0.0122 0.06 -0.02 0.055 -0.03 0.05 -0.04 0.046 -0.05 0.045 -15 -10 8 5 10 15 -15 -10 -5 5 10 15 Table angle (deg) Table angle (deg) Figure 3. Experimental data (a) Derive the dynamic equations for the electromechanical system. Obtain a linearized approximation about an equilibrium where the input voltage V = 0. (b) Determine the transfer function G(s)=- e(s) V(s)