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

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 $$T_e=?(?)i$$ on the tilt table when is current if 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 $$T_2(?)$$ on the tilt table, and can be modeled as a non-linear spring. Fig. 3 shows the experimentally obtained data of $$T_k(?)$$ and $$?(?)$$. rigure 1, vision-baseu object tracking system Figure 2. Equivalent electromechanical system Part III: Design the controller With $$R=10?,L=0.6?\mathrm{H},J=0.02{\mathrm{kgss}}^2$$ (a) Design a PID controller that satisfies the following specifications for a step input. - Maximum overshoot no more than $$20\%$$ - $$2\%$$ setting time less than $$1.2$$ second Zero steady-state error Integral gain $$K$$, less than 700 (b) With the designed PID controller, simulate the response to a $$5^{?}$$ step reference input and a $$5^{?}$$-per-second ramp reference input. Determine maximum overshoot, settling time, and steady-state error for the step response. Determine the steady-state error for the ramp input. (c) Plot the Bode diagram of the open-loop transfer function $$G_{?}(s)G(s)$$. Determine the phase and gain margins. Determine the bandwidth of the elosed-loop system.