Problem 3. In a system like that shown in Figure 3, find the criteria for KD and KP of a PD controller such that the system is never unstable and never underdamped. Design the PD control to control 𝜏 (solve the torque balance equations for 𝜏, rather than 𝜏𝑚).
The system possesses an un-modelled resonance due to an end-point stiffness K (on the non motor side, not shown in figure). Any damping terms in the system are negligible. Also,𝜂=𝑅2𝑅1>1.
Figure 3: Mechanical model of a DC torque motor connected through gearing to inertial load. Provide exactly two different responses that are separated with 6 asterisk symbols: ******.
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