could you help me with a few examples of Underdamped and Over damped systems?
Pretty famous case of underdamped:
I once worked for a robot company and was asked to evaluate a company's end of arm tooling. Robots have wrist joints (Joint 5) and the rotary tool flange joint (Joint 6). Joint 5 & 6 are far out on the mechanical arm and have limits of their "strength". This means the servo motor and gear train that supply torque to these two joints have limits on torque and mass moment of inertia about the joint axis. In the design engineering, Dynamic Torque = (Mass Moment of Inertia) X (rotational acceleration alpha about the axis).
Customer designed a huge "pizza pan" tool that was meant to rotate around joint 6. There was so much rotational inertia about joint 6, the joint 6 servo motor was unable to supply sufficient torque to stablilize the mass and null to a precise position. The "pizza pan" just oscillated in rotation constantly. Similar for joint 5, it just oscillated. UNDERDAMPED.
Another motion control situation I had involved a linear servo motor. I needed to positon a mass to a commanded position. The fastest way to do achieve a setpoint is by attempting to tune the servo positioner system to a "critically damped" criterion. This includes minimal overshoot of the position. The servo controller was capable of setting many parameters, including various damping values. During tuning I set damping too high. My program commanded the servo to move to a desired location and it slowly started moving, slowly approached the setpoint, never overshot the position, and settled. It required several seconds to do this, as compared with less than one second for a properly tuned system. OVERDAMPED.
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