Case Study Summaries
Described here are two very common, yet different, cases that affect motor sizing. Case 1 is when the control system has to move a load from position A to position B and repeat. Case 2 is where the control system has to track (or reject) a disturbance signal. In each case power dissipated in the motor is the ultimate driving factor.
In case 1, the dissipated power is primarily a function of the duty cycle of motion, the moving mass (or inertia), and the acceleration reached during the move and is independent of servo loop bandwidth. In this case, the “backbone” of the motion trajectory is the same independently of servo bandwidth (within the amount of servo tracking error).
In case 2, however, dissipated power is largely driven by the servo bandwidth. Higher bandwidth servos ask the controller to track higher frequencies, which means higher accelerations and higher motor forces. In our example, a 2x increase in servo bandwidth created 6x more dissipated power in the motor.
In both cases, servo bandwidth is ultimately governed by servo stability, meaning gain margin and phase margin must always be met. In some cases like case 2 described here, the servo bandwidth might not be limited by stability, but by allowable dissipated power.
In both cases, dissipated power is used to size the motor. The load mass (or inertia), its acceleration, and its duty cycle all combine to affect motor power dissipation.