Is a high gain good in the speed control example?

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First, one needs to be cautious about defining what "good" means when designing control laws. There are trade-offs between various performance measures, including steady-state error, disturbance rejection, robustness, and other things we did not mention in today's lecture like response time. Therefore, it is impossible to optimize all of them.

In this example, a high gain is good at reducing the steady-state error (\(v_\mathrm{des}-v\)) and rejecting external disturbances coming from \(F_\mathrm{hill}\). However, it will not be desirable if one does not want the magnitude of \(F_\mathrm{eng}\) to be large.