Is a high gain good in the speed control example?

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.

--Shuo