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 (Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_\mathrm{des}-v} ) and rejecting external disturbances coming from Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_\mathrm{hill}} . However, it will not be desirable if one does not want the magnitude of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_\mathrm{eng}} to be large.

--Shuo