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A steering mirror for a telescope has a maximum angular acceleration of 100 rad/sec^2 and hard...

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Physics

A steering mirror for a telescope has a maximum angularacceleration of 100 rad/sec^2 and hard stops at +/- 30 the softwarecontrolling it runs at 200 hz. If the mirror hits the hard stop atfaster than 15 rad/sec, it can damage the hard stops. To preventthis, a “soft stop” is implemented in its software.

What is the largest value the soft stop can be set at thatwill ensure no damage is done to the hard stops in the event thatthe controller goes unstable and starts commanding the maximumacceleration? If the sample rate is increased to 500 Hz “, howclose to the hardstops can the soft stops be safely set?

Provide answers in degrees to 4 significant figures.

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