Controls: Completely reconstructible system?

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SUMMARY

The discussion centers on the state-space representation of a car model defined by the equation v(dot) ̇= -av+bθ, where v(t) is speed and θ(t) is throttle angle. The participants seek to determine if the pair (A,C) is completely reconstructible, equating this concept with complete observability. The conclusion drawn is that complete reconstructibility implies that the system's internal states can be fully determined from the output measurements, which is critical for effective control system design.

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Kaydee371
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Consider the following model of a car, where v(t) is the speed and θ(t) is the throttle
angle

v(dot) ̇= -av+bθ

where a and b are positive constants. Now express the model in state space form with the states as position and velocity, assuming the measured output is the velocity. Is (A,C) completely reconstructible? Interpret your answer.

This is a confusing area of controls for me. Any help would be greatly appreciated, thanks!
 
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Hi, were you able to get the state-space representation?

Is "completely reconstructible" the same as "completely observable"?
 

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