Controls: Completely reconstructible system?

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The discussion revolves around expressing a car model in state space form, focusing on speed and throttle angle. Participants seek clarity on whether the pair (A,C) is completely reconstructible and how it relates to complete observability. There is confusion regarding the terminology, specifically if "completely reconstructible" equates to "completely observable." The conversation highlights the need for assistance in understanding these control concepts. Overall, the thread emphasizes the complexities of state space representation in control systems.
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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