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Observability question

Observability question

Observability question

If I have an encoder on a rotating joint, I know the position, and if I differentiate, I know I can get velocity and acceleration. If my state space controller requires velocity and acceleration, does that mean I am able to observe those values? Observability doesn't necessarily mean you need a instrument to directly measure it, does it? Many thanks for your help!

RE: Observability question

The fundamental answer to your question is yes, these values are observable. There are a couple of important caveats, however.

In real state-space control, these values are not obtained by differentiation. Instead, they are computed by a mathematical model of the plant in response to the control effort, with correction from the actual position measurement each cycle.

Second, do not count on these observed states being incredibly accurate, given resolution and computational limitations.

Curt Wilson
Delta Tau Data Systems

RE: Observability question

Differentiation and double differentiation can result in extremely noisy and/or pathological behavior. For example, if your position data resolution is poor, multiple samples might have the same value for a while before jumping to a new value. This would result in zero velocity followed by near infinite velocity spikes. Likewise, any position noise can be differentiated into velocity spikes. If your controller is not designed to handle this, it can behave erratically.

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