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How do I proceed with finding the transfer function? The concept of (Laplace transform) transfer functions are applicable for linear systems. So, you need to linearise your equations of motion. Linearisation uses the concept of Taylor series. In the example given in your question, that reduces to removing the term $\dot{\theta}^2$. This comes from the ...

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The arduino does impose some limits. But a classical frequency identification is build from a few steps: As the other comments already suggest, the design of a suitable input. As mentioned, a sinusoidal input (I actually recommend multisine) is suitable to accurately identify the response of a few frequencies. White noise or band-limited white noise can ...

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The input is a scaling factor between 1 and 0 that is multiplied with the area of the valve. Do note that for most valves, putting the valve half open does not mean the throughput area is half the total area, so you might want to link that in an equation. $$\frac{dM_{gas}}{dt} = u(t)A_{valve}\rho V_f$$ $$0\leq u(t) \leq 1$$ Which also instantly leads to an ...

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Typically, the output of the controller is the input to the valve. Depending on the sophistication of the valve model, it could be either the voltage or the valve opening in % or mm (or similar).

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If $\alpha$ has units of angle and $\tau$ has units of torque, then $I$ has units of moment of inertia. It is likely to be the moment of inertia about the axis which is being controlled. The block is very likely a plain gain block which multiplies the angular acceleration signal with the value of the moment of inertia. Published papers usually have a ...

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