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As you pointed out, there are many state-space realizations of one particular transfer function. The reason is that a transfer function only represents the input-output behavior of a system (observable and controllable dynamics) and not the internal states. That being said, you can directly write state-space realizations from a transfer function with the so-...


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First, typically when you're exerting a force on something and getting a position, the acceleration varies instantaneously with force. A more or less universal equation of motion for a single-axis linear system would be $m \ddot x = f_v(\dot x) + f_p(x)$. For a mass-spring-damper system, it'd be $m \ddot x = b \dot x + k x$. So you can easily express that ...


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