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System Dynamics Modeling

Deriving the system dynamics is systematically done using free-body diagrams, one diagram per body: The sign of spring and damper forces are easily determined by considering the motion of one state ...
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Calculating the transfer function of this block diagram

Assuming scalars (i.e. SISO systems): $$\begin{align} C&=E_1G_3+E_2G_2\\ E_1&=R-CH\\ E_2&=E_1G_1-CG_4=(R-CH)G_1-CG_4\\ \end{align}$$ Hence $$\begin{align}C&=(R-CH)G_3+((R-CH)G_1-CG_4)...
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How to get difference equation from this block diagram

You can label each node and form a matrix equation: You get equations: $$\begin{align}x_0&=x[n]\\ x_1&=-x_0+x_3+x_4\\ x_2&=2x_1\\ x_3&=z^{-1}x_0+2x_4\\ x_4&=z^{-1}x_2+z^{-1}x_5\\ ...
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