$\frac{?}{117}$

$90\%$

Problem $5\mathrm{.}14$

W

The figure below shows an linesr bydrsulie setustor driven by a four$-$way control valve. The valve is ened to direct presuer to either the epper or lower chambers of the cylinder A re$.$ lief valve $R_F$ in set as a desired pressure $P_s$ which is kept constant

Find a statespace model of this system in terma of energy variables. Use $P_n,F$ and $P_r$ as inputs to your model. The variable $x$ describes the position of the spool. The control valve is characterised by the for monlinear resiston $R_{1}dots{R}_4.$ The CCRs for each resistor is of the form:

$Q_i={}_{R_d^{-1}}^{-1}(P_{i}x),i=1$dots$4$