Consider the mechanical system given in Figure 1. di(t) and dz(t) are the displacements of the two blocks with respect to their nominal positions (when no any force exist). vi(t) and valt) are the velocities of the two blocks, respectively. vit) vy(t) K2 Ki 00000 M M f(t) dit) de(t) Figure 1: Mechanical system An external force f(t) is applied to the system as the input. Assume that the movement of blocks 1 and 2 is opposed by viscous friction forces given by fo(t) = Divi(t), fp,(t) = D2v2(t) Choose the state vector to be x(t) = [d (t) d (t) v(t) tx(t)]" (1) Derive the state-space model of the system. Assume the output of the system, y(t), is the velocity of the second block.
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