Determine a state-space representation for the system shown in Figure P3.35. The motor inductance is negligible, the motor constant is Km = 10, the back electromagnetic force constant is Kb = 0.0706, the motor friction is negligible. The motor and valve inertia is J = 0.006, and the area of the tank is 50 m2. Note that the motor is controlled by the armature current ia (t). Let x1 (t) = h(t), x2 (t) = (t), and 3 . x (t) = (t)

Assume that q1 (t) = 80(t), where (t) is the shaft angle. The output flow is q0 (t) = 50h(t).

FIGURE P3.35 One-tank system. ia(t) R + 10 Amplifier v;(t) K = 50 va(t) v(t) Valve 8(t) qi(t) h(t) Reservoir 90(t)