(Solution) - Determine a state space representation for the system shown in Figure -(2025 Original AI-Free Solution)

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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, Let x1 = h, x2 = ?, and x3 = d?/dt. Assume that q1 = 80?, where ? is the shaft angle. The output flow is q0 = 50h(t).
Figure P3.35
One-tank system.