7. Consider the two interact tanks system shown in the figure below. In this system the inlet flow into tank 1 is controlled through the valve Vi. The opening of this valve is regulated through a DC motor. Find the describing differential equations that can relate the input voltage Va(t) of the DC motor to the output flow rate Qout (t). Ra and La are resistance and inductance of the DC motor coil and, respectively, Jm Bm Km, Tm and 0m are moment of inertia, viscous damping ratio, spring constant, load torque and angular position of the motor shaft. The tanks have cross sectional area of A₁ and A₂ respectively, while the valves have cross-sectional area of Av2 and Av3 and discharge coefficient of Cd₂ and Cd₂ respectively. The flow though the control valve Vi is given as: Qin = Qsupply Ke Om where K, is a known constant. •

7. Consider the two interact tanks system shown in the figure below. In this system the inlet flow into tank 1 is controlled through the valve Vi. The opening of this valve is regulated through a DC motor. Find the describing differential equations that can relate the input voltage Va(t) of the DC motor to the output flow rate Qout (t). Ra and La are resistance and inductance of the DC motor coil and, respectively, Jm Bm Km, Tm and 0m are moment of inertia, viscous damping ratio, spring constant, load torque and angular position of the motor shaft. The tanks have cross sectional area of A₁ and A₂ respectively, while the valves have cross-sectional area of Av2 and Av3 and discharge coefficient of Cd₂ and Cd₂ respectively. The flow though the control valve Vi is given as: Qin = Qsupply Ke Om where K, is a known constant. •

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter11: Transient Stability

Section: Chapter Questions

Problem 11.18P

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