me352_hw2 - flow(in cubic centimeter per minute to h 2...

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1 ME 352 System Dynamics and Control Homework #2 Due: Friday 18.03.2011 1. Given the dc servomotor and load in Figure - P1, represent the system in state space, where the state variables are the armature current, i a , load displacement, θ L , and angular velocity ω L . Assume that the output is the angular displacement of the armature. Do not neglect armature inductance. Note that there is a gear in the system. 2. Find the transfer function, G(s)=V 0 (s)/V i (s), for the operational amplifier circuits shown in Figure – P2. Figure – P2 3. A laboratory experiment in the flow of water through is sketched in Figure P-3. Assume that ( ) 1 2 1 0 1 out w p p R = - describes flow through the equal-sized holes at points A , B , or C . (a) With holes at A and C but none at B , write the equations of motions for this system in term of h 1 and h 2 . Assume that h 3 =20 cm , h 1 > 20 cm and h 2 <20 cm . When h 2 =10 cm, the outflow is 200 g/min. (b) At h 1 =30 cm and h 2 =10 cm , compute a linearized model and the transfer function from pump
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Unformatted text preview: flow (in cubic centimeter per minute) to h 2 . Figure - P1 Gear 2 4. The equations for heating a house are 1 2 1 ( ) q T T R =-and 1 T q C = & and, in a particular case, can be written with time in hours as h h dT T T C Ku dt R-=-, where -C is the termal capacity of the house (BTU/ o F), -T h is the temperature in the house ( o F), -T is the temperature outside the house ( o F), -K is the heat rating of the furnace (=90,000 BTU/hr), -R is the thermal resistance ( o F per BTU/hr), -u is the furnace switch (=1 if the furnace is on an =0 if the furnace is off). It is measured that, with the outside temperature at 32 o F and the house is at 60 o F, the furnace raises the temperature 2 o F in 6 min (0.1 hr). With the furnace off, the house temperature falls 2 o F in 40 min. What are the values of C and R for the house? Pump h 1 h 2 h 3 A B C Figure – P3 h 3 h 2...
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