hwk10

# hwk10 - angle y H is the gain of the speedometer and r H is...

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ME 375 HOMEWORK #10 Spring 2010 Out: April 7, 2010 Due: April 14, 2010 PROBLEM 1 : (30%) Given Find: (a) Differential equation relating r P 3 to s P . (b) Natural frequency and damping ratio for 5 1 sec/ 001 . 0 in lb R = , 5 2 sec/ 005 . 0 in lb R = lb in C f / 1000 5 = , and 5 2 / sec 010 . 0 in lb I = (c) MATLAB response ) ( 3 t P r for unit step change in s P . PROBLEM 2 : (40%) (a) Problem 7.22 in Palm. In particular, find the transfer function ) ( ) ( 2 s Q s H mi . (HINT: develop the equations for the gage pressures at the bottom of each tank, then convert these pressures to the heights of the two tanks. Also note that q mi is the mass flow rate, which is simply the volumetric flow rate q times the density ρ .) (b) Problem 7.23 in Palm. (See HINT above.)

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PROBLEM 3 : (30%) Consider the automobile speed control system depicted in the following figure, where R is the desired speed, Y is the actual speed of the car, and W is the road grade (in percent) which represents the slope of the road. The constant K is the control input (the throttle
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Unformatted text preview: angle), y H is the gain of the speedometer, and r H is input scaling factor. a s A + and a s B + represent the vehicle speed dynamics as a first order system. (a) Find the transfer functions from W ( s ) to Y ( s ) and from R ( s ) to Y ( s ). (b) Assume the desired speed is a constant reference r , so that s r s R ) ( = . Assume that the road is level, so ) ( = t w . What are the conditions on the gains K , r H and y H to guarantee that ) ( lim r t y t = ∞ → . Include both the open-loop (assuming = y H ) and feedback cases ( ≠ y H ) in your discussion. (c) Assume that a constant grade disturbance s w s W ) ( = is present in addition to the reference input. Using the same gains as in part (b), what is the steady-state speed of the car ) ( lim t y t ∞ → ? Include both the open loop and feedback cases....
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## This note was uploaded on 12/22/2011 for the course ME 375 taught by Professor Meckle during the Fall '10 term at Purdue.

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hwk10 - angle y H is the gain of the speedometer and r H is...

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