hw10 - ME 375 HOMEWORK#10 Fall 2009 Out Nov 4 2009 Due Nov...

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ME 375 HOMEWORK #10 Fall 2009 Out: Nov. 4, 2009 Due: Nov. 11, 2009 PROBLEM 1 : (30%) A DC motor is driving a load as shown in the following figure. The motor has a Back-EMF constant b K , a torque constant T K , an armature inductance a L , and a resistance a R . The rotor has an inertia A J and a viscous friction B . The load has an inertia L J . The two inertias are connected by a shaft with a spring constant L K and an equivalent viscous damping L B . (a) Write the equations of motion for the motor and the load dynamics. (b) Draw the block diagram of the complete system. (c) Find the transfer function from the input voltage ) ( s E i to the angular position of the load ) ( s L Θ . PROBLEM 2 : (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 angle), y H is the gain of the speedometer, and r H is input scaling factor.
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