ME461 Homework 1 - space form with r v as input and v as...

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ME461 Homework 1# (Due Date: Thurday, 6 th week ) Problem1(20’) Problem2 (30’) (a) Write the equation of motion for the speed and forward motion of the car shown in figure, assuming that the engine imparts a force u as shown. Take the Laplace transform of the resulting differential equation and find the transfer function, between the input u and output v. (b) Use MATLAB to find the response of the velocity of the car for the case in which the input jumps from u=0 at time t=0 to a constant u=500N thereafter. Assume the car mass m=1000Kg and b= 50 N.sec/m (c) If we use ) ( v v K u r - = Where r v =reference speed K=constant This is a “Proportional” Control law in which the difference between r v and the actual speed is used as a signal to speed the engine up or slow down. Derive the equations of motion in state
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Unformatted text preview: space form with r v as input and v as output. (d) How would changing the value of K affect the speed with which the closed loop system would settle in at its final level, given a unit step input as the reference input (in other words, how does changing of K affect the speed of response of the closed loop system) . Try several values of K , create step responses for the corresponding closed loop systems and comment on your results. Problem 3.(30) An armature-controlled dc motor is driving a load. The input voltage is 5V. The speed at t=2 second is 30 rad/s, and the steady speed is 70 rad/s when -t , Determine the transfer function ) ( / ) ( s V s Problem 4 (20) Find the transfer function for the block diagram shown in below....
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ME461 Homework 1 - space form with r v as input and v as...

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