# HW12 - ME 375 Out Thur April 23 Due Wed April 29 HOMEWORK...

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ME 375 HOMEWORK 12 Spring 2009 Out: Thur., April 23 Due: Wed., April 29 PROBLEM 1 (30%) Given the following expression for the denominator of the closed-loop transfer function for a system that uses a proportional controller K : 2 1 10 ( 2)( 10 34) K ss s += ++ + (a) Determine the roots of this characteristic equation when K = 0. (b) To get an idea of where the roots go when K gets large, determine the imaginary axis crossings. (Hint: set s = j ω and solve for and K .) (c) Sketch the root locus on graph paper. You can use Matlab command rlocus to help you. (d) Determine the range of gain K for which this system is stable. PROBLEM 2 (35%) The dynamics of one axis of a Cartesian robot with compliance in the power transmission element are described by the following transfer function: () 2 22 1 2 Xs Fs = + Since vibration during motion is to be minimized, it has been suggested that the acceleration ax = ±± be used for feedback. (a) Determine the transfer function that relates the transformed acceleration A 2 ( s ) to the transformed force F ( s ).

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HW12 - ME 375 Out Thur April 23 Due Wed April 29 HOMEWORK...

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