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hw7 - proportional controller and with the wind disturbance...

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ME 475 HOMEWORK #7 Spring 2011 PROBLEM 1 : Given : Find : (a) Plot frequency response of G(s) in MATLAB. (b) Static gain of G(s) from frequency response. (c) y ss (t) when r(t) = A sin( ω t). (d) Output at steady state if r(t) = 10sin(15t). (e) Output at steady state if r(t) = 5 sin(2t) + 10 sin(15t). PROBLEM 2 : Given : Here: v d (t) & v(t) are the desired and actual speeds, respectively [ft/sec] T(t) = throttle position [degrees] f(t) = engine force [lb f ] W(t) = wind force [lb f ] Suppose , and the car weighs 3000 lb f . Find : (a) The physical law that relates to the summing junction preceding the block 1/ms. (b) The controller gain for a proportional controller so that the closed loop system is critically damped. (c) An expression for the steady-state speed v(t) of the closed-loop system with your

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Unformatted text preview: proportional controller and with the wind disturbance W(t): Y(s) R(s) G(s) f inertia engine controller + v G(s) − W + v d T + 2 where Which component(s) of the wind will have the biggest effect on the speed? (d) The total response v(t) (using the MATLAB lsim command). How does it compare with your prediction in part (c)? PROBLEM 3 : FPE, Prob. 6.19, parts (a), (b), and (d), p. 396. Use K = 1 for parts (a) and (b). Given : (a) (b) Find : Sketch the Nyquist plot for each system and compare with that obtained using the MATLAB nyquist command. (d) Using your plots, estimate the range of K for which each system is stable, and qualitatively verify your result using a rough sketch of a root-locus plot....
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hw7 - proportional controller and with the wind disturbance...

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