For a discrete time unit step input x(kT), the output y(kT) of a system is shown below, Part (a) ? 30 Marks Obtain the Z-transform of the output signal y(kT). Part (b) ? 30 Marks Find out the discrete time system transfer function G(z)=Y(z)/X(z) Part (c) ? 50 Marks Rewrite this system in a difference equation form, and verify your result by reproducing the first five terms (k=0, 1, 2, 3 & 4) of the output signals for a unit step input.
ELE3105 COMPUTER CONTROLLED SYSTEMS – JUNE 2007 Page 1 Question XXXXXXXXXXMarks - - For a discrete time unit step input x(kT), the output y(kT) of a system is shown below, y(kT) 1 0.5 … … … … 0 XXXXXXXXXX XXXXXXXXXX XXXXXXXXXX XXXXXXXXXXt Part (a XXXXXXXXXXMarks Obtain the Z-transform of the output signal y(kT). Part (b XXXXXXXXXXMarks Find out the discrete time system transfer function G(z)=Y(z)/X(z) Part (c XXXXXXXXXXMarks - - Rewrite this system in a difference equation form, and verify your result by reproducing the first five terms (k=0, 1, 2, 3 & 4) of the output signals for a unit step input. Question XXXXXXXXXXMarks A digital control system is shown below. C(z) R(z) G (z) ZOH G (s) + C P - Part (a XXXXXXXXXXMarks c G (s) = K For a plant given by , show how an appropriate sampling rate can be p s + c chosen using system Bode plots and cut-off frequency. Part (b XXXXXXXXXXMarks - - 1 A controller G (z) = is derived for the above system. Given K=c=1, find out the C - 1 - 2 az + bz system closed-loop transfer function T(z)=C(z)/R(z) Part (c XXXXXXXXXXMarks - - -T -2T Given a=e and b=e , where T is the sampling interval, determine the stability of the above system. Page 1 of 6ELE3105 COMPUTER CONTROLLED SYSTEMS – JUNE 2007 Page 2 Question XXXXXXXXXXMarks - - (a) Electrical System (b) Mass-spring-damping system Take one of the above systems into consideration. For system (a), the input is v(t) and the output is v (t). For system (b), the input is f(t) and the output is x (t). (Notes: you can choose C 1 system (a) or (b). However you must stick with that system for all the following questions) Part (a XXXXXXXXXXMarks Assuming zero initial conditions, write a differential equation to represent the system input- output relationship. Then work out its model G(s) in a transfer function form. Part (b) -- 30...
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