# soln6a - ECE320 Solution Notes 6 Cornell University Spring...

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ECE320 Solution Notes 6 Spring 2006 Cornell University T.L.Fine 1. Consider the negative feedback system shown in Figure 1. f g e u S S 1 2 + - Figure 1: Negative Feedback System The subsystem S 1 is an amplifier by K . The subsystem S 2 is an integra- tor (the derivative of its output equals its input). On the Blackboard 320 site, under Course Documents/Matlab Programs, you will find dfield7.m written by Professor John Polking at Rice and my brief summary Notes to dfield7 . You can use this program to numerically solve first-order differen- tial equations. (a) Let the input f ( t ) = 1. For each of the three values of gain K given by 0 . 1 , 1 . 0 , 10 provide plots of the output starting from initial condition g (0) = 0. Run dfield7.m for a time interval [ - 2 , 10] and an amplitude range of [ - 3 , 3]. See Figures 2 and 3. (b) Repeat (a) for f ( t ) = cos(5 * t ). See Figures 4 and 5. (c) Repeat (a) for f ( t ) = t 2 . See Figures 6 and 7. (d) What qualitative understandings can you reach about changing the value of gain K and about the ability of this control system to track rapidly chang- ing inputs? Pay attention to the amplitude of the response as compared with that of f . Larger K provides more accurate and faster tracking. Note that in (b) the waveform shape is reasonable but the amplitude is off. In (c), we have plotted t 2 using a dotted line on the K = 10 Figure 7. The system output g does not quite follow the desired trajectory but is close to it.

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• Spring '06
• FINE
• Amplifier, Zürich Hauptbahnhof

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