Assignment 4 Solutions 2009

Thefo llowingrules

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Unformatted text preview: lex transfer funct ion as a funct ion of w Take the logarithm o f the AR funct ion. Plot log(w) vs log(AR). This is the magnitude plot of the Bode diagram. Find the argument (theta ) of the complex function. Plot log(w) vs theta. This is the phase angle plot of the Bode diagram. The fo llowing rules help in drawing Bode diagrams for systems in series. If g(s) = g1(s) g2(s) g3(s), then log(AR) = log(AR1) + log(AR2) + log(AR3) f = f 1 + f 2 + f 3 2 where AR, AR1, AR2, AR3 are the amplitude ratios and f, f 1, f 2, f 3 are phase angles o f g, g1, g2, g3 respectively. Or, you can just use the “Bode” command in MATLAB. B ode Diagrams Fr om: U( 1) 0 --- g2(s ) __ g1(s ) - 100 - 150 0 To: Y (1) Phas e (deg); Magnitude (dB) - 50 - 100 --- g2(s ) __ g1(s ) - 200 - 300 10-1 100 101 102 Frequenc y (rad/ s ec ) 3. A process has the fo llowing transfer funct ion: g ( s = ) 4 + 1 (as ) (5 + 1 ( + 1 ) s ) s ) For the fo llowing values of the parameter a, · a = 10 · a = 2 · a = 0. 5 · a = -1 Compute the responses for a step­change of magnitude 0.5 and plot in a...
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