Assignment_3_2007_Solutions

10 concentrationaftereachtankcannowbecalculated

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Unformatted text preview: t ö 1 æ t ö ö ù - / 10 ç t c ( ) = 0 13ê1 - e . 1 + + + ç ÷ + ç ÷ ÷ú 5t ç 10 2! ç 10 ÷ è ø 3! è 10 ø 4! è 10 ø ÷ ú ê è øû ë Concentration after each tank can now be calculated, III. Draw the Bode diagrams of the transfer funct ions below, g ( s = 1) 1 (3 + 1)( + 1) s s g 2 ( s = ) 1 (3 + 1)( + 1)( . s + 1) s s 0 1 Comment on the differences observed in the diagrams and their practical implicat ions. Solution: To draw the Bode diagrams, use the fo llowing steps: ü ü ü ü ü ü Replace s = jw in the transfer funct ion Find the magnitude (AR) of the complex 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 funct ion. 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 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, g...
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