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Crc Press Mechatronics Handbook 2002 By Laxxuss Episode 3 Part 5

Tham khảo tài liệu 'crc press mechatronics handbook 2002 by laxxuss episode 3 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | data was then found with the MATLAB software.13 The transfer-function between the applied input voltage V_ t and the output of the inductive sensor y t was found to be G1 s Y s Vx 5 í a Cl y 1 Q 18 91 5.544 X 10 s - 7.528 X 109s 1.476 X 10 s - 4.571 X 10 s 9.415 X 10 6 4 5 9 4 13 3 17 2 21 25 s 1.255 X 104s 1.632 X 10 s 1.855 X 10 s 6.5 X 10 s 6.25 X 10 s 1.378 X 10 23.134 with units of V V. Equation 23.135 was scaled by the inductive sensor gain 30  V and the transferfunction between the applied voltage V_ t and the actual displacement of the piezo-tube xp t is given by G2 s Xp s V_ s __1.663 X 107s4 - 2.258 X 1011 s3 4.427 X 1016s2 - 1.371 X 1020s 2.825 X 1025 s6 1.255 X 104s5 1.632 X 109s4 1.855 X 1013s3 6.5 X 1017s2 6.25 X 1021s 1.378 X 1025 23.135 with units of  V. Time Scaling of a Transfer-Function Model We present below an approach for rescaling time for G2 s from seconds s to milliseconds ms . We briefly recall the time scaling property of the Laplace transform presented in 1 Chapter 3 section 1.4 . Let F s be the Laplace transform of f t i.e. L f t A F s 23.136 1 T 1 . . 1 T 1 . r .XT 1 . 1 1 r 1 where L denotes the Laplace transform operator. Now consider a new time scale defined as t at where a is a constant. The Laplace transform of f t f at is given by L1 s f t f at -1__FI __ I F s a ya J 23.137 Using relation 23.137 we can reduce the coefficients of G2 s by changing the time units of both the input signal u t and output signal y t as follows G s Y s Y s a a Y s a G Tsh U s U s a a U s a yaj 23.138 Therefore to rescale time for G2 s from seconds s to millisecond ms we choose t at 0.001t and the new rescaled transfer G2 s becomes G 2 s a 0.001 G2 1000s - 16.63s4 - 225.8s3 4.427 X 104s2 - 1.371 X 105s 2.825 X 107 G2 s -1--------1-------------_- ------------_-_-----------11-------------1--------------1 s6 12.55s5 1.632 X 10 s 1.855 X 10 s 6.5 X 105s 6.25 X 106s 1.378 X 107 23.139 13The MATLAB command invfreqs gives real numerator and .