tailieunhanh - 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 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 X 10 s - X 109s X 10 s - X 10 s X 10 6 4 5 9 4 13 3 17 2 21 25 s X 104s X 10 s X 10 s X 10 s X 10 s X 10 with units of V V. Equation 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 X 107s4 - X 1011 s3 X 1016s2 - X 1020s X 1025 s6 X 104s5 X 109s4 X 1013s3 X 1017s2 X 1021s X 1025 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 . Let F s be the Laplace transform of f t . L f t A F s 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 Using relation 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 Therefore to rescale time for G2 s from seconds s to millisecond ms we choose t at and the new rescaled transfer G2 s becomes G 2 s a G2 1000s - - X 104s2 - X 105s X 107 G2 s -1--------1-------------_- ------------_-_-----------11-------------1--------------1 s6 X 10 s X 10 s X 105s X 106s X 107 13The MATLAB command invfreqs gives real numerator and .