Tham khảo tài liệu 'the mems handbook introduction & fundamentals (2nd ed) - m. gad el hak part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Fundamentals of Control Theory 14-3 TABLE Laplace Transform Pairs for Basic Functions F t F s 1 Unit impulse 8 t 1 1 2 Unit step 1 t s 1 3 t IF n 4 tn n 1 2 3 . sn 1 1 5 e at s a 6 i e n s a n 1 7 sin cot . co s2 co2 8 s cos cot s2 co2 9 e a cos bt s a s a 2 b2 10 e sill bt b s a 2 b2 Example As a simple example consider the differential equation x x 0 x 0 0 x 0 1 Taking the Laplace transform of the equation yields s2X s - sx 0 - x 0 X s 0 Algebraic manipulation gives 1 X s s2 . I Consequently from the table of Laplace transform pairs x t sin t For more examples see Ogata 1997 Raven 1995 Kuo 1995 and Franklin et al. 1994 . Due to the convolution property of Laplace transforms aconvenient representation of a linear control system is the block diagram illustrated in Figure . In such a block diagram each block contains the Laplace transform of the differential equation representing that component of the control system that relates the block s input to its output. Arrows between blocks indicate that the output from the preceding block is transferred to the input of the subsequent block. The output of the preceding block multiplies the contents of the block to which it is an input. Simple algebra will yield the overall transfer function of a block diagram representation for a system. 2006 by Taylor Francis Group LLC 14-4 MEMS Introduction and Fundamentals FIGURE Typical block diagram representation of a control system. FIGURE Generic block diagram including transfer functions. Example The transfer function for the system illustrated in Figure can be computed by observing that E s R s - Y s S s and Y s E s C s A s P s which can be combined to yield Y s _ C s A s P s R s 1 C s A s P s S s A more complete exposition on block diagram algebra can be found in any of the previously cited undergraduate texts. Note that the numerator and denominator of the transfer function will typically be polynomials in .
