PROCESS CONTROL - EXAMPLE 6.1 : In a Laplace Transform Table, the Laplace transfer function of f(t) is F(s). When d(t) = f(t) then 1 = F(s). When x(t) = f(t) then X(s) = F(s). If d(t) is the impulse of a spring when d(t) = kx(t), then derive the equation for the impulse of a spring as X(s) in term of k. Next question : A controller has a transfer function a and the other controller has a transfer function b. The overall transfer function of both controllers is ab. What is the transfer function overall when both controllers have similar transfer function 1 / (Cs + k)?
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PROCESS CONTROL - ANSWER 6.1 : For f(t), d(t) = kx(t). Transform such equation to F(t) gives 1 = kX(s) then X(s) = 1 / k. Next answer : Overall transfer function for 2 controllers in combination is 1 / (Cs + k) x 1 / (Cs + k) = 1 / [ (Cs + k) (Cs + k) ]. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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