Problem 2 A lead lag element is described by the transfer function p(s) K(Tas 1) (TS 1) T O a) What is the ordinary differential equation implied by this transfer function (1) b) Consider the output response y(t) of this system to a step input of magnitude A (A 0) for the case of Ta 0 and K 0 Sketch the response using information provided from the Initial and Final Value theorems Clearly label the initial and final values of y(t) and the initial slope of the response Note do not rely on an analytical solution when drawing this sketch 1

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Question: Problem 2. A lead-lag element is described by the transfer function p(s) = K(Tas +1) (TS+1) T > O a) What is the ordinary

Problem 2. A lead-lag element is described by the transfer function p(s) = K(Tas +1) (TS+1) T > O a) What is the ordinary differential equation implied by this transfer function? (1) b) Consider the output response y(t) of this system to a step input of magnitude A (A > 0) for the case of Ta 0. Sketch the response using information provided from the Initial and Final Value theorems. Clearly label the initial and final values of y(t) and the initial slope of the response. Note: do not rely on an analytical solution when drawing this sketch! 1

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