Problem 2. A lead-lag element is described by the transfer function p(s) = K(Tas +1) (TS+1)...

 

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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 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