This problem concerns the use of Laplace transforms on a first-order system written in standard (gain/time...

 

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This problem concerns the use of Laplace transforms on a first-order system written in standard (gain/time constant) formo To gulfolie bony(s) u(s) K = P1(s) = TS+1 T>0, 0 0, (2) (3) Take advantage of linearity, the Principle of Superposition, and your knowledge of standard forms/responses to obtain a detailed sketch of the plant response to this input. Please assume that T> 37 and clearly label the initial and final values of y(t). Apply superposition; please obtain a "high insight" solution that does not rely on the Initial or Final Value Theorems, or a manual derivation of an analytical solution for this input. Use the IVT (only) to obtain the initial slope of the response. Include both y(t) and u(t) in your sketch in the same plot. Listen carefully to the instructor directions in this regard. b) Repeat part a), but this time consider a plant consisting of a simple integrator P(s) = K ' S 0 < K <1 (4) Assume that the duration of T is such that 0 < KT < 1; as before, plot the responses of y(t) and u(t) in the same plot. 92 493 c) For Extra Credit. Consider the problem in b), but this time sketch the response for a pulse of duration such that KT > 1. rod at od nisano (d This problem concerns the use of Laplace transforms on a first-order system written in standard (gain/time constant) formo To gulfolie bony(s) u(s) K = P1(s) = TS+1 T>0, 0 0, (2) (3) Take advantage of linearity, the Principle of Superposition, and your knowledge of standard forms/responses to obtain a detailed sketch of the plant response to this input. Please assume that T> 37 and clearly label the initial and final values of y(t). Apply superposition; please obtain a "high insight" solution that does not rely on the Initial or Final Value Theorems, or a manual derivation of an analytical solution for this input. Use the IVT (only) to obtain the initial slope of the response. Include both y(t) and u(t) in your sketch in the same plot. Listen carefully to the instructor directions in this regard. b) Repeat part a), but this time consider a plant consisting of a simple integrator P(s) = K ' S 0 < K <1 (4) Assume that the duration of T is such that 0 < KT < 1; as before, plot the responses of y(t) and u(t) in the same plot. 92 493 c) For Extra Credit. Consider the problem in b), but this time sketch the response for a pulse of duration such that KT > 1. rod at od nisano (d