Given the Transfer Function model of a first-order system as [G(s)=frac{a}{s+a},] (a) Calculate the time constant, settling

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Given the Transfer Function model of a first-order system as

\[G(s)=\frac{a}{s+a},\]

(a) Calculate the time constant, settling time, rise time and pole location for the three first-order systems where the values of a are 1,2 and 3), respectively.

(b) Using MATLAB plot the unit-step responses of the three systems in one diagram.

(c) Compare the calculated and experimentally determined (MATLAB) time constant, settling time and rise time for each of the three systems.

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