For the transfer functions

(a) Derive an analytical expression for the step response to a unit step change. Evaluate the step-response coefficients, {S_i}, for a sampling period of Δt = 1.
(b) What value of model horizon N should be specified in order to ensure that the step-response model covers a period of at least 99% of the open-loop settling time? (That is, we require that NΔt ‰¥ t₉₉ where t₉₉ is the 99% settling time.)

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Зе-2 Gp(8) = G, = G = 1 (15s + 1)(10s + 1)