A process (including sensor and control valve) can be modeled by the transfer function,

(a) Derive an analytical expression for the response to a unit step change in the input.
(b) Suppose that the maximum allowable value for the model horizon is N = 30. What value of the sampling period Δt should be specified 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.) Use the analytical solution and this value of Δt to obtain a step-response model in the form of Eq. 20-1.

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4(1 – 3s) G(s) = (15s + 1)(5s + 1)