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 ?t 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 N?t ? t99 where t99 is the 99% setting time.) Use the analytical solution and this value of r to obtain a step-response model in the form of Eq. 20-1.

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Set No. Δt (i) (ii) 40 40 40 40 5 20 2. 20 0.01 10 0.1 10 3. (iv)