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 Icirc 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 Icirc t yen t 99 where t 99 is the 99 settling time ) Use the analytical solution and this value of Icirc t to obtain a step response model in the form of Eq 20 1 4(1 3s) G(s) (15s 1)(5s 1)

Question: 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

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

4(1 – 3s) G(s) = (15s + 1)(5s + 1)

(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 Î”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 NÎ”t ‰¥ t₉₉ where t₉₉ is the 99% settling time.) Use the analytical solution and this value of Î”t to obtain a step-response model in the form of Eq. 20-1.

4(1 3s) G(s) = (15s + 1)(5s + 1)

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