Consider the following empirical model of a pilot-scale distillation column (Wood and Berry, 1973)[ XD(s) XB(s) ] = [12.8e^-s/16.7s+1 -18.9e^-3s/21s+1 6.6e^-7s/10.9s+1 -19.4e/-3s/14.4s+1 ] [ R(s) S(s) ] (18-12) where the notation is defined in Fig.18.1b. Suppose that a multiloop control system cons

Question

Consider the following empirical model of a pilot-scale distillation column (Wood and Berry, 1973)

[latex]\left[ \begin{matrix} X_{D}(s) \ X_{B}(s) \end{matrix} ight] = \begin{bmatrix} \frac{12.8e^{-s} }{16.7s+1} & \frac{-18.9e^{-3s} }{21s+1} \ \frac{6.6e^{-7s} }{10.9s+1} & \frac{-19.4e^{-3s} }{14.4s+1} \end{bmatrix} \left[ \begin{matrix} R(s) \ S(s) \end{matrix} ight] (18-12)[/latex]

where the notation is defined in Fig. 18.1b. Suppose that a multiloop control system consisting of two PI controllers is used. Compare the closed-loop set-point changes that result if the [latex]X_{D}-R/X_{B} -S[/latex] pairing is selected and
(a) A set-point change is made in each loop with the other loop in manual
(b) The set-point changes are made with both controllers in automatic Assume that the controller settings are based on the ITAE tuning method for set-point changes in Chapter 12.

Accepted Answer

Table 18.1 shows the single-loop ITAE settings, and Fig. 18.5 shows simulation results for set-point changes for each controlled variable. The ITAE settings provide satisfactory

Table 18.1 Controller Settings for Example 18.1

[latex]τ_{I} (min)[/latex]	[latex]K_{c} [/latex]	Controller Pairing
16.37	0.604	[latex]x_{D} − R[/latex]
14.46	−0.127	[latex]x_{B} − S[/latex]

set-point responses for either control loop when the other controller is in manual (solid line). However, when both controllers are in automatic, the control loop interactions produce very oscillatory responses especially in [latex]x_{B} [/latex](dashed line). McAvoy (1983) has discussed various approaches for improving the performance of the multiloop controllers. See Exercise 18.1 for a similar MIMO control problem where the loops also exhibit oscillations.

Question 18.1: Consider the following empirical model of a pilot-scale dist...

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