SIMPLIFIED AND GENERALIZED STEADY-STATE DECOUPLERS FOR THE WOOD AND BERRY DISTILLATION COLUMN. Design steady-state decouplers for the Wood and Berry column using both the simplified and the generalized approaches.

Question

SIMPLIFIED AND GENERALIZED STEADY-STATE DECOUPLERS FOR THE WOOD AND BERRY DISTILLATION COLUMN.

Design steady-state decouplers for the Wood and Berry column using both the simplified and the generalized approaches.

Accepted Answer

The simplified steady-state decouplers are easily obtained by retaining only the steady-state gains of the transfer function elements; the results are:

[latex]g_{I_{1}} = - \frac{-18.9}{12.8} = 1.48[/latex] (22.61)

and

[latex]g_{I_{2}} = - \frac{6.6}{-19.4} = 0.34[/latex] (22.62)

and these will be implemented on the real process as:

[latex]u_{1} = v_{1} + 1.48 v_{2}[/latex] (22.63)

and

[latex]u_{2} = 0.34 v_{1} + v_{2}[/latex] (22.64)

For the generalized decoupler on the other hand, we have, upon taking the inverse of:

[latex]K = \begin{bmatrix} 12.8 & -18.9 \ 6.6 & -19.4 \end{bmatrix} [/latex] (22.65)

and multiplying by:

[latex]K_{R} = \begin{bmatrix} 12.8 & 0 \ 0 & -19.4 \end{bmatrix} [/latex] (22.66)

we would obtain:

[latex]G_{I} = \begin{bmatrix} 2.01 & 2.97 \ 0.68 & 2.01 \end{bmatrix} [/latex] (22.67)

and these will be implemented as:

[latex]u_{1} = 2.01 v_{1} + 2.97 v_{2}[/latex] (22.68)

and

[latex]u_{2} = 0.68 v_{1} + 2.01 v_{2}[/latex] (22.69)

Note that these same results could have been obtained by setting s= 0 in the dynamic decoupler results obtained in Example 22.2.
In principle we would expect the simplified approach and generalized approach to give the same result for steady-state decoupling. That this is true may be seen by dividing Eqs. (22.68) and (22.69) by the common factor 2.01 to obtain Eqs. (22.63) and (22.64). However, the single-loop controller gains in each case will also differ by the factor 2.01.

Question 22.5: SIMPLIFIED AND GENERALIZED STEADY-STATE DECOUPLERS FOR THE W...

Related Answered Questions

Verified Answer:

Verified Answer:

PARTIAL DYNAMIC DECOUPLING FOR THE HULBERT AND WOODBURN WET-GRINDING CIRCUIT. Hulbert and Woodburn [3] have reported the control of a wet-grinding circuit whose transfer function model, obtained by experimental means, is given by: [y1 y2 y3] = [119/217s + 1 153/337s + 1 -21/10s + 1 ...

Verified Answer:

A GENERALIZED DECOUPLER FOR THE WOOD AND BERRY DISTILLATION COLUMN. Using the generalized decoupling approach, design a decoupler for the Wood and Berry distillation column, the same system of Example 22.1. ...

Verified Answer:

SIMPLIFIED DECOUPLER DESIGN FOR THE WOOD AND BERRY DISTILLATION COLUMN. Using the simplified decoupling approach, design a decoupler for the Wood and Berry distillation column whose transfer function model was given in Example 20.6, Eq. (20.26). ...

Verified Answer: