Process Dynamics, Modeling, and Control by Babatunde A. Ogunnaike, W. Harmon Ray | 9780195091199 | 0195091191 | Holooly

Control Systems

Process Dynamics, Modeling, and Control

122 SOLVED PROBLEMS

Question: 22.8

DEGENERACY AND DECOUPLING CONTROL OF THE STIRRED MIXING TANK SYSTEM. Let us consider the stirred mixing tank expanded with an additional heater as in Example 21.10. If we fix the heater at a constant power and only consider the hot and cold stream flowrates as inputs, the linearized model is given ...

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Under Condition 1, the steady-state gain matrix is...

Question: 22.7

PARTIAL STEADY-STATE DECOUPLING OF THE PRETT AND GARCIA HEAVY OIL FRACTIONATOR. Prett and Garcia presented in Ref. [7] a 7 x 5 transfer function model for a heavy oil fractionator column. Here we will consider the partial decoupling of this system by focusing on a 2 x 2 subsystem involving the top ...

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The steady-state gain matrix for this subsystem is...

Question: 22.5

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. ...

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The simplified steady-state decouplers are easily ...

Question: 22.4

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 ...

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Under the indicated conditions, the transfer funct...

Question: 22.2

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. ...

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The transfer function matrix in question is: [late...

Question: 22.1

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). ...

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Recalling the transfer function matrix for this pr...

Question: C.7

PARTIAL FRACTION EXPANSION: REPEATED ROOTS IN z-TRANSFORMS. Obtain a partial fraction expansion of the function: y(z) = 0.8 – 0.3z^-1/(1 – z^-1)² (1 – 0.5z^-1) (C.106) ...

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Because of the repeated pole at z = 1, we wish to ...

Question: C.6

SOLUTION OF A FIRST-ORDER DIFFERENCE EQUATION BY z-TRANSFORMS, AND PARTIAL FRACTION EXPANSION. Use z-transforms to solve the first-order difference equation: y(k) = 0.7y(k – 1) + 1.5u(k – 1) (C.101) given that u(k) = 1 for all k. (That is, find the unit step response of the first-order system whose ...

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By taking z-transforms of both sides and rearrangi...

Question: 15.6

CONTROLLER TUNING USING AN APPROXIMATE PROCESS MODEL. Consider again the three-tank process of Example 15.1 and now design PI and PID controllers based on the approximate model Eq. (15.33) determined from the process reaction curve in Example 15.5. Compare the responses to a set-point change using ...

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Based on all of the tuning rules discussed above, ...

Question: C.5

PARTIAL FRACTION EXPANSION: R(s) NOT STRICTLY PROPER. Obtain a partial fraction expansion for the function: R(s) = (s² + 4s + 3)/(s² + 9s + 20) ...

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Factoring both the numerator and the denominator q...

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