Process Dynamics and Control-Solution Manual 4th. Edition by Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellichamp, Francis J. Doyle | Holooly

Process Dynamics and Control-Solution Manual [EXP-2817]

410 SOLVED PROBLEMS

Question: 8.9

(a) For the digital velocity P and PD algorithms, show how the set point enters into calculation of Δpk on the assumption that it is not changing, that is, ysp is a constant. (b) What do the results indicate about use of the velocity form of P and PD digital control algorithms? (c) Are similar

Verified Answer:

a) Let the constant set point be denoted by [latex...

Question: 3.16

(a) The differential equation d^2 y/dt^2 + 6dy/dt + 9y = cos t has initial conditions, y(0) = 1, y′(0) = 2. Find Y(s) and, without finding y(t), determine what functions of time will appear in the solution. (b) If Y(s) = s + 1/s(s^2 + 4s + 8), find y(t).

Verified Answer:

a) Take the Laplace transform:

\lef...

Question: 14.19

(a) Using the process, sensor, and valve transfer functions in Exercise 11.21, find the ultimate controller gain Kcu using aBode plot. Using simulation, verify that values of Kc > Kcu cause instability. (b) Next fit a FOPTD model to G and tune a PI controller for a set-point change. What is the

Verified Answer:

(a)

G=G_{p} G_{v} G_{m}=\frac{2 e^{-1.5 s}}...

Question: 18.14

(Modified from McAvoy, 1983). A decanter shown in Fig. E18.14 is used to separate a feed that consists of two completely immiscible liquids, a light component and a heavy component. Because of the large difference in their densities, the two components form separate liquid phases very rapidly after

Verified Answer:

In this case, an RGA analysis is not needed. The m...

Question: 18.23

A 4 × 4 control system has the following gain matrix: K = [9.82 4.49 1.40 4.56 8.99 5.47 1.68 5.24 4.59 5.80 2.31 7.33 2.41 4.33 2.82 8.92] Assess the potential difficulty of control using singular value analysis. Should any outputs or inputs be eliminated to achieve better control?

Verified Answer:

Applying SVA analysis: Determinant of

K =| ...

Question: 22.4

A batch operation is used to heat a liquid to a specified temperature. There is a start button, a stop button, inlet/outlet valves, and limit sensors for low tank level (LL) and high tank level (LH). Flow is performed by gravity transfer. The process steps are (a) Push the start button to start the

Verified Answer:

Information Flow Diagram Ladder Logic Diagram Sequ...

Question: 19.8

A batch reactor converts component A into B, which in turn decomposes into C: k1 k2 A → B → C where k1 = k10e^−E1/RT and k2 = k20e^−E2/RT. The concentrations of A and B are denoted by x1 and x2, respectively. The reactor model is dx1/dt = −k10x1e^−E1/RT dx2/dt = k10x1e^−E1/RT − k20x2e^−E2/RT Thus,

Verified Answer:

The reactor equations are:

\frac{d x_{1}}{d...

Question: 22.10

A batch reactor converts component A into B, which in turn decomposes into C: k1 k2 A → B → C where k1 = k10e^−E1∕RT and k2 = k20e^−E2∕RT. The concentrations of A and B are denoted by x1 and x2, respectively. The reactor model is dx1/dt = −k10x1e^−E1∕RT dx2/dt = k10x1e^−E1∕RT − k20x2e^−E2∕RT Thus,

Verified Answer:

The reactor equations are:

\begin{aligned}&...

Question: 6.8

A blending tank that provides nearly perfect mixing is connected to a downstream unit by a long transfer pipe. The blending tank operates dynamically like a first-order process. The mixing characteristics of the transfer pipe, on the other hand, are somewhere between plug flow (no mixing) and

Verified Answer:

a) Transfer Function for the blending tank: [latex...

Question: 11.7

A block diagram for internal model control, a control technique that is considered in Chapter 12, is shown in Fig. E11.7. Transfer function Gp denotes the process model, while Gp denotes the actual process transfer function. It has been assumed that Gv = Gm = 1 for simplicity. Derive closed-loop

Verified Answer:

Using block diagram algebra

\begin{aligned}...

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