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Understanding Process Dynamics and Control

Costas Kravaris, Ioannis K. Kookos

Chapter 11

BLOCK-DIAGRAM REDUCTION AND TRANSIENT-RESPONSE CALCULATION IN A FEEDBACK CONTROL SYSTEM - all with Video Answers

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Chapter Questions

00:13

Problem 1

Simplify the block diagram shown in Figure P11.1.

Kara Merfeld
Kara Merfeld
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00:22

Problem 2

Simplify the block diagrams shown in Figure P11.2.
(a)
(b)
(c)

Rashmi Sinha
Rashmi Sinha
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00:30

Problem 3

Simplify the block diagram shown in Figure P11.3.

Julie Silva
Julie Silva
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00:22

Problem 4

Simplify the block diagram shown in Figure P11.4.

Rashmi Sinha
Rashmi Sinha
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00:22

Problem 5

Simplify the block diagram shown in Figure P11.5.

Rashmi Sinha
Rashmi Sinha
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Problem 6

Consider the closed-loop system shown in Figure P11.6, where the transfer function of the process is that of a second-order system, i.e.
$$
G_p(s)=\frac{k_p}{\tau^2 s^2+2 \zeta \tau s+1}
$$
If the controller is a P controller $\left(G_c(s)=k_c\right)$
(a) determine the closed-loop transfer function
(b) determine the offset to a unit step change of the set point.

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Problem 7

Repeat Problem 11.6 for the case of an integral-only controller with transfer function $G_c(s)=k_I / s$.

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01:53

Problem 8

Repeat Problem 11.6 for the case of a real proportional-derivative controller with transfer function $G_c(s)=k_c\left(1+\tau_D s\right) /\left(1+\alpha \tau_D s\right)$

Chai Santi
Chai Santi
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Problem 9

Consider the closed-loop system shown in Figure P11.6 where the process is a firstorder system, i.e.
$$
G_p(s)=\frac{k_p}{\tau_p s+1}
$$
If the controller is an integral-only controller $\left(G_c(s)=k_I / s\right)$
(a) determine the closed-loop transfer function
(b) determine the offset to a unit step change of the set point.

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01:12

Problem 10

Repeat Problem 11.9 for the case of a real PD controller with transfer function $G_c(s)=k_c\left(1+\tau_D s\right) /\left(1+\alpha \tau_D s\right)$.

Amit Srivastava
Amit Srivastava
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01:13

Problem 11

Consider the system of two tanks in series shown in Figure P11.11, where the volume of the liquid in each tank ( $V_1$ and $\left.V_2\right)$ is constant. The volumetric flowrate of the feed stream is $F$ (constant) and its temperature is $T_0(t)$ and varies significantly (disturbance). A heating coil has been installed in the first tank to control the temperature of its liquid content by adjusting the amount of heat exchanged between the heating medium and the liquid in the tank is $Q(t)$ (manipulated variable).
(a) Derive the transfer function between $T_{s p}$ and $T_2$.
(b) Derive the transfer function between $T_0$ and $T_2$.
(c) If the controller is a $\mathrm{P}$ controller, calculate the offset for a unit step change in either $T_{s p}$ or $T_0$.

Manik Pulyani
Manik Pulyani
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