Process Dynamics and Control 3rd Edition Chapter 12 Problem 3E Solution - Chegg.com

Process Dynamics And Control 3rd Edition Chapter 12 Problem 3E Solution | Chegg.com

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Chegg Guided Solutions for Process Dynamics and C Chapter 12 Problem 3E CH12

3E

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Printing Disabled Step 2 of 11 Write the expressions for controller settings derived from Equation (1). CH12 2E

…… (2)

…… (3) Consider the process transfer function. …… (4)

Compare Equations (1) and (4).

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Step 3 of 11 (a) Determination of the PI controller settings for the design using direct synthesis method follows: Substitute 2 for

, 0.2 for

, 1 for

, 0.2 for

in Equation (2).

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Process Dynamics And Control 3rd Edition Chapter 12 Problem 3E Solution | Chegg.com

Substitute 1 for

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in Equation (3).

Therefore, the PI controller settings

and

are

and

.

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Step 4 of 11 (b) Determination of the PI controller settings for the design using direct synthesis method follows: Substitute 2 for

Substitute 1 for

, 0.2 for

, 1 for

, 1.0 for

in Equation (2).

in Equation (3).

Therefore, the PI controller settings

and

are

, and

.

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Step 5 of 11 (c)

Consider the design relation for integral of Time Absolute Error (ITAE) of disturbance input a …… (5) Where, for the proportional mode for the integral mode.

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Process Dynamics And Control 3rd Edition Chapter 12 Problem 3E Solution | Chegg.com

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Refer Table 12.3 for the values of A and B. Substitute

for

in Equation (5).

…… (6) Substitute

for

in Equation (5).

…… (7) For P mode, substitute 2 for

For I mode, substitute 2 for

The PI controller settings are

, 0.2 for

, 0.2 for

and

, 1 for

, 1 for

, 0.859 for A, and

for B, in Equati

, 0.674 for A, and

and

for B, in Equatio

.

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Step 6 of 11 (d) The design relation for integral of Time Absolute Error (ITAE) of set point input is, …… (8) Where, for the proportional mode for the integral mode.

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Process Dynamics And Control 3rd Edition Chapter 12 Problem 3E Solution | Chegg.com

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Refer to Table 12.3 for the values of A and B. Substitute

for

in Equation (5).

…… (9) Substitute

for

in Equation (5).

…… (10) For P mode, substitute 2 for

, 0.2 for

For I mode, substitute 2 for

, 0.2 for

The PI controller settings are

, 1 for

, 0.586 for A, and

, 1 for

,

for B, in Equati

for A, and

, and

for B, in Eq

.

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Step 7 of 11 (e) A conservative controller setting typically has small values of The direct synthesis method in part (b) has

and large values of

, and

The controller using direct synthesis method in part (b) gives more conservative settings. The ITAE method in part (c) has

, and

.

The controller using ITAE method in part (c) gives less conservative settings.

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Process Dynamics And Control 3rd Edition Chapter 12 Problem 3E Solution | Chegg.com

Thus, controller in the The controller in

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gives more conservative settings. gives less conservative settings.

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Step 8 of 11 (f) Steps to create the SIMULINK model:

• Take the required blocks from the library browser and connect all the blocks as in Figure 1

• Double click the step response block and set step time value as 1, initial value as 1 and fin

• Double click the transfer function block (Transfer Fcn) and set numerator coefficients as [2 denominator coefficients as [1 1].

• Double click the PID controller block and change the controller to PI type. Set the PI contr form. Set the

value as 0.42 and

value as 1 for part (b) controller. Set the

value

value as0.49 for part(c) controller. • Double click the transport delay block and set the delay value of input as 0.2 • Double click the simout block and change the parameter to array. • Run the SIMULINK model using F5 key. Consider the Figure 1.

Figure 1 Provide feedback (0) http://www.chegg.com/homework-help/process-dynamics-and-control-3rd-edition-chapter-12-problem-3e-solution-9780470128671

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Process Dynamics And Control 3rd Edition Chapter 12 Problem 3E Solution | Chegg.com

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Step 9 of 11 Type the following in the MATLAB command window and press enter. plot(tout,simout,tout,simout1) legend('controller b)','controller c)'); Provide feedback (0)

Step 10 of 11

The comparison of closed-loop step response to a unit step disturbance for controller b) and shown in Figure 2.

Figure 2 Provide feedback (0)

Step 11 of 11

Therefore, the simulation of closed-loop step response to a unit step disturbance is execute is drawn. Provide feedback (0)

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Process Dynamics And Control 3rd Edition Chapter 12 Problem 3E Solution | Chegg.com

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Process Dynamics And Control 3rd Edition Chapter 12 Problem 3E Solution | Chegg.com

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