Exercise 1.9 shows two possible ways to design a feedback control loop to obtain a desired rate of liquid flow. Assume that in both Systems I and II, the flow transmitter is direct-acting (i.e., the output increases as the flow rate increases). The control valve in System I is “air-to-open, meaning

Question

Exercise 1.9 shows two possible ways to design a feedback control loop to obtain a desired rate of liquid flow.

Assume that in both Systems I and II, the flow transmitter is direct-acting (i.e., the output increases as the flow rate increases). The control valve in System I is "air-to-open," meaning that an increasing pressure signal from the controller will open the valve more, thus increasing the flow rate (See Chapter 9). On the other hand, the control valve in System II is "air-to-close." The dynamics for both of the valves are negligible.

(a) For each of these valves, what is the sign of its gain, [latex]K_{v}[/latex] ?

(b) Which controller must be direct-acting? Reverse-acting?

Use physical arguments to support your answers.

(c) What sign should the controller gain have for each case?

Accepted Answer

a)

System I (air-to-open valve): as the signal to the control valve increases, the flow through the valve increases [latex]\Rightarrow K_{v}>0[/latex].

System II (air-to-close valve): as the signal to the control valve increases, the flow through the valve decreases [latex]\Rightarrow K_{v}<0[/latex].

b)

System I: Flow rate too high [latex]\Rightarrow[/latex] need to close valve [latex]\Rightarrow[/latex] decrease

controller output [latex]\Rightarrow[/latex] reverse acting controller

Or: [latex]\quad[/latex] Process gain [latex]+[/latex]

[latex]\quad[/latex][latex]\quad[/latex][latex]\quad[/latex]Valve gain [latex]+[/latex]

Controller gain must be [latex]+[/latex] (which means reverse acting)

System II: Flow rate too high [latex]\Rightarrow[/latex] need to close valve [latex]\Rightarrow[/latex] increase

controller output [latex]\Rightarrow[/latex] direct acting controller.

Or: [latex]\quad[/latex] Process gain [latex]+[/latex]

[latex]\quad[/latex][latex]\quad[/latex][latex]\quad[/latex]Valve gain [latex]-[/latex]

Controller gain must be [latex]-[/latex] (which means direct acting)

c)

System I: [latex]K_{c}>0[/latex].

System II: [latex]K_{c}<0[/latex].

Question 8.4: Exercise 1.9 shows two possible ways to design a feedback co...

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