The CAP question published in the January InTech has a serious terminology problem. It asks for the transfer function for C(s)/R(s), where C(s) is the output and R(s) is one of the inputs to the diagram, the other input being D(s).
Using the division sign for the transfer function is misleading and incorrect. Basic manipulation of the equations that represent inputs and outputs in the diagram leads to:
Clearly, the ratio C(s)/R(s) will only be represented by answer A when D(s) is identically zero.
Answer A is actually the transfer function G1 that relates C(s) to the input R(s). G1 is just one of the transfer functions that can be defined, and it is not equal to C(s)/R(s).
In the literature:
Luyben (Process modeling, simulation and control for chemical engineers) shows a similar equation: X(s) = G1×L(s) + G2×SP(s).
He never calls G1 the transfer function for X(s)/L(s); he refers to G1 and G2 simply as the first and second transfer functions in the equation (and then names them the regulator and the servo transfer functions, respectively).
Seborg et al (Process dynamics and control) use the same equation as the CAP question, except they use L instead of D: C(s) = G1×R(s) + G2×L(s).
The next step is to arrive at C(s)/R(s) = G1. But before getting to this point, there is a note: "for the moment, consider set-point changes only." In other words, the book states L(s) = D(s) = 0 is a condition for C(s)/R(s) = G1.
Roberto Werneck, Rio de Janeiro, Brazil
Any process has many, possibly even hundreds of "inputs," i1, i2, i3, … and maybe as many or even more "outputs," o1, o2, o3, … Most of the inputs are disturbances of some type, even though they might not be recognized as such: A weather change, a change in steam pressure to a unit operation, a change in air pressure to a valve, a change in the heat transfer coefficient of a heat exchanger, a flow rate change in some obscure part of the process, an operator changing a set point, and on and on. Outputs can be just as wide ranging-flow rates, temperatures, pressures, etc., even if they are not measured.
Even in block diagrams like the one in the question, just because disturbances are not shown does not mean they do not exist.
It is legitimate to consider the transfer function from any one of the inputs such as ia, to any one of the outputs, such as ob. One writes that transfer function as ob divided by ia. It is true that the value of ob is not simply the transfer function times ia-it is really the sum of the transfer functions from each of the hundreds of inputs to that output, times the value of the corresponding input. The example in InTech used the two inputs shown, but all the other inputs were ignored in the example. Inherent in the transfer function concept is that a transfer function from one input to one output assumes all the other inputs are zero. Otherwise transfer functions would be meaningless. With this concept, the answer is correct as stated.
Two possible choices
The Certification Review CCST question in the May InTech is ambiguous in that it does not state the type of service in which the valve is installed.
If the service was such that increasing flow resulted in decreasing pressure drop, then the answer B would be correct. If the pressure drop remained relatively constant (two pressure controlled tanks with minimum piping and control valve in between) then the answer would be linear, or D. The answer could be D or B. It depends on the service and that is what should be added to the question ... a description of the service. If the service was such that increasing flow resulted in decreasing pressure drop (a circuit with a centrifugal pump for instance), then indeed answer B would be correct.
Len Klochek, P.Eng.
Thank you for the much-needed "The Final Say" by Hans D. Baumann in the May InTech, which I received today. From my business as an executive headhunter, I have long known of the efficiencies of ITW. But the contrast between Southwest Airlines and Delta is amazing.
Regarding Baumann's deep concern that Congress "will prevent further mega-mergers between large airlines," check out the comments T. Boone Pickens made in a recent issue of Fast Company magazine, "Not exactly an inspiring vision of Congress": "The leadership is absolutely, totally pissy in Congress-a real conglomeration of fruitcakes. I mean pitiful people." I believe he has nailed it. As long as United, Continental, American, etc., continue to feed the Congressional PACs, why should they care about the terrible airline inefficiencies? They will surely allow Hewlett-Packard to buy out EDS, which also surely means a Restrain of Trade.
Thank you once again for Baumann's insights published in InTech.
Roy A. Bobo II, Houston