Modern Control Engineering

158 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems

B–4–11.Consider the controller shown in Figure 4–53. The

input is the air pressure pimeasured from some steady-state

reference pressure and the output is the displacement yof

the power piston. Obtain the transfer function Y(s)Pi(s).

P

–

B–4–12.A thermocouple has a time constant of 2 sec. A

thermal well has a time constant of 30 sec. When the ther-

mocouple is inserted into the well, this temperature-

measuring device can be considered a two-capacitance

system.

Determine the time constants of the combined thermo-

couple–thermal-well system. Assume that the weight of the

thermocouple is 8 g and the weight of the thermal well is

40 g. Assume also that the specific heats of the thermocouple

and thermal well are the same.

aa

bb

Airpi(Input)

y(Output)

x

k

Bellows

Figure 4–53

Controller.

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