Methods and systems for controlling rate and output of heat exchanger fluids

Abstract

Systems, methods and devices are disclosed for controlling fluids parameters in a heat exchanger. In one embodiment, an apparatus for controlling a heat exchanger system may include a first controller and a second controller. Each controller may control an actuator associated with a parameter of the heat exchanger system. Each controller may include a feedback gain and a cross coupling gain. The cross coupling gain may cross couple the system inputs to the actuators. The parameters are the temperature and the mass flow rate. The heat exchanges fluids are the heat transfer fluid and the controlled fluid.

Description

BACKGROUND

The present invention relates, in general, to process control, and more particularly to controlling the rate and output of a controlled fluid through a heat exchanger. More specifically, the present invention relates to methods and systems for controlling a plurality of parameters of a heat exchanger system such as the temperature and the mass flow rate of a controlled fluid.

Many chemical processes may require control of a plurality of parameters. For example, control of a heat exchanger may involve control of parameters such as temperature and mass flow rate of one of more fluids in a heat exchanger system. Some heat exchanger systems include two fluids: a heat transfer fluid and a controlled fluid. Typically, the mass flow rates or temperatures of both fluids to a heat exchanger may be independently controlled by actuators. Moreover, changes in the mass flow rates of one of both input fluids of a heat exchanger may lead to large changes in temperature. Consequently, temperature tracking in many heat exchangers may be poor.

A change in the mass flow rate of the controlled fluid in the heat exchanger may propagate through the entire system within a few seconds. Concomitant with the change in mass flow rate, however, is a change in temperature of the controlled fluid. As a result, a temperature gradient may be established within a heat exchanger system, and this gradient may propagate through the system within tens of seconds or minutes following a change in mass flow rate. Thus, many control systems for heat exchangers do not function well in response to a change in a desired temperature or desired mass flow rate of the controlled fluid. Moreover, due to actuator dynamics, many control systems cannot maintain a desired temperature following a large change in the desired mass flow rate of the controlled fluid.

SUMMARY

The present invention relates, in general, to process control, and more particularly to controlling the rate and output of the controlled fluid through a heat exchanger.

More specifically, the present invention relates to methods and apparatus for controlling a plurality of parameters of a heat exchanger system such as the temperature and the mass flow rate of a controlled fluid.

In a first aspect of the invention, a method of maintaining a desired first parameter of a controlled fluid in a heat exchanger system, comprises the steps of measuring a second parameter of the controlled fluid; varying an input to a first parameter actuator as a function of the second parameter of the controlled fluid; measuring the first parameter of the controlled fluid; and varying the input to the first parameter actuator to reduce an error of the first parameter of the controlled fluid indicative of the difference between the measured and desired values of first parameter.

Additionally, the method comprises the steps of varying an input to a second parameter actuator as a function of the first parameter of the controlled fluid; measuring the second parameter of the controlled fluid; and varying the input to the second parameter actuator to reduce an error of the second parameter of the controlled fluid indicative of the difference between the measured and desired values of the second parameter.

A second aspect of the invention, a method of maintaining a desired temperature of a controlled fluid in a heat exchanger system, comprises the steps of measuring a parameter of the controlled fluid; varying an input to a temperature actuator as a function of the parameter of the controlled fluid; measuring a temperature of the controlled fluid; and varying the input to the temperature actuator to reduce an error of the temperature of the controlled fluid indicative of the difference between the measured and desired temperature.

Additionally, when the parameter of the controlled fluid is a mass flow rate, the method comprises the steps of varying an input to a parameter actuator as a function of the temperature of the controlled fluid; measuring the parameter of the control fluid; and varying the input to the parameter actuator to reduce an error of the parameter of the controlled fluid indicative of the difference between the measured and desired values of the parameter.

In a third aspect, a method of maintaining desired parameters of a controlled fluid in a heat exchanger system, wherein the controlled fluid has one or more parameters, and the heat transfer fluid has a parameter, the method comprises the steps of measuring a first parameter of the controlled fluid; and varying an input to a first actuator of the parameter of the heat transfer fluid as a function of an error of the first parameter of the controlled fluid indicative of the difference between the measured and desired values of the first parameter of the controlled fluid.

Additionally, the method comprises the steps of measuring the second parameter of the controlled fluid; and varying an input to a second actuator of the second parameter of the controlled fluid as a function of the second parameter of the controlled fluid.

In a fourth aspect, an apparatus for controlling one or more parameters of a first fluid or a second fluid of a heat exchanger system, wherein the heat exchanger includes a first fluid having one or more parameters and a second fluid having one or more parameters, the apparatus comprises a first controller controlling a first parameter of the heat exchanger system; a second controller controlling a second parameter of the heat exchanger system; and a first cross coupling gain coupling an input of the first controller and an output of the second controller.

In a fifth aspect, an apparatus for controlling one or more parameters of a heat exchanger system, the heat exchanger including a heat transfer fluid and a controlled fluid, the apparatus comprises a first controller controlling an input to a first actuator, the first actuator controlling a first parameter of the heat exchanger system; a second controller controlling an input to a second actuator, the second actuator controlling a second parameter of the heat exchanger system; and a first cross coupling gain coupling an input of the first controller and an output of the second controller.

In another aspect, a system for controlling one or more parameters of a heat exchanger, the heat exchanger including a heat transfer fluid and a controlled fluid, the system comprises a heat exchanger; a first actuator controlling a first parameter of the heat exchanger; a second actuator controlling a second parameter of the heat exchanger; a first parameter monitor; a second parameter monitor; and a controller for controlling the heat exchanger. The controller comprises a first controller controlling an input to the first actuator; a second controller controlling an input to a second actuator; and a first cross coupling gain the first controller and the second controller.

The features and advantages of the present invention will be readily apparent to those skilled in the art upon a reading of the description of the exemplary embodiments which follows.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present disclosure and advantages thereof may be acquired by referring to the following description taken in conjunction with the accompanying drawings wherein:

FIG. 1 is a block diagram of a system for controlling the controlled fluid of a heat exchanger according to the present invention;

FIG. 2 is a block diagram of a system for controlling the controlled fluid of a heat exchanger according to the present invention;

FIG. 3 is a schematic diagram of one embodiment of a control circuit according to the present invention;

FIG. 4 is one embodiment of a control circuit according to the present invention; and

FIG. 5 is another embodiment of a control circuit according to the present invention.

FIG. 6 illustrates a diagram of the implementation of a temperature control system according to the present invention.

FIG. 7 represents different graphs showing the mass flow rate and temperature as functions of time in response to a change in temperature in an example of a nitrogen system.

FIG. 8 represents different graphs showing the heat build valve performance where two valves are implemented, each on a separate hydraulic loop.

The present invention may be susceptible to various modifications and alternative forms. Specific embodiments of the present invention are shown by way of example in the drawings and are described herein in detail. It should be understood, however, that the description set forth herein of specific embodiments is not intended to limit the present invention to the particular forms disclosed. Rather, all modifications, alternatives and equivalents falling within the spirit and scope of the invention as defined by the appended claims are intended to be covered.

DETAILED DESCRIPTION

The present invention relates, in general, to process control, and more particularly to controlling the rate and output of the controlled fluid through a heat exchanger.

The details of the present invention will now be described with reference to the figures. In some embodiments, the present invention comprises methods for controlling the mass flow rate and temperature of a fluid. For example, some cementing or fracturing processes related to the production of hydrocarbons may require a fluid, e.g., nitrogen, having a desired temperature (T_D) and a desired mass flow rate (dM_D/dt). As used herein, “T” denotes temperature, “M” denotes mass, and “dM/dt” denotes mass flow rate. In one embodiment, the present invention may be used in a process requiring nitrogen at a desired temperature of about 100° F. Typically, liquid nitrogen stored at about −320° F. is used as the source of nitrogen. A heat exchanger may be used to increase the temperature of the nitrogen from its source temperature of about −320° F. to about 100° F.

A heat exchanger may include two fluids: a heat transfer fluid and a controlled fluid. Typically, the controlled fluid is the fluid whose temperature and/or mass flow rate is being controlled, and the heat transfer fluid is a fluid functioning as an energy source from which energy is transferred to the controlled fluid (when the temperature of the controlled fluid is being increased) or as an energy sink to which energy is transferred from the controlled fluid (when the temperature of the controlled fluid is being decreased). In one embodiment of the present invention, it may be desirable to control the temperature and mass flow rate of a controlled fluid. For example, it may be desirable to maintain a flow of nitrogen at constant temperature, and at the same time vary the mass flow rate of the nitrogen.

Turning to FIG. 1, a block diagram of one embodiment of a heat exchanger system for controlling the temperature and mass flow rate of a controlled fluid according to the present invention is depicted. As shown in FIG. 1, the controlled fluid nitrogen may be derived from liquid nitrogen stored in tank 180. Pump 190 may pump nitrogen through heat exchanger 350. As the nitrogen passes through heat exchanger 350, the temperature of the nitrogen is increased. The heat exchanger system also includes Pump 160. Pump 160 pumps the heat transfer fluid through heat exchanger 350. Certain embodiments of the present invention control the mass flow rate or temperature of the controlled fluid exiting heat exchanger 350. In other embodiments, the mass flow rate or temperature of the heat transfer fluid of heat exchanger 350 may be controlled.

Various types of pumps may be selected for pumps 160 and 190. In one embodiment, pumps 160 and 190 may be positive displacement pumps. For example, nitrogen may be pumped at a pressure of about 1,000-15,000 psi and at a volume of about 340,000 ft³/hour using a positive displacement pump. One skilled in the art with the benefit of this disclosure will recognize other types of pumps and fluid moving devices that may be used in the present invention.

Another embodiment of the present invention for controlling the temperature and mass flow rate of the controlled fluid is shown in FIG. 2. FIG. 2 includes nitrogen storage tank 180, pump 190 for pumping the nitrogen through heat exchanger 350, and pump 160 for pumping the heat transfer fluid through heat exchanger 350. The system shown in FIG. 2 may also include heat exchanger 250 for controlling the temperature of the heat transfer fluid. As depicted in FIG. 2, the controlled fluid of heat exchanger 250 functions as the heat transfer fluid of heat exchanger 350. The system depicted in FIG. 2 also includes pump 240 and valve 230 for pumping and controlling the flow of the controlled fluid through heat exchanger 250. In another implementation, more than one valve similar to valve 230 can be implemented. One skilled in the art with the benefit of this disclosure will recognize that the present invention may be implemented with one, two, or more heat exchangers. In the same way, more than one pumps 190, 160 or 240 can be implemented on each loop. Additionally, in another embodiment, valve 230 may be included in the system shown in FIG. 1.

In one embodiment, a heated hydraulic fluid may be used as the heat transfer fluid, and water may be used as the controlled fluid of heat exchanger 250. A heat throttle valve having a high pressure and low pressure side may be selected as valve 230. For example, the high pressure side of valve 230 may be maintained around 4000 psi, and the low pressure side may be maintained around 200 psi. The output temperature of the hydraulic fluid from heat throttle valve 230 may be estimated according to the following equation:
T_out=T_in+(V/C)(ΔP),
where T_out is the temperature of the heated hydraulic fluid at the output of the throttle valve, T_in is the temperature at the input of the throttle valve, V is the specific volume of hydraulic fluid that is passing through the throttle valve, C is the specific heat of the hydraulic fluid, and ΔP is the pressure drop across the heat throttle valve (e.g., 3800 psi for the previous example).

One skilled in the art with the benefit of this disclosure will recognize the desirability of controlling the temperature and mass flow rate of the controlled fluid (e.g., nitrogen) of heat exchanger 350 shown in FIGS. 1 and 2. One embodiment of a control circuit for controlling temperature and mass flow rate of a controlled fluid is shown in FIG. 3. The control circuit shown in FIG. 3 includes a first controller for controlling first parameter actuator 308 and a second controller for controlling a second parameter actuator 328. Control of actuators 308 and 328 in turn control the output of heat exchanger 350. The first controller includes a first feedback gain 304 having as an input the output of summation block 302. In the embodiment shown in FIG. 3, the input to first feedback gain 304 is an error between a desired first parameter and a measured first parameter.

In FIG. 3, the second controller includes a second feedback gain 324 having as an input the output of summation block 322. In the same way, the first controller includes a first feedback gain 304 having as an input the output of summation block 302. As shown in FIG. 3, the inputs to second feedback gain 324 and first feedback grain are respectively error between a desired second parameter 321 and a measured second parameter 362, and error between a desired first parameter 301 and a measured first parameter 364.

A first cross coupling gain 330 having as an input the output of summation block 322 may be used to couple the second controller to the first controller. In the embodiment shown in FIG. 3, the input to first cross coupling gain 330 is an error between a desired second parameter and a measured second parameter. The first cross coupling gain 330 may couple the error associated with the second parameter to the first controller. In this fashion, the heat exchanger system may respond quickly to an increase in a second parameter such as the desired temperature, without greatly affecting the first parameter such as mass flow rate. Consequently, the input to the first cross coupling gain 330 may also be the input to the second feedback gain 324.

A second cross coupling gain 312 having as an input the output of summation block 302 may also be included to couple the first controller to the second controller. In the embodiment shown in FIG. 3, the input to second cross coupling gain 312 is an error between a desired first parameter and a measured first parameter. Consequently, the input to the first feedback gain 304 may also be the input to the second cross coupling gain 312.

A third cross coupling gain 310 having as an input a desired first parameter may also be used to couple the first controller to the second controller. Second cross coupling gain 312 and third cross coupling gain 310 may couple the desired first parameter and the error associated with the desired first parameter to the second controller. In this fashion, the heat exchanger system may respond quickly to an increase in a desired first parameter such as a desired mass flow rate of a controlled fluid without a significant change in a desired second parameter such as temperature.

The outputs of respectively first cross coupling gain 330 and second coupling gain 312 are the inputs of summation blocks 306 and 326. Summation block 306 is used for subtracting the output of first cross coupling gain 330 to the output of first feedback gain 304 and for feeding the input of first parameter actuator 308. Summation block 325 is used for adding the outputs of second feedback gain 324, third cross coupling gain 310 and second cross coupling gain 312 and for feeding the input of second parameter actuator 328.

The measured first parameter and measured second parameter of the embodiment shown in FIG. 3 may fed back with unitary gain. One skilled in the art with the benefit of this disclosure will recognize that the measured parameters may be processed through one or more filters or transfer functions before being fed back to the summation blocks 322 and 302. For example, a feedback transfer function may be used to introduce or correct for a time lag in the control system of FIG. 3.

Another embodiment of the present invention is shown in FIG. 4. In this example, the first parameter is the controlled fluid mass flow rate, the second parameter is the temperature of the controlled fluid. For the example shown in FIG. 4, the first parameter actuator is the controlled fluid mass flow rate actuator 408, and the second parameter actuator is the heat transfer fluid actuator 428. One skilled in the art with the benefit of this disclosure will recognize that the temperature of the controlled fluid may be controlled by controlling either the temperature or the mass flow rate of the heat transfer fluid. The heat transfer mass flow rate actuator 428 output and the controlled fluid mass flow rate actuator 408 output may be used to control heat exchanger 350. Moreover, the first and second feedback gains may be selected to be proportional-integral-derivative (PID) controllers 404 and 424, respectively. The measured temperature 462 and the measured mass flow rate 464 of the controlled fluid are fed back to the second and first cross coupling gains, respectively. The first, second, and third cross coupling gains 430, 412, and 410 in the example of FIG. 4 have been selected to be K₁, K₂, and K₃, respectively.

The first controller for controlling the controlled fluid mass flow rate actuator 408 for the example depicted in FIG. 4 includes PID controller 404 as a feedback gain. The PID controller 404 input is an error between a desired mass flow rate and a measured mass flow rate. And the second controller for controlling the heat transfer fluid mass flow rate includes PID controller 424 as a feedback gain. The PID controller 424 input is an error between a desired temperature and a measured temperature. A proportional cross coupling gain K₁, referred as 430, couples the error associated with a desired temperature to the output of PID controller 404. The combination of the output of PID controller 404 and the output of cross coupling gain K₁ is used as the input to controlled fluid mass flow rate actuator 408. Cross coupling gain K₂, referred as 412, couples the error associated with a desired and measured mass flow rate of the controlled fluid to the output of PID controller 424. Cross coupling gain K₃, referred as 410, couples the desired mass flow rate of the controlled fluid to the output of PID controller 424. The combination of the output of PID controller 424 and the outputs from cross coupling gains K₂ and K₃ is used as the input to the working fluid mass flow rate actuator 428.

As shown in FIG. 4, the output of a summation block 426 which sums the outputs of the PID controller 424 and cross couple gains K₂, K₃ is the input of the heat transfer fluid actuator 428. In the same way, the output of a summation block 406 which subtracts the output of cross coupling gain K₁ to the output of the PID controller 404 is the input of controlled fluid mass flow rate actuator 408.

The typical input to a PID controller may be an error function, wherein the error function is calculated as the difference between a desired parameter and a measured parameter. In the case of the first controller for controlling the controlled fluid mass flow rate actuator, the desired parameter may be a desired mass flow rate, and the measured parameter may be the measured mass flow rate of the controlled fluid of heat exchanger 350. The outputs of PID controllers 404 and 424 function to drive the temperature error and mass flow rate error to zero. The temporal response to a PID controller may be given by the following equation: $u\left(t\right)=K_{p}e\left(t\right)+K_i\int e\left(t\right)dt+K_d\frac{de\left(t\right)}{dt},$
where K_p, K_i, K_d are constants for the proportional, integral, and derivative terms, respectively, of the PID controller, and ε(t) is an error function as a function of time.

The temporal response of the PID controller may be transformed to the frequency domain through the use of a Laplace transform. The Laplace transform of the temporal response of a PID controller may be given by the following equation: $U\left(s\right)=\left(K_p+\frac{K_i}{s}+K_{d}s\right)E\left(s\right).$

One skilled in the art with the benefit of this disclosure will recognize that the methods, devices, and systems of the present invention may be applied to digital signals, as well as analog signals. The digital signals may be processed using digital transform functions, including, but not limited to, Z transforms, Fast Fourier transforms, wavelet transforms.

The input to PID controller 404 for the example depicted in FIG. 4 is the error ε_dM, which is the error between the desired mass flow rate of the controlled fluid dM_D/dt and the measured mass flow rate of the controlled fluid of the heat exchanger dM_M/dt. The output from PID controller 404 may be connected to summation block 406. The output of the first cross coupling gain 430 is fed negatively into summation block 406. The input to first cross coupling gain 430 may be an error ε_T, which is the error between the desired temperature of the-controlled fluid T_D and the measured temperature of the controlled fluid of the heat exchanger T_M. As depicted in FIG. 4, first cross coupling gain 430 includes a proportional transfer function K₁. One skilled in the art with the benefit of this disclosure will recognize that the selection of the constant K₁ and the constants associated with the PID controller 404 may be determined empirically and optimized, if necessary. Furthermore, in other embodiments, the first feedback gain 404 may be chosen to have other transfer functions such as a PI controller.

The mass flow rates of the heat transfer fluid and the controlled fluid may be inputted into the system through, inter alia, a pump, valve, or blower. The mass flow rate of the heat transfer fluid may be controlled by the error in the desired temperature output of the controlled fluid and the error in the desired mass flow rate of the controlled fluid. The mass flow rate of the controlled fluid may also be controlled by the error in the desired temperature output of the controlled fluid and the error in the desired mass flow rate of the controlled fluid. By cross coupling the inputs, the mass flow rate of the heat transfer fluid and the controlled fluid may be driven by the desired mass flow rate and desired temperature of the controlled fluid.

The output of first cross coupling gain 430 may improve system performance through, inter alia, cross coupling the error ε_T associated with the desired temperature T_D to the controller for controlling the mass flow rate actuator 408 of the controlled fluid. For example, if the desired temperature T_D increases, ε_T will accordingly increase, and consequently the input to the controlled fluid mass flow rate actuator 408 will decrease, which in turn should permit more energy per mass to be added to the controlled fluid resulting in an increase in the temperature of the controlled fluid. Similarly, a decrease in the desired temperature T_D should lead to an increase in the controlled fluid mass flow rate, which in turn should lead to a decrease in the temperature of the controlled fluid.

More generally, the control system depicted in FIG. 4 may include a second controller for controlling the mass flow rate actuator 428 of the heat transfer fluid. The second controller may comprise a second feedback gain 424. The second cross coupling gain 412, and the third cross coupling gain 410 may couple the second controller to the first controller. As previously discussed, a PID controller may be chosen as the second feedback gain 424. One skilled in the art with the benefit of this disclosure will recognize that the transfer function of the second feedback gain 424 may include other functions and variants including a PI controller.

In the embodiment shown in FIG. 4, second cross coupling gain 412 includes a cross coupling gain K₂. The input to second cross coupling gain 412 may be the error ε_dM between the desired mass flow rate of the controlled fluid dM_D/dt and the measured mass flow rate of the controlled fluid dM_M/dt. Additionally, third cross coupling gain 410 may include a proportional gain K₃. The desired mass flow rate of the controlled fluid dM_D/dt may be selected as the input to third cross coupling gain 410. The outputs of second feedback gain 412 and third feedback gain 410 may combined along with the output from second feedback controller 424 at summation block 426.

The second cross coupling gain 412 and the third cross coupling gain 410 may cross couple the desired mass flow rate dM_D and the error ε_dM in the desired mass flow rate to the control of the mass flow rate of the heat transfer fluid. For example, as the desired mass flow rate of the controlled fluid increases, the output of the second cross coupling gain 412 and the third cross coupling gain 410 increase, which in turn, increases the input to the heat transfer fluid mass flow rate actuator 428. Consequently, the mass flow rate of the heat transfer fluid should increase.

An increase in the desired mass flow rate of the controlled fluid absent an increase in the mass flow rate and/or temperature of the heat transfer fluid should reduce the time available for the controlled fluid to absorb energy from the heat transfer fluid. Consequently, the amount of energy transfer between the two fluids of the heat exchanger may be reduced. However, if the energy capacity of the heat transfer fluid is increased through, for example, increasing the mass flow rate of the controlled fluid, then an increase the temperature of the working fluid would be expected.

In the embodiment shown in FIG. 4 an increase in the mass flow rate of the controlled fluid, which in isolation, would tend to decrease the temperature of the controlled fluid, may be offset by increasing the heat transfer fluid mass flow rate. As a result, an increase in the desired mass flow rate of the controlled fluid in FIG. 4 would increase not only the desired mass flow rate M_D, but also the error dM_D/dt associated with the desired mass flow rate. Thus, when the desired temperature is increased, the third cross coupling gain 410 may add energy to the controlled fluid by increasing the mass flow rate of the heat transfer fluid. Additionally, when the error rate of the desired temperature is large, e.g., a large change in the desired temperature, the second cross coupling function 412 also adds additional energy to the controlled fluid by increasing the mass flow rate of the heat transfer fluid.

These increases associated with the desired mass flow rate are fed forward through second and third cross coupling functions 412 and 410, which in turn result in an increase the mass flow rate of the heat transfer fluid. The increase in the mass flow rate of the heat transfer fluid in combination with an increase in the mass flow rate of the controlled fluid provides the system the ability to increase the desired mass flow rate of the controlled fluid without resulting in a large change in the temperature of the controlled fluid. In other words, the cross coupling gains K₂ and K₃ link changes in the mass flow rate input of the controlled fluid to changes in the actuator of the heat transfer fluid mass flow rate such that an increase in mass flow rate of the controlled fluid will result in a minimal increase in the output temperature T_out of the heat exchanger.

One skilled in the art with the benefit of this disclosure will recognize that energy may be added to a heat exchanger system by increasing the mass flow rate of the heat transfer fluid or by increasing the temperature of the heat transfer fluid.

As depicted in the example of FIG. 5, the second parameter actuator may be chosen as the heat transfer temperature actuator. Consequently, the system performance may be improved by the use of the cross coupling gains K₁, K₂, and K₃ respectively referred as 530, 512 and 510. For example, the system depicted in FIG. 5 can maintain a relatively constant temperature following an increase in the desired mass flow rate of the controlled fluid.

The example depicted in FIG. 5 includes PID controllers 504 and 524, heat transfer fluid temperature actuator 528, controlled fluid mass flow rate actuator 508, and heat exchanger 350. The input to PID controller 524 is a controlled fluid temperature error ST generated by summation element 522. The input to PID controller 504 is a controlled fluid mass flow rate error ε_dM/dt generated by summation element 502. The temperature error, mass flow rate, and mass flow rate error may be fed forward through cross coupling gains K₁, K₂, and K₃ as shown in FIG. 5.

The cross coupling gains K₁, K₂, and K₃, referred as 530, 512 and 510, may cross couple the mass flow rate and the energy input to improve temperature control. For example, a temperature error may be amplified by gain K₁ and fed negatively through a summation block 506 into the mass flow rate input to slow the mass flow rate of the controlled fluid when there is a temperature offset. The summation block 506 also receives the output of PID controller 504. Additionally, the desired mass flow rate of the controlled fluid may be amplified by gain K₃ to feed forward an approximated energy input required for a specified mass flow rate. The mass flow rate error may also be used to approximate an additional energy input required to respond to a specific mass flow rate. For example, the mass flow rate error may be amplified by K₂ to boost the energy input during the occurrence of a large change in mass flow rate of the controlled fluid. The cross coupling terms working in conjunction with the PID control loops may improve temperature control of a controlled fluid with a variable mass flow rate. Cross coupling gains K₂ and K₃ are positively fed through a summation block 526 into the heat transfer fluid temperature actuator 528. The summation block 506 also receives the output of PID controller 524.

In one embodiment, the present invention includes a method for controlling a plurality of parameters of a heat exchanger system comprising at least a heat exchanger. The heat exchanger system may include a heat transfer fluid and a controlled fluid. The method includes determining a first parameter error and determining a second parameter error. The method also includes generating a first and second control signals. The first control signal is the output from a first controller which in turn may control a first actuator. The second control signal is the output from a second controller which also in turn may control a second actuator. Additionally, a first coupling gain couples the first controller and the second controller.

In another one embodiment, the present invention includes an apparatus for controlling a plurality of parameters of a heat exchanger system comprising at least a heat exchanger. The heat exchanger may include a heat transfer fluid and a controlled fluid. The apparatus may include a first controller controlling a first parameter of the heat exchanger system, a second controller controlling a second parameter of the heat exchanger system, and a first cross coupling gain coupling the first controller and the second controller.

In still another embodiment, the present invention includes an apparatus for controlling a plurality of parameters of a heat exchanger system comprising at least a heat exchanger. The heat exchanger may include a heat transfer fluid and a controlled fluid. The apparatus may include a first controller controlling an input to a first actuator, a second controller controlling an input to a second actuator, and a first cross coupling gain coupling the first controller and the second controller. The first actuator may control a first parameter of the heat exchanger system, and the second actuator may control a second parameter of the heat exchanger system.

In yet another embodiment, the present invention includes a system for controlling a plurality of parameters of a heat exchanger system comprising at least a heat exchanger. The heat exchanger may include a heat transfer fluid and a controlled fluid. The system may include a first actuator, a second actuator, a first parameter monitor, a second parameter monitor, and a controller for controlling the heat exchanger. The first actuator may control a first parameter of the heat exchanger, the second actuator may control a second parameter of the heat exchanger. The controller may include a first controller controlling an input to the first actuator, a second controller controlling an input to a second actuator, and a first cross coupling gain coupling the first controller and the second controller.

To facilitate a better understanding of the present invention, the following examples in FIGS. 6, 7 and 8 of exemplary embodiments are given. In no way should the following examples be read to limit the scope of the invention.

FIG. 6 illustrates a diagram of the implementation of the temperature control system. Conceptually the system does not change from the designs shown in the previous figures except that the heat transfer fluid temperature actuator in the present case is more complex and is now under reference 628.

In the implementation as shown in FIG. 6, the first and second parameters are respectively the mass flow rate and the temperature of the controlled fluid. A feedback gain is selected to be proportional-integral-derivative (PID) controller 624 whose input is the error between the desired and measured temperature (T_D−T_M) which is the output of a summation block 622. The PID controller 624 controls a N₂ diverter valve 629 which in turn controls an exhaust heat exchanger 631 and H₂O to N₂ heat exchanger 632. Both the exhaust heat exchanger 631 and the H₂O to N₂ heat exchanger 632 feed positively a summation block 630. The output of summation block 630 is then used to feed back negatively the summation block 622 with a first control loop.

Within the heat transfer fluid temperature actuator 628, the H₂O to N₂ heat exchanger 632 is also connected to the output of an hydraulic to H₂O heat exchanger 633 which is controlled by one or more hydraulic heat valve(s) 637. The output of the hydraulic to H₂O heat exchanger 633 is used a second control loop 638 that will be described more in detail later on. In one implementation, the hydraulic to H₂O heat exchanger 633 is cooperative with a comingling chamber 636 whose input is connected to a switch 634 which also feeds the hydraulic to H₂O heat exchanger 633. The output of the comingling chamber 636 is connected to a switch 635 which feeds the hydraulic to H₂O heat exchanger 633.

Not only is the heat transfer fluid temperature actuator 628 controlled by PID controller 624, but it is also controlled by an additional controller block. This additional controller block receives two types of inputs: Rate_D and (T_D+66 ), where Rate_D represents the desired mass flow rate, T_D the desired temperature and Δ the slight variation. A proportional transfer function K_r, referred as 600, is applied to the input Rate_D and positively fed to a summation block 601 which also receives the input (T_D+Δ). The output of summation block 601 is then fed to another summation block 603 which is also negatively fed by the control loop input. The output of summation block 603 is then fed into a PID controller 605 which is used to control the hydraulic heat valve(s) 637 through a summation block 626.

The summation block 626 is also positively fed with a proportional transfer function K_ffd referred as 610 which has Rate_D as an input. K_ffd can be considered as a feed forward transfer function of Rate_D. Furthermore, the summation block 626 is also positively fed forward with another input. The Rate_D is fed to a First Order lag transfer function 605 before it is fed to a derivative function 607 and a proportional transfer function K_d referred as 612. The gains K_d and K_ffd can be respectively assimilated to K₂ and K₃ of FIGS. 4 and 5 which are fed forward to summation block 626.

The second control loop 638 that negatively feed back the output of the hydraulic to H₂O heat exchanger 633 to one of the inputs of the summation block 603 enables to feed the input of the PID 605 with the error between the desired and the measured temperatures of H₂O.

FIG. 7 shows different graphs in the case of the temperature control main component. In this system, the nitrogen is the controlled fluid, and the mass flow rate and temperature are functions of time in response to a change in temperature.

FIG. 7 shows a graph of the temperature control main components. It contains the nitrogen rate, also referred as Rate-multiBy (curve A), the nitrogen output temperature, also referred as Spare discharge Temp (curve B₂), the water input to the water to nitrogen heat exchanger (curve B₁), and the nitrogen diverter valve position (curve C). As is shown, the water temperature control is slow, it is also fluctuating due to the co-mingling chamber receiving hot water from the engine. As shown on the graph, the output temperature starts off too high, it then returns to the desired temperature of 70 degrees. At each rate increase, it drop slightly then returns to the set point. Under manual control, the industry standard, the temperature is control to within 30 degrees of set point, with this control I can control it to within 4 degrees during step changes and within 1 at steady state.

As shown in FIG. 7, the Rate-multiBy (curve A) depicts the mass flow rate out of the pump of nitrogen in standard cubic feet per minute (scfm). The control system is controlling this rate. When the rate changes the required energy input changes to maintain the temperature setpoint. The setpoint of the temperature (curve B₂) is 70 degrees F. When the system first starts there is excess energy in it, therefore the temperature (curve B₂) starts at about 86 degrees. It then returns to the setpoint and limit cycles at + or −1 degree. The limit cycle is caused by the diverter valve which is only a on/off system, leading it to over/under shoot. After it has hit steady state the rate (curve A) is increased from 2000 scfm to 3000 scfm, at which point the temperature (curve B₂) undershoots then overshoots about 3 or 4 degrees before it settles out at the setpoint.

Due to the fact the rate can change without prior knowledge (the operator just changes the rate setpoint and the controller goes to that setpoint) there will always be some change in temperature. To mitigate this behavior the control system uses the feed forward gains K2, K3, and Kr. Gain K1 would also improve the performance, but it was not implemented because this unit is required to track a rate command from another unit, therefore, I can not effect the rate from the temperature error.

This system could be used with other fluids. We do use CO2 in fracturing. But this control system could be used with any system in which a fluid/gas is heated (or cooled) to a specified setpoint with a changeable output rate. The only thing that would change between using N2 or another fluid, such as CO2, would be the required heated. Therefore the system would have to be tuned relative to the fluid, but the overall control system would not change.

FIG. 8 illustrates different graphs showing the heat build valve performance. There are two valves, each on a separate hydraulic loop.

In the diagram, T_D represents the desired nitrogen output temperature, rate_D is the desired nitrogen rate. On the unit there are 2 heat exchangers that control the output nitrogen temperature: A water to nitrogen parallel flow heat exchanger (shown as “H₂O to N₂ Heat Exchanger”) and a heat exchanger using the exhaust gas from the engines (“exhaust Heat Exchanger”). After testing the unit it was found that the water to nitrogen heat exchanger had a response time that was very slow, about 3 minutes, therefore an exhaust heat exchanger is implemented, which had a response of a few seconds, to run the fine control of the temperature.

Control loop #1 controls a diverter valve that itself controls the flow of nitrogen between the exhaust heat exchanger and water to nitrogen heat exchanger. Under normal operating conditions about 80-90% of the nitrogen is flowing to the water to nitrogen heat exchanger, the rest is going to the exhaust heat exchanger. Control loop #1 is closed around the output nitrogen temperature.

Control loop #2 controls the position of a heat build valve in the hydraulic system. The hydraulic oil is then fed into a hydraulic to water heat exchanger, the water is then fed into the water to nitrogen heat exchanger. This control loop is used to maintain a specified water temperature that is dependant on the desired output nitrogen temperature and the designed rate.

To help the system when rate changes occur, two feed forward terms are included. As shown in FIG. 5 from the current application draft, they represent gain K2 and K3. In this case, the differential feed forward term is implemented from the desired rate only. In the present example the desired rate is in the form of step functions, and send it through a 1st order lag. This signal is then differentiated to get a decaying impulse input. The reason of this differentiation is that the rate control is very fast, within a few seconds, and it is expected that the effect of the asked for rate change on the temperature control to have a longer effect. Another subsystem to notice is the H₂O co-mingling chamber. This takes the cooling water from the engines and mixes in with the water in the heat exchanger system. The valve that controls this is only on or off, therefore, it is designed to turn on at a certain rate (currently set to 1900 scfm).

FIG. 8 also illustrates graphs where the maximum pressure allowed is 4000 psi in each hydraulic loop. It can be noted that the Hyd heater Valve position (curve C₁), which drives the hyd heater pressure (curve D₂), holds the pressure to 4000 psi and begins to reroute the input into the cryo valve. In the same way, the cryo Valve position (curve C₂) is driving the cryo Pressure (curve D₁).

From FIG. 8, it can be seen that there is always pressure in the hyd heater pressure (curve D₂) during operation and there is pressure in the cryo pressure (curve D₁) during higher rates. This is used to perform two operations:

1) If the engines are under load (due to driving the pressure in the system) the exhaust will increase in temperature, allow for more energy to be extracted from the exhaust/N2 heat exchanger, and

2) The two operations are used to increase the hydraulic oil temperature, which will increase the water temperature, which will then increase the heat available for N2.

The present invention is well-adapted to carry out the objects and attain the ends and advantages mentioned as well as those which are inherent therein. While the invention has been depicted, described, and is defined by reference to exemplary embodiments of the invention, such a reference does not imply a limitation on the invention, and no such limitation is to be inferred. The invention is capable of considerable modification, alternation, and equivalents in form and function, as will occur to those ordinarily skilled in the pertinent arts and having the benefit of this disclosure. The depicted and described embodiments of the invention are exemplary only, and are not exhaustive of the scope of the invention. Consequently, the invention is intended to be limited only be the spirit and scope of the appended claims, giving full cognizance to equivalents in all respects.

Claims

1. A method of maintaining a desired first parameter of a controlled fluid in a heat exchanger system, comprising the steps of:

measuring a second parameter of the controlled fluid;

varying an input to a first parameter actuator as a function of the second parameter of the controlled fluid;

measuring the first parameter of the controlled fluid; and

varying the input to the first parameter actuator to reduce an error of the first parameter of the controlled fluid indicative of the difference between the measured and desired values of first parameter.

2. The method of claim 1 further comprising the steps of:

varying an input to a second parameter actuator as a function of the first parameter of the controlled fluid;

measuring the second parameter of the controlled fluid; and

varying the input to the second parameter actuator to reduce an error of the second parameter of the controlled fluid indicative of the difference between the measured and desired values of the second parameter.

3. The method of claim 2 further comprising the steps of:

generating a first control signal from a first controller, wherein the first controller controls the first parameter actuator; and

generating a second control signal from a second controller, wherein the second controller controls the second parameter actuator.

4. The method of claim 3 wherein:

a first cross coupling gain couples an input of the first controller with an output of the second controller; and

a second cross coupling gain couples an input of the second controller with an output of the first controller.

5. The method of claim 3 wherein a third cross coupling gain couples the desired first parameter with an output of the second controller.

6. The method of claim 1 wherein the first controller comprises a first feedback gain having an input being derived from a desired first parameter of the heat exchanger system.

7. The method of claim 6 wherein the first feedback gain is one of a proportional (P) gain, proportional-integral (PI) controller gain, and a proportional-integral-derivative (PID) controller gain.

8. The method of claim 7 wherein the input to the first feedback gain is a function of the desired and measured first parameter.

9. The method of claim 1 wherein the second controller comprises a second feedback gain having an input being derived from a desired second parameter of the heat exchanger system.

10. The method of claim 9 wherein the second feedback gain is one of a proportional (P) gain, proportional-integral (PI) controller gain, and a proportional-integral-derivative (PID) controller gain.

11. The method of claim 10 wherein the input to the second feedback gain is a function of the desired and measured second parameter.

12. The method of claim 1 wherein the first cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

13. The method of claim 1 wherein the first parameter of the controlled fluid is the temperature of the controlled fluid.

14. The method of claim 13 wherein the second parameter of the controlled fluid is the mass flow rate of the controlled fluid.

15. A method of maintaining a desired temperature of a controlled fluid in a heat exchanger system, comprising the steps of:

measuring a parameter of the controlled fluid;

varying an input to a temperature actuator as a function of the parameter of the controlled fluid;

measuring a temperature of the controlled fluid; and

varying the input to the temperature actuator to reduce an error of the temperature of the controlled fluid indicative of the difference between the measured and desired temperature.

16. The method of claim 15 wherein the parameter of the controlled fluid is a mass flow rate.

17. The method of claim 16 further comprising the steps of:

varying an input to a parameter actuator as a function of the temperature of the controlled fluid;

measuring the parameter of the control fluid; and

varying the input to the parameter actuator to reduce an error of the parameter of the controlled fluid indicative of the difference between the measured and desired values of the parameter.

18. The method of claim 17 further comprising the steps of:

generating a first control signal from a first controller, wherein the first controller controls the temperature actuator; and

generating a second control signal from a second controller, wherein the second controller controls the parameter actuator.

19. The method of claim 18 wherein:

a first cross coupling gain couples an input of the first controller with an output of the second controller; and

a second cross coupling gain couples an input of the second controller with an output of the first controller.

20. The method of claim 18 wherein a third cross coupling gain couples the desired first parameter with an output of the second controller.

21. A method of maintaining desired parameters of a controlled fluid in a heat exchanger system, wherein the controlled fluid has one or more parameters, and the heat exchanger includes a heat transfer fluid having a parameter, the method comprising the steps of:

measuring a first parameter of the controlled fluid; and

varying an input to a first actuator of the parameter of the heat transfer fluid as a function of an error of the first parameter of the controlled fluid indicative of the difference between the measured and desired values of the first parameter of the controlled fluid.

22. The method of claim 21 further comprising the steps of:

measuring the second parameter of the controlled fluid; and

varying an input to a second actuator of the second parameter of the controlled fluid as a function of the second parameter of the controlled fluid.

23. The method of claim 22 further comprising the steps of:

varying the input to the first actuator to reduce the error of the first parameter of the controlled fluid; and

varying the input to the second actuator to reduce an error of the second parameter of the controlled fluid indicative of the difference between the measured and desired values of the second parameter of the controlled fluid.

24. The method of claim 23 further comprising the steps of:

generating a first control signal from a first controller, wherein the first controller controls the first actuator; and

generating a second control signal from a second controller, wherein the second controller controls the second actuator.

25. The method of claim 24 wherein:

a first cross coupling gain couples an input of the first controller with an output of the second controller;

a second cross coupling gain couples an input of the second controller with an output of the first controller; and

a third cross coupling gain couples the desired first parameter with an output of the second controller.

26. The method of claim 25 wherein:

the first and second parameters of the controlled fluid are respectively the temperature and the mass flow of the controlled fluid; and

the parameter of the heat transfer fluid is the temperature of the heat transfer fluid.

27. A method of maintaining desired parameters among a plurality of parameters of a heat exchanger system, wherein the heat exchanger system includes a first fluid having one or more parameters and a second fluid having one or more parameters, the method comprising the steps of:

measuring a first parameter of the first fluid; and

varying an input to a first actuator of the second fluid as a function of an error of the first parameter of the first fluid indicative of the difference between the measured and desired values of the first parameter of the first fluid.

28. The method of claim 27 further comprising the steps of:

measuring a second parameter of the first fluid; and

varying an input to a second actuator of the second parameter of the first fluid as a function of the second parameter of the first fluid.

29. The method of claim 28 further comprising the steps of:

varying the input to the first actuator to reduce the error of the first parameter of the first fluid; and

varying the input to the second actuator to reduce an error of the second parameter of the first fluid indicative of the difference between the measured and desired value of the second parameter of the first fluid.

30. The method of claim 29 further comprising the steps of:

generating a first control signal from a first controller, wherein the first controller controls the first actuator; and

generating a second control signal from a second controller, wherein the second controller controls the second actuator.

31. The method of claim 30 wherein:

a first cross coupling gain couples an input of the first controller with an output of the second controller;

a second cross coupling gain couples an input of the second controller with an output of the first controller; and

a third cross coupling gain couples the desired first parameter with an output of the second controller.

32. The method of claim 31 wherein:

the first and second parameters of the controlled fluid are respectively the temperature and the mass flow rate of the controlled fluid; and

the parameter of the heat transfer fluid is the temperature of the heat transfer fluid.

33. An apparatus for controlling one or more parameters of a first fluid or a second fluid of a heat exchanger system, wherein the heat exchanger includes a first fluid having one or more parameters and a second fluid having one or more parameters, the apparatus comprising:

a first controller controlling a first parameter of the heat exchanger system;

a second controller controlling a second parameter of the heat exchanger system; and

a first cross coupling gain coupling an input of the first controller and an output of the second controller.

34. The apparatus of claim 33 further comprising a second cross coupling gain coupling an input of the second controller and an output of the first controller.

35. The apparatus of claim 34 wherein the first and second cross coupling gain include at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

36. The apparatus of claim 33 further comprising a third cross coupling gain coupling a desired first parameter of the heat exchanger and an output of the second controller.

37. The apparatus of claim 36 wherein the third cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

38. The apparatus of claim 33 wherein the first controller comprises a first feedback gain having an input being derived from a desired first parameter of the heat exchanger system.

39. The apparatus of claim 38 wherein the first feedback gain is one of a proportional (P) gain, proportional-integral (PI) controller gain, and a proportional-integral-derivative (PID) controller gain.

40. The apparatus of claim 39 wherein the input to the first feedback gain is a function of the desired first parameter and a measured first parameter.

41. The apparatus of claim 33 wherein the second controller comprises a second feedback gain having an input being derived from a desired second parameter of the heat exchanger system.

42. The apparatus of claim 41 wherein the second feedback gain is one of a proportional (P) gain, proportional-integral (PI) controller gain, and a proportional-integral-derivative (PID) controller gain.

43. The apparatus of claim 42 wherein the input to the second feedback gain is a function of the desired second parameter and a measured second parameter.

44. The apparatus of claim 33 wherein the first cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

45. The apparatus of claim 33 wherein the first parameter includes at least one of a temperature and a mass flow rate of the first fluid.

46. The apparatus of claim 33 wherein the second parameter includes at least one of a temperature and a mass flow rate of the first fluid.

47. The apparatus of claim 33 wherein the first fluid is one of a heat transfer fluid and a controlled fluid.

48. The apparatus of claim 33 wherein the first parameter includes at least one of a temperature of the second fluid.

49. The apparatus of claim 33 wherein the second parameter includes at least one of a temperature and mass flow rate of the second fluid.

50. The apparatus of claim 33 wherein the second fluid is one of a heat transfer fluid and a controlled fluid.

51. An apparatus for controlling one or more parameters of a heat exchanger system, wherein the heat exchanger includes a heat transfer fluid and a controlled fluid, the apparatus comprising:

a first controller controlling an input to a first actuator, wherein the first actuator controls a first parameter of the heat exchanger system;

a second controller controlling an input to a second actuator, wherein the second actuator controls a second parameter of the heat exchanger system; and

a first cross coupling gain coupling an input of the first controller and an output of the second controller.

52. The apparatus of claim 51 further comprising a second cross coupling gain coupling an input of the first controller and an output of the second controller.

53. The apparatus of claim 52 wherein the second cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

54. The apparatus of claim 51 further comprising a third cross coupling gain coupling the desired first parameter with an output of the second controller.

55. The apparatus of claim 54 wherein the third cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

56. The apparatus of claim 51 wherein the first controller comprises a first feedback gain having an input, wherein the input to the first feedback gain is derived from a desired first parameter of the heat exchanger system.

57. The apparatus of claim 56 wherein the first feedback gain is one of a proportional (P) gain, proportional-integral (PI) controller gain, and a proportional-integral-derivative (PID) controller gain.

58. The apparatus of claim 57 wherein the input to the first feedback gain is a function of the desired first parameter and a measured first parameter.

59. The apparatus of claim 51 wherein the second controller comprises a second feedback gain having an input, wherein the input to the second feedback gain is derived from a desired second parameter of the heat exchanger system.

60. The apparatus of claim 59 wherein the second feedback gain is one of a proportional (P) gain, proportional-integral (PI) controller gain, and a proportional-integral-derivative (PID) controller gain.

61. The apparatus of claim 60 wherein the input to the second feedback gain is a function of the desired second parameter and a measured second parameter.

62. The apparatus of claim 51 wherein the first cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

63. The apparatus of claim 51 wherein the first parameter includes at least one of a temperature and a mass flow rate of the controlled fluid.

64. The apparatus of claim 51 wherein the second parameter includes at least one of a temperature and a mass flow rate of the controlled fluid.

65. A system for controlling one or more parameters of a heat exchanger, wherein the heat exchanger includes a heat transfer fluid and a controlled fluid, the system comprising:

a heat exchanger;

a first actuator, wherein the first actuator controls a first parameter of the heat exchanger;

a second actuator, wherein the second actuator controls a second parameter of the heat exchanger;

a first parameter monitor;

a second parameter monitor; and

a controller for controlling the heat exchanger, the controller comprising: a first controller controlling an input to the first actuator; a second controller controlling an input to a second actuator; and a first cross coupling gain coupling the first controller and the second controller.

66. The system of claim 65 further comprising a second cross coupling gain coupling an input of the first controller and an output of the second controller.

67. The system of claim 66 wherein the second cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

68. The system of claim 65 further comprising a third cross coupling gain coupling the desired first parameter with an output of the second controller.

69. The system of claim 68 wherein the third cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

70. The system of claim 65 wherein the first controller comprises:

a first feedback gain having an input, wherein the input to the first feedback gain is derived from a desired first parameter of the heat exchanger system.

71. The system of claim 70 wherein the first feedback gain is one of a proportional (P) gain, proportional-integral (PI) controller gain, and a proportional-integral-derivative (PID) controller gain.

72. The system of claim 71 wherein the input to the first feedback gain is a function of the desired first parameter and a measured first parameter.

73. The system of claim 65 wherein the second controller comprises a second feedback gain having an input, wherein the input to the second feedback gain is derived from a desired second parameter of the heat exchanger system.

74. The system of claim 73 wherein the second feedback gain is one of a proportional (P) gain, proportional-integral (PI) controller gain, and a proportional-integral-derivative (PID) controller gain.

75. The system of claim 74 wherein the input to the second feedback gain is a function of the desired second parameter and a measured second parameter.

76. The system of claim 65 wherein the first cross coupling gain includes at least one of a proportional (P) gain, a proportional-integral (PI) gain, and a proportional-integral-derivative (PID) gain.

77. The system of claim 65 wherein the first parameter includes at least one of a temperature and a mass flow rate of the controlled fluid.

78. The system of claim 65 wherein the second parameter includes at least one of a temperature and a mass flow rate of the controlled fluid.