Industrial process control apparatus and method

A control system and method are provided for an industrial process operation, wherein a controller is coupled with a process control member and has a gain that is adjustable in accordance with a predetermined relationship of the controller reference iteration interval and the controller actual execution interval.

CROSS-REFERENCE TO RELATED APPLICATIONS 
The present application is related to two concurrently filed patent 
applications (Ser. No. 367,828 and 367,830 filed Apr. 12, 1982) by the 
same inventor, which are assigned to the same assignee as the present 
application, and which are entitled "Industrial Process Control Apparatus 
and Method", the disclosures of which are incorporated herein by 
reference. 
BACKGROUND OF THE INVENTION 
It is known in the prior art that the control of non-linear combustion 
process operations such as combustion chamber pressure in boilers, 
furnaces or soaking pits is influenced by automatic control of the exhaust 
stack damper position. A piston-type servomotor utilizing compressed air 
is linked to the damper to control its movement. Many exhaust stacks rely 
on natural draft to draw the flue gas upward for discharge into the 
atmosphere. It is the reliance on natural draft only which introduces 
marked non-linearities in the relationship between the combustion chamber 
pressure and stack damper position. Contributing to this non-linearity is 
the resistance to flow introduced by the presence of a recuperator or 
economizer through which the spent gases pass, for purposes of preheating 
the air of combustion in the case of a furnace, or for preheating the 
water in the case of a boiler. Also, the stack draft itself tends to fall 
as the flow of flue gases increases, because the draft is a function of 
the flow as well as of the temperature difference between the top and the 
bottom of the stack. The updraft or suction at the bottom of the stack 
tends to be reduced for a constant temperature difference as the velocity 
of the flue gas coming into the bottom of the stack is increased. 
The difficulty of controlling combustion chamber pressure in these 
environments is compounded by the common practice of discharging the flue 
gases of a plurality of combustion processes through a common stack. This 
difficulty is because of the tendency toward interaction of the dampers 
associated with each independent combustion process. An example of these 
problems is well illustrated by the circumstances of soaking pit 
operation. 
Soaking pits are located in the steel production cycle between the basic 
oxygen furnace (BOF) where ingots are produced, and the slabbing mill. The 
BOF produces ingots of steel, either stainless or carbon steel. These 
ingots sit outside on trucks for a long period and cool off before they 
are placed in the slabbing mill. The purpose of the soaking pits is to 
raise the ingots to the desired rolling temperature, and because it takes 
quite a while for the heat to penetrate through the large tonnage of metal 
in each ingot, a soaking pit cycle may take eight hours between charging 
the ingots in the pit and withdrawing them for passage to the slabbing 
mill. 
A typical arrangement would have these pits in batteries of three, with 
nine such batteries altogether, for a total of twenty-seven pits. The 
outlet duct from each of the pits in a battery is connected to a common 
stack provided for the battery of three pits and through which the flue 
gases are exhausted to the atmosphere. However, each pit has its own 
damper, which is a hinged, butterfly-type valve, moved by a piston-type 
servo motor that operates with compressed air. There is always some 
minimum opening of the pit damper to afford purging of the pit. 
In industrial combustion processes, natural draft is commonly relied upon 
to draw the exhaust gases into the atmosphere, rather than induced draft 
fans, so that movement of the damper on one pit changes the pressure in 
the common duct and creates an interaction within the battery of pits as 
each damper moves in an attempt to maintain the pressure in its respective 
pit. There can be a constant instability that persists between the three 
pit pressure control systems, even through the combustion control, which 
is on the front-end of each pit for controlling the air and gas ratios, 
works well. Because the differential pressure is higher across their 
valves, interaction in the control of air and gas is not as significant as 
contrasted with interactions which take place through the stack. 
The exhaust stack arrangement is such that an attempt is made to recover 
some of the heat going up the stack and transmit it to the input air of 
combustion through the use of recuperators which preheat the air before it 
gets to the burners. 
The gases from each pit in a given battery flow through a separate exhaust 
system with its own damper, and a common stack is provided after the 
individual dampers. The natural draft characteristic of the system is 
critical in that it changes the normal pressure drop versus flow 
relationships and the damper position controller gain relationship to 
flow. Control of the damper position on each pit is very sensitive because 
the flow rates are not that high and changes in damper position cause 
changes in draft within a matter of two or three seconds. 
The combustion controls associated with each pit respond to the independent 
variable of temperature which is the product of the combustion process. 
Temperature in the pit regulates the gas flow, and the gas flow regulates 
the air flow, and as is commonly found on combustion systems, a 
cross-coupling and ratio adjustment exists between the air and gas flows 
arranged so that neither can get out of step with the other while 
providing a desired fuel quantity and air/fuel ratio. 
The control for each damper senses the actual static pressure in the 
associated pit, and this pressure should be controlled quite closely. If 
it is too low, or a highly negative pressure, then cold air can be sucked 
in and the pit cannot properly heat up the ingots. Ingot scaling will also 
occur. If it is too high, or a positive pressure, the hostile atmosphere 
within the pit might be blown out into the shop which is both a fire 
hazard and dangerous to shop personnel. 
Conventional pit firing utilizes a modulated firing technique in which the 
temperature excursions in a temperature versus time profile continuously 
modulate the fuel gas flow to maintain whatever temperature is specified 
in the profile for that pit. The fuel gas flow would be fully on when the 
pit is first started, and gradually tapers off to some very low value as 
the desired soaking temperature is approached. These pits are not only 
capable of being fired in the conventional way with modulated firing, but 
can also be fired with a technique called pulse-firing, with which the pit 
interactions discussed earlier can become very troublesome. 
Pulse-firing creates tremendous disturbances which are not present with 
modulated firing where there is some trimming taking place all the time. 
This is because the pulse-firing technique involves firing the pit at full 
blast to bring it up to desired temperature as quickly as possible. The 
fuel gas is then cut off completely and the pit cools down slightly, from 
about 2480.degree. F. to 2372.degree. F. At 2372.degree. F. the fuel gas 
is turned on again. About 21/2-3 minutes later, when the temperature again 
reaches about 2480.degree. F., the gas is turned off again. The firing 
operation keeps pulsing up and down like this all the time, with the pulse 
being simply a complete full blast on or nothing at all. As the soaking 
condition is approached, the duration of the off time increases because 
the whole atmosphere surrounding the ingots is hotter and more uniform in 
temperature, so there is less decay in temperature when the gas is turned 
off. An indication that soaking temperature has been reached is provided 
by the increase in duration of the off time to a certain magnitude. 
The nature of the pulse-firing technique is such that it introduces very 
severe changes in the input fuel gas flow every time the pulse occurs. 
Thus, the interaction between the pits can become very significant. 
Clearly, both the magnitude and rate of change in flow are large when this 
occurs and the effect on the other pits is severe. Further, because the 
pits are at different stages in their heating cycles, there can be no 
synchronism in the sequence of pulsing in the respective pits. 
The pulse-firing technique has many advantages over modulated firing. Two 
of the major benefits of the pulse firing technique are improved heat 
utilization and increased yield of ingots through reduced scale formation. 
These stem from the fact that the pulse-firing technique exhibits only two 
states; firing the pit at full bore or not at all. With modulated firing, 
a very low fuel gas flow requires a lot of excess air to provide the 
necessary turbulence, which is not very efficient. When firing at full 
bore under pulse firing, on the other hand, the air/fuel ratio can be 
adjusted downward so that it is much closer to stoichiometric and nearer 
to a slightly reducing atmosphere. This also makes the excess air much 
lower and therefore the ingots do not scale as much leading to a better 
ingot yield. Overall, pulse-firing is much more efficient in terms of heat 
utilization. 
It can be readily seen that the pulse-firing technique greatly magnifies 
the aforementioned interactions between the individual pit damper control 
systems and greatly complicates the operation of any one damper control 
system. This is because the typical 2,400 pounds per hour of fuel gases 
which were flowing suddenly stop. The sudden curtailment of fuel gas flow 
in any particular pit calls for a step change in damper position owing to 
the sudden increase in natural draft as the affected damper shuts down, 
and the other pits close in their dampers in response to the sudden 
increase in draft. There is a tendency for a damper movement on one pit to 
affect the control of pressure in the others, leading to instability 
unless the damper position controllers are detuned. 
The present invention overcomes these problems, resulting in a control 
system which exhibits greater stability and higher speed of improved 
accuracy and response over a 100% load range. This invention has 
commercial value because of the large number of pits and furnaces to which 
part or all of the invention applies whether they are operating in 
batteries or alone. The improved accuracy and response of the system 
permits the adjustment of the furnace pressure set point closer to 
atmospheric pressure, to reduce the amount of cold air leaking in through 
the furnace cover, with an associated saving in fuel gas being provided. 
SUMMARY OF THE INVENTION 
The present invention relates to the control of an industrial process 
operation with a control member, such as a soaking pit having a movable 
exhaust gas damper. A control assembly member controller loop is provided 
in which automatic adjustment of the controller gain is provided in 
relation to a comparison of the controller reference iteration interval 
and the controller actual execution interval, for any variations in the 
magnitude of the actual execution interval in a provided sample data 
algorithm.

GENERAL DESCRIPTION OF A PREFERRED EMBODIMENT 
The non-linear combustion process control apparatus and method in 
accordance with the present invention is operative to provide an improved 
operation of the individual pressure control systems associated with each 
of several combustion processes such as furnaces, soaking pits or boilers, 
any one of which is equipped with a recuperator or economizer through 
which spent flue gases pass for discharge into a common stack subject to 
natural draft. Each pressure control system determines the position of a 
damper which acts to maintain a desired furnace combustion pressure, and 
the position of the damper is changed in response to the output of a 
damper position control program implemented with a microprocessor computer 
apparatus, with one such microprocessor being applied to control a battery 
of three soaking pits. 
The herein disclosed simulation and analysis of a soaking pit, its flue gas 
path and pit pressure control system addresses the following process 
characteristics, which are also common to furnaces and boilers: 
(1) The three soaking pits are typically discharged into a common exhaust 
gas stack, and while each pit is provided with its own damper, the pit 
pressure control loops exhibit interaction through the common stack due to 
the sudden changes in flow induced by the pulse-firing associated with 
each pit. 
(2) The availability of only natural or stack draft to pull the exhaust 
gases from the pits reinforces these interactions and introduces 
non-linearities in the system. 
(3) Large combustion process level changes typically occur over short 
periods of time presenting the danger that positive combustion chamber 
pressure will be created during these changes. 
(4) The inherent cycle time limitations of a microprocessor create a 
varying iteration interval which has an effect on control system 
stability. Also, microprocessor memory space considerations dictate the 
need for control programs which are compact. 
The present invention simulates the flue gas pressure drop in the exhaust 
train of equipment from the pit, across the recuperators, the duct work 
and the stack damper. The simulation is incorporated in a control 
algorithm that anticipates, for a given battery of pits, the position 
change on at least one other damper if a particular damper is moved. 
Similarly, the change in position of a third damper produced by the 
movement of the second damper is anticipated. Resolution of this 
decoupling before any damper position change is made and related with 
modification of all damper positions simultaneously, minimizes the 
undesired pit operation interaction. The control of the three pits as here 
described by one microprocessor facilitates this decoupling control 
procedure. The aforementioned resolution for each of pit A, pit B, and pit 
C is provided by passage through a decoupling matrix to generate the 
respective resolved damper position outputs which are a synthesis of the 
three initially desired damper position outputs, and then the individual 
dampers are moved simultaneously. 
The herein disclosed application of the decoupling algorithm acts to 
minimize the undesired interaction of the individual pit pressure control 
systems which is introduced by the very severe changes in gas flow 
inherent in the pulse-firing technique. Implementation of the decoupling 
algorithm on a microprocessor-based computer accomplishes the purpose of 
the algorithm through the inherent discontinuities of a logical device. A 
set of system information is gathered, processed, and that set is passed 
back again in a processed form. 
The decoupling concept is useful in other process applications, such as in 
steam turbine-generator control and in energy management systems, where 
several turbo generators with extraction valves, governors, and reducing 
valves, are applied in a system. Changes made to the control devices 
associated with any one generator, if made on a serial basis, will cause a 
response from another generator due to natural feedback and thereby 
complicate the procedure of trying to bring the whole plant to a new 
desired steam/power distribution level. For example, to decouple a 
plurality of devices from one another, the decoupling concept permits 
assessment of the effect the desired change on any one device will have on 
the others, so that the resolved desired change for each can be generated 
and implemented simultaneously on al the devices. In boiler control 
systems, it is a widespread practice to pass the flue gases from several 
boilers into a common flue and this creates similar interaction problems 
where there is a load change in response to a change in process steam 
demand. 
The non-linearity of the behavior of the respective dampers and soaking 
pits creates the need for a control operation in which both the current 
damper position and the gain on the damper position controller are 
adjusted in response to the total amount of fuel being fired. The herein 
disclosed control operation incorporates a non-linear feed-forward signal 
and variable gain control operation for accomplishing these adjustments. 
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT 
Referring now to FIG. 1, a prior art flue gas path for a battery 19 of 
three soaking pits is shown. The components associated with the second pit 
and the third pit, respectively, are designated a and b in FIG. 1 and the 
description applies to each of the three soaking pits. Each pit includes a 
pit chamber 10 which is supplied with the products of combustion of coke 
oven gas 12 at a temperature of approximately 2550.degree. F. and flow 
rate of approximately 5000 pounds per hour. The exhaust gases are drawn 
out of the pit chamber 10 at a temperature of about 2200.degree. F. and 
are passed through a gas/air heat exchanger or recuperator 14 and leave at 
a temperature of about 1000.degree. F. to pass through an adjustable 
damper 16 on the way through outlet duct 20 to the stack 18, which stack 
18 is common to the battery 19 of three similar soaking pits. The draft 
condition within the pit 10 is assumed to be -0.1 inches of water, which 
is increased to -0.727 inches of water leaving the recuperator 14, then 
leaving the damper 16 further increased to -0.9627 inches of water, 
reaching -1.1688 inches of water at the bottom of the stack 18. As shown 
in FIG. 1, each pit has its own damper 16, with the three pits discharging 
into the outlet duct 20 at sequential points. A prior art combustion 
control apparatus 11 is shown including two independent controllers (C) 22 
and 24 operative with respective flow transmitters (FT) 23 and 25, with 
the controller 22 being operative with the air control loop and the 
controller 24 being operative with the fuel gas flow control loop, with a 
ratio function provided by a multiplier 26 between them to provide a 
desired fuel to air ratio. Each independent controller derives its set 
point from a fuel gas demand disturbance signal 48 provided by a master 
temperature controller (PIDTC) 28 which is controlled by a set point 30 
and a feedback signal 31 from a temperature thermocouple 32 and 
temperature transmitter (TT) 34 operative with the pit. In addition, a 
prior art damper position proportional plus integral controller apparatus 
(PIC) 36 is shown which operates from the combination of an externally 
adjustable root proportional gain (k.sub.o) 37, a set point signal 38, and 
a pressure feedback signal 40 which is fed from a pressure transmitter 
(PT) 42 and obtained via pressure tap 41 in the pit 10. The controller 
apparatus 36 outputs to a servomotor positioner (SMP) 44 that mechanically 
controls the position of the damper 16. 
In FIG. 2 there is shown a similar battery 19 of three soaking pits, with 
each pit 10 including a combustion control apparatus 11 similar to the 
combustion control apparatus 11 shown in FIG. 1. The position controller 
15 is supplied in a feed-forward manner with the external disturbance fuel 
gas demand signal 48 which is passed to a characterizer 49 and is then 
processed through the lead/lag control block 50 to provide a modified 
feed-forward signal 51 which is fed to the summer (.SIGMA.) 52 at which 
point the output 53 from the damper position PI controller 36 is added to 
generate the desired damper position signal 57 which is compared to the 
present actual damper position signal in comparator (.DELTA.) 59 to 
generate a desired delta position signal 58 so transforming the output of 
the combined PI controller and lead/lag control block into the velocity 
algorithm form. The desired delta position signal 58 is fed to a 
decoupling control 56 which generates a modified delta signal 61 which is 
then fed to a summer (.SIGMA.) 60 within damper position control 62 and at 
which point the modified delta signal 61 is added to the present damper 
position to provide the new desired damper position signal 63, which is 
used to update the present damper position register 45. The updated 
position signal 64 is fed to the servomotor positioner 44 for the damper 
16. In addition, the updated position signal 64 corresponding to the new 
actual position of the damper 16 is also fed to a variable gain control 
block 54 within the damper position control 15, which variable gain 
control block 54 acts to vary the gain of the damper position PI 
controller 36 as a function of damper position. 
A second soaking pit includes a pit chamber 10a and a recuperator 14a 
operative through a damper 16a with the common stack 18. The pressure of 
pit chamber 10a from pressure tap 41a and the feed-forward signal 48a of 
the fuel gas demand for the pit chamber 10a are supplied to the damper 
position control 15a. The desired damper position signal is compared to 
the present actual damper position signal in a comparator to generate a 
desired delta position signal 58a which is supplied to the decoupling 
control 56. The modified delta signal 61a is generated and fed to a summer 
to provide the new desired damper position signal which is used to update 
the present damper position register within the damper position control 
62a. The new actual position of the damper 16a as represented by signal 
64a is then fed both to the servomotor positioner 44a and to a variable 
gain control block 54a within the damper position control 15a which 
variable gain control block is used to vary the damper position controller 
gain. 
A third soaking pit includes a pit chamber 10b and a recuperator 14b 
operative through a damper 16b with the common stack 18. The pressure of 
pit chamber 10b from pressure tap 41b and the feed-forward signal 48b of 
the fuel gas demand for the pit chamber 10b are supplied to the position 
controller 15b. The desired damper position signal is compared to the 
present actual damper position signal in a comparator to generate a 
desired delta position signal 58b which is supplied to the decoupling 
control 56. The modified delta signal 61b is generated and fed to a summer 
to provide the new desired damper position signal which is used to update 
the present damper position register within the damper position control 
62b. The new actual position of the damper 16b as represented by signal 
64b is then fed both to the servomotor positioner 44b and to a variable 
gain control block 54b within the damper position control 15b which 
variable gain control block is used to vary the damper position controller 
gain. 
In FIG. 3 there is shown a control loop function block diagram which 
includes the damper position control 15 having a damper position PI 
controller 36 which is fed by the error signal 39 generated in a node by 
the comparison of a positive set point signal 38 and a negative pressure 
feedback signal 40. The position controller 15 is supplied in a 
feed-forward manner with the fuel gas demand signal 48 which is passed to 
a characterizer 49 and is then processed through the lead/lag control 
block 50 to provide a modified feed-forward signal 51 which is fed to the 
summer 52 at which point the output 53 from the damper position PI 
controller 36 is added to generate the desired damper position signal 57 
which is compared to the present actual damper position signal in 
comparator 59 to generate a desired delta position signal 58 so 
transforming the output of the combined PI controller and lead/lag control 
block into the velocity algorithm form. The desired delta position signal 
58 is fed to a decoupling control 56 which generates a modified delta 
signal 61 which is then fed to a summer 60 within damper position control 
62 at which point the modified delta signal 61 is added to the present 
damper position to provide the new desired damper position signal 63, 
which is used to update the present damper position register 45. The 
updated position signal 64 is fed to the servomotor positioner 44 for the 
damper 16. In addition, the updated position signal 64 corresponding to 
the new actual position of the damper 16 is also fed to a variable gain 
control block 54 within the damper position control 15, which variable 
gain control block 54 acts to vary the gain of the damper position PI 
controller 36 as a function of damper position. 
The program flow chart shown in FIGS. 4A, 4B and 4C functionally 
corresponds with the function block diagram shown in FIG. 3. FIGS. 4A and 
4B illustrate the determination of the desired change in damper position 
for each of three pits, one after the other. Then FIG. 4C illustrates the 
operation of the decoupling algorithm, with the hysteresis if any being 
added, such that the final damper position for each pit is determined. 
In FIG. 4A, block 200 is the start of the program loop for each of three 
pits. In block 202 there is calculated the desired damper position in 
terms of fuel flow, and this is a non-linear function. In block 204 the 
net input to the lead/lag algorithm is calculated as the absolute 
difference between the new desired damper position and the desired damper 
position value calculated at the last iteration of the program. The lead 
term OUT is then calculated in block 206 taking the value of the input and 
the past error into account. In block 208 the ratio of the new input to 
the previous input is calculated, and in block 210 this ratio is less than 
0.1; this indicates that the feed-forward term has ceased to change and 
has become steady state so the lead term OUT should be made 0, since it 
should not become negative. In block 212, whatever value the term OUT has 
become, whether it is equal to the lead term or 0, we add to OUT the value 
of the lag term. In block 214, the registers used to pass data from one 
iteration to another are updated. The register PAST DAMP is made equal to 
the new value of damper position. The register LLAGREG is made equal to 
the new value of OUT and the register PAST ERROR is made equal to present 
value IN. The total feed-forward signal is then computed in block 216 and 
consists of the raw feed forward signal damper position calculated in 
block 202, plus the output of the lead/lag algorithm calculated in block 
212. These two combined form the total feed-forward signal. This is then 
checked in block 218 against upper and lower constraints to make sure that 
it lies within the value of 0 to 1 which is the range of the damper 
position itself. A check is made in block 219 of the value of TEMP, which 
is a ratio of input to past error determined at bock 208. If the value of 
TEMP is less than 0.1, it means that the reset register of the controller 
has to be modified as the lag term begins to decay, since there has been 
reached a steady state operation, and there is no lead term, only a lag 
term and the decay of the lag term now should impact immediately on the 
reset register of the controller to avoid the damper being moved 
unnecessarily during the decay of the lead/lag algorithm. The feed-forward 
signal should predominate during the steady state situation. In block 220 
this anticipation is calculated, and this block forms a termination of the 
lead/lag algorithm portion of the total pit pressure controller program. 
Starting in block 222 with the PI controller, the change in damper 
position is first made 0, and in block 224 the desired set point of the 
controller is computed as a function of air flow, since leakage through 
the recuperator requires raising the set point of the pit pressure to 
reduce the quantity of leakage. The set point tends to rise with total 
flow through the recuperator, so this is an adjustment to offset 
recuperator leakage. After computing the set point of the control loop, in 
block 226 the error difference between the set point and the actual value 
of the pit pressure is modified for the actual .DELTA.T which the program 
is running under, so the correction for .DELTA.T is applied to the error. 
In FIG. 4B, at block 228 the variable gain is computed as a function of the 
desired damper position and this variable gain is then multiplied by the 
fixed gain to provide the total proportional gain for the controller. The 
final input to the controller in bock 230 is equal to the corrected error 
from block 226 multiplied by the total gain calculated in block 228. In 
block 232 it is determined if the controller is on automatic control, and 
in block 234 it is determined whether the pit cover is on or not. For a 
pit under control the cover should be on, and if so at block 236. The 
reset register is updated including the anticipation of the lead/lag decay 
calculated in block 220. In block 238, the sum of the proportional, reset 
and feed-forward terms is calculated and this provides the total desired 
damper position for a particular pit. In block 240, the combined output is 
then checked against upper and lower limits and constrained to within a 
range of 0 to 1, which is the full range of damper position. In block 242 
if the output has not been constrained, the flow sheet moves forward to 
the end of the do loop, if the output has been constrained, then in block 
244 the reset register must be modified to take account of the 
constraining. At block 246 the change in damper position between this 
iteration and the previous iteration is calculated for each pit. 
If the controller is on manual at step 232, then in block 248 there is 
calculated any change due to a change in manual signal which the operator 
has imposed, such that if the operator has the damper position control on 
manual and has changed the damper position, it is necessary to take that 
change into account. In block 250, the controller reset register is 
adjusted to match the manual signal so that a bumpless transfer can be 
made when next going back to automatic control. In block 252 the register 
of the lead/lag algorithm is set to 0 to again provide bumpless transfer 
from the state the system is in at the moment to switching at a later time 
from manual to automatic. 
If at block 234 the pit cover is off then the pit ought to be shut down, 
and in block 254 if the cover is off the damper is moved to the 5% open 
position, since there must be some minimum opening to make sure that the 
fuel gases can escape from the pit and then proceed to block 250. 
The program operation so far described in relation to FIGS. 4A and 4B is 
repeated three times, once for each pit, and the output at block 256 is 
the total desired damper position as the sum of all of these different 
components. 
The program shown in FIG. 4C follows block 256 and is the decoupling 
algorithm. Having established the desired change in damper position for 
each pit, the decoupling algorithm provides the resolved change in damper 
position for each pit, taking interactions into account. Block 260 is the 
start of the decoupling algorithm for each pit. At block 262 the resolved 
change in damper position TOT is set equal to the sum from j equals l to j 
equals 3 of the product of the change in damper position times the matrix 
(I, J). In block 264 the magnitude of a hysteresis effect is inserted into 
the code. If the ratio of the change of damper position to hysteresis at 
block 266 is less than unity, the hysteresis effect is set to 0 in block 
268. This implements the change in damper position that was already 
calculated. Otherwise the hysteresis effect AA is retained. From the 
resolved change in damper position, at step 270 the final damper position 
is calculated in terms of the previous position plus the effect of 
hysteresis plus the resolved change. 
DESCRIPTION OF FEED-FORWARD/LEAD-LAG CONTROL OPERATION 
In FIG. 2, a modified feed-forward signal 51 is provided in which the 
desired damper position is estimated in accordance with the fuel gas 
demand signal 48 representing the quantity of fuel gas that is being 
fired. The feed-forward mode is used to adjust each pit damper in 
accordance with the major changes in fuel gas flow. 
Feed-forward involves the anticipation of a change in related parameters, 
such as fuel and air flow, which will eventually impact the combustion 
chamber pressure. The pressure is a feedback signal, but air and fuel flow 
determine a feed-forward signal because they will take place before the 
change in pressure has occurred. The feed-forward characteristic is a 
prediction of the damper position corresponding to the new flue gas flow 
and is affected by the non-linearity of the particular process system 
characteristics. Non-linearity, while not as marked with an induced draft 
system as in a natural draft system, is always a factor. The 
characteristics of the damper position versus flow equation given in (3) 
below are developed by the regression analysis of fuel flow versus damper 
position data obtained under steady-state conditions over a wide range of 
flows. The characterizer 49 is a piece of firmware which contains this 
equation. 
There is included an absolute lead/lag algorithm which operates on the fuel 
gas demand signal 48 to provide the modified feed-forward signal 51 which 
ensures that each damper is open more than is needed during transient 
conditions of the combustion chamber pressure to provide a safety feature 
that prevents the flue gases from blowing out into the shop generally and 
creating a dangerous situation for a human operator. This is a different 
kind of algorithm from that which is commonly used in an ordinary lead/lag 
context such as that of a compensator on a feedback signal which assumes a 
sinusoidal and continuous input disturbance. In the case under 
consideration, the process disturbance is monotonic, not sinusoidal, and 
the standard Laplace lead/lag function is not suitable for the desired 
control operation because it decays too quickly when the change ceases. 
Also, the standard lead/lag algorithm designed for use in the feedback 
mode reverses in its behavior when a negative rate of change is detected 
in the signal which it receives. For these reasons it is inappropriate for 
use in the feed-forward mode where the object is to have a lead/lag 
contribution which is always positive and decays gracefully once the 
signal approaches steady state. The present invention addresses these 
problems by including a feed-forward lead/lag algorithm which features 
maintenance of the lead component until after the change has ceased, at 
which point the lag component or decay commences. Another feature is the 
positive nature of the output under all conditions. 
As the fuel flow increases, the modified feed-forward signal 51 operates to 
achieve the desired position of the damper 16 in anticipation of the 
increased flow. The lead/lag feature of the modified feed-forward signal 
51 operates to make the damper position change such that the change is 
more than is otherwise necessary, tending to create a negative pressure 
during the resulting transient condition of operation. Similarly, when the 
fuel flow drops, the controlled closing movement of the damper 16 will lag 
behind the fuel, again creating more suction than is really needed during 
the resulting transient condition of operation. The modified feed-forward 
signal 51 attempts to establish new system equilibrium with some 
precision. However, because the equilibrium based on only the modified 
feed-forward signal 51 is not absolutely precise, the summer 52 adds to it 
the output 53 of the damper position PI controller 36 which, because it is 
fed from the pressure transmitter 42 monitoring the internal pit pressure, 
will integrate out any resultant error that might persist in the latter 
pressure during the steady-state operation after any transient has died 
away. 
To anticipate the required damper position change corresponding to an 
increase in the rate of fuel firing, the lead/lag network incorporates a 
lead/lag algorithm having the basic transfer function as follows: 
##EQU1## 
where C(S) is the controlled variable and R(S) is the reference variable, 
T.sub.1 is the lead time constant, T.sub.2 is the lag time constant and k 
is the gain. 
The value of the modified feed-forward signal 51 is added to the output 53 
of the PI Controller 36 in line 158 of the control program listing 
included in Appendix A. However, in the past, the rapid decay in this 
value with constant input has caused an unnecessary change in the position 
of the damper 16 which must be integrated out through the PI algorithm of 
controller 36, to restore equilibrium. One improvement of the present 
invention is to correct the reset register of the PI algorithm of 
controller 36 internally by the amount of the decay in the lead/lag 
algorithm output immediately as it is calculated, to avoid the controller 
36 unnecessarily disturbing the damper. 
DESCRIPTION OF VARIABLE GAIN CONTROL OPERATION 
For purposes of operating the damper position control system, the desired 
relationship is the change in damper position for a change of pressure, 
which relationship cannot be derived directly, so it is derived indirectly 
from a combination of relationships that can be measured. One of these is 
the relationship between a change of pressure in the pit and the change of 
input mass flow for a constant stack draft and fixed damper position. The 
other relationship is the change in damper position for a change of input 
mass flow, or the feed-forward characteristic. The product of the 
transformed partial differentials in each of these relationships 
determines a third relationship which is the change of pressure to the 
change of damper position. Because the change of pressure is caused by the 
change of damper position which, in turn, is caused by a change of 
pressure, this third relationship becomes the system gain. 
The non-linearities in flue gas flow introduced by the resistance of the 
recuperator or economizer and the reliance on natural draft create the 
need for the variable gain feature which acts to obtain a constant system 
gain over the whole range of system operation. Reliance on natural draft 
introduces non-linearities in the flow because with natural draft, for an 
increase in the flow of flue gases the draft tends to fall. The draft is a 
function of the temperature difference between the top and the bottom of 
the stack and the velocity of the flue gases. The up-draft inherent in a 
rising column of hot air tends to create a low pressure at the bottom of 
the stack. The draft or suction at the stack bottom tends to be reduced, 
for a constant temperature difference, as the velocity of the flue gas 
flowing into the bottom of the stack increases so as to increase the 
pressure at the bottom. With natural draft, the suction tends to decrease 
with increased flue gas flow, as compared with an induced draft fan 
application, where the suction tends to increase with increased flue gas 
flow as the fan speeds up to force the increase in suction. 
Application of control theory stability criteria dictates that the system 
gain, which is the product of the disturbance gain and the controller 
gain, should be unity or less. The partial differential derived from the 
damper pressure relationship, or dD/dP, is the variable gain of the damper 
position controller. When the combined damper position controller gain is 
multiplied by the predicted process response as reflected by the partial 
differential dP/dD, the overall system gain should be less than unity. 
Thus, 
##EQU2## 
where (1+(1/T(s)) is the Laplace transfer function 47 for a PI controller, 
((dD/dP).multidot.K.sub.o) is the consolidated proportional gain 46, and 
k.sub.o is the root proportional gain 37. 
Because the root proportional gain of the damper position controller is a 
value which can be set externally, the overall system gain can be 
determined. In the present invention there is a variable gain which is a 
function of the actual damper position. The more open the damper becomes, 
the larger the controller gain becomes because the change of damper 
position for a given change of pressure has to become greater. This is 
because the stack draft is decreasing with increased flue gas flow, and a 
greater change in damper opening is therefore required. As the flow 
increases, the damper must be moved more to get the same change of 
pressure in the pit. 
Analysis of the flow relationships on an empirical or theoretical basis 
reveals that the gain on the system has a very non-linear characteristic. 
The method of theoretical analysis is now described. 
The herein disclosed theoretical plant model was exercised in the control 
program listing of Appendix A, eliminating the effect of flow differences 
on pit pressure and, assuming a constant value for stack draft (-1.1688 
inches H.sub.2 O) and pit pressure (-0.1 inches H.sub.2 O), i.e., 
establishing an equality between input mass flow and flue gas flow. The 
flue gas flow W through the recuperator/damper/stack system was thus 
established over the range of damper position D of 10% through 100% and 
the flow/damper position relationship is plotted in curve 96 in FIG. 5. 
The curve relates the independent variable, flue gas flow (or mass flow in 
lb./hr.), to damper position. Regression of the data from which this curve 
was plotted gives the equation: 
EQU D=0.17742E-03W-0.74227E-7W.sup.2 +0.14334E-10W.sup.3 (3) 
The flue gas flow equation was also regressed from this curve, and 
indicates that gas flow is a function of the damper position. Thus, 
##EQU3## 
Thus, the partial differential of this relationship is: 
##EQU4## 
Curve 98 in FIG. 5 plots the inverse of this relationship, 
.DELTA.D/.DELTA.W, and indicates by how much the flow into the pit should 
change to correspond to a change in damper position. 
For varying damper positions over the range 10% to 100%, the flows with pit 
pressures of -0.1 inches H.sub.2 O and zero inches H.sub.2 O respectively 
were established and the partial differential of flue gas flow with 
respect to pit pressure, .DELTA.W/.DELTA.P, is plotted in curve 100 of 
FIG. 6 and defined by the flow/pressure relationship: 
##EQU5## 
For purposes of establishing a soaking pit combustion pressure control 
system, a key part in the analysis of soaking pit operation is the 
establishment of the damper/pressure relationship. The forward gain 
associated with the tuning of a PI controller may be defined as the change 
in damper position corresponding to the flow produced by a change in pit 
pressure. This is obtained by taking the two partial differentials, both 
in terms of damper position D, and dividing them. Thus, the 
damper/pressure relationship is: 
##EQU6## 
Curve 102 in FIG. 6 is the damper/pressure relationship, or change of 
damper position for a change of pressure. The primary stimulus in the 
system is a change of pit pressure, or furnace pressure, which through the 
controller produces a change in damper position. 
By evaluating the rather complicated expression of equation 7 for various 
values of D and plotting the results, curve 102 in FIG. 6 can be obtained. 
By regressing this curve, the variable gain is found: 
##EQU7## 
Clearly, this must be constrained to some low value greater than zero if 
the controller is to continue to function. It must also never reverse in 
sign. 
In order to incorporate the adjustable tuning constant k.sub.o in previous 
equation (2), the above expression must be modified as follows to 
establish the consolidated proportional gain: 
##EQU8## 
The purpose of the foregoing analysis is to identify that in a non-linear 
system, the damper/pressure relationship can be developed as shown in 
equation 7. This relationship is strikingly non-linear and it is clear 
that a variable gain control 54 would be desirable, the gain being varied 
as a function of damper position. 
DESCRIPTION OF COMPENSATION CONTROL OPERATION FOR ITERATION INTERVAL 
VARIATIONS 
The damper position PI controller is implemented in a programmed 
microprocessor. With a fixed iteration interval, the reset time constant 
can be adjusted to achieve system stability. However, because the 
microprocessor duty cycle may change, the actual iteration interval 
(.DELTA.t) may be subjected to unwanted changes. The PI controller will 
not exhibit the right behavior unless such changes in the actual .DELTA.t 
are compared to the reference .DELTA.t and a compensating adjustment is 
made by modifying the basic Laplace transfer function for the overall 
controller gain. In the herein disclosed PI controller, with a base or 
reference iteration interval of a quarter of a second, for example, if the 
actual iteration interval slips to one second, the gain will be decreased 
in a compensating fashion by .DELTA.t compensator 43 to maintain former 
system stability. 
The stack damper simulation as incorporated in the control program listing 
of Appendix A was exercised with a proportional only controller, the reset 
time constant being set to 10000. The gain on the control loop was then 
increased in steps until the loop became unstable. The associated gain and 
loop natural frequency S were then noted as 2.09 and 2.5 sec. 
respectively. 
A common rule of thumb (see Rutherford, C. I., The Practical Application of 
Frequency Response Analysis to Automatic Process Control, Proc. Inst. 
Mech. Eng., Vol. 162, No. 3, pp 334-343, 1950) is to divide the gain (G) 
that produces instability by 
##EQU9## 
to obtain k.sub.o, the gain for a damped oscillation thus: 
##EQU10## 
The reset time constant may be established by assuming that the controller 
is to have a 9.degree. phase lag .phi.. The reset time constant T can be 
computed from the relationship: 
##EQU11## 
For .phi.=9.degree., T/S=0.995 or close to unity. The above rule of thumb 
was evolved in the course of the tuning of analog control systems in which 
the iteration interval .DELTA.t approaches zero. Where .DELTA.t has a 
finite value which is large compared to the time constant of the plant, it 
has become apparent that the effective gain of the system is proportional 
to the value of .DELTA.t. This is not unexpected in a sampled data system 
in which the change in pressure is proportional to the product of time and 
the difference between pit inlet and outlet flows. 
A common DDC algorithm for a PI controller having the transfer function: 
##EQU12## 
can be expressed in this case in its sample data form as: 
##EQU13## 
The normal transfer function for a PI controller can be applied to express 
the change in damper position for a given change of pressure coming into 
the controller. Thus, 
##EQU14## 
The iteration interval is represented by .DELTA.t which corresponds to the 
sampling time. Use of a reference .DELTA.t of a quarter of a second or 
less allows the sample data algorithm to approximate the theoretical 
relationships. 
If the reference iteration interval is chosen to be 0.25 seconds for a 
specific process control application, and the gain and reset time 
constants are established accordingly, then for uniform dynamic behavior 
of the control loop regardless of the value of the actual iteration 
interval .DELTA.t, (14) should be modified as follows: 
##EQU15## 
In this way the control loop settings can be established in a rational 
manner and automatically compensated for variations in the actual 
controller execution interval. As the rationale for this innovation the 
following explanation is offered. Equation (15) can be rewritten in the 
form: 
##EQU16## 
In a system containing a first order process lag, a given difference in 
flow rates will produce a response in the form of a pressure change which 
is directly proportional to the time of duration. Thus by adjusting 
k.sub.o, the experimentally determined root proportional gain or tuning 
constant, by the ratio .DELTA.t.sub.REF /.DELTA.t, the effect on system 
gain remains constant regardless of the value of .DELTA.t. 
The ability to automatically modify k.sub.o is important in systems where 
the value of .DELTA.t cannot be assured, such as where a microprocessor 
with a high duty cycle might slip. If, in the course of slipping, the same 
dynamic behavior is maintained, the stability of the control is improved 
regardless of changes in the iteration interval. 
DESCRIPTION OF DECOUPLING CONTROL OPERATION 
Each damper position control system is operationally independent until the 
desired change in damper position is generated. Before that change is 
implemented, the desired change in the other two damper positions is 
calculated. Having established by how much each damper position should 
change in order to maintain its own pit pressure, the effect on the other 
pits is evaluated. The coupling here is different from pit to pit because 
of the way in which the flue gas ducts are connected and the pressure 
drops existing therein. A net change is generated through a simultaneous 
equation, and the resolved desired change is added simultaneously to the 
present position on each pit damper. Otherwise, if these changes are made 
one at a time, they will react undesirably with each other by disturbing 
each other's pit pressure controller unnecessarily. By anticipating the 
undesired interactions and implementing the resolved desired changes all 
at once, such interactions are minimized. The algorithms used for the 
control of each damper position are exercised once per second. 
The diagram of FIG. 2 shows a decoupling control 56 incorporating a 
decoupling algorithm. Whenever the damper on any one pit opens, the volume 
of gas leaving that pit will increase, as will the stack flow loss 
however. The associated reduction in net stack draft will also affect the 
flows from the other pits and cause their dampers to tend to open slightly 
in response; but with some lag, which can cause inter-loop instability if 
the interaction is sufficiently large. To avoid this occurring the 
following decoupling algorithm is used, which takes the estimated damper 
position change associated with each pit, resolves these, and passes back 
a resolved change to each damper position servo motor. The decoupling 
algorithm looks at the effect that any individual desired damper position 
change will have on the other pit dampers. Once these are resolved, it is 
the resolved changes that are actually used to shift the damper positions. 
The decoupling algorithm shown in lines 181-191 of Appendix A is organized 
so that the desired change in damper position .DELTA.D.sub.i for each of 
the 3 loops is first calculated. Knowing the interaction factor between 
each pit, the coupled changes in damper position .DELTA.D.sub.i * may be 
calculated as follows: 
##EQU17## 
It should be noted that k.sub.11, K.sub.22, and k.sub.33 are all unity. The 
resultant change in damper position, array V, can be calculated as 
follows: 
EQU V.sub.i =V.sub.i-1 +.DELTA.D.sub.i * (19) 
And the reset registers R can be readjusted so as to be equal to: 
EQU R.sub.i =V.sub.i -GAIN.sub.i .multidot.ERR.sub.i (20) 
It is seen that the code multiplying a 3.times.3 matrix by an array is very 
short and should have little impact on microprocessor duty cycle. The 
decoupling effect can be eliminated by making matrix MATR in line 187 an 
identity matrix. 
Some pit dampers are very large and the servo mechanism and linkage 
combined can exhibit hysteresis to small signal changes. To offset this, a 
small hysteresis factor HYST has been introduced in line 188 which, added 
to the desired position in line 191, can ensure that this hysteresis is 
offset. 
The velocity algorithm has been used to permit the decoupling feature to be 
included. It has however been coded in lines 133-146 as an absolute 
position algorithm, the output from which is then subtracted from the 
previously calculated output to provide the new desired change in damper 
position. Note that all control loops must be calculated before the 
decoupling algorithm is applied. 
DESCRIPTION OF PLANT MODEL 
The plant model of the flue gas path including the pit chamber 10, the 
recuperator 14, the damper 16 and the common stack 18 as shown in FIG. 2 
may be defined mathematically as shown in the program listing in Appendix 
A and as follows, in terms of the driving force for the system, i.e., 
pressure. Each of the model constants is then evaluated based on stated 
assumptions. 
For the purpose of control system simulation, it will be assumed that the 
pit 10 is provided with a leak-free cover. 
##EQU18## 
For a 1/3600 lb per second change in mass of air in the pit, the change in 
pit pressure= 
##EQU19## 
Therefore, 
##EQU20## 
ins H.sub.2 O/lb per hr per sec 
The pressure drop across the recuperator 14 varies directly as the flow 
through it, thus: 
EQU .DELTA.P.sub.2 =k.sub.2 .multidot.W.sub.o.sup.2 (25) 
Assume that the pressure drop across the recuperator is 0.627 ins. H.sub.2 
O with a mass gas flow of 5000 lb/hr. 
Then from (24) 
EQU k.sub.2 =0.627/5000.sup.2 =2.508.multidot.10.sup.-8 (26) 
For a damper position D, and assuming a constant discharge characteristic, 
the flow may be calculated from: 
##EQU21## 
It should be noted that, in order to avoid dividing by zero, the stack 
draft in the model should have a minimum value of, say 1%. Also that, 
within the overall model, .DELTA.P.sub.3 cannot fall below the stack 
draft. 
Assume that the pressure drop across the damper is 0.23577 ins H.sub.2 O 
with the damper 80% open and passing a mass gas flow of 5000 lb/hr. 
Then, from (28): 
##EQU22## 
In accordance with Perry, R. H., Chemical Engineer Handbook, McGraw Hill 
1963, pp 9-43, the theoretical stack draft may be derived as follows, 
where: 
##EQU23## 
Assuming that the stack height is 125 feet, the barometric pressure is 29.5 
ins. Hg, ambient temperature of 60.degree. F. and a mean stack temperature 
of 1000.degree. F., Then from (30): 
##EQU24## 
Again, in accordance with Perry, R. H., Chemical Engineer Handbook, McGraw 
Hill 1963, pp 9-43, stack flow loss may be estimated from the following, 
where: 
##EQU25## 
Assume a stack diameter of 6.83 ft., Then from (33): 
##EQU26## 
To determine the flue gas flow as a function of damper position, a pressure 
balance within the system shown in FIG. 1 may be defined for pit A as 
follows: 
##EQU27## 
Substituting the appropriate equivalents gives 
##EQU28## 
Which, being a standard, quadratic equation, can be solved in the usual way 
for the flow W.sub.o through pit A. A similar procedure will apply to the 
flow through pits B and C. 
In Appendix B there is included a control program listing to control a 
plurality of soaking pits, such as shown in FIGS. 2 and 3. 
In Appendices A and B there are included control program listings relating 
to the herein disclosed control of a non-linear combustion process. The 
control program listing is written in the Fortran language which is 
available for use with a variety of microprocessors. Many of these 
microprocessors have already been supplied to customers, including 
technical instruction manuals and descriptive documentation to explain to 
persons skilled in this art the operation of the microprocessor apparatus. 
This control program listing is included to provide an illustration of one 
suitable embodiment of the present invention that has been developed. This 
control program listing at the present time is more or less a development 
program and has not been extensively debugged through the course of 
practical operation for the real time control of the above operation. It 
is well known by persons skilled in this art that most real time control 
application programs contain some bugs or minor errors, and it usually 
takes varying periods of actual operation time to identify and routinely 
correct the more critical of these bugs. 
##SPC1## 
##SPC2## 
##SPC3##