COORDINATION IN MULTILAYER PROCESS CONTROL AND OPTIMIZATION SCHEMES
Technical Field of the Invention
The present invention relates to dynamic load control.
Background of the Invention
Controls have been developed for a variety of different load control processes. For example, in steam generation plants, several boilers and/or other types of steam generators generate steam and supply the steam to a common header. If individual pressure controllers with integral action running in parallel were used to control the boilers, instability in the operation of the boilers could result.
Therefore, pressure in the header is typically controlled by a single master pressure controller (MPC) that produces a total energy reguirement (usually in terms of fuel feed) for the plant input. An energy allocation module divides the total energy requirement into separate fuel feed demands (i.e., set points) for the individual boilers.
The division of the total energy requirement implemented by the energy allocation module should be cost optimized according to varying economic conditions (such as price of fuels and electricity, environmental
limits, etc.) and according to various constraints such as total production demand, technological constraints, runtime hours, and life time consumption. The underlying optimization problem is well known and has been solved in a variety of ways and with various levels of complexity since the 1960's. For example, Real Time Optimizers have been implemented in order to optimize the cost of operating one or more loads.
These Real Time Optimizers have detected a steady state load requirement and then have provided control signals that optimize the cost of operating the loads based on this steady state load requirement. In order to operate in this fashion, the Real Time Optimizers have had to wait for transient process disturbances to settle out so that a steady state condition exists before such Optimizers can invoke their optimization procedures. However, for processes with slow dynamics and/or high levels of disturbances, the dependence of Real Time Optimizers on steady state information substantially deteriorates the performance of the control system, as no optimization is performed during the transients created by disturbances such as changes in set point and/or changes in load.
While predictive controllers have been used in the past, predictive controllers have not been used with
Real Time Optimizers such that the Real Time Optimizers dynamically respond to target load values of the predicted process variables projected to the end of a prediction horizon. In one embodiment of the present invention, predictive controllers and Real Time
Optimization are combined in this fashion in order to more effectively control loads during disturbances such as changes in set point and changes in load.
Summary of the Invention
According to one aspect of the present invention, a process control system for controlling a load comprises a predictive controller and a real time optimizer. The predictive controller predicts an energy requirement for the load at prediction points k = 0, 1, -2, . . . , K based on a steady state target energy requirement for the load. The real time optimizer determines an optimized dynamic energy demand requirement for the load at the prediction points k = 0, 1, 2, . . ., K based on the predicted energy requirement, and controls the load based on the dynamic energy demand requirement.
According to another aspect of the present invention, a process control method for controlling loads 1, 2, . . ., N comprises the following: predicting, in a predictive controller, an energy requirement for each of
the loads 1, 2, . . . , N at prediction points k = 0, 1,
2, . . ., K based on a steady state target allocation for each of the loads 1, 2, . . ., N; determining, in a real time optimizer, a dynamic energy demand requirement for each of the loads 1, 2, . . . , N at prediction points k =
0, 1, 2, . . . , K based on the predicted energy requirements; and, controlling the loads 1, 2, . . . , N based on the dynamic energy demand requirements.
According to yet another aspect of the present invention, a process control method for controlling loads
1, 2, . . ., N comprises the following: predicting, by way of a predictive controller, a total energy requirement for the loads 1, 2, '. . ., N at prediction points k = 0, 1, 2, . . . , K; allocating, by way of a real time optimizer, the total energy requirement to the loads 1, 2, . . . , N at the prediction points k = 0, 1,
2, . . . , K based on a steady state target for each of the loads 1, 2, . . ., N; determining, by way of the real time optimizer, a dynamic energy demand requirement for each of the loads 1, 2, . . . , N at the prediction points k = 0, 1, 2, . . . , K based on the allocated energy requirements; and, controlling the loads 1, 2, . . . , N based on the dynamic energy demand requirements .
Brief Description of the Drawings
These and other features and advantages will become more apparent from a detailed consideration of the invention when taken in conjunction with the drawings in which:
Figure 1 illustrates a control system according to an embodiment of the invention;
Figure 2 illustrate graphs useful in explaining the present invention; and, Figure 3 illustrates a flow chart depicting the operation of the control system shown in Figure 1.
Detailed Description
In one embodiment of the present invention, real-time, on-line, optimized dynamic allocation of time varying total demand among loads, taking into account various constraints, is provided. The resulting dynamic
allocation is composed of a target allocation Fl'arg(k) and
a dynamic portion w " (k)AF"" (k) that is proportional to the
loads' dynamic weights w "(k) for loads i = 1, . . ., N.
The target allocation Fl nas (k) is provided by a Real Time
Optimizer using load cost curves which can be evaluated from efficiency or consumption curves, etc. Likewise,
the loads' dynamic weights w " (k) may also be set by the
Real Time Optimizer or by an operator.
The algorithm that implements the optimized dynamic allocation is used with a model-based predictive controller. In this case, a steady state load balance at the end of a prediction horizon can be predicted as the target value for computation of the target economic allocation, and dynamic deviations in the transient part of the prediction period can be allocated in proportion to the dynamic weights. In this way, the system of the present invention need not wait for loads to achieve a steady state condition following a disturbance to economically control the loads.
Moreover, because a predictive controller is used, rate of change constraints, in addition to the absolute constraints, are introduced so as to provide a positive impact on the stability of the control process and on the stresses and life time of the control system equipment . The algorithm that is implemented by the control system may be modular. For example, the target
allocation F'iae(k) is provided by an optimization routine
using the loads' cost curves which can be evaluated from efficiency curves, etc. This modular structure allows the addition of new features that, for example, take into
account burner configuration, fuel mixing, etc. without changing the basic algorithm. An off-line what-if analysis as a decision support tool is also possible using existing routines. As shown in Figure 1, a control system 10 includes a predictive controller 12, a Real Time
Optimizer 14, and a plurality of loads lβi - lβN. For
example, the loads 16χ - 16N can be boilers, turbines,
compressors, chillers, etc. Thus, if i = 1, 2, . . . , N
designates the loads lβi - 16N in Figure 1, then N
designates the number of loads.
The predictive controller 12 suitably senses the load requirements (e.g., pressure, and/or fuel feed,
and/or temperature, etc.) of the loads 16ι - lβN and
provides a predicted total load energy demand Ftot to the real time optimizer 14 that divides the total load energy demand Ftot according to a predicted target allocation
E r (/c) into individual allocated fuel feed demands (or
set points) F^ly"(k) for the individual loads 16ι - 16N.
The predictive controller 12 may be any of the controllers supplied by Honeywell under part numbers HT- MPC3L125, HT-MPC3L250, HT-MPC3L500, HT-MPC6L125, HT- MPC6L250, and HT-MPC6L500, or may be any other predictive controller that projects a system response to a set
point, load, or other disturbance. The real time optimizer 14 may be any of the real time optimizers supplied by Honeywell under part numbers HT-ELA3L125, HT- ELA3L250, HT-ELA3L500, HT-ELA6L125, HT-ELA6L250, and HT- ELA6L500, or may be any other real time optimizer that can be modified so as to react to load change predictions in order to cost effectively allocate load demand among a plurality of loads.
Because the predictive controller 12 is a predictive controller, the total load energy demand Ftot is a trajectory, i.e., a sequence of values corresponding to a sequence of prediction times k up to a prediction horizon K, where k = 0, 1, . . ., K. Accordingly, the total load energy demand Ftot may be given by the following equation:
F"" = (F""(1), F"" (1), ..., F"" (K)) ( 1 )
The dynamic allocation trajectories Fl dy"(k) for
the loads are determined by the real time optimizer 14 in two steps. First, the unconstrained allocation
trajectories Fl""c""s,r (k) are determined for the loads i = 1,
2, . . ., N. Second, the unconstrained allocation
trajectories F™'" ( ) for the loads i = 1, 2, . . ., N
are modified to satisfy constraints and to approach the unconstrained allocation as much as possible (in the sense of minimum least squares of deviations) in order to
obtain the dynamic allocation trajectories F "(k) .
In the first step, the unconstrained allocation
trajectories Fι u"c"nslr (k) are defined by means of two sets of
parameters: (1) the target allocation Fl'asi(k) , and (2) the
dynamic weights w "(k) . Accordingly, the unconstrained
allocation trajectories /V""""""' ( k) are defined according to
the following equation:
F~'r (k) = F;ars (k) + wf"' (k)AF"" (k) (2 )
where
ΔE"" (k) = F"" (k) - F! (k) ( 3 :
•=ι
for each load i = 1, 2, . . ., N and for each trajectory point k = 0, 1, . . ., K.
The target allocation F'aϊS(k) corresponds to
values around (or near) which the unconstrained
allocation F™" ' (k) varies, and the dynamic weights w?y" (k)
are an indication of the sensitivities of the loads 16ι -
16N to the changes in the total load demand.
Figure 2 illustrates an example of dynamic fuel feed allocation with the samples on the left side of the vertical dashed line representing historical data and the samples on the right side of the vertical dashed line representing predicted (modeled) trajectories. The
samples may be taken at time instants t^ = kTs, where Ts
is a given sampling period. The total load energy demand Ftot shown in the left graph is allocated between a boiler (load) Bl as shown in the top right graph and a boiler (load) B2 as shown in the bottom right graph. The dashed curves 20 and 22 represent the unconstrained allocation
trajectories F%comtr (k) and F™{onstr (k) for loads Bl and B2,
respectively. The solid line curve in the graph on the left represents the total load energy demand Ftot predicted by the predictive controller 12, and the solid line curves in the graphs on the right represent the
dynamically allocation fuel feeds (set points) El=1 n(-c) and
?(k) for loads Bl and B2, respectively, as produced by
the real time optimizer 14. The horizontal solid lines represent absolute limits that are placed on the total load energy demand Ftot and the dynamically allocation
fuel feeds (set points) Fι=^n(k) and F^(k) , respectively.
The horizontal dashed lines represent the target
allocations F'arg(k) . Moreover, for the example shown in
Figure 2, the ratio of the dynamic weights used for loads Bl and B2 are assumed to be given by the following equation:
w β. αyynn i .=1 (k)
(4) w dyn ι=2 (k)
Accordingly, the changes in total energy load
demand AF"" (k) are divided into the loads 16ι - 16N
proportionally to the dynamic weights so that the allocated load energy requirement (e.g., fuel feed value)
is composed of the target value Fy' g(k) plus a portion
from the transient deviations AF"" (k) . The dynamic
weights may be provided by the operator. Alternatively, the dynamic weights may be calculated automatically. For example, they may be calculated automatically based on the number of running coal pulverizers, burners, etc. A balance condition exists where the sum over
the loads l β - 16N of the target allocations ^jFl'ars (k) is
equal to total load energy demand Ftot(k) in equation (3).
In the balance condition, AF"" (k) is zero, and the
following relationship:
∑F,mc"m,r(k) = F""(k) (5)
;=1
is fulfilled for each trajectory point k, assuming that the non-negative dynamic weights are normalized to 1 according to the following equation:
f 4"(*) = l (6)
As discussed above, the target allocation
F'ars(k) is the prediction horizon for load i and is
allocated to load i by the real time optimizer 14 based upon various economic conditions. The target allocation
E ar8(/c) may be evaluated from offsets.
As indicated by Figure 2, the target allocation
F'a's(k) is assumed to be constant during the prediction
period unless the target allocation Ft'ars(k) is
significantly changed, such as by the operator. When the
target allocation Ft laιe(k) is significantly changed, linear
interpolation from the old value to the new one, instead
of using the new value for the whole prediction period, may be used in order to assure bumpless operation.
If the target allocation F'aIS(k) is set (such as
by the operator as indicated above) so that it is time- invariant up to the next operator intervention, the sum
of the target allocation F'are(k) over all loads cannot
follow the time-varying target of the total load energy demand Ftot, i.e., the value of the total load energy demand Ftot at the end of prediction horizon. However, the appreciable balance condition can be fulfilled if the
target allocations Fl""s(k) are evaluated using offsets F"ϋ
as given by the following equation:
where Fav is determined from the following balance condition:
N N
Ftot (K) = ∑ F;** = ∑ Ft off + NF ( 8 )
(=1 .=1
Thus , even if offsets (defining differences between
N loads) are constant, the term ^^'arg is time varying and
/=1 equal to Ftot(K)
As indicated above, the dynamic weights w y" (k)
may be set by the operator. The dynamic weights w "(k)
are assumed to be constant during the prediction period unless they are significantly changed by the operator. If they are changed, they may be ramped using a linear
interpolation algorithm. Also, the dynamic weights w y"(k)
are normalized to 1 as discussed above in relation to equation (6) .
As indicated above, the unconstrained
allocation trajectories F~'r (k) do not need to satisfy
constraints. On the other hand, the dynamic allocation
trajectories F?y"(k) are required to be constrained.
Constraints imposed by the real time optimizer 14 may be generated by the operator. Alternatively and/or additionally, constraints may be algorithm-generated constraints that are propagated from slave controllers on all levels of a sub cascade. Also, constraints may be time varying. Moreover, constraints may be absolute
limits (such as low and high limits F, m (k) and F,mm (k) on
the dynamic allocation trajectories F y"(k) ) f and
constraints may be rate of change limits (such as
decremental and incremental limits F~(k) and F (/),
respectively) .
While absolute constraints must not be violated, rate of change constraints can be violated. However, such a violation should be highly penalized so as to avoid undesired thermal stress, which may have a negative impact on the life of the control system equipment .
In the second step of calculating the dynamic
allocation trajectories F*"(/), the dynamic allocation
trajectories ,*"(/) are calculated based on the
unconstrained allocation trajectories F""cons"' (k) . The
dynamic allocation trajectories Fl dy"(k) must satisfy the
total load energy demand Ftot (as the unconstrained
allocation trajectories ^""""""' (k) must also do) according
to the following equation:
In addition, the dynamic allocation trajectories ,*"(/)
are constrained by the absolute constraints, considered as hard constraints, and the rate of change constraints, considered as soft constraints in that they can be violated by arbitrary (although highly penalized) values z,(k) .
These constraints are given by the following expressions :
< Fdy" < F" (10)
F- < f ?dyynn _ z ≤ p + (11)
where
dn _ fori = \,...,N (12)
Expressions similar to expressions (12) can be written
for Ft mm , F,max , F~ , F; , and zx. Each of the vectors F " ,
^min ^ ^a ^ - ^ p+ ^ an(^ _,^ ^as a corresponding dimension
K + 1. Also, expressions similar to expression (13) can be written for Fmιn, F"13 , F", and F+. Each of the vectors Fdyr^ pπαn^ pmax^ γ- ^ and F+ has a correSponding dimension
N(K + 1) .
A difference vector AF "' is defined according
to the following equation :
AF. ayn DFT dyn -F, (14)
where D is a (K + 1) by (K + 1) difference matrix given by the following equation:
and where F°cl are (K + 1) dimensional vectors having the
corresponding loads' actual input energy requirements (such as boilers' actual fuel feed) in the first component and zeros elsewhere as given by the following equation:
(pact \
The actual input energy requirements F"" may be sensed by
appropriate sensors located at the energy inputs of the
loads 16ι - lβN.
Variables z±(k) are introduced in order to penalize violation of the rate of change constraints. If
Zi(k) is equal to zero (no penalty), AFl dy"(k) must lie
within rate of change limits according to the
inequalities (11). If AFdy"(k) is not within corresponding
limits, the variable zι(k) is equal to the deviation of
AF? "(k) from the range (-F'(k), F,+ (k)) , and the limit
violation penalty defined as the norm of z becomes nonzero .
The dynamic demand allocation Fdyn is obtained by minimizing the penalty for the deviation of Fdyn from the unconstrained allocation Funconstr and for violation of the rate of change limits. That is, the dynamic allocation Fdyn is obtained by minimizing the following function:
f(F,z) = p ■ dyn _ τjunconstr + z ( 17 ) β(i) 2(2)
with respect to variables Fdyn and z, subject to constraints (9)— (11) . It should be noted that the vector
■vunconstr in equation (17) has a dimension 2N(K + 1) similar to the right hand side of equation (13). Function (17) is a quadratic programming problem with dimension 2N(K +
1) -
The square N (K + 1) by N(K + 1) norm matrices (l) and Q(2) can be chosen as diagonal matrices with elements depending only on boiler i, not on trajectory points k. Accordingly, these matrices may be given by the following equations:
qω = wo)j (19)
where j = 1, 2, where I is a (K + 1) by (K + 1) unity
matrix, and where w,(1) and w,(2) are penalty weights for i
1, N. The penalty weights w; (i) ' and wιX;2) ' may be
defined by the process engineer during the optimizer commissioning,
The control algorithm as described above may be implemented by the control system 10 according to the flow chart shown in Figure 3. With k equal to a current value, the total energy load demand Fot(k) is projected by the predictive controller 12, at a block 30 of this flow chart, for each point k out to the horizon K. The
change in Ftot(k), i.e., ΔF""(/c) , is calculated at a block
32 using equation (3) using the predicted steady state
target allocations F'aτe(k) set by the real time optimizer
14 as discussed above. Alternatively, the target
allocations F'are(k) may be determined in accordance with
equations (7) and (8) as discussed above. Also, the
unconstrained allocation trajectories Fl""c°"s"' (k) are
calculated at a block 34 using equation (2), where the
target allocations Fl'a!S(k) are as used at the block 32,
where the dynamic weights w m(k) may be set, for example,
by the operator, and where the total energy load demand Ftot(k) is provided by the block 30.
The dynamic demand allocation trajectories
Fl dy"(k) are then determined at a block 36 in accordance
with equations (17), (18), and (19), and the difference
vector AF*" is determined at a block 38 in accordance
with equations (14), (15), and (16). Constraints are
applied to the dynamic allocation trajectories Fj dy"(k) and
the difference vector ΔF,.*" at a block 40 in accordance
with equations (9), (10), and (11). At a block 42, the
constrained dynamic demand allocation trajectories F yn (k)
are used to control energy supplied to the respective loads 1, . . . , N.
The algorithm at a block 44 then waits for the next time k before repeating the operations of the blocks (30)-(44) . Certain modifications of the present invention has been described above. Other modifications of the invention will occur to those skilled in the art. For example, although the present invention has been described above with specific reference to the control of loads such as boilers, the present invention may be used in connection with a variety of other control processes.
Also as described above, the target allocation
F rg(/) is provided by a Real Time Optimizer.
Alternatively, the target allocation Farg(/) may be set by
an operator.
Accordingly, the description of the present invention is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the best mode of carrying out the invention. The details may
be varied substantially without departing from the spirit of the invention, and the exclusive use of all modifications which are within the scope of the appended claims is reserved.