Source: http://www.google.com/patents/US6745088?dq=%22Meaning-based+advertising+and+document+relevance+determination%22
Timestamp: 2016-05-24 16:02:13
Document Index: 61547151

Matched Legal Cases: ['Application No. 60', 'art 2102', 'art 2104', 'art 2106', 'art 2202', 'art 2204', 'art 2206', 'art 2302', 'art 2304', 'art 2306', 'art 2402', 'art 2404', 'art 2406', 'art 2502', 'art 2504', 'art 2506', 'art 2602', 'art 2604', 'art 2606', 'application No. 60']

Patent US6745088 - Multi-variable matrix process control - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign inPatentsComputer-implemented system and method for controlling a processing apparatus having at least one independently controlled manipulated variable and at least one controlled variable responsive to the manipulated variable, using a robust multi-variable controller which defines an expected variation in...http://www.google.com/patents/US6745088?utm_source=gb-gplus-sharePatent US6745088 - Multi-variable matrix process controlAdvanced Patent SearchPublication numberUS6745088 B2Publication typeGrantApplication numberUS 09/878,711Publication dateJun 1, 2004Filing dateJun 11, 2001Priority dateJun 30, 2000Fee statusPaidAlso published asCA2411378A1, CN1449511A, EP1299778A2, US20020016640, WO2002003150A2, WO2002003150A3Publication number09878711, 878711, US 6745088 B2, US 6745088B2, US-B2-6745088, US6745088 B2, US6745088B2InventorsRonald A. GagneOriginal AssigneeThe Dow Chemical CompanyExport CitationBiBTeX, EndNote, RefManPatent Citations (10), Non-Patent Citations (2), Referenced by (41), Classifications (25), Legal Events (4) External Links: USPTO, USPTO Assignment, EspacenetMulti-variable matrix process control
US 6745088 B2Abstract
Computer-implemented system and method for controlling a processing apparatus having at least one independently controlled manipulated variable and at least one controlled variable responsive to the manipulated variable, using a robust multi-variable controller which defines an expected variation in magnitude for each controlled variable as a respective function of each manipulated variable via use of a set of at least two models. The model set has a dynamic response inertial characteristic. The two models are derived from a Reference Model (the traditional model defined in Dynamic Matrix Control). The multi-model set further enables adaptation of the models and gains during real-time use.
I claim: 1. A computer-implemented system for controlling a processing apparatus having at least one independently controlled manipulated variable and at least one controlled variable responsive to said manipulated variable, comprising:
a set of at least two models for defining an expected variation in magnitude for each controlled variable as a respective function of each manipulated variable, said model set having a dynamic response inertial characteristic; and means for implementing a change defined from said model set to modify said manipulated variable in said processing apparatus. 2. The system of claim 1 further characterized by means for adapting said models during real-time use.
4. A computer-implemented system for controlling a processing apparatus having at least one independently controlled manipulated variable and at least one controlled variable responsive to at least one said manipulated variable and further responsive to process disturbances originating independently of said manipulated variable, comprising:
means for measuring the magnitude of each controlled variable; a set of at least two models for defining an expected variation in magnitude for each controlled variable as a respective function of a manipulated variable disturbance instance in each manipulated variable; means for determining, from said set of models, an estimated modeling error value in interaction of one said controlled variable with all said manipulated variables in achieving a manipulated variable modification; means for determining an estimated process disturbance value from said controlled variable magnitude and said estimated modeling error value; means for defining a first portion of desired change in the present value of at least one manipulated variable from said estimated modeling error value; means for defining a second portion of desired change in the present value of at least one manipulated variable from said estimated process disturbance value; and means for implementing said first and second desired change portions to modify said manipulated variable. 5. The system of claim 4 wherein said model set incorporates a dynamic response inertial characteristic, said system further characterized by means for acquiring an inertial characteristic value so that said dynamic response inertial characteristic can be achieved in said model set.
6. The system of claim 5 further compromising means for adapting said model set during real-time use.
7. The system of claim 4 further compromising means for determining divergent response behavior in said controlling.
8. A computer-implemented system for of an apparatus having at least one independently controlled manipulated variable and at least one controlled variable responsive to at least one said independently controlled manipulated variable, comprising:
means for defining a set of consecutive discrete intervals of time in a time-dependent function; means for introducing, in each independently controlled manipulated variable, a manipulated variable disturbance instance of predefined magnitude, said disturbance instance prompting a response in each controlled variable; means for measuring the magnitude of each controlled variable; a controller; means for defining, respective to each response, at least one time-dependent functional characterization of said controlled variable magnitude over said set of consecutive discrete intervals of time on a time-axis, said functional characterization having a zero-time time-axis attribute, a maximum-time time-axis attribute, a dead-time time-axis attribute, a response gain attribute, a ramp-rate attribute, a steady-state time-axis attribute, a curvilinear portion disposed between the time-axis position of said dead-time time-axis attribute and the time-axis position of said steady-state time-axis attribute, a ramped portion disposed between the time-axis position of said dead-time time-axis attribute and the time-axis position of said maximum-time time-axis attribute, and a homaloidal portion disposed between the time-axis position of said steady-state attribute and the time-axis position of said maximum-time time-axis attribute, each discrete time interval for one said response having the same time duration, said homaloidal portion having a zero value for an integrating controlled variable response, said ramped portion having a zero value for a non-integrating controlled variable response, and each functional characterization for one said response having identically valued zero-time time-axis attributes, response gain attributes, ramp-rate attributes, and maximum-time time-axis attributes; means for acquiring a first said time-dependent functional characterization respective to the response from measuring an effected change in said magnitude of a controlled variable after introducing said disturbance instance, said first functional characterization having a first said dead-time time-axis attribute, a first said steady-state time-axis attribute, a first said curvilinear portion, a first said homaloidal portion, and a first said ramped portion having its functional derivative equivalent to said ramp-rate attribute at said maximum-time time-axis attribute; means for inverting said first time-dependent functional characterization into said controller; means for deriving a second said time-dependent functional characterization from said first time-dependent functional characterization, said second functional characterization having a second dead-time attribute in first predefined diminishing offset from said first dead-time attribute, a second steady-state attribute in second predefined diminishing offset from said first steady-state attribute, a second curvilinear portion in first predefined functional offset from said first curvilinear portion, a second homaloidal portion in extrapolation of said first homaloidal portion, and a second ramped portion in extrapolation of said first ramped portion; means for deriving a third said time-dependent functional characterization from said first time-dependent functional characterization, said third functional characterization having a third dead-time attribute in first predefined superadditive offset from said first dead-time attribute, a third steady-state attribute in second predefined superadditive offset from said first steady-state attribute, a third curvilinear portion in second predefined functional offset from said first curvilinear portion, and a third homaloidal portion in truncation of said first homaloidal portion, and a third ramped portion in truncation of said first ramped portion; means for determining a desired change in the value of a manipulated variable in real-time from said second time-dependent functional characterization, said third time-dependent functional characterization, the magnitude of at least one controlled variable, and said controller; and means for implementing said desired change to modify said manipulated variable. 9. The computer-implemented system of claim 8, said means for determining a desired change in the value of a manipulated variable in real-time determining said desired change from said first time-dependent functional characterization, said second time-dependent functional characterization, said third time-dependent functional characterization, the magnitude of at least one controlled variable, and said controller.
10. The computer-implemented system of claim 9 wherein said first, second, and third time-dependent functional characterizations define three models in a model set, said model set incorporating a first dynamic response inertial characteristic between said first and second time-dependent functional characterizations and a second dynamic response inertial characteristic between said first and third time-dependent functional characterizations, said system further characterized by means for acquiring a first inertial characteristic value and a second inertial characteristic value so that said first and second dynamic response inertial characteristics can be respectively achieved in said model set.
11. The system of claim 10 further characterized by means for adapting said model set during real-time use.
12. A computer-implemented system for controlling a processing apparatus having at least one independently controlled manipulated variable and at least one controlled variable responsive to at least one said manipulated variable and further responsive to process disturbances originating independently of said manipulated variable, comprising:
means for measuring the magnitude of each controlled variable; a model set for defining an expected variation in magnitude for each controlled variable as a respective function of a manipulated variable disturbance instance in each manipulated variable; means for determining, from said model set an error value in interaction of one said controlled variable with all said manipulated variables in achieving a manipulated variable modification; means for defining a desired change in the present value of at least one manipulated variable from said error value; means for implementing said desired change to modify said manipulated variable; and means for determining divergent response behavior in said controlling. 13. The computer-implemented system of claim 12 further characterized by means for counteracting said divergent response behavior.
defining an expected variation in magnitude for each controlled variable as a respective function of each manipulated variable from a set of at least two models, said model set having a dynamic response inertial characteristic; and implementing a change defined from said model set to modify said manipulated variable in said processing apparatus. 15. The method of claim 14 further comprising the step of adapting said models during real-time use.
measuring the magnitude of each controlled variable; defining an expected variation in magnitude for each controlled variable as a respective function of a manipulated variable disturbance instance in each manipulated variable from a set of at least two models; determining, from said set of models, an estimated modeling error value in interaction of one said controlled variable with all said manipulated variables in achieving a manipulated variable modification; determining an estimated process disturbance value from said controlled variable magnitude and said estimated modeling error value; defining a first portion of desired change in the present value of at least one manipulated variable from said estimated modeling error value; defining a second portion of desired change in the present value of at least one manipulated variable from said estimated process disturbance value; and implementing said first and second desired change portions to modify said manipulated variable. 18. The method of claim 17 wherein said model set incorporates a dynamic response inertial characteristic, said method further characterized by the step of acquiring an inertial characteristic value so that said dynamic response inertial characteristic can be achieved in said model set.
19. The method of claim 18 further characterized by the step of adapting said model set during real-time use.
20. The method of claim 17 further characterized by the step of determining divergent response behavior in said controlling.
21. A method for computer-implemented controlling of an apparatus having at least one independently controlled manipulated variable and at least one controlled variable responsive to at least one said independently controlled manipulated variable, comprising the steps of:
defining a set of consecutive discrete intervals of time in a time-dependent function; introducing, in each independently controlled manipulated variable, a manipulated variable disturbance instance of predefined magnitude, said disturbance instance prompting a response in each controlled variable; measuring the magnitude of each controlled variable; providing a controller; defining, respective to each response, at least one time-dependent functional characterization of said controlled variable magnitude over said set of consecutive discrete intervals of time on a time-axis, said functional characterization having a zero-time time-axis attribute, a maximum-time time-axis attribute, a dead-time time-axis attribute, a response gain attribute, a ramp-rate attribute, a steady-state time-axis attribute, a curvilinear portion disposed between the time-axis position of said dead-time time-axis attribute and the time-axis position of said steady-state time-axis attribute, a ramped portion disposed between the time-axis position of said dead-time time-axis attribute and the time-axis position of said maximum-time time-axis attribute, and a homaloidal portion disposed between the time-axis position of said steady-state attribute and the time-axis position of said maximum-time time-axis attribute, each discrete time interval for one said response having the same time duration, said homaloidal portion having a zero value for an integrating controlled variable response, said ramped portion having a zero value for a non-integrating controlled variable response, and each functional characterization for one said response having identically valued zero-time time-axis attributes, response gain attributes, ramp-rate attributes, and maximum-time time-axis attributes; acquiring a first said time-dependent functional characterization respective to the response from measuring an effected change in said magnitude of a controlled variable after introducing said disturbance instance, said first functional characterization having a first said dead-time time-axis attribute, a first said steady-state time-axis attribute, a first said curvilinear portion, a first said homaloidal portion, and a first said ramped portion having its functional derivative equivalent to said ramp-rate attribute at said maximum-time time-axis attribute; inverting said first time-dependent functional characterization into said controller; deriving a second said time-dependent functional characterization from said first time-dependent functional characterization, said second functional characterization having a second dead-time attribute in first predefined diminishing offset from said first dead-time attribute, a second steady-state attribute in second predefined diminishing offset from said first steady-state attribute, a second curvilinear portion in first predefined functional offset from said first curvilinear portion, a second homaloidal portion in extrapolation of said first homaloidal portion, and a second ramped portion in extrapolation of said first ramped portion; deriving a third said time-dependent functional characterization from said first time-dependent functional characterization, said third functional characterization having a third dead-time attribute in first predefined superadditive offset from said first dead-time attribute, a third steady-state attribute in second predefined superadditive offset from said first steady-state attribute, a third curvilinear portion in second predefined functional offset from said first curvilinear portion, and a third homaloidal portion in truncation of said first homaloidal portion, and a third ramped portion in truncation of said first ramped portion; determining a desired change in the value of a manipulated variable in real-time from said second time-dependent functional characterization, said third time-dependent functional characterization, the magnitude of at least one controlled variable, and said controller; and implementing said desired change to modify said manipulated variable. 22. The method of claim 21, said step of determining a desired change in the value of a manipulated variable in real-time determining said desired change from said first time-dependent functional characterization, said second time-dependent functional characterization, said third time-dependent functional characterization, the magnitude of at least one controlled variable, and said controller.
23. The method of claim 22 wherein said first, second, and third time-dependent functional characterizations define three models in a model set, said model set incorporating a first dynamic response inertial characteristic between said first and second time-dependent functional characterizations and a second dynamic response inertial characteristic between said first and third time-dependent functional characterizations, said method further characterized by the step of acquiring a first inertial characteristic value and a second inertial characteristic value so that said first and second dynamic response inertial characteristics can be respectively achieved in said model set.
24. The method of claim 23 further characterized by the step of adapting said model set during real-time use.
measuring the magnitude of each controlled variable; a model set for defining an expected variation in magnitude for each controlled variable as a respective function of a manipulated variable disturbance instance in each manipulated variable; determining, from said model set, an error value in interaction of one said controlled variable with all said manipulated variables in achieving a manipulated variable modification; defining a desired change in the present value of at least one manipulated variable from said error value; implementing said desired change to modify said manipulated variable; and determining divergent response behavior in said controlling. 26. The method of claim 25 further characterized by the step of counteracting said divergent response behavior.
This application claims the benefit of U.S. Provisional Application No. 60/215,453 filed Jun. 30, 2000.
Optimized operation of manufacturing systems is valued for providing benefits in profitability, productivity, environmental impact, and high product quality. The increasing capability of low cost computers to deliver resolution of complex control approaches has advanced optimized operation to incorporate techniques which could not have been economically explored even a few years ago. One of the techniques enabled at a relatively early stage of computer use in control was Dynamic Matrix Control, a form of feed-forward control based upon a method where outputs, or controlled variables, are predicted to move in the context of known control settings and current data. Feed-forward methodologies are, in many cases, superior to feedback methodologies which wait until process disturbances have actually changed the controlled variables before controller action is taken. Indeed, an ideal controller provides both feed-forward and feedback action in sufficient capability to achieve optimal operation.
Dynamic Matrix Control is discussed in U.S. Pat. No. 4,349,869 for a DYNAMIC MATRIX CONTROL METHOD which issued on Sep. 14, 1982 to David M. Prett, Brian L. Ramaker, and Charles R. Cutler. This patent is incorporated herein by reference. Dynamic Matrix Control has helped in solving control issues related to limitations in future controller response in the context of a decision at a particular time, accommodation of the full set of conditions in a system being controlled, complexity in multiple influences, and non-linear impacts respective to disturbance.
FIG. 1 presents a system overview.
FIG. 2 exhibits multi-variable controller logical detail.
FIG. 3 shows a basic control system block diagram.
FIG. 4 demonstrates a multi-variable control system block diagram.
FIG. 5 presents a time-dependent non-integrating-model characterization.
FIG. 6 presents a multiple-model non-integrating-model characterization.
FIG. 7 shows non-integrating-model set inertial characteristics.
FIG. 8 exhibits a time-dependent integrating-model functional characterization.
FIG. 9 demonstrates a multiple-model integrating-model characterization.
FIG. 10 presents integrating-model set inertial characteristics.
FIG. 11 shows multi-variable control general actions in deploying a multi-model system.
FIG. 12 presents model construction steps.
FIG. 13 exhibits dead-time time-axis attribute determination in a model.
FIG. 14 demonstrates Steady-state time-axis attribute determination in a model.
FIG. 15 shows ramp-portion determination detail in a model.
FIG. 16 presents curvalinear-portion determination detail in a model.
FIGS. 17A and 17B presents controller operation detail.
FIGS. 18A-18E exhibits adaptation methodology detail.
FIG. 19 shows future controlled variable requirement definition detail.
FIG. 20 demonstrates controlled variable prediction detail.
FIGS. 21A-21C presents output from a simulator for a regular DMC operating in a situation of model mismatch in modeling parameters.
FIGS. 22A-22C presents output from a simulator for the robust controller of the preferred embodiments operating in the situation of model mismatch of FIG. 21.
FIGS. 23A-23C presents output from a simulator for a regular DMC operating in a situation of model mismatch in gains.
FIGS. 24A-24C presents output from a simulator for the robust controller of the preferred embodiments operating in the situation of model mismatch of FIG. 23.
FIGS. 25A-25C presents output from a simulator for a regular DMC operating in a situation of controller model inversion.
FIGS. 26A-26C presents output from a simulator for the robust controller of the preferred embodiments operating in the situation of model inversion of FIG. 25.
The Controller for the multi-variable controller is defined by essentially inverting the first time-dependent functional characterization (the Primary Model).
In implementing the models, an inertial characteristic value is input into the database of the model-variable controller so that the dynamic response inertial characteristics are achieved in the model set. The inertial characteristics (establishing robustness in response) are (a) different for the “Slow side” of the Primary Model and for the “Fast side” of the Primary Model, or (b) the two inertial characteristics are identical. In this regard, the first, second, and third time-dependent functional characterizations define three models in a model set, the model set incorporating a first dynamic response inertial characteristic between the first and second time-dependent functional characterizations and a second dynamic response inertial characteristic between the first and third time-dependent functional characterizations.
After the inertial characteristics have been input, the Primary Models are defined by introducing, in each independently controlled Manipulated Variable, a Manipulated Variable disturbance instance of predefined magnitude, the disturbance instance prompting a response in each Controlled Variable. The magnitude of each Controlled Variable is then measured, retained, and used in definition of the Primary Model according to traditional DMC practice (reference previously discussed U.S. Pat. No. 4,349,869).
In implementing use of the multivariable controller, a number of different approaches are possible.
M(t)={a (t)}, where t=0, 1*Δt, 2*Δt, 3*Δ, . . . np*Δt Equation 1
M(t)=Z(M*(t))=a0+a1*z −1 +a2*z −2+etc. Equation 2
In defining the “Fast Model” and the “Slow Model”, substitutions of the time variable into M*(t) are performed; the aim of the substitution is to contract (Fast Model) or expand (Slow Model) the function of the Reference Model along the time axis.
t=t fast/(1.0−F r1) yielding t fast=(1.0−F r1)*t. Equation 3
t fast=(1.0−F r1)*t d+(1.0−F r2)*(t−t d). Equation 4
t slow=(1.0+F r3)*t. Equation 5
t slow=(1.0+F r3)*t d+(1.0+F r4)*(t−t d). Equation 6
The portion after tslow>tfinal is dropped.
Fr1, Fr2, Fr3, and Fr4 are robustness factors. The robustness factors are positive adjustable values usually in the numeric range of 0-0.5, but they can be of greater magnitude. The fact that the time-referenced model contraction and expansion are treated differently before and after dead time allows for more flexibility in building the limit models (the “Slow Model” and the “Fast Model” are collectively “limit models” defining the “envelope” around the “Reference Model”). In this regard, (a) the veritable dead-time of the operational apparatus being controlled and (b) the veritable transient trajectory of the operational apparatus being controlled (as characterized in each model with a “curvilinear portion” as further described herein) both are subject to time-variance and/or to measurement error; the flexibility afforded by the independent methods (1) in “Reference Model” expansion to the “Slow Model” and (2) in “Reference Model” contraction to the “Fast Model” facilitates the robust operational response enabled by the preferred embodiments. Furthermore, the “Slow” and “Fast” Models need this flexibility when either of these limit models solves to be essentially proximate to the Reference Model.
t=tfast=tslow. Equation 7
F rk(i,j)=F r(global)+F r(whole MV i)+F r(whole CV i)+F rk(specific to a Reference Model instance). Equation 8
The requirement that each Frk(i,j) be a positive number is still valid, but this does not prevent other components in the above equation from having a negative value. In this regard, a local Fr may be negative with the effect that the net Frk(i,j) is of lower magnitude than Fr(global) even as Frk(i,j) is positive (or even zero).
When all instances of Fr(i,j) have been chosen, the models have been properly extended (if necessary), and M*fast and M*slow have been calculated, then M*fast and M*slow are written into sampled form (or Z-transform form). The diagram and discussion respective to FIG. 16 illustrates a computer-implemented approximative process which yields equivalent results to the above formalized models. The process involves interpolation of the Reference Model M (already in z-transform form).
x i =f*a i+(1.0−f)*a i+1 Equation 9
The controller block uses the usual least-squares equation of traditional DMC to evaluate the final moves in the manipulated variables; but, in the preferred embodiments, the calculation of E(i) is different from the previous art in DMC—in this regard, the traditional calculation is:
ΔU=(A t WA)−1 �A t W�E Equation 10
(AtWA)−1 is also denoted as the “ATA” matrix herein and AtW�E is also denoted as the “ATE” matrix herein.
ΔU=(A t WA)−1 �A t W�F(models, Y, . . . ) Equation 11
where F is a function dependant of process measurements Y, and errors based on limits models are used. In this regard, F(models, Y, . . . ) has replaced E in the ΔU=(AtWA)−1�AtW�E equation.
For each CV there are at least two predictions: the one from the Fast Model CVfast and the one from the Slow Model CVslow. Optionally, the prediction from the Reference Model is used along with at least one limit model. The predictions are obtained as in traditional DMC practice with: CV  ( i , k ) = ∑ j = 1 N  ∑ l = 1 np  ( a  ( i , j , l ) * Δ   U  ( j , k + l - 1 ) . Equation��12 However, in the preferred embodiments, there are at least two prediction blocks: one for the Slow Model and one for the Fast Model. It is also preferable to maintain the prediction from the Reference Model, but, again, this is optional.
Y*=f(CV fast(t), CV slow(t), Y, etc.). Equation 13
CV max=Max(CV fast(t−k), CV slow(t−k)) {∀k|−d<k<+d} CV min=Min(CV fast(t−k), CV slow)(t−k))d=0,1,2 or 3 (chosen)
CV mean=(CV fast +CV slow)/2.0 Equations 14-16
CVmean=CVreference at the expense of more computing, but it might be preferred insofar as a better estimate is achieved. Equation 17
The extension {∀k|−d<k<+d} within the predicted values expands the choice of predicting models to those having less and more dead time. So, if d=3, for example, then this function actually uses at least 14 different models, with each model generating different responsive behavior:
If Y>CV fast then Y*=Y−CV fast +CV fast +CV slow If Y<CV fast then Y*=Y−CV fast +CV slow Otherwise Y*=CV mean. Equations 18-20
Another possible function (that has the benefit of being continuous) is the following as obtained by defining a function φ to normalize variations in the predicted CV's: Φ = Y - ( CV fast + CV slow ) 2  CV fast - CV slow  ; Equation��21 it is possible to calculate the desired Y* according to Y * =  CV fast + CV slow 2 + ( Y - ( CV fast + CV slow 2 ) ) *  ( 1 - 1 1 + a   Φ n ) . Equation��22 The value of “a” and “n” are adjusted to provide a behavior that fits statistical expectation. For example, a=1.5 and n=4 produces a function that has desirable effects:
it returns Y* equal to the measured CV when far away from CVfast or CVslow; and
The function term ( 1 - 1 1 + a   Φ n ) Equation��23 is a confidence function that is zero (or close to zero) when the measured output is within the Slow and Fast predictions. In the first example, the confidence interval is defined by CVmax and CVmin. In both cases, the function is a scaling sensitivity factor. The function also jumps (increases) toward unity when the measured output moves away from the predictions; this indicates a confidence that the measured output indicates a strong deviation in the plant (apparatus in operation) needing correction. Also, CVmean (i.e., (CVfast+CVslow)/2) is optionally replaced by CVreference (if available).
ΔU=(A t WA)−1 �A t W(Y*−CV mean). Equation 24
The model prediction based on the Reference Model at time tk for each CV(i) can be written as: CV  ( i , k ) = ∑ j = 1 N  ∑ l = 1 np  ( a  ( i , j , l ) * Δ   U  ( j , k + l - 1 ) Equation��25 and this is transformed into a larger sampled time interval and into a difference equation: Δ   CV s  ( i , k ) =  ∑ j = 1 N  ∑ l = 1 r  ( a  ( i , j , s * l ) - a  ( i , j , s * ( l - 1 ) ) ) * Δ   U s  ( j , k + l - 1 ) Equation��26 where: N is the number of MV's and FF's
λ(k)=λ0 (k−1) Equation 27
where λ0 is adjusted to lie usually between 0.9 and 1.0.
V (i,k) =f(CV slow , CV fast , CV reference , MV, Y) and 0.0<V (i,k)<1.0, Equation 28
If CVslow≠CVfast if Y>CV slow and Y>CV fast then V(i,k)=0.0,
if Y<CV slow and Y<CV fast then V(i,k)=0.0,
V(i,k)=Min(|Y−CV fast |,|Y−CV slow|)/|CV fast −CV slow)|,
Finally, if ΔUs(j,k) is not monotonic within its “s” time interval according to its historical record, then V(i,k)=0.0.
|ΔUs|<Σk i |ΔU t+i| Equation 34
Optionally, a part of the proposed scaling sensitivity factor determines the V function: V  ( i , k ) = ( 1 1 + a   Φ n ) . Equation��35 Whatever the choice, this function is chosen by the user to eliminate (or minimize) the effect of model mismatch caused by model parameters other than gain by using the predictions obtained from at least two limit models. The selected function varies according to the characteristics of the process such as (a) a deterministic process with few disturbances or (b) a process characterized by strong stochastic disturbances. The function V has the effect of (a) screening data containing the most valuable information for adapting the process gains and (b) rejecting some of the transients and disturbances introducing errors in the adaptation process.
ΔCV s(i,k)=ΔCV s(i,k)*(λ(k) *V (i,k)). Equation 36
This forms the matrix “C” used to solve the following minimization of sum-of-squared error: S  ( i ) = ∑ k  ( λ ( k ) * V  ( i , k ) ) * E  ( i , k ) 2 = ∑ k  H  ( k ) * E  ( i , k ) 2 , Equation��37 the summation being done on available historical data E  ( i , k ) =  Δ   Y s  ( i , k ) - Δ   CV s  ( i , k ) =  Δ   Y s  ( i , k ) - ∑ j = 1 N  ∑ l = 1 r  Δ   G  ( i , j ) *  ( a  ( i , j , l ) - a  ( i , j , l - 1 ) ) * Δ   U s  ( j , k + l - 1 ) . Equations��38-39 To minimize S(i), a set of changes in gain is introduced to provide multipliers of the actual “a” values of each model. These are the ΔG(i,j) multiplying each term of the summation (Equation 39). Therefore, there are as many ΔG as there are models. For future reference, ΔU and ΔCV quantities are collectively denoted as “delta-s quantities”.
ΔG(i)=(C t HC)−1 �C t HΔY(i) (repeated for each CV i). Equation 40
M=M�ΔG(i). Equation 41
ΔG=(C t HC)−1 �C t HΔY Equation 42
For eigenvalues: G reference=T−1 �λ�T; Equation 43
For singular values: G reference =U�Σ�V. Equation 44
The matrix λ or Σ contains the characteristic values to monitor. For an ill-conditioned matrix, it is necessary (a) to detect a change of sign in one characteristic value of the process and then (b) to responsively implement the equivalent change of sign in the model gains to produce the same sign in all the characteristic values and add to the controller stability.
For eigenvalues: G* ref,slow,fast =T −1 �λ*�T; Equation 45
For singular values: G* ref,slow,fast =U�Σ*�V. Equation 46
λ*i,t=max(ε,(0.1−h)*λreference, min(ε,(1.0+h)*λreference,λ*i,t))
λ*i,t=λ*i,t +f*(λ*i,t−λ*i,t−1) with f chosen 0.0<f<1.0 Equations 47 and 48
f=g(statistics of past λ). Equation 49
ΔCVs(i,k) and ΔMVs(i,k) Equation 50
ΔMV s(i,k)=ΔMV s(i,k)*V (i,k);
ΔCV s(i,k)=ΔCV s(i,k)*V (i,k). Equations 51 and 52
For eigenvalues: A=T�ΔCV s and B=T�ΔMV s; Equation 53
For singular values: A−U −1 �ΔCV s and B=V�ΔMV s. Equation 54
When divergence is detected, changes in the model gains G(i,j) (corresponding to the value of λ or Σ, but with the sign inverted) are introduced to produced λd or Σd. This means that (for eigenvalues) the following transformation is accomplished for any small eigenvalues (other eigenvalues may have been adapted as well): ( λ λ …  + ɛ …  λ ) ⇒ ( λ λ …  - ɛ …  λ ) . Equation��55 The new vector, denoted as λd with inverted characteristic values, is then used to back-calculate the final gains:
For eigenvalues: G d ref,slow,fast =T −1�λd T; Equation 56
For singular values: G d ref,slow,fast =U�Σ d �V. Equation 57
Turning now to FIG. 17, Controller Operation 1700 shows the operational process of MV Determination Logic 206 and Controller 402. In History Update Step 1702, data for existing MV, FF, and CV variables is transmitted to History Block 414 for archival and use in Adaptation Block 416. The history is built for N input (CV) variables, L feed-forward (FF) variables, and M output (MV) variables. In Adaptation Decision Step 1704, an estimated process disturbance value (from the Controlled Variable magnitude) and the estimated modeling error value are calculated. The estimated model error value and the estimated process disturbance error value are then used to determine the need for further adaptation of either tuning data or model data. Details in Model Adaptation Step 1722 (given a YES answer from Adaptation Decision Step 1704) are discussed in Adaptation Methodology Detail 1800 of FIGS. 18A-18E. In CV Prediction Step 1706, the Primary (Reference), Slow, and Fast Models are used to predict steady-state Controlled Variable values. The predictions are done for N input (CV) variables, L feed-forward (FF) variables, and M output (MV) variables. Further detail in this is shown in Future CV Requirement Definition Detail 1900 of FIG. 19. In Steady-State MV Definition Step 1708, Linear Program 426 is called to define steady-state Manipulated Variable values. These values are defined for N input (CV) variables and M output (MV) variables. In Dynamic Matrix Build Step 1710, the Dynamic (ATA) Matrix is rebuilt if tuning is to be changed, if the models are to be changed, or if this is the first execution instance of the process of Controller 402. The ATA Matrix has a dimension of M�M, where M=N (CV variables) multiplied by the number of future MV moves for each MV. In Future CV Requirement Definition Step 1712, necessary future shifts in Controlled Variable values are determined from setpoints and other predicted future values as acquired from the database of Control Computer Logic 120 in CV Data Acquisition Step 1720. Further detail in Future CV Requirement Definition Step 1712 is shown in CV Prediction Detail 2000 of FIG. 20. The shifts are determined for M output variables. In MV Change Definition Step 1714, the ATE matrix and Dynamic Matrix are solved to define incremental changes in Manipulated Variables. In MV Implementation Step 1716, the incremental Manipulated Variable changes are implemented and the process returns to Data Acquisition Step 1718; this affects each of N input variables. In Data Acquisition Step 1718, MV, CV, and FF variables are read from Control Computer Logic 120 (via Communication Interface 106). In CV Data Acquisition Step 1720, setpoints and other predicted future values are acquired from the database of Control Computer Logic 120 along with necessary future shifts in Controlled Variable values.
Factor Modification Decision 1804, the “forgetting factor” is applied to the most senescent data in Archival Logic 222 via use in determining individual discount factors. In C Matrix Build Step 1802 and other steps of Adaptation Methodology Detail 1800, “differential form” is sometimes also termed “difference form”. The C Matrix is dimensioned as M�N where N is the number of MV and FF variables and M is the number of increments in time horizon used.
L=maximum predicted CV−minimum predicted CV Equations 58-60
error=x*(1.0−exp(−x*x)) OR
error=x*(1.0−1.0/(1+a*x{circumflex over ( )}n))
Error=setpoint−function(Fast predicted CV, Slow predicted CV) Equation 61
In the example, a simulation of an operating apparatus is controlled in FIGS. 21, 23, and 25 with a classic DMC. In respectively comparative FIGS. 22, 24, and 26, the same simulation of the operating apparatus is controlled using the robust multi-variable controller of the preferred embodiments. In the FIGS. 21-22 comparison, the model is “affected” with an identical shift in a model parameter between the simulation of the plant and the model used in the controller. In the FIGS. 23-24 comparison, the model is “affected” with an identical shift in a gain parameter between the simulation of the plant and the model used in the controller. In the FIGS. 25-26 comparison, the model is “affected” with an identical controller model (characteristic value) inversion. In reading the simulation output time charts, note that the right hand scale of the time charts defines the quantitative value of the MV variable, whereas the left hand scale defines the SP and CV quantitative values.
FIG. 21 presents output 2100 from a simulator for a regular DMC operating in a situation of model mismatch in modeling parameters. Output 2100 contains time chart 2102 for the actions of CV1 and MV1 time chart 2104 for the actions of CV2 and MV2, and time chart 2106 for the actions of CV3 and MV3. FIG. 21 shows the regular DMC in the situation of model mismatch between the simulation of the operating apparatus and the model used in the controller (the case is a 3�3 with model mismatch in only the first model; in this regard, the dead time is incorrectly modeled). The move suppression factor is set to unity. Equal concern errors are also all unity. The simulation is normalized internally so that all values of CV and MV begin at 50.0. The process gains are usually in the 0 to 3.0 range. The figure shows the instability induced in the DMC by a single small error in the dead time model in only one model out of 9 (i.e. 3�3). Each other model parameter is strictly equal between the apparatus simulation and the model of the controller. The dead time error in the first model is about 20%. This error makes the controller unstable in all the 3 CV's; the traditional cure is to increase move suppression but at the expense of controller reaction time to external disturbance and to set point changes.
FIG. 22 presents output 2200 from a simulator for the robust controller of the preferred embodiments operating in the situation of model mismatch of FIG. 21. Output 2200 contains time chart 2202 for the actions of CV1 and MV1, time chart 2204 for the actions of CV2 and MV2, and time chart 2206 for the actions of CV3 and MV3. FIG. 22 shows the robust controller in face of the same model mismatch as FIG. 21 (the case is the same 3�3 with model mismatch in only the first model; the dead time is again incorrectly modelized). The move suppression factor is set to unity. Equal concern errors are also all unity. The simulation is normalized internally so that all values of CV and MV start at 50.0. The figure shows the resulting stability of the robust multivariable controller. The controller is not gaining stability at the expense of the reaction time, and, therefore, disturbances and set point changes can be handled faster than the regular DMC. The robustness is so substantial that move suppression can be zero (i.e. turned off) if there is any reason to do so.
FIG. 23 presents output 2300 from a simulator for a regular DMC operating in a situation of model mismatch in gains. Output 2300 contains time chart 2302 for the actions of CV1 and MV1, time chart 2304 for the actions of CV2 and MV2, and time chart 2306 for the actions of CV3 and MV3. FIG. 23 shows the regular DMC without adaptation. The case is a 3�3 with model mismatch in only the gains of all models. The move suppression factor is set to unity. Equal concern errors are also all unity. The simulation is normalized internally so that all values of CV and MV start at 50.0. The process gains are usually in the 0 to 3.0 range with errors in the range 0 to 50%. The figure shows the instability induced in the DMC by the gain errors. The DMC controller is unstable in all the 3 CV's.
FIG. 24 presents output 2400 from a simulator for the robust controller of the preferred embodiments operating in the situation of model mismatch of FIG. 23. Output 2400 contains time chart 2402 for the actions of CV1 and MV1, time chart 2404 for the actions of CV2 and MV2, and time chart 2406 for the actions of CV3 and MV3. FIG. 24 shows the robust controller with adaptation. The case is the same 3�3 as used in FIG. 23 with model mismatch in only the gains of all models. The move suppression factor is set to unity. Equal concern errors are also all unity. The simulation is normalized internally so that all values of CV and MV start at 50.0. The process gains are usually in the 0 to 3.0 range with errors in the range 0 to 50%. The figure shows some initial instability in the robust controller (area of 2408); this is a learning period. After this learning period, the controller exhibits nearly perfect response to set point changes since it derives, from past data, the correct model gains that match the actual process to the control model. Note also, in comparing the peak in the area of 2408 of FIG. 24 with the comparable peak area of 2308 of FIG. 23, that the controller of FIG. 24 shows less overshoot above the setpoint SP; this demonstrates the efficiency with which the described embodiment of the multi-model controller reacts to the operating system.
FIG. 25 presents output 2500 from a simulator for a regular DMC operating in a situation of controller model (characteristic value) inversion. Output 2500 contains time chart 2502 for the actions of CV1 and MV1, time chart 2504 for the actions of CV2 and MV2, and time chart 2506 for the actions of CV3 and MV3. Note that (a) the set point change at time t=100 triggers the inverted response and (b) the controller diverges very rapidly since the move suppression is set to unity.
FIG. 26 presents output 2600 from a simulator for the robust controller of the preferred embodiments operating in the situation of model (characteristic value) inversion of FIG. 25. Output 2600 contains time chart 2602 for the actions of CV1 and MV1, time chart 2604 for the actions of CV2 and MV2, and time chart 2606 for the actions of CV3 and MV3. Again, the set point change at time t=100 triggers the inverted response, and the controller initially diverges—but not as rapidly as the regular DMC of FIG. 25. Inversion detection then triggers inversion of the characteristic value in all models; this process effectively occurs at time t=120. As should be apparent, the inversion is initiated at an earlier relative moment when a different choice of controller parameters are used. The move suppression factor is set to unity. A comparison of FIGS. 25 and 26 shows the value in the described embodiments of (a) determining divergent response behavior in the controlling process and then (b) counteracting the identified divergent response behavior to stabilize the controller.
The described embodiments are achievable within a number of computer system architectural alternatives. In one alternative, an embodiment is facilitated within the context of a multi-process environment wherein different databases, data sections, and logical engines (logical sub-sections which read data, write data, calculate data, and make decisions in data computational processes) within the computer-implemented logic are simultaneously installed and activated with dynamically active data transfer linkages, facilitated either directly or indirectly via the use of a data common and/or an application program interface (APIs). In another alternative, the different databases, data sections, and logical engines are facilitated within the context of a single process environment wherein different components are sequentially activated by an operating technician with linkages facilitated either directly or indirectly via the use of data commons or data schema dedicated to interim storage. In yet another alternative, the different databases, data sections, and logical engines are deployed within the context of a single process environment wherein (a) some components of the different databases, data sections, and logical engines are accessed and activated by an operating technician with linkages facilitated either directly or indirectly via the use of data commons or data schema dedicated to interim storage, and (b) the other components within the different databases, data sections, and logical engines are accessed and activated by calls from previously activated with linkages facilitated either directly or indirectly via the use of data commons or data schema dedicated to interim storage. In one alternative, the multi-variable controller is implemented and executed on one physical computer. In another alternative, the controller is facilitated on different platforms where the results generated by one engine are transferred by an operating technician to a second or other plurality of the different databases, data sections, and logical engines executing on different computer platforms, although a separate operating system is needed on each platform. In yet another alternative, controller is facilitated on a plurality of computer platforms interconnected by a computer network, although a separate operating system is needed on each platform and the operating system further incorporates any networking logic that is needed to facilitate necessary communications via such a computer implemented communication network. A relatively small controller according to the described embodiments is deployed on a computer having an Intel 80486 CPU with a 33 MHz clock, 10 Megabytes of RAM Memory, and a 100 Megabyte Hard Disk using a Windows '95 operating system from Microsoft Corporation. A larger controller according to the described embodiments is deployed on a Vaxstation 4000m90 having 128 Megabytes of RAM and a (at least) 500 Megabyte Hard Disk from Compaq Computer Corporation. Many of the different gradations of architectural deployment within the context of the above overview are considered by the applicants to be generally apparent, and the illustration of present invention can be conveniently modified by those of skill, given the benefit of this disclosure, to achieve the utility of the present invention within the context of the above computer system architectural alternatives without departing from the spirit of the present invention once given the benefit of the disclosure.
Patent CitationsCited PatentFiling datePublication dateApplicantTitleUS4349869Oct 1, 1979Sep 14, 1982Shell Oil CompanyDynamic matrix control methodUS4698745 *Feb 7, 1985Oct 6, 1987Kabushiki Kaisha ToshibaProcess control apparatus for optimal adaptation to a disturbanceUS5394322 *Jul 22, 1993Feb 28, 1995The Foxboro CompanySelf-tuning controller that extracts process model characteristicsUS5432885 *Sep 24, 1992Jul 11, 1995Mitsubishi Denki Kabushiki KaishaRecurrent fuzzy inference apparatusUS6253113 *Aug 20, 1998Jun 26, 2001Honeywell International IncControllers that determine optimal tuning parameters for use in process control systems and methods of operating the sameUS6278899 *Oct 6, 1998Aug 21, 2001Pavilion Technologies, Inc.Method for on-line optimization of a plantUS6381504 *Dec 31, 1998Apr 30, 2002Pavilion Technologies, Inc.Method for optimizing a plant with multiple inputsUS6438532 *Jan 23, 1998Aug 20, 2002Kabushiki Kaisha ToshibaAdjustment rule generating and control method and apparatusUS6529814 *May 14, 2001Mar 4, 2003Nissan Motor Co., Ltd.System and method for controlling vehicle velocity and inter-vehicle distanceUS6587108 *Jul 1, 1999Jul 1, 2003Honeywell Inc.Multivariable process matrix display and methods regarding same* Cited by examinerNon-Patent CitationsReference1U.S. Patent Ser. No. 09/482,386, filed Jan. 12, 2000.2U.S. Provisional application No. 60/215,453, filed Jun. 30, 2000.Referenced byCiting PatentFiling datePublication dateApplicantTitleUS6952620 *Sep 30, 2003Oct 4, 2005Sap AktiengesellschaftDeclaring application dataUS7039559 *Mar 10, 2003May 2, 2006International Business Machines CorporationMethods and apparatus for performing adaptive and robust predictionUS7113834 *Apr 21, 2003Sep 26, 2006Fisher-Rosemount Systems, Inc.State based adaptive feedback feedforward PID controllerUS7203554 *Mar 16, 2004Apr 10, 2007United Technologies CorporationModel predictive controller with life extending controlUS7231264 *Mar 19, 2004Jun 12, 2007Aspen Technology, Inc.Methods and articles for detecting, verifying, and repairing collinearity in a model or subsets of a modelUS7317953Dec 2, 2004Jan 8, 2008Fisher-Rosemount Systems, Inc.Adaptive multivariable process controller using model switching and attribute interpolationUS7444191Oct 4, 2005Oct 28, 2008Fisher-Rosemount Systems, Inc.Process model identification in a process control systemUS7451004 *Sep 30, 2005Nov 11, 2008Fisher-Rosemount Systems, Inc.On-line adaptive model predictive control in a process control systemUS7551969Sep 25, 2006Jun 23, 2009Fisher-Rosemount Systems, Inc.State based adaptive feedback feedforward PID controllerUS7660649 *Feb 9, 2010Optimal Innovations Inc.Resource management using calculated sensitivitiesUS7738975Oct 2, 2006Jun 15, 2010Fisher-Rosemount Systems, Inc.Analytical server integrated in a process control networkUS7856280 *Aug 2, 2006Dec 21, 2010Emerson Process Management Power & Water Solutions, Inc.Process control and optimization technique using immunological conceptsUS7856281 *Nov 7, 2008Dec 21, 2010Fisher-Rosemount Systems, Inc.On-line adaptive model predictive control in a process control systemUS8036760Oct 11, 2011Fisher-Rosemount Systems, Inc.Method and apparatus for intelligent control and monitoring in a process control systemUS8046096Oct 25, 2011Fisher-Rosemount Systems, Inc.Analytical server integrated in a process control networkUS8280533Jun 22, 2009Oct 2, 2012Fisher-Rosemount Systems, Inc.Continuously scheduled model parameter based adaptive controllerUS8332057Dec 11, 2012University Of New BrunswickMethod of multi-dimensional nonlinear controlUS8509924Dec 10, 2010Aug 13, 2013Emerson Process Management Power & Water Solutions, Inc.Process control and optimization technique using immunological conceptsUS8527252 *Jul 28, 2006Sep 3, 2013Emerson Process Management Power & Water Solutions, Inc.Real-time synchronized control and simulation within a process plantUS8706267Oct 28, 2008Apr 22, 2014Fisher-Rosemount Systems, Inc.Process model identification in a process control systemUS8756039 *Dec 3, 2010Jun 17, 2014Fisher-Rosemount Systems, Inc.Rapid process model identification and generationUS20030195641 *Apr 21, 2003Oct 16, 2003Wojsznis Wilhelm K.State based adaptive feedback feedforward PID controllerUS20040143815 *Sep 30, 2003Jul 22, 2004Markus CherdronDeclaring application dataUS20040181370 *Mar 10, 2003Sep 16, 2004International Business Machines CorporationMethods and apparatus for performing adaptive and robust predictionUS20040249481 *Mar 19, 2004Dec 9, 2004Qinsheng ZhengMethods and articles for detecting, verifying, and repairing collinearity in a model or subsets of a modelUS20050149209 *Dec 2, 2004Jul 7, 2005Fisher-Rosemount Systems, Inc.Adaptive multivariable process controller using model switching and attribute interpolationUS20050209713 *Mar 16, 2004Sep 22, 2005Fuller James WModel predictive controller with life extending controlUS20060015194 *Mar 19, 2004Jan 19, 2006Qingsheng ZhengMethods and articles for detecting, verifying, and repairing collinearity in a model or subsets of a modelUS20070021850 *Sep 25, 2006Jan 25, 2007Fisher-Rosemount Systems, Inc.State Based Adaptive Feedback Feedforward PID ControllerUS20070078529 *Sep 30, 2005Apr 5, 2007Fisher-Rosemount Systems, Inc.On-line adaptive model predictive control in a process control systemUS20070100477 *Mar 19, 2004May 3, 2007Qingsheng ZhengMethods and articles for detecting, verifying, and repairing collinearity in a model or subsets of a modelUS20070142936 *Oct 2, 2006Jun 21, 2007Fisher-Rosemount Systems, Inc.Analytical Server Integrated in a Process Control NetworkUS20080027704 *Jul 28, 2006Jan 31, 2008Emerson Process Management Power & Water Solutions, Inc.Real-time synchronized control and simulation within a process plantUS20080125881 *Aug 2, 2006May 29, 2008Emerson Process Management Power & Water Solutions, Inc.Process control and optimization technique using immunological conceptsUS20090058185 *Jul 7, 2008Mar 5, 2009Optimal Innovations Inc.Intelligent Infrastructure Power Supply Control SystemUS20090143872 *Nov 7, 2008Jun 4, 2009Fisher-Rosemount Systems, Inc.On-Line Adaptive Model Predictive Control in a Process Control SystemUS20090265021 *Oct 22, 2009University Of New BrunswickMethod of multi-dimensional nonlinear controlUS20090319060 *Jun 22, 2009Dec 24, 2009Fisher-Rosemount Systems, Inc.Continuously Scheduled Model Parameter Based Adaptive ControllerUS20100228363 *Sep 9, 2010Fisher-Rosemount Systems, Inc.Analytical server integrated in a process control networkUS20110144772 *Dec 10, 2010Jun 16, 2011Emerson Process Management Power & Water Solutions, Inc.Process control and optimization technique using immunological conceptsUS20110218782 *Dec 3, 2010Sep 8, 2011Fisher-Rosemount Systems, Inc.Rapid process model identification and generation* Cited by examinerClassifications U.S. Classification700/29, 700/34, 700/71, 318/561, 703/2, 700/46, 700/67, 700/28, 700/31International ClassificationG06F11/14, G05B11/32, G05B13/02, G05B17/02, G05B11/36, G05B13/04Cooperative ClassificationG05B17/02, G05B13/042, G05B13/048, G05B11/36, G05B11/32European ClassificationG05B11/32, G05B13/04D, G05B17/02, G05B11/36, G05B13/04BLegal EventsDateCodeEventDescriptionMar 11, 2004ASAssignmentOwner name: DOW CHEMICAL COMPANY, THE, MICHIGANFree format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:GAGNE, RONALD A.;REEL/FRAME:015060/0581Effective date: 20000726Sep 21, 2007FPAYFee paymentYear of fee payment: 4Sep 19, 2011FPAYFee paymentYear of fee payment: 8Nov 19, 2015FPAYFee paymentYear of fee payment: 12RotateOriginal ImageGoogle Home - Sitemap - USPTO Bulk Downloads - Privacy Policy - Terms of Service - About Google Patents - Send FeedbackData provided by IFI CLAIMS Patent Services