Controlling a manufacturing process with a multivariate model
View Patent ↗A method, controller, and system for controlling a manufacturing process (batch-type or continuous-type) with a multivariate model are described. Dependent variable data and manipulated variable data are received. Dependent variable data represents values of uncontrolled process parameters from a plurality of sensors. Manipulated variable data represents controlled or setpoint values of controllable process parameters of a plurality of process tools. A predicted operational value, multivariate statistic, or both are determined based on the received data, and operating parameters of the manufacturing process are determined based on the predicted score, multivariate statistic, or both.
1. A computer-implemented method for controlling a batch-type manufacturing process with a finite duration, the method comprising:
receiving dependent variable data and manipulated variable data associated with the batch-type manufacturing process, the dependent variable data including measured past and present values of a first set of process parameters observed by one or more sensors, the manipulated variable data including measured past and present values of a second set of process parameters measured from a plurality of process tools, wherein the first set of process parameters, representative of dependent variables, and the second set of process parameters, representative of manipulated variables, are X-type variables in the batch-type manufacturing process;
determining, using a multivariate model of the manufacturing process, one or more multivariate statistics based on at least the dependent variable data and the manipulated variable data, wherein each multivariate statistic, which comprises a Hotelling value, a residual standard deviation value, a principal component score or a partial least squares component score, measures a deviation of the batch-type manufacturing process from a multivariate space of normal process behavior;
determining future values of the manipulated variables by optimizing an objective function that comprises J=θ Y (Y SP −Y pred ) 2 +θ MV (E MV ) 2 +θ DModX (E DModX ) 2 +θ T2 (E T2 ) 2 +θ t (E t ) 2 , wherein (i) Y SP represents at least one setpoint or target value for Y-type yield variables representative of yield or quality at the end of the finite duration of the batch-type manufacturing process, (ii) Y pred represents at least one predicted value for the yield variables, (iii) E MV represents an amount of deviation in the manipulated variable data from a desired trajectory subject to a penalty weight θ MV , (iv) E DModX represents an amount of the residual standard deviation value subject to a penalty weight θ DModX , (v) E T2 represents an amount of the Hotelling value subject to a penalty weight θ T2 , (vi) E t represents an amount of the principal component score or the partial least squares component score subject to a penalty weight θ t , (vii) and θ Y represents a penalty weight;
adjusting at least one of the second set of process parameters based on the future values of the manipulated variables.
2. The method of claim 1 , wherein the second set of process parameters, represented by the manipulated variables, are controlled during the manufacturing process.
3. The method of claim 2 , wherein the first set of process parameters, represented by the dependent variables, are not directly controlled during the manufacturing process.
4. The method of claim 1 , further comprising modifying the present or future values of the manipulated variables based on the past or present values of the manipulated variables and of the dependent variables.
5. The method of claim 1 , wherein determining future values of the manipulated variables further comprises satisfying a controller objective.
6. The method of claim 5 , wherein satisfying a controller objective comprises optimizing the objective function by associating process data, values for the yield variables, result data, or any combination thereof of the manufacturing process.
7. The method of claim 6 , wherein the objective function includes one or more constraints on the dependent variable data, the manipulated variable data, values for the yield variables, the multivariate statistic, or any combination thereof.
8. The method of claim 7 , wherein the one or more constraints are user-specified.
9. The method of claim 7 , wherein the one or more constraints are associated with penalties for deviating from the multivariate model.
10. The method of claim 5 , wherein the controller objective is the objective function comprising a quadratic-type function and satisfying the controller objective further comprises minimizing a parameter of the objective function.
11. The method of claim 1 , further comprising;
determining desired values for the yield variables or desired multivariate statistic associated with the end of the finite duration of the batch type manufacturing process; and
adjusting the second set of process parameters based on the future values of the manipulated variables to achieve at least one of the desired values for the yield variables or the desired multivariate statistic.
12. The method of claim 1 , further comprising estimating future values of the dependent variables using a dependent variable model based on the future values of the manipulated variables, the past or present values of the dependent variables, or any combination thereof.
13. The method of claim 1 , wherein optimizing the object function penalizes deviation of the multivariate statistic from the multivariate model.
14. The computer-implemented method of claim 1 , further comprising:
estimating future values of the dependent variables based on the future values of the manipulated variables; and
providing at least one of the future values of the dependent variables or the future values of the manipulated variables as inputs to the multivariate model.
15. The computer-implemented method of claim 1 , further comprising:
estimating the predicted value for the yield variables based on the future values of the manipulated variables; and
providing the predicted value for the yield variables as inputs to the objective function.
16. A multivariate controller for a batch-type manufacturing process with a finite duration, the controller comprising:
a hardware control module in communication with a plurality of process tools and a plurality of sensors to monitor manipulated variable data from the process tools and dependent variable data from the sensors, the control module including a multivariate model for determining one or more multivariate statistics based on at least the manipulated variable data and the dependent variable data, each multivariate statistic comprising a Hotelling value, a residual standard deviation value, a principal component score or a partial least squares component score, and each multivariate statistic measuring a deviation of the batch-type manufacturing process from a multivariate space of normal process behavior,
wherein the dependent variable data includes measured past and present values of a first set of process parameters observed by the plurality of sensors and the manipulated variable data includes measured past and present values of a second set of process parameters, wherein the first set of process parameters, representative of dependent variables, and the second set of process parameters, representative of manipulated variables, are X-type variables in the batch-type manufacturing process; and
a hardware solver module to: i) receive, from the multivariate model, the one or more multivariate statistics, and ii) optimize an objective function using the multivariate statistics determined from the multivariate model to generate future values of the manipulated variables for providing to the plurality of process tools, wherein the objective function comprises J=θ Y (Y SP −Y pred ) 2 +θ MV (E MV ) 2 +θ DModX (E DModX ) 2 +θ T2 (E T2 ) 2 +θ t (E t ) 2 , wherein (i) Y SP represents at least one setpoint or target value for Y-type yield variables representative of yield or quality at the end of the finite duration of the batch-type manufacturing process, (ii) Y pred represents at least one predicted value for the yield variables, (iii) E MV represents an amount of deviation in the manipulated variable data from a desired trajectory subject to a penalty weight θ MV , (iv) E DModX represents an amount of the residual standard deviation value subject to a penalty weight θ DModX , (v) E T2 represents an amount of the Hotelling value subject to a penalty weight θ T2 , (vi) E 1 represents an amount of the principal component score or the partial least squares component score subject to a penalty weight θ t , (vii) and θ Y represents a penalty weight.
17. The controller of claim 16 , wherein the controller adjusts one or more parameters of the plurality of process tools based on the future values of the manipulated variables.
18. The controller of claim 16 , wherein the solver module is adapted to provide the future values of the manipulated variables to a score model to generate predicted values for the solver module of one or more statistical data.
19. The controller of claim 18 , wherein the score model provides the predicted statistical data to the control module and the solver module.
20. The controller of claim 16 , wherein the solver module is adapted to provide the future values of the manipulated variables to a dependent variable model to estimate future values of the dependent variables.
21. The controller of claim 20 , wherein the dependent variable model provides the future values of the dependent variables to the multivariate model to improve future determination of the multivariate model.
22. The controller of claim 16 , wherein the solver module generates the future values of the manipulated variables based on a controller objective.
23. The controller of claim 22 , wherein the controller objective optimizes the objective function comprising a quadratic-type function associated with the manufacturing process.
24. The controller of claim 22 , wherein the controller objective includes one or more constraints on the dependent variable data, the manipulated variable data, values for the yield variables, the multivariate statistic, or any combination thereof.
25. The controller of claim 24 , wherein the one or more constraints are user-specified.
26. The controller of claim 24 , wherein the one or more constraints are associated with penalties for deviating from the multivariate model.
27. The controller of claim 16 , wherein the solver module is a constrained optimization solver.
28. The controller of claim 16 , wherein the control module comprises the solver module.
29. A system for controlling a batch-type manufacturing process with a finite duration, the system comprising:
a hardware data acquisition means for acquiring manipulated variable data associated with the manufacturing process, including measured past and present values of a set of process parameters measured from a plurality of process tools; and acquiring dependent variable data associated with the manufacturing process, including measured past and present values of a second set of process parameters observed by a plurality of sensors, wherein the first set of process parameters, representative of dependent variables, and the second set of process parameters, representative of manipulated variables, are X-type variables in the batch-type manufacturing process;
a hardware multivariate control means incorporating a multivariate statistical model for receiving at least the manipulated variable and dependent variable data and determining multivariate statistical information that measures a deviation of the batch-type manufacturing process from a multivariate space of normal process behavior, wherein the multivariate statistical information comprises one or more of a Hotelling value, a residual standard deviation value, a principal component score or a partial least squares component score;
a hardware process control means for determining future values of the manipulated variables by optimizing an objection function using at least the multivariate statistical information determined by the multivariate control means, the objective function comprising J=θ Y (Y SP −Y pred ) 2 +θ MV (E MV ) 2 +θ DModX (E DModX ) 2 +θ T2 (E T2 ) 2 +θ t (E t ), wherein (i) Y SP represents at least one setpoint or target value for Y-type yield variables representative of yield or quality for the end of the finite duration of the batch-type manufacturing process, (ii) Y pred represents at least one predicted value for the yield variables, (iii) E MV represents an amount of deviation in the manipulated variable data from a desired trajectory subject to a penalty weight θ MV , (iv) E DModX represents an amount of the residual standard deviation value subject to a penalty weight θ DModX , (v) E T2 represents an amount of the Hotelling value subject to a penalty weight θ T2 , (vi) E t represents an amount of the principal component score or the partial least squares component score subject to a penalty weight θ t , (vii) and θ Y represents a penalty weight,
wherein the process control means is configured to adjust at least one of the second set of process parameters representative of manipulated variables based on the future values of the manipulated variables.
30. The system of claim 29 , wherein the future values of the manipulated variables determined by the process control means optimize or satisfy a control objective.