Robust steady-state target calculation for model predictive control
First Claim
1. A method of controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, G represents system gain parameters, and where J is a function of G, said method comprising the steps of;
(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description and where {tilde over (J)} is said objective function J applied to {tilde over (G)};
(b) computing steady-state targets for said system-manipulated input variables u such that all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description.
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Accused Products
Abstract
A method and apparatus for steady-state target calculation that explicitly accounts for model uncertainty is disclosed. In accordance with one aspect of the invention, when model uncertainty is incorporated, the linear program associated with the steady-state target calculation can be recast as a highly structured nonlinear program. In accordance with another aspect of the invention, primal-dual interior point methods can be applied to take advantage of the resulting special structure. For a system having characteristic gain parameters G having a known uncertainty description, the present invention provides a method and apparatus for selecting steady-state targets for said system-manipulated variables such that all system-controlled variables will remain feasible at steady-state for all possible values of the parameters G within the known uncertainty description. A nominal estimate {tilde over (G)} of the system parameters G is made, and in accordance with another aspect of the invention, the steady-state targets are selected such that when {tilde over (G)}=G, the system is driven to an operational steady-state in which the objective function is extremized.
59 Citations
37 Claims
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1. A method of controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, G represents system gain parameters, and where J is a function of G, said method comprising the steps of;(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description and where {tilde over (J)} is said objective function J applied to {tilde over (G)};
(b) computing steady-state targets for said system-manipulated input variables u such that all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
- y=GΔ
-
9. A method of controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters, said method comprising the steps of;(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description;
(b) extremizing said objective function J by solving the nonlinear equation
subject to
- y=GΔ
-
10. A method of controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G is a matrix representing system gain parameters, said method comprising the steps of;(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description;
(b) ascribing minimum and maximum bounds to elements of G;
(c) extremizing said objective function J by solving the linear equation
subject to
- y=GΔ
-
11. A method of controlling a system in accordance with an objective function J, wherein the operation of said system is describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters, said method comprising the steps of;(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description;
(b) extremizing said objective function J by solving the nonlinear equation
subject to
- y=GΔ
-
12. An apparatus for controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters having a known uncertainty description, and where J is a function of G, said apparatus comprising;(a) an estimator for deriving a nominal estimate {tilde over (G)} of said system gain parameters G, where {tilde over (G)} has a known uncertainty description and where {tilde over (J)} is said objective function J applied to {tilde over (G)};
(b) a computing circuit, responsive to at least one past value of said system-controlled output variables and of said system-manipulated input variables to compute steady-state targets for said system-manipulated input variables u such that all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19)
(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description and where {tilde over (J)} is said objective function J applied to {tilde over (G)};
(b) computing steady-state targets for said system-manipulated input variables u such that all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description.
- y=GΔ
-
20. An apparatus for controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters having a known uncertainty description, and where J is a function of G, said apparatus comprising;(a) estimator means for deriving a nominal estimate {tilde over (G)} of said system gain parameters G, where {tilde over (J)} is said objective function applied to {tilde over (G)};
(b) computing means, responsive to at least one past value of said system-controlled output variables and of said system-manipulated input variables to compute steady-state targets for said system-manipulated input variables u such that all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description. - View Dependent Claims (21, 22, 23, 24, 25, 26, 27)
- y=GΔ
-
28. An apparatus for controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters having a known uncertainty description, said apparatus comprising;(a) an estimator for deriving a nominal estimate {tilde over (G)} of said system gain parameters G;
(b) computation circuitry responsive to at least one past value of said system-controlled output variables and of said system-manipulated input variables, and responsive to said nominal estimate {tilde over (G)}, for extremizing said objective function J by solving the equation
subject to
- y=GΔ
-
29. An apparatus controlling a system in accordance with an objective function J, wherein the operation of said system is describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters having a known uncertainty description, said method comprising the steps of;(a) estimator circuitry for deriving a nominal estimate {tilde over (G)} of said system gain parameters G;
(b) computation circuitry, responsive to at least one past value of said system-controlled output variables and of said system-manipulated input variables, and responsive to said nominal estimate {tilde over (G)}, for extremizing said objective function J by solving the equation
subject to
- y=GΔ
-
30. An apparatus for controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=G Δ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters having a known uncertainty description, said apparatus comprising;(a) estimator means for deriving a nominal estimate {tilde over (G)} of said system gain parameters G;
(b) computing means responsive to at least one past value of said system-controlled output variables and of said system-manipulated input variables, and responsive to said nominal estimate {tilde over (G)}, for extremizing said objective function J by solving the equation
subject to
- y=G Δ
-
31. An apparatus controlling a system in accordance with an objective function J, wherein the operation of said system is describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters having a known uncertainty description, said apparatus comprising;(a) estimator means for deriving a nominal estimate {tilde over (G)} of said system gain parameters G;
(b) computing means, responsive to at least one past value of said system-controlled output variables and of said system-manipulated input variables, and responsive to said nominal estimate {tilde over (G)}, for extremizing said objective function J by solving the equation
subject to
- y=GΔ
-
32. A controller for controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, G represents system gain parameters, and where J is a function of G, the controller comprising (a) a processor and (b) a program storage device that is readable by said processor and that comprises instructions that, when executed, cause the controller to perform the steps of;(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description and where {tilde over (J)} is said objective function J applied to {tilde over (G)};
(b) computing steady-state targets for said system-manipulated input variables u such that all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description.
- y=GΔ
-
33. A computer program product for controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, G represents system gain parameters, and where J is a function of G, the computer program embodied on a computer readable medium and comprising instructions that, when executed, cause a computing apparatus to perform the steps of;(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description and where {tilde over (J)} is said objective function J applied to {tilde over (G)};
(b) computing steady-state targets for said system-manipulated input variables u such that all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description.
- y=GΔ
-
34. A method of controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, G represents system gain parameters, and where J is a function of G, said method comprising the steps of;(a) modeling said system according to an equation Δ
y={tilde over (G)}Δ
u, where {tilde over (G)} is a nominal estimate of G and has a known uncertainty description and where {tilde over (J)} is said objective function J applied to {tilde over (G)};
(b) computing steady-state targets for said system-manipulated input variables u such that;
(i) all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description; and
(ii) said objective function {tilde over (J)} is extremized;
wherein as {tilde over (G)} approaches G, said computed steady-state targets approach those steady-state targets that extremize J, subject to said known uncertainty description. - View Dependent Claims (35)
- y=GΔ
-
36. An apparatus for controlling a system in accordance with an objective function J, the operation of said system being describable by an equation Δ
- y=GΔ
u, where y represents one or more system-controlled output variables, u represents one or more system-manipulated input variables, and G represents system gain parameters having a known uncertainty description, and where J is a function of G, said apparatus comprising;(a) estimator means for deriving a nominal estimate {tilde over (G)} of said system gain parameters G, where {tilde over (J)} is said objective function applied to {tilde over (G)};
(b) computing means, responsive to at least one past value of said system-controlled output variables and of said system-manipulated input variables to compute steady-state targets for said system-manipulated input variables u such that;
(i) all of said system-controlled output variables will remain feasible at steady-state for all possible values of the system gain parameters within said known uncertainty description; and
(ii) said objective function {tilde over (J)} is extremized;
wherein as {tilde over (G)} approaches G, said computed steady-state targets approach those steady-state targets that extremize J, subject to said known uncertainty description. - View Dependent Claims (37)
- y=GΔ
Specification