Modeling and Control for Highly Variable and Nonlinear Systems
First Claim
1. A method of describing a measured response from a process receiving at least one inputs and producing at least one responses, said process having nonlinearities of at least one of a minimum input or minimum amount of accumulated input to produce a non-minimal response measurement and a maximum response measurement, on a second scale accounting for said nonlinearities where the process is modeled as a process linear on the second scale, by converting the response according to a slope and offset comprising:
- (a) defining said slope as the range of inputs or range of accumulated inputs that produces a range of measurable responses that are neither minimal nor maximal responses, divided by said range of measurable responses over said range of inputs or accumulated inputs;
(b) defining an offset parameter as an input or quantity of accumulated inputs required to establish a non-minimal measurable response; and
(c) calculating the second response as the measured response multiplied by said response, plus the offset.
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Abstract
The present invention relates generally to methods of modeling and handling of nonlinearities for application of automatic control to systems with high inter-process variance and nonlinearities. The variance and nonlinearities make these systems difficult to control. Variance is accounted for by replacing the mathematical model of the system with a more representative model from a modelset that may or may not be chosen based on characteristics of the system under test, and then adapting using recursive estimation techniques. Nonlinearities defined by threshold to response and maximal responses are incorporated into linear models relating accumulated inputs to response. Example implementations in relation to automated drug delivery for neuromuscular blocking drugs through warning, advisory and closed-loop control systems are discussed.
17 Citations
51 Claims
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1. A method of describing a measured response from a process receiving at least one inputs and producing at least one responses, said process having nonlinearities of at least one of a minimum input or minimum amount of accumulated input to produce a non-minimal response measurement and a maximum response measurement, on a second scale accounting for said nonlinearities where the process is modeled as a process linear on the second scale, by converting the response according to a slope and offset comprising:
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(a) defining said slope as the range of inputs or range of accumulated inputs that produces a range of measurable responses that are neither minimal nor maximal responses, divided by said range of measurable responses over said range of inputs or accumulated inputs; (b) defining an offset parameter as an input or quantity of accumulated inputs required to establish a non-minimal measurable response; and (c) calculating the second response as the measured response multiplied by said response, plus the offset. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A method of calculating a linear response model for a process receiving at least one inputs and producing at least one responses, said process having nonlinearities, where said nonlinearities include at least one of a minimum input or minimum amount of accumulated input to produce a non-minimal response and a maximum response, comprising:
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(a) administering at least one standard input to the process; (b) recording one or more responses produced by the standard input; (c) assembling a dataset of matched response and time datapoints where response datapoints comprise non-minimal and non-maximal response measurements, and time datapoints comprise time of measurement; (d) adjusting the dataset to correct for the nonlinearities on a second scale accounting for said nonlinearities, where the process is modeled as a process linear on the second scale by converting the response data according to a slope defined as the range of inputs or range of accumulated inputs that produces a range of measurable responses that are neither minimal nor maximal responses, divided by said range of measurable responses over said range of inputs or accumulated inputs; and
an offset defined as an input or quantity of accumulated inputs required to establish a non-minimal measurable response; and
calculating the adjusted response on the second scale as the measured response multiplied by said response plus the offset;(e) estimating at least one parameters for at least one mathematical function to describe the adjusted dataset; and (f) calculating at least one continuous set of datapoints described by the at least one function whose parameters are derived in step (e). - View Dependent Claims (9, 10, 11, 12)
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13. A method of adapting a model of a process comprising at least one equation said equation including a set of at least one parameters, said model translating at least one input into at least one response, and said model beginning as at least one of an initial model taken from a modelset comprising one or more models of like processes similar in mathematical construct but with one or more differences in the at least one parameters or built as a mathematical function of the models in the modelset, comprising:
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(a) collecting measurement data related to at least one measured responses; (b) estimating model parameters to adapt the model of a process to the collected data; and (c) evaluating said model of a process for comparative performance versus other process models in the modelset, and replacing the at least one parameters of the model of a process with the set of at least one parameters of another similar in mathematical construct process model from the modelset. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20)
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21. A system for indicating when at least one response of a process will reach at least one setpoint, the system comprising:
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(a) a user interface for receiving process related data including process characteristics and inputs administered, and for displaying information including warnings; (b) a communications interface through which the system obtains data from at least one sensor; (c) a model of the process'"'"' at least one response comprising at least one equation said equation including a set of at least one parameters, said model translating at least one input into at least one response; (d) a computing mechanism operatively connected to the communications interface to receive the sensor data and connected to the user interface to receive input from the user and to present data to the user, the computing mechanism configured to use the model of the process'"'"' at least one response to estimate current and future responses; (e) memory operatively connected to the computing mechanism for storing and retrieving sensor data and data relevant to the computation, and for storing programs for operation by the computing mechanism; and (f) a modelset comprising one or more models of like processes similar in mathematical construct but with one or more differences in the at least one parameters; where said model begins as at least one of an initial model taken from the modelset or is built as a mathematical function of the models in the modelset, and is adapted by steps comprising; (i) collecting measurement data related to at least one measured responses; (ii) estimating the at least one parameters to adapt the model of a process to the collected data; and (iii) evaluating said model of a process for comparative performance versus other process models in the modelset, and replacing the at least one parameters of the model of a process with the set of at least one parameters of another similar in mathematical construct process model from the modelset. - View Dependent Claims (22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51)
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Specification