Super-linear approximation of dynamic property values in a process control environment

A system for improving processor performance for simulating at least one physical process control environment, comprising:

• a processor,
• a non-transitory computer-readable medium;
• wherein said non-transitory computer-readable medium comprises instructions configured and arranged for generating a process simulation using said processor, said instructions comprising:
• creating a mathematical model,
• generating a super-linear Taylor series expansion of the mathematical model;
• wherein said super-linear Taylor series expansion calculation comprises:
• determining a rigorous value,
• generating a linear difference between a current independent property value and a previous independent property value,
• generating a linear derivative of the linear difference,
• generating a negative of the linear derivative,
• generating a logarithmic difference between a logarithm of the current independent property value and a logarithm of the previous independent property value,
• generating a logarithmic derivative of the logarithmic difference,
• adding the rigorous value, the linear derivative, the negative linear derivative, and the logarithmic derivative to obtain a super-linear approximation;
• wherein said previous independent property value represents a mathematical model property value during a previous time, and
• wherein said current independent property value represents a mathematical model property value during a current time;
• and
• wherein said determining the rigorous value comprises one of:
• generating a mathematical model solution for the current time,
• using a previously obtained super-linear approximation,
• wherein said previously obtained super-linear approximation is the solution to a previous super-linear Taylor series expansion calculation;
• and
• wherein the obtaining the super-linear approximation does not comprise generating second order derivatives;
• and
• wherein the rigorous value, the linear derivative, the negative linear derivative, and the logarithmic derivative are all first-order terms;
• and
• wherein said processor is configured and arranged to control at least one component of the at least one physical process control environment based on the super-linear approximation.

A non-transitory processor readable medium having processor-executable instructions stored thereon configured and arranged to generate a super-linear approximate value of a dynamic physical property associated with an industrial process, the instructions comprising:

• receiving one or more values of the dynamic physical property,
• generating at least one first-order series expansion of at least one dynamic equation modeling at least part of the dynamic physical property,
• generating a super-linear approximate value of the dynamic physical property based on the first-order series expansion,
• generating the super-linear approximate value over a range of values of the dynamic physical property, and
• simulating, using a simulation module, at least part of the industrial process based at least in part on the super-linear approximate value;
• wherein the at least one dynamic equation is a mathematical model of at least part of the dynamic physical property;
• and
• wherein generating the at least one first-order series expansion does not result in terms with second order derivatives.

A system for controlling a component of a process comprising:

• a processor configured and arranged to be coupled to a process comprising the component;
• a super-linear approximation system producing a plurality of results for use by the processor to determine a current super-linear approximate value, said super-linear approximation system comprising:
• a subtraction-differentiation module adapted to perform a subtraction operation and a differentiation operation on a previous property value and a current property value to determine a result thereof;
• a negation module adapted to perform a negation operation on the result of the subtraction-differentiation module to determine a result thereof;
• a logarithm-subtraction-differentiation module adapted to perform a logarithm operation, a subtraction operation, and a differentiation operation on the previous property value and the current property value to determine a result thereof;
• a first summation module adapted to perform an addition operation on the result of the subtraction-differentiation module, the result of the negation module, the result of the logarithm-subtraction-differentiation module, and a previous rigorously calculated property value, wherein a result of the addition operation comprises a current super-linear approximate property value;
• and
• wherein the processor is adapted to perform a repeated simulation of the process based at least in part on a dynamic equation representing a mathematical model of the dynamic property, the dynamic equation solved as a function of the current super-linear approximate value to determine a converged solution for the dynamic equation based at least in part on the current super-linear approximate property value;
• and
• wherein the processor is configured and arranged to control the component based at least in part on the converged solution.

A method for simulating at least one physical process control environment, comprising:

• providing a processor,
• providing a non-transitory computer-readable medium;
• wherein said non-transitory computer-readable medium comprises instructions configured and arranged for generating a process simulation using said processor, said instructions comprising the steps of:
• creating a mathematical model,
• generating a super-linear Taylor series expansion of the mathematical model;
• wherein said super-linear Taylor series expansion calculation comprises the steps of:
• determining a rigorous value,
• generating a linear difference between a current independent property value and a previous independent property value,
• generating a linear derivative of the linear difference,
• generating a negative of the linear derivative,
• generating a logarithmic difference between a logarithm of the current independent property value and a logarithm of the previous independent property value,
• generating a logarithmic derivative of the logarithmic difference,
• adding the rigorous value, the linear derivative, the negative linear derivative, and the logarithmic derivative to obtain a super-linear approximation;
• wherein said previous independent property value represents a mathematical model property value during a previous time, and
• wherein said current independent property value represents a mathematical model property value during a current time;
• and
• wherein said determining the rigorous value step comprises one of:
• generating a mathematical model solution for the current time,
• using a previously obtained super-linear approximation;
• wherein said previously obtained super-linear approximation is the solution to a previous super-linear Taylor series expansion calculation;
• and
• wherein the obtaining the super-linear approximation does not comprise generating second order derivatives;
• and
• wherein the rigorous value, the linear derivative, the negative linear derivative, and the logarithmic derivative are all first-order terms;
• and
• wherein said processor is configured and arranged to control at least one component of the at least one physical process control environment based on the super-linear approximation.