Dynamic Optimization of Industrial Processes via Linearization
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Solution Overview
Problem
Existing industrial processes face challenges in optimizing both measured and unmeasured process variables to minimize objective functions subject to constraints, particularly in non-linear dynamic systems where steady-state conditions are not consistently maintained.
Innovation Solution
A method and system that utilize Wiener-Hammerstein block-oriented nonlinear models to relate state vector values over time, allowing for the minimization of steady-state objective functions by linearizing memory-less nonlinearities and solving the problem as a sequence of linear static optimization problems, even during transients, using linear programming techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If non-linear dynamic optimization is applied to industrial processes, then optimization accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent segments the non-linear dynamic optimization problem into multiple linear sub-problems by dividing the time horizon into discrete intervals and linearizing the system dynamics within each interval. This allows the complex non-linear problem to be solved as a sequence of simpler linear programming problems, reducing computational complexity while maintaining optimization accuracy.
Solution Approach 2:
The patent introduces an intermediary linearization step that transforms the non-linear system into a linear approximation. By using linearization techniques as an intermediary, the complex non-linear optimization is converted into a manageable linear programming problem that can be solved efficiently while still capturing the essential dynamics of the original system.
2Adaptability or versatility
If dynamic optimization during transients is implemented, then process control flexibility is improved, but mathematical model complexity increases
Solution Approach 1:
The patent applies dynamics by formulating the optimization to handle time-varying conditions and transient states. The model incorporates dynamic behavior through time-dependent constraints and objective functions, allowing the system to adapt to changing conditions while using linear programming techniques to manage the mathematical complexity.
Solution Approach 2:
The patent changes parameters by transforming the non-linear dynamic problem into a linear programming problem with time-varying parameters. By allowing parameters to change with time and using linearization, the system achieves flexibility in handling transient conditions without requiring complex non-linear mathematical models.
3Manufacturing precision
If both measured and unmeasured process variables are optimized, then comprehensive process optimization is improved, but data reconciliation difficulty increases
Solution Approach 1:
The patent applies universality by creating a unified linear programming framework that simultaneously handles both measured and unmeasured process variables. The model integrates data reconciliation and optimization into a single multi-functional system, allowing comprehensive process optimization while managing data reconciliation through consistent linear mathematical relationships.
Data Source
AI summary
Enables minimization of steady-state objective function P(z∞), subject to a set of constraints zmin≦z∞≦zmax, and under the assumption that the values of the state vector, z, at different points in time related via a model expressed in dynamic open equation format Q(z∞, zk, zk-1, zk-2, . . . , zk-n)=0, where z∞ is predicted final value of state vector, z, and zk, zk-1, zk-2, . . . , zk-n are current and previous values of state vector, z. Determines optimum operation of an industrial process having steady-state objective function P(z∞), including: receiving outputs from the process; minimizing steady-state objective function P(z∞) subject to set of constraints zmin≦z∞≦zmax; wherein values of state vector at different times are related via model of form Q(z∞, zk, zk-1, zk-2, . . . , zk-n)=0; to minimize objective function P(z∞). Industrial process to be optimised may include measured and unmeasured process variables.