Nonlinear Process Decomposition via Local Linear Models
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing model-based process control methods for nonlinear processes face challenges in accurately representing dynamics, particularly in industries like chemicals, polymers, and pulp and paper, due to the complexity and cost of nonlinear models, as well as issues with numerical stability and optimal transitions between operating points.
Innovation Solution
A method for decomposing the nonlinear process into multiple local linear models using fuzzy classification and Monte Carlo simulations, ensuring smooth switching and maintaining closed-loop stability, which reduces the number of models needed while preserving prediction quality and stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If nonlinear dynamic models are used for nonlinear model predictive control, then the control accuracy and ability to handle process nonlinearity are improved, but the model complexity and computational burden increase significantly
Solution Approach 1:
The patent divides the nonlinear process into multiple local linear models, each valid in a specific operating region. This segmentation allows the complex nonlinear system to be represented by simpler linear models that can be computed efficiently while maintaining accuracy within their respective regions.
Solution Approach 2:
The patent applies local linearization by creating models that are accurate locally around specific operating points rather than attempting a global nonlinear model. Each local model has optimized parameters for its specific region, providing high accuracy where needed while keeping individual model complexity low.
2Reliability
If first principles based nonlinear models are built, then the physical accuracy and understanding of the process are improved, but the cost and time required to develop the model increase
Solution Approach 1:
The patent creates simplified linear copies of the nonlinear process behavior around different operating points. These linear models capture the essential dynamics without requiring complex first principles derivations, reducing development cost and time while maintaining sufficient accuracy for control applications.
Solution Approach 2:
The patent changes the model representation from fixed first principles parameters to adaptive local parameters that vary with operating conditions. This allows the model to maintain physical accuracy across different regions while using simpler parameter structures that are easier and cheaper to identify from data.
3Adaptability or versatility
If a large number of local linear models are created to cover the operating range, then the coverage and adaptability are improved, but the computational burden and complexity of model switching increase
Solution Approach 1:
The patent merges adjacent local models through smooth transition functions and overlapping validity regions. This combining approach reduces the effective number of discrete models needed while maintaining continuous coverage across the operating range, simplifying the switching logic and reducing computational burden.
Solution Approach 2:
The patent implements dynamic model selection and smooth transitions between models based on real-time operating conditions. Rather than statically switching between discrete models, the system dynamically weights and combines models based on current state, providing continuous adaptability with reduced complexity.
4Stability of the object's composition
If smooth switching between local models is implemented, then the stability and continuity of control are improved, but the complexity of the switching strategy increases
Solution Approach 1:
The patent ensures continuous control action during model transitions by using overlapping validity regions and smooth weighting functions. The useful control action continues uninterrupted as the system transitions between local models, maintaining stability without requiring complex switching logic.
Solution Approach 2:
The patent introduces smooth transition functions as intermediaries between discrete local models. These intermediary functions provide continuous blending of model outputs during transitions, ensuring stability and avoiding abrupt changes while keeping the switching strategy relatively simple.
Data Source
AI summary
Multiple models for various stages of a non-linear process control are developed by clustering perturbation data obtained from the nonlinear process so as to permit multiple local data regions to be identified as a function of substantial similarity between the data, wherein the data of first data set represent the non-linear process. A discrete model corresponding to each of the local data regions is generated. The number of the discrete models may be reduced as a function of prediction error between actual outputs of the process and predicted outputs of the models and as a function of a gap metric based on closed loop similarity and frequency response similarity between the models.