Loop-Shaping Controller Design Using Weighted Coprime Factorization
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Solution Overview
Problem
Conventional process control systems face challenges in accurately modeling and controlling industrial processes due to uncertainties and disturbances, leading to suboptimal performance and stability issues.
Innovation Solution
The method involves obtaining a preliminary model of the system, constructing a weighted model using coprime factorization, and iteratively determining parameters to minimize weighted coprime uncertainty, ensuring a stability margin greater than the uncertainty, and designing a controller based on this final model.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional PID controllers are used with traditional tuning methods, then the control system is simple to implement, but the system performance and stability are suboptimal due to uncertainties and disturbances
Solution Approach 1:
The patent performs system identification and model construction before controller design, obtaining a preliminary model of the process system. This preliminary modeling action enables subsequent robust controller synthesis that accounts for uncertainties, improving stability without requiring complex adaptive mechanisms during operation.
Solution Approach 2:
The patent transforms the controller design problem by changing parameters from traditional PID tuning to robust control parameters including coprime factorizations, stability margins, and weighted uncertainty bounds. This parameter transformation enables systematic handling of uncertainties while maintaining design tractability.
2Measurement precision
If a high-order accurate model is used for system identification, then the model precision is improved, but the controller design and implementation becomes more complex
Solution Approach 1:
The patent extracts the essential dynamic characteristics of the process system through system identification, separating the dominant behavior from higher-order effects. The coprime factorization methodology extracts stable and unstable components independently, enabling accurate representation of critical dynamics while simplifying the overall model structure for controller design.
Solution Approach 2:
The patent segments the model representation into coprime factors (stable and unstable parts) and further divides the frequency domain into weighted uncertainty regions. This segmentation allows targeted modeling of critical frequency ranges while simplifying less critical regions, achieving accuracy where needed without unnecessary complexity elsewhere.
3Reliability
If robust control design accounting for all uncertainties is implemented, then the stability margin is improved, but the computational burden and design time increase
Solution Approach 1:
The patent applies weighted uncertainty modeling that focuses computational effort on the most critical uncertainty regions rather than treating all uncertainties equally. By weighting uncertainties according to their impact on stability and performance, the design achieves robustness against critical disturbances while avoiding excessive computation on less significant uncertainties.
Solution Approach 2:
The patent changes the design approach from exhaustive uncertainty analysis to a parameterized robust control framework using stability margins and weighted norms. This parameterization transforms an intractable infinite-dimensional problem into a manageable optimization problem with finite parameters, significantly reducing design time while maintaining robustness guarantees.
Data Source
AI summary
One method includes obtaining a preliminary model associated with a system to be controlled and constructing a weighted model using one or more weighting factors. The method also includes identifying a final model of the system using the preliminary and weighted models, where the final model has a stability margin that is greater than an uncertainty associated with the final model. The method further includes controlling the system using a controller designed based on the final model. Another method includes identifying a first model associated with a system to be controlled, performing model order reduction to identify a second model, and controlling the system using a controller designed based on the second model. Performing the model order reduction includes reducing a weighted coprime factor model uncertainty between the first and second models.