Polytopic Reduced-Order Model for HVAC Parameter Adaptation
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Solution Overview
Problem
Existing methods for controlling systems governed by parametric partial differential equations (PDEs), such as HVAC airflow, struggle with parameter-dependent dynamics, leading to poor estimation and control performance.
Innovation Solution
A computer-implemented method using a polytopic reduced-order model (ROM) generator that combines classic ROM methods with polytopic modeling and adaptive estimation and control, allowing for online adaptation to track unknown physical parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a classical reduced-order model (ROM) is used that does not include explicit dependence on physical parameters, then the model structure is simpler and easier to implement, but the estimation and control performance deteriorates when the system dynamics are strongly parameter-dependent
Solution Approach 1:
The patent applies dynamics by making the ROM adaptive and parameter-dependent. Instead of using a fixed classical ROM structure, the invention dynamically adjusts the model to track unknown physical parameters in real-time, allowing the model structure to evolve with changing system conditions while maintaining computational efficiency
Solution Approach 2:
The patent implements parameter changes by transitioning from a parameter-independent classical ROM to a parameter-dependent polytopic ROM. The model explicitly incorporates physical parameters through polytopic interpolation between local models, enabling the system to adapt to varying parameters such as room geometry, temperature, and window status
2Reliability
If a polytopic model with online adaptation is applied to track unknown physical parameters, then the estimation and control performance improves, but the computational complexity and processing requirements increase
Solution Approach 1:
The patent applies segmentation by dividing the parameter space into multiple polytopes, each associated with a local reduced model. This segmentation allows the complex parameter-dependent system to be broken down into manageable local models that can be independently constructed and then interpolated, reducing the overall computational burden compared to a single global model
Solution Approach 2:
The patent implements partial action by using a weighted combination of local models rather than requiring a complete global model for all parameter values. The polytopic interpolation uses only the necessary local models relevant to the current parameter regime, avoiding the computational expense of maintaining and evaluating all possible parameter configurations
3Adaptability or versatility
If polytopic modeling with weighted combination of local models is used, then the model adapts smoothly to parameter variations, but the number of local models and computational resources required increase
Solution Approach 1:
The patent applies universality by designing local reduced models that can serve multiple purposes across different parameter regimes. Each local model is constructed to be valid within its polytope region and can be reused through polytopic interpolation, eliminating the need to create entirely new models for each parameter value and reducing the total number of models required
Data Source
AI summary
A polytopic reduced-order model (ROM) generator is provided for a polytopic reduced-order model (ROM) used by an optimization controller in a heating, ventilation and air conditioning system. The physica model generator includes an interface circuit to receive a training dataset via a network connected to a simulation computer, a memory to store the polytopic ROM for predicting dynamics of airflow in the room, the training dataset, and instructions for calculating the parameters of the polytopic ROM, a processor to calculate the parameters of the polytopic ROM. The calculations include computing a global projection operation from high-dimensional state to reduced state, computing a global lifting operation from reduced state to high-dimensional state, constructing local reduced models of reduced state dynamics for each physical parameter value in the training dataset, and generating the polytopic ROM by combining a weighted average of the local reduced models with projection and lifting between reduced state and full state.