Method and system for scalable embedded model predictive control of HVAC systems
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Solution Overview
Problem
Existing model predictive control (MPC) methods for HVAC systems are not feasible on low-cost, resource-limited embedded computing platforms due to scalability issues and computational complexity, particularly in solving large-scale optimization problems with matrix inversion.
Innovation Solution
A computationally efficient and scalable solution for large-scale model predictive building control using a first-order method with a novel UV factorization of the constraint matrix, allowing for real-time control on low-cost embedded devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional model predictive control methods are used for HVAC systems, then control accuracy is improved, but computational complexity increases making it infeasible on low-cost embedded platforms
Solution Approach 1:
The constraint matrix H is segmented into two factors U and V through UV-factorization, where U contains orthonormal columns. This segmentation transforms the original complex matrix inversion problem into simpler operations involving diagonal matrices, reducing computational complexity while preserving control accuracy.
Solution Approach 2:
The patent changes the parameter representation by transforming the optimization problem to work with the factorized matrix structure. Instead of directly inverting the constraint matrix H, the method uses the factorized form with diagonal matrices UUT and VTV, changing the computational parameters from general matrix operations to diagonal matrix operations that are computationally lighter.
2Measurement precision
If large-scale optimization problems are solved with matrix inversion, then control precision is improved, but real-time control capability deteriorates
Solution Approach 1:
The constraint matrix is segmented into factors U and V, enabling the optimization problem to be solved through simpler diagonal matrix operations rather than full matrix inversion. This segmentation maintains solution precision while dramatically reducing computational time, enabling real-time control for large-scale HVAC systems.
Solution Approach 2:
The method changes the computational parameters by working with the factorized matrix structure and diagonal matrices instead of the original constraint matrix. This parameter transformation allows solving large-scale optimization problems faster while maintaining the precision required for accurate HVAC control.
3Adaptability or versatility
If scalable models are used for large-scale buildings, then system adaptability is improved, but computational complexity increases
Solution Approach 1:
The UV-factorization segments the constraint matrix into structured factors that exploit the sparsity and structure of large-scale HVAC systems. This segmentation enables scalable models to be used across different building sizes while keeping computational complexity manageable through efficient diagonal matrix operations.
Solution Approach 2:
The factorized matrix approach provides a universal solution that can be applied to HVAC systems of various scales. The same UV-factorization methodology works for both small and large-scale buildings, making the system adaptable and versatile without requiring different computational approaches for different system sizes.
Data Source
AI summary
A physics model of a building is linearized around an operating point. Measurements received from sensors define a system state of the HVAC system. The linearized physics model is used as an equality constraint for a model predictive controller that determines a next control input to the HVAC system based on the system state by solving an optimization problem for a time horizon of size N. A constraint matrix H of the equality constraint is decomposed into factors of U and V matrices such that UUT and VT V are both diagonal matrices. An objective function of the model predictive controller is optimized by iteratively solving a linear system of equations that includes inverses of UUT and VT V to determining a sequence of inputs for a horizon of the model predictive controller. A first input of the sequence of inputs to is used to control the HVAC system.