Method and system for scalable embedded model predictive control of HVAC systems
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 UU T and V T 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 UU T and V T 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.
1. A method comprising:
determining a physics model of a building and linearizing the physics model around an operating point, the linearized physics model defining thermodynamic relationships between zones of the building and a heating, ventilation, and air-conditioning (HVAC) system;
receiving measurements from sensors, the measurements defining a system state of the HVAC system;
using the linearized physics model 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;
decomposing a constraint matrix H of the equality constraint into factors of a first matrix U and a second matrix V such that UU T and V T V are both diagonal matrices;
optimizing an objective function of the model predictive controller by iteratively solving a linear system of equations that includes inverses of UU T and V T V to determining a sequence of inputs for a horizon of the model predictive controller; and
applying a first input of the sequence of inputs to control the HVAC system.
2. The method of claim 1 , wherein an augmented Lagrangian method is used to optimize the objective function in view of the equality constraint and other equality and inequality constraint.
3. The method of claim 1 , wherein optimizing the objective function of the model predictive controller comprises finding, in a first iteration a first factor comprising the inverse of the diagonal matrix UU T and a second factor comprising the inverse of the diagonal matrix V T V and reusing the first and second factors in subsequent iterative steps.
4. The method of claim 3 , wherein the iterations involve using the first and second factor to update primal variables of the model predictive controller and Langrangian multipliers.
5. The method of claim 1 , wherein the model predictive controller is formatted as a quadratic problem that involves optimizing a quadratic objective function subject to a set of linear equality and linear inequality constraints.
6. The method of claim 5 , wherein the set of linear inequality constraints comprise upper and lower bound constraints on states and control inputs.
7. The method of claim 6 , wherein the upper and lower bound constraints on states comprise zone temperature bounds and the upper and lower bound constraints on control inputs comprise control input bounds.
8. The method of claim 1 , wherein the receiving of the measurements, the determination of the sequence of inputs, and the applying of the first input to control the HVAC system occurs in real-time on one or more local computing devices.
9. The method of claim 8 , further comprising implementing a security policy wherein the one or more local computing devices determine the sequence of inputs independently of a cloud computing service.
10. The method of claim 8 , wherein the one or more local computing devices comprises two or more local computing devices that cooperatively execute the model predictive controller.
11. A system comprising:
a heating, ventilation, and air-conditioning (HVAC) system of a building comprising two or more zones;
sensors that measure a system state of the HVAC system; and
a hardware controller configured via instructions to:
determine a physics model that is linearized around an operating point, the linearized physics model defining thermodynamic relationships between the two or more zones of the building;
use the linearized physics model as an equality constraint for a model predictive controller that determines a next control input to the HVAC system based on the system state;
decompose a constraint matrix H of the equality constraint into factors of a first matrix U and a second matrix V such that UU T and V T V are both diagonal matrices;
optimize an objective function of the model predictive controller by iteratively solving a linear system of equations that includes inverses of UU T and V T V to determining a sequence of inputs for a horizon of the model predictive controller; and
apply a first input of the sequence of inputs to control the HVAC system.
12. The system of claim 11 , wherein an augmented Lagrangian method is used to optimize the objective function in view of the equality constraint and other equality and inequality constraint.
13. The system of claim 11 , wherein optimizing the objective function of the model predictive controller comprises finding, in a first iteration a first factor comprising the inverse of the diagonal matrix UU T and a second factor comprising the inverse of the diagonal matrix V T V and reusing the first and second factors in subsequent iterative steps.
14. The system of claim 13 , wherein the iterations involve using the first and second factor to update primal variables of the model predictive controller and Langrangian multipliers.
15. The system of claim 11 , wherein the model predictive controller is formatted as a quadratic problem that involves optimizing a quadratic objective function subject to a set of linear equality and linear inequality constraints.
16. The system of claim 15 , wherein the set of linearity inequality constraints comprise upper and lower bound constraints on states and control inputs.
17. The system of claim 11 , the measuring of the system state, the determination of the sequence of inputs, and the applying of the first input to control the HVAC system occurs in real-time occurs in real-time.
18. The system of claim 11 , wherein the HVAC system services two or more buildings, and wherein the linear physics model defines the thermodynamic relationships between zones of the two or more buildings.
19. The system of claim 11 , wherein the hardware controller comprises two or more controllers that cooperatively execute the instructions.
20. The system of claim 11 , wherein the instructions further cause the hardware controller to determine the sequence of inputs independently of a cloud computing service.