Navier-stokes based indoor climate control

1. A data processor, comprising outputs to provide control signals to one or more actuators, wherein said data processor jointly resolves a set of coupled optimization problems of the following form

z Φ k =arg min z Φ ([ S Φ k+1 O ] z Φ −{tilde over (Φ)} k+1 ) T Q Φ k ([ S Φ k+1 O ] z Φ −{tilde over (Φ)} k+1 )+([ OI ] z Φ ) T R Φ k ([ OI ] z Φ )

subject to [ A Φ k −B Φ k ] z Φ −b′ Φ k (Φ k ,e Φ k )=0

wherein the control signals are to activate said one or more actuators to change at least one variable of an indoor climate, wherein:

z

Φ

=

[

Φ

q

Φ

]

is an augmented state-vector comprising a vector Φ specifying the spatial distribution of a climate related variable with respect to a plurality of spatial cells, and a source term q Φ to be resolved, said source term corresponding to an activation of said one or more actuators to result from said control signals and wherein

z

Φ

k

=

[

Φ

k

+

1

q

Φ

k

]

is the solution found for point in time k, {tilde over (Φ)} k+1 being a vector specifying a setpoint specified for said climate related variable at point in time k+1 for at least a part of said plurality of cells, e Φ k are boundary conditions relevant for said climate related variable at point in time k, S is a selection matrix, selecting cells for said distribution having a setpoint, O is the zero matrix, I is the identity matrix and Q and R are weighting matrices that specify the relative importance attached to tracking the setpoint and complying with energy consumption budgets, respectively, and

wherein A Φ is a matrix that defines the development of vector Φ as a function of one or more other vectors of climate related variables,

wherein B Φ is a matrix that maps the source terms for field Φ to the cell field values affected by those source terms, and wherein the data processor provides the control signals in accordance with the source term q Φ .

2. The data processor according to claim 1 , wherein jointly resolving the set of coupled optimization problems involves the following steps:

an update step, comprising the following sub-steps to be carried out in arbitrary order,

update (S1u) the air velocity field u and associated source term field q u for a first spatial direction (x) by optimizing the air velocity field u for said direction,

update (S1y) the air velocity field v and associated source term field q v for a second spatial direction (y) by optimizing the air velocity field v for said direction,

update (S1w) the air velocity field w and associated source term field q w for a third spatial direction (z) by optimizing the air velocity field z for said direction,

update (S1T) the temperature field T and associated source term field q T by optimizing the temperature field T,

calculate (S2) the pressure field (P),

apply a relaxation step (S3), and

check for convergence, otherwise repeat the previous steps S1-S3.

3. A data processing method for controlling at least one variable of an indoor climate, the data processing method comprising

jointly resolving a set of coupled optimization problems of the following form:

z Φ k =arg min z Φ ([ S Φ k+1 O ] z Φ −{tilde over (Φ)} k+1 ) T Q Φ k ([ S Φ k+1 O ] z Φ −{tilde over (Φ)} k+1 )+([ OI ] z Φ ) T R Φ k ([ OI ] z Φ )  (5a)

subject to [ A Φ k −B Φ k ] z Φ −b′ Φ k (Φ k ,e Φ k )=0

wherein:

z

Φ

=

[

Φ

q

Φ

]

is an augmented state-vector comprising a vector Φ specifying the spatial distribution of a climate related variable with respect to a plurality of spatial cells, and a source term q Φ to be resolved, and

wherein

z

Φ

k

=

[

Φ

k

+

1

q

Φ

k

]

is the solution found for point in time k, {tilde over (Φ)} k+1 being a vector specifying a setpoint specified for said climate related variable at point in time k+1 for at least a part of said plurality of cells, e Φ k are boundary conditions relevant for said climate related variable at point in time k, S is a selection matrix, selecting cells for said distribution having a setpoint, O is the zero matrix, I is the identity matrix and Q and R are weighting matrices for tracking and energy consumption, and

wherein AΦ is a matrix that defines the development of vector Φ as a function of one or more other vectors of climate related variables, and

wherein BΦ is a matrix that maps the source terms for field Φ to the cell field values affected by those source terms,

the method further comprising providing control signals in accordance with said source terms, said control signals activating one or more actuators to change said at least one variable of said indoor climate.

4. A method according to claim 3 , further comprising

receiving sensory data indicative for sensed values from climate related variables in an indoor space as the data indicative for values of indoor climate related variables, and

driving said one or more actuators by said control signals.

5. The method according to claim 4 , comprising providing the vector {tilde over (Φ)} specifying a setpoint and the boundary conditions e Φ k as constants.

6. The method according to claim 4 , comprising providing the vector {tilde over (Φ)} specifying a setpoint and/or the boundary conditions e Φ k as variables.

7. The method according to claim 6 , comprising jointly resolving the set of equations for one time step at a time.

8. The method according to claim 6 , comprising jointly resolving the set of equations for a plurality of time steps and based on predicted values for the vector {tilde over (Φ)} specifying the setpoint and/or the boundary conditions e Φ k .

9. The method according to claim 3 , wherein the source terms (q k ) that are calculated in response to the provided setpoint values ({tilde over (Φ)} k ) and boundary conditions (e Φ k ) are indicative for the one or more actuators to be used in a design and their required settings.

10. A climate control system for controlling a climate in an indoor space, comprising

a plurality of sensors configured to sense climate related variables in said indoor space, and to provide, to a controller, sensory data indicative for sensed values for said variables,

a plurality of actuators configured to control said climate related variables in said indoor space, and

the controller configured to jointly resolve a set of coupled optimization problems comprising

z Φ k =arg min z Φ ([ S Φ k+1 O ] z Φ −{tilde over (Φ)} k+1 ) T Q Φ k ([ S Φ k+1 O ] z Φ −{tilde over (Φ)} k+1 )+([ OI ] z Φ ) T R Φ k ([ OI ] z Φ )

subject to [ A Φ k −B Φ k ] z Φ −b′ Φ k (Φ k ,e Φ k )=0,

wherein:

z

Φ

=

[

Φ

q

Φ

]

is an augmented state-vector comprising

a vector Φ specifying spatial distribution of a climate related variable with respect to a plurality of spatial cells, and

a source term q Φ to be resolved, said source term corresponding to an activation of one or more actuators to result from control signals,

wherein

z

Φ

k

=

[

Φ

k

+

1

q

Φ

k

]

is a solution found for point in time k, {tilde over (Φ)} k+1 being a vector specifying a setpoint specified for said climate related variable at point in time k+1 for at least a part of said plurality of cells, e Φ k are boundary conditions relevant for said climate related variable at point in time k, S is a selection matrix, selecting cells for said distribution having a setpoint, O is the zero matrix, I is the identity matrix and Q and R are weighting matrices for tracking and energy consumption,

wherein A Φ is a matrix that defines the development of vector Φ as a function of one or more other vectors of climate related variables,

wherein B Φ is a matrix that maps the source terms for field Φ to the cell field values affected by those source terms, and

wherein the controller is further configured to provide said control signals to said plurality of actuators to activate the plurality of actuators, in accordance with the source term q Φ , to change at least one variable of an indoor climate.

11. The climate control system of claim 10 , wherein the controller is configured to jointly resolve the set of coupled optimization problems by:

executing a plurality of update operations in arbitrary order, further comprising

updating an air velocity field u and associated source term field q u for a first spatial direction (x) by optimizing the air velocity field u for said direction,

updating an air velocity field v and associated source term field q v for a second spatial direction (y) by optimizing the air velocity field v for said direction,

updating an air velocity field w and associated source term field q w for a third spatial direction (z) by optimizing the air velocity field z for said direction, and

updating a temperature field T and associated source term field q T by optimizing the temperature field T,

calculating a pressure field (P),

applying a relaxation operation, and

checking for convergence, wherein the controller is otherwise configured to repeat the update operations, calculating the pressure field, and applying the relaxation operation.

12. The climate control system of claim 10 , further comprising a mapping unit for mapping said sensory data onto the plurality of cells.

13. The climate control system of claim 10 , wherein the vector {tilde over (Φ)} specifying the setpoint for said climate related variable is uniform for at least a part of said plurality of cells.

14. The climate control system of claim 10 , wherein the vector {tilde over (Φ)} specifying the setpoint for said climate related variable is non-uniform for at least a part of said plurality of cells.

15. A design system comprising:

a data processor configured to jointly resolve a set of coupled optimization problems comprising

z Φ k =arg min z Φ ([ S Φ k+1 O ] z Φ −{tilde over (Φ)} k+1 ) T Q Φ k ([ S Φ k+1 O ] z Φ −{tilde over (Φ)} k+1 )+([ OI ] z Φ ) T R Φ k ([ OI ] z Φ )

subject to [ A Φ k −B Φ k ] Z Φ −b′ Φ k (Φ k ,e Φ k )=0,

wherein:

z

Φ

=

[

Φ

q

Φ

]

is an augmented state-vector comprising

a vector Φ specifying spatial distribution of a climate related variable with respect to a plurality of spatial cells, and

a source term q Φ to be resolved, said source term corresponding to an activation of one or more actuators to result from control signals,

wherein

z

Φ

k

=

[

Φ

k

+

1

q

Φ

k

]

is a solution found for point in time k, {tilde over (Φ)} k+1 being a vector specifying a setpoint specified for said climate related variable at point in time k+1 for at least a part of said plurality of cells, e Φ k are boundary conditions relevant for said climate related variable at point in time k, S is a selection matrix, selecting cells for said distribution having a setpoint, O is the zero matrix, I is the identity matrix and Q and R are weighting matrices for tracking and energy consumption,

wherein A Φ is a matrix that defines the development of vector Φ as a function of one or more other vectors of climate related variables,

wherein B Φ is a matrix that maps the source terms for field Φ to the cell field values affected by those source terms,

wherein the data processor is further configured to provide said control signals to activate a plurality of actuators, in accordance with the source term q Φ , to change at least one variable of an indoor climate, and

wherein the source terms (q k ) calculated by the design system in response to the provided setpoint values ({tilde over (Φ)} k ) and boundary conditions (e Φ k ) are indicative for the plurality of actuators to be used in the design and their settings.

16. The design system of claim 15 , wherein the data processor is configured to jointly resolve the set of coupled optimization problems by:

executing a plurality of update operations in arbitrary order, further comprising

updating an air velocity field u and associated source term field q u for a first spatial direction (x) by optimizing the air velocity field u for said direction,

updating an air velocity field v and associated source term field q v for a second spatial direction (y) by optimizing the air velocity field v for said direction,

updating an air velocity field w and associated source term field q w for a third spatial direction (z) by optimizing the air velocity field z for said direction, and

updating a temperature field T and associated source term field q T by optimizing the temperature field T,

calculating a pressure field (P),

applying a relaxation operation, and

checking for convergence, wherein the controller is otherwise configured to repeat the update operations, calculating the pressure field, and applying the relaxation operation.

17. The design system of claim 16 , wherein the data processor is further configured to

receive sensory data indicative for sensed values from climate related variables in an indoor space as the data indicative for values of indoor climate related variables, and

drive the plurality of actuators by said control signals.

18. The design system of claim 17 , wherein the data processor is further configured to provide the vector {tilde over (Φ)} specifying a setpoint and the boundary conditions e Φ k as constants.

19. The design system of claim 17 , wherein the data processor is further configured to provide the vector {tilde over (Φ)} specifying a setpoint and/or the boundary conditions e Φ k as variables.