Navier-stokes based indoor climate control

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:
• zΦk=arg minzΦ([SΦk+1O]zΦ−{tilde over (Φ)}k+1)TQΦk([SΦk+1O]zΦ−{tilde over (Φ)}k+1)+([OI]zΦ)TRΦk([OI]zΦ) (5a)
• subject to [AΦk−BΦk]zΦ−b′Φk(Φk,eΦk)=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 qΦ 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, eΦk 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.

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
• zΦk=arg minzΦ([SΦk+1O]zΦ−{tilde over (Φ)}k+1)TQΦk([SΦk+1O]zΦ−{tilde over (Φ)}k+1)+([OI]zΦ)TRΦk([OI]zΦ)
• subject to [AΦk−BΦk]zΦ−b′Φk(Φk,eΦk)=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 qΦ 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, eΦk 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 AΦ is a matrix that defines the development of vector Φ as a function of one or more other vectors of climate related variables,
• wherein BΦ 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 qΦ, to change at least one variable of an indoor climate.

A design system comprising:

• a data processor configured to jointly resolve a set of coupled optimization problems comprising
• zΦk=arg minzΦ([SΦk+1O]zΦ−{tilde over (Φ)}k+1)TQΦk([SΦk+1 O]zΦ−{tilde over (Φ)}k+1)+([OI]zΦ)TRΦk([OI]zΦ)
• subject to [AΦk−BΦk]ZΦ−b′Φk(Φk,eΦk)=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 qΦ 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, eΦk 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 AΦ is a matrix that defines the development of vector Φ as a function of one or more other vectors of climate related variables,
• wherein BΦ 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 qΦ, to change at least one variable of an indoor climate, and
• wherein the source terms (qk) calculated by the design system in response to the provided setpoint values ({tilde over (Φ)}k) and boundary conditions (eΦk) are indicative for the plurality of actuators to be used in the design and their settings.