MANAGEMENT

CROSS-REFERENCE TO RELATED APPLICATION

This is a non-provisional application claiming the benefit of U.S. provisional application serial number 61/489,004, filed May 23, 2011, the contents of which are incorporated by reference herein in their entirety.

GOVERNMENT LICENSE RIGHTS

This invention was made with U.S. Government support under Contract No.: DE-EE- 0003843 awarded by Department of Energy. The U.S. Government has certain rights in this invention.

BACKGROUND

1. Technical Field

The present disclosure relates to modeling tools, and more particularly to methods for constructing a thermal dynamics model.

2. Discussion of Related Art

Heuristic rule -based control (RBC) is widely used in the building industry for building automation systems (BASs). System dynamics modeling plays an important role in model-based control and constructing a model can be challenging under realistic engineering conditions.

For standard industry practices, field engineers need to walk through the target building, define "if-then-else" style rules based on experience, implement the rules in control sequence, then conduct field tests. A Proportional Integral Derivative (PID) controller is typically the only feedback control in the building. The process is not optimized for energy saving.

BRIEF SUMMARY

According to an embodiment of the present disclosure, a method for controlling a building automation system includes determining a plurality of set points using a hybrid building model comprising a plurality of analytical models for a plurality of thermal zones of a building and a plurality of data-driven models for a plurality of actuators controlling an environment within the thermal zones and controlling the actuators according to the set points.

According to an embodiment of the present disclosure, a method for constructing a thermal dynamics model includes creating a plurality of zone thermal models corresponding to respective zones of a building, receiving a plurality of actuator models, generating a plurality of virtual set points based on the zone thermal models and a feedback parameter of the building, and generating a plurality of set points configured to control a plurality of actuators of the building corresponding to the actuator models based on the virtual set points and the plurality of actuator models.

According to an embodiment of the present disclosure, a control system includes a plurality of actuators of a building automation system, a knowledge base comprising a plurality of zone thermal models, a plurality of actuator models, and a plurality of inverse actuator models, and a controller comprising a core and a linearizer, wherein the core receives the plurality of zone thermal models and outputs virtual set points to the linearizer, and the linearizer receives the plurality of actuator models and the plurality of inverse actuator models and outputs set points for controlling the plurality of actuators. BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the present disclosure will be described below in more detail, with reference to the accompanying drawings:

FIG. 1 shows a model of an exemplary building;

FIG. 2 shows a control system block diagram according to embodiments of the present disclosure;

FIG. 3 is a diagram of a Model Predictive Control (MPC) system according to an embodiment of the present disclosure;

FIG. 4 is a diagram of a run time system including an MPC system according to an embodiment of the present disclosure;

FIG. 5A is an MPC with feedback linearization according to embodiments of the present disclosure;

FIG. 5B is an MPC with feedback linearization method according to embodiments of the present disclosure; and

FIG. 6 is an exemplary system for constructing a thermal dynamics model according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Hereinafter, a hybrid approach to constructing a thermal dynamics model is described. The thermal dynamics model may be used for building an integrated control under the guidance of control theory. According to an embodiment of the present disclosure, a Model Predictive Control (MPC) based controller may be developed using feedback linearization. A method for model development may be coupled with controller

development. For purposes of providing a detailed description, an exemplary building is described having a thermal, ventilation, lighting systems, etc. More particularly, the building is described as being equipped with a plurality of actuators. The actuators may include air diffusers, motorized windows, air handlers, dehumidifiers, water based thermal systems such as fan coil and radiant panel units for local cooling, water mullions, etc. As shown in FIG. 1, there are 13 zones (areas) in the building, less than the number of actuators. In FIG. 1, the actuators include chillers 101, radiant cooling/heating panels 102, water mullions 103, and temperature, humidity, and carbon dioxide systems 104.

A control system block diagram is shown in FIG. 2. In FIG. 2, "reference" is the desired output; "error" is reference minus the output; "input" is the signal from a controller 201 to a plant 202, such as the building; "plant" is the object being controlled; "output" includes the sensor measurements from the plant, such as temperature or humidity.

In control theory, control systems may use feedback loops. The term "system model" or "model," in this context, is the mathematical description of the plant. Models may be in the form of a state space or transfer function. Equation (1) is a form of discrete state space model for a linear time invariant (LTI) system, where k is the discrete time, e.g., the iteration number; x, u, y are the state variable, input and output, respectively.

Transfer function is the notion of output versus input in Laplace space, which is associated with frequency domain. The Laplace space is a linear operator of a function f(t) with a real argument t (t≥ 0) that transforms it to a function F(s) with a complex argument s . Equation (2) is one example of a transfer function. γ

r(s) -

X (2)

Each state space model can be converted into a set of transfer functions, and the set of transfer functions may be converted into a state space model. The set of transfer functions may be a transfer matrix. This connection allows for a study of a control system from both time domain and frequency domain.

FIG. 3 is the system block diagram of an exemplary MPC controller 300. In the context of building control, "plant" is the building model 301; v is a measured disturbance, such as weather conditions; r represents set points to the controller; d is an unmeasured disturbance. An MPC core 302 may minimize a cost function in the form of Equation (3),

subject to:

^U (j)[k+i\k] ^G where n is the length of a prediction horizon; Wi, W ₂ , and W ₃ are weighting factors that designate the importance of tracking performances versus energy consumption; footnotes . _(;) or . _{( )} are the j-th or j ^' -th variable; head notes u and u are the lower and upper limits, respectively. Given the flexibility of MPC framework, sophisticated constraints, such as upper and lower limits on u , Au , and y , can be considered.

According to an embodiment of the present disclosure, an MPC controller is configured to process signals within a building system given certain models. The building system may be non-linear. ,

An exemplary implementation of the MPC controller 400 is shown in FIG. 4 and FIGs. 5A-B. The MPC controller 400 of FIG. 4 and FIG. 5A uses a feedback linearization technique.

Referring to FIG. 4, an engineering system 401 comprises a plurality of zone thermal models 402 and inverse actuator models 403 derived from the actuator models. The zone thermal models 402 are built from data collected at the building. The actuator models may be built based on data sheets, specifications, etc., from an actuator manufacturer. For example, the data sheets may specify the output of an actuator, for example, in cubic feet per minute (CFM), given certain input control voltages. The actuator models capture this information and are used to create the inverse actuator models.

An inverse model may be an inverse curve of a CFM/input control voltage curve, for answering questions such as what input is needed to achieve 100 CFM of airflow. According to an embodiment of the present disclosure, actuator models are reusable, such that, if a roof top unit is replaced the model of a new roof top unit may replace the model of the roof top unit being removed in the engineering system 401 without needing to collect additional data or calibrate the building model. That is, in the case of a modular building model, actuator models may be added, deleted, exchanged, etc. without affecting the remaining models or components.

According to an embodiment of the present disclosure, the zone thermal models 402 are mathematical analytical models input to a MPC core 404 and the inverse actuator models 403 are data-driven models input to a linearizer 405. Each inverse actuator model 403 models a certain actuator. Thus, the inverse actuator models 403 are reusable and may be implemented in different applications. For example, the same actuator model may be used by different MPC controllers for controlling the same model actuator 406 disposed in different buildings.

The reusable the inverse actuator models 403 enable robust analysis in a frequency domain. Frequency domain analysis enables robust control and stability analysis in control theory. Frequency domain methods, such as Bode plots, may be used to test stability of physical control systems. In frequency domain approaches, the system response is studied with respect to sinusoid input signals of difference frequencies. Due to Flourier transfer, any time domain signal is a linear combination of sinusoid signals of different frequencies. Thus, if the control system has desirable behaviors for different input sinusoid signals, the control system characteristics may be ensured, such as stability and robustness, under different time domain inputs.

The MPC core 404 may further receive feedback parameter 407 from a sensor 408 of the building and comfort constraints and/or energy optimization objectives, c 409, for controlling the output virtual set points to the linearizer 405.

According to an embodiment of the present disclosure, feedback linearization may be used to reconfigure a nonlinear system into a linear system using inverse functions in the control flow. For example, given a nonlinear dynamic system in Equation (4), where the notations are defined as in Equation (1), a linearized input may be found such that

Equation (5) holds.

To illustrate the concept using an example, assuming a system with nonlinear dynamics:

one can define

where f is the actuator model. Thus, a linear function may be obtained as:

As shown in Equation (6) and FIG. 5B, the controller may solve for virtual set points as a linear system (S501), then find the associated set points (S502). The value of

the set points may be sent to the plant (S503). In this example, may be derived from

f . For a generic nonlinear function f , the analytical solution of may not exist. For example, the water mullions do not have an analytical inverse function. Numerical solutions may be found based on nonlinear optimization approaches.

Referring again to FIGs. 5A-B, an MPC controller (501) includes in an MPC core (502). The MPC core (502) is a linear MPC solver for actuator models formulated in Equation (4). The MPC core (502) considers coupling among different actuators (S501). The output of the MPC core (502) may include the heat, Q, from each actuator system to the plant. One or more inverse functions (503) determine and output control variables u (S502), such as valve openings of water mullions given the output of the MPC core (502). There is no coupling between the inverse functions. Further, the inverse functions are non-linear. The MPC controller (501) sends the control variables u to the plant (504 - S503). Although the plant (504) is nonlinear, the augmented system (505) in FIG. 5A is linear time invariant (LTI), which simplifies the control problem.

The feedback linearization may be used to divide a building model into a set of problems. The modeling problem may be divided into zone thermal models and actuator models, and the modeling problem may be solved step-wise.

An LTI system may be easier to control as compared to a non- linear time varying system. That is, a global optimal solution for a generic nonlinear system may be more challenging than LTI systems.

Each building has a unique zone (e.g., room) thermal dynamics, which are governed by the same mathematical equations with different parameters. The actuator models f and f ^-1 are building-independent. Possible model reuse allows for multiple use cases.

If more actuators are installed in the same building, the room model and the actuator models may be reused. For example, if one more cooling system is installed, another set of parameters may be added to characterize the impacts of this cooling system to each zone. In the linear room model, existing parameters in the zone thermal model(s) does not need to be changed.

For model reuse purposes, the first principle model system may use existing methods such as Trnsys (a graphically based software environment used to simulate the behavior of transient systems) or EnergyPlus. The zone thermal models in Trnsys may be realized in TYPE56 following physics laws, such as that described by Equation (4). Simulation data may be used to identify the parameters in Equation (4). A zone thermal model may be created with a data driven approach. For example, define the zone temperature vector at

the k-th time step; the temperature of zone i at the k-th time step; the linearized input

are the column vectors for heat

from the actuator systems. The system input , where actuator

system inputs, are the valve openings from 0% to 100%; u ^T cw[k] is the binary

input to turn on or off certain actuator systems. Let Q _L be the thermal load of each zone and

T _0A[k the outdoor temperature.

An exemplary zone thermal model is given in Equation (7), where k and f are unknown constants. Equation (7) may be converted into standard state space model in Equation (8), where v is a measurable disturbance to MPC. Thus:

A heating mode model may be used to create of inverse function. Pseudo code for heating mode model is shown in Table 1.

Table 1: Water Mullion Heating Mode

T_SW: Water temperature;

MKGH: Water flow rate in kilograms per hour (kg/hr). M is the same flow rate in grams per minute (gpm).

N=4: Number of pipes for each set of Water Mullions.

T_A: Ambient temperature.

T_REW0=0.7845*(T_SW* 1.8+32)+15.369;

C1=(T_SW* 1.8+32-80)/40*0.0268+0.1351 ;

C2=T_REW0-C1*72;

C3=0.3199*(M/0.23) ^Λ 3-1.0182*(M/0.23) ^Λ 2+1.1185*(M/0.23)+0.5798;

T_REWl=Cl.*(T_A*1.8+32)+C2;

T_REW=(C3.*T_REWl-32)/1.8;

Q=(MKGH*4.186.*(T_SW-T_REW))*N;

If the analytical inverse function does not exist, there is no analytical mapping from C3 to M. In this case, a numeric solution may be acquired using, for example, a Matlab nonlinear optimization function such as fsolve. For example, a Matlab function may be created, e.g., WaterMullionHeat, which implements the actuator model in Table 1. The inverse function is shown in Table 2, where use Q (heat), water and environment temperature as input, and the output is Mullion valve opening.

Table 2: Water Mullion Inverse Function

global Q WaterTemp EnvTemp;

F0=227; % initial value

Valve = fsolve(@ WaterMullionHeat, F0)/MaxFlow;

According to an embodiment of the present disclosure, a hybrid building model is constructed using first principle modeling methods to create mathematical analytical models for the zones following physics and data-driven models fitted using experimental (or simulation) data for the actuators. That is, a data-driven model is a hybrid model using first principle modeling methods for zone thermal models and creating the actuator models using data-driven modeling methods. The first principle model seeks to determine a physical quantity starting directly from established laws of physics without making assumptions such as empirical or fitted parameters.

It is to be understood that embodiments of the present disclosure may be implemented in various forms of hardware, software, firmware, special purpose processors, or a combination thereof. In one embodiment, a software application program is tangibly embodied on a non-transitory computer-readable storage medium, such as a program storage device or computer-readable storage medium, with an executable program stored thereon. The application program may be uploaded to, and executed by, a machine comprising any suitable architecture. Referring to FIG. 6, according to an embodiment of the present disclosure, a computer system (block 601) for constructing a thermal dynamics model includes, inter alia, a CPU (block 602), a memory (block 603) and an input/output (I/O) interface (block 604). The computer system (block 601) is generally coupled through the I/O interface (block 604) to a display (block 605) and various input devices (block 606) such as a mouse, keyboard, medical scanners, power equipment, etc. The display (block 605) may be implemented to display the rules, e.g., as the rules evolve during evaluation, ranking and refinement or as an output set of rules. The support circuits can include circuits such as cache, power supplies, clock circuits, and a communications bus. The memory (block 603) can include random access memory (RAM), read only memory (ROM), disk drive, tape drive, etc., or a combination thereof. The present invention can be implemented as a module (block 607) of the CPU or a routine stored in memory (block 603) and executed by the CPU (block 602) to process input data (block 608). For example, the data may include image information from a camera, which may be stored to memory (block 603) As such the computer system (block 601) is a general purpose computer system that becomes a specific purpose computer system when executing the routine of the present disclosure. The computer system (block 601) may further include a GPU (block 609) for image processing.

The computer platform (block 601) also includes an operating system and micro instruction code. The various processes and functions described herein may either be part of the micro instruction code or part of the application program (or a combination thereof) which is executed via the operating system. In addition, various other peripheral devices may be connected to the computer platform such as an additional data storage device and a printing device.

It is to be further understood that, because some of the constituent system components and method steps depicted in the accompanying figures may be implemented in software, the actual connections between the system components (or the process steps) may differ depending upon the manner in which the system is programmed. Given the teachings of the present disclosure provided herein, one of ordinary skill in the related art will be able to contemplate these and similar implementations or configurations of the present disclosure.

Having described embodiments for constructing a thermal dynamics model, it is noted that modifications and variations can be made by persons skilled in the art in light of the above teachings. It is therefore to be understood that changes may be made in embodiments of the present disclosure that are within the scope and spirit thereof.