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A software framework for model predictive control with GenOpt

Brian Coffey a,*, Fariborz Haghighat b, Edward Morofsky c, Edward Kutrowski c

a University of California, Berkeley, USAb Concordia University, Montreal, Canadac Public Works and Government Services, Ottawa, Canada

1. Introduction

There is currently a strong demand for very low energy

commercial buildings. Passive technologies, such as increased

insulation and climate-appropriate orientation and window

placements, are likely to account for part of the demanded

efficiency improvements. But active technologies, such as low

energy HVAC and variable-transmissivity window systems, are

also expected to play a significant role in most low energy

commercial buildings. Such low energy active systems can also

play a role in demand response by shedding or shifting electrical

load when necessary, which will likely become even more

important with more intermittent renewable electricity produc-

tion being added to the grid. Better integrated supervisory control

strategies are neededto fully address the potentials andchallenges

presented by these very low energy systems and by demand

response control objectives.

One such advanced control strategy is model predictive control

(MPC), where a building model is used within the supervisory

control system, automatically testing at each control time-stepvarious possible set-point configurations with simulations before

choosing the best one for use in the building. Optimization

algorithms determine set-points, rather than relying on rule-based

approaches that specify set-points based on schedules or in

response to particular conditions. There has been a modestamount

of research on MPC for buildings applications, but this body of

research is growing quickly and is expected to grow further in the

next few years. The underlying motive of the research presented in

this paper is to facilitate future research in this area by developing

a standard approach and software for model predictive control

(and for non-predictive model-based control) that can be easily

applied by buildings researchers to many different cases.

A Java software framework based around GenOpt [1] is

presented, along with an example MPC algorithm for use within

it, and an example case study. A beta version of the software is

freely available at [2]. It allows the use of any text-based

simulation tool and simplifies the setup process for simulation-

based studies or real-time implementations. It also facilitates the

use of optimization starting points and dynamic search-space

constraints based on the results of previous time-steps and on

heuristic rules, which is a promising and often overlooked

technique in MPC for buildings.

2. Background

2.1. Model predictive control in buildings research

Although still relatively uncommon in building engineering,

MPC has seen extensive research and application in other fields,

particularly in chemical, electrical and mechanical engineering

(see [3,4] for seminal papers, and [5] for an example application).

Within the buildings research field, the idea of MPC for

supervisory control was noted at least as early as 1988 [6], but

because of its computational requirements it has not received

much research attention until the past decade. It has been applied

to a number of different types of systems by buildings researchers,

often using standard simulation tools for the online building

Energy and Buildings 42 (2010) 10841092

A R T I C L E I N F O

Article history:

Received 15 December 2009

Accepted 29 January 2010

Keywords:

Building simulation

Optimization

Model predictive control

Demand response

A B S T R A C T

There is a growing interest in integrated control strategies for building systems with numerous

responsive elements,such as solarshadingdevices,thermal storage and hybrid ventilationsystems, both

for energy efficiency and for demand response. Model predictive control is a promising way of

approaching this challenge. This paper presents a flexible software framework for model predictive

controlusing GenOpt, along with a modified geneticalgorithmdeveloped foruse withinit, and appliesit

to a case study of demand response by zone temperature ramping in an office space. Various areas for

further research and development using this framework are discussed.

2010 Elsevier B.V. All rights reserved.

* Corresponding author.

E-mail addresses: [email protected] , [email protected]

(B. Coffey).

Contents lists available at ScienceDirect

Energy and Buildings

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n b u i l d

0378-7788/$ see front matter 2010 Elsevier B.V. All rights reserved.

doi:10.1016/j.enbuild.2010.01.022
mailto:[email protected]:[email protected]://www.sciencedirect.com/science/journal/03787788http://dx.doi.org/10.1016/j.enbuild.2010.01.022http://dx.doi.org/10.1016/j.enbuild.2010.01.022http://www.sciencedirect.com/science/journal/03787788mailto:[email protected]:[email protected]

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models. Research interest seems to be growing, and building

controls problems have recently attracted MPC experts from

outside of the buildings research field.

Theuse of MPCfor energyminimization through ice storage and

active building mass thermal storage has been studied by Henze

et al.: a real-time implementation experiment was carried out for

the control of a building with these systems, using a 24-h future

horizon and a 1-h controller time-step, with TRNSYS used for the

building model and Matlab used to control the optimization [7,8].

They noted some of the expected technical glitches (such as sensor

malfunctions and problems with information passing), but aside

from this the approach was generally successful, except for a few

points in time where the optimization algorithm was stuck in local

minima and actually performed worse than the default strategy

would have. They have also analyzed various aspects of MPC that

are peripheral to the central concept but essential in its

application: they have studied the importance of forecast and

model accuracy [9]; worked on the development of a method for

automated model calibration to ensure continued accuracy over

time [10]; and worked on the development of a hybrid control

system that attempts to incorporate the aspect of continual

updating (found in the learning-algorithm approach to control)

with the MPC approach [11,12].

The problem of determining the optimal start time for heatinghas been considered by a number of researchers. One such study

brought together researchers from Honeywell Controls Systems

Ltd. and the University of Strathclyde, and worked out some of the

interfacing concerns between a standard control system and a

simulation tools (ESP-r in particular) and optimizer [13]. A

modification of the optimal start problem was also considered

by Kummert et al. [14,15], who looked at the optimal control of

passive solar buildings with night setback, in an attempt to

minimize the energy consumption while also minimizingoccupant

discomfort due to morning undercooling and afternoon over-

heating. A simplified model (a linear state-space representation)

was used and the optimization was done by quadratic program-

ming.

Non-predictive model-based control has also been used by anumber of buildings researchers, for example in daylighting

research (controlling blinds and lights) by Mahdahvi et al. Their

experimental work has focused on the control of automated

shading devices [1618], using lighting simulation tools such as

LUMINA, but they have also considered control for natural

ventilation [19]. The purpose of using simulation in these cases

is to capture the complexities of a snapshot of the system, rather

than to capture the systems dynamics, so no prediction horizon

was used in these studies.1 Other examples of non-predictive

model-based supervisory control include studies of VAV control

(using highly simplified and fast-running system models) [20,21],

andchilled water plant control (using detailed TRNSYSmodels, but

conceived not for real-time implementation but for derivation of

heuristic control rules, so it did not have to contend with thecomputation time challenge associated with global HVAC control

using a detailed simulation model) [22].

It is also worth noting the extensive existing research and

applications of neural network control in building systems. An

illustrative example of how this approach can be conceived in a

way that is similar to the MPC approach (with a neural-network

empirical online model instead of a physics-based online model) is

the EDIFICIO project carried out by a number of European research

agencies and headed by a group from EPFL [23]. Clarke [24]

outlined the differences between these learning-algorithm

approaches and the model-based approach, and discusses the

advantages and disadvantages of each. In general, learning-

algorithm based controllers are easier to install and operate, and

do not have the same concerns about model accuracy or

computation time that MPC has. But unlike model-based

controllers, learning-algorithm controllers usually require an in

situ learning period before use, they do not deal well with physical

or occupant-use changes in the building, and they tend not to

perform well under anomalous conditions. And since they lack any

building physics in their internal calculations, they cannot be used

to explain why particular conditions or configurations produce

particular effects, so they are of less use in building diagnostics or

retrofit than arethe models used in MPC. But the ability to improve

performance over time, as embodied by these learning-algorithm

approaches, is a useful feature that could be incorporated into

software and methodologies for MPC.

Recent and ongoing research in MPC for buildings is being

carried out by research teams involving both buildings experts andMPC experts. Recent collaborative work between UC Berkeley,

Lawrence Berkeley National Lab and United Technologies Corpo-

ration has implemented MPC for a campus chilled water storage

system [25], and there is an ongoing research project on MPC in

buildings involving ETH Zurich, Siemens, EMPA Dubendorf and

MeteoSwiss [26].

2.2. Simulation, optimization and controls software

There is a broad collection of commonly used building energy

simulation software available, but most of this was created with

design applications in mindand tends not to beideal for use for the

online model in MPC because of slow run times, lack of optimizer

access to the underlying equations, and difficulties in re-initializing the model states for a particular time-step (most

require a warm-up period). Some existing programs (e.g. TRNSYS,

SPARK) present fewer difficulties for use in MPC than others, but

they are still not ideal.

Thedevelopmentof a Modelica library of buildings components

[27] is currently underway, in part to try to address these

problems. Some MPC researchers have turned to the creation of

models from scratch in Matlab (which is the tool of choice for

controls researchers, and the Matlab MPC Toolbox [28] is helpful)

or the creation of Matlab lookup tables off-line by simulating the

modeled components over their range of expected input condi-

tions and then using these lookup tables as the model in the on-

line optimization instead of using the first-principles directly.

This development of more controls-friendly building simula-tion tools is helpful. But it will require some time, and buildings

researchers and practitioners who are more familiar with the

standard building simulation tools may wish to use these for MPC

studies in the near-term. And those for whom the software cost is

prohibitive will always prefer to use free or inexpensive tools. As

such, the software framework described herein was constructed to

make use of any text-based simulation software (so either existing

or new-generation tools can be used), and uses GenOpt [1] for the

optimization.

GenOpt was developed in an effort to simplify and standardize

the process of optimization with building simulation. It is a Java

program and is freely downloadable. It essentially acts as an

interface between any text-based building simulation program

and any optimization algorithm. It has a standard library of

1 Note that the use of predicted values over a future horizon is necessary for any

system involving energy storage, but it may also be necessary for any system in

which there is a penalty incurred for changing control configurations. For example,

if the system requires x kWh to change the position of a solar shading device, and

such an action would save less than x kWh over any one particular controller time-

step, thisactionwould notbe selectedwithout theconsideration of furtherpointsin

the future, even though one change in position might save substantial energy over

the course of a day. So a prediction horizon may still be desired in solar shading

applications if an energy or occupant-distraction penalty is considered for position

changes.

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optimization algorithms, which includes generalized pattern

search algorithms, particle-swarm algorithms and algorithms for

parametric studies, and the library can be extended by the user by

adding new optimization algorithms.

3. Framework

The development of the software framework aims to provide a

free MPC tool that researchers and practitioners can use alongsidetheir modeling software of choice. It essentially acts as an

extension of GenOpt, providing the organization necessary to

use it as the optimizer in a model-based controller that is

connectedto a central building control system, andproviding some

functionality specifically appropriate to MPC problems. We begin

by looking at the MPC problem definition, then describe the

GenOpt-based framework developed to address it.

3.1. Generic problem definition

Fig. 1 provides a simple illustration of model predictive control,

where the projected control sequence over the prediction horizon

is determined by an online optimization with a system model. It

can be used for multi-input multi-output control of nonlinear

dynamic systems, and is most often applied to systems with slow

dynamics, application-critical and possibly nonlinear state con-

straints (as in many chemical process applications), and/or

complex interactions between inputs and outputs. Buildings

applications rarely have critical state constraints, but many

supervisory problems have complex interactions between com-

ponents (e.g. between solar shading, space cooling and lighting),

combined with relatively slow dynamics. The supervisory control-

lertime-step in buildings applications could range from minutes to

days. Since the objective function is evaluated by running a

simulation of the online model, there is an important tradeoff that

must be made between the controller time-step, the computation

time required by the simulation, and the precision (and global-vs-

local characteristics) of the optimizer.

Each time that the controller is asked to determine new valuesfor the control variables, it is facedwith the optimization problem

defined by the setof Eqs. (1)(4) (inan energyminimization case)

or the set of Eqs. (5)(8) (in a demand minimization case), where

g1 is the objectivefunction (theoutput of the online model),g2 are

theconstraintson the state andoutput (whichmay be nonlinear),

f maps the evolution of the system states (the evolution of the

model states),p is a terminal cost,and Uare the input constraints.

Note that for non-predictive control, one can use same ideas but

set t 1 as a constant, eliminate the terminal cost p and ignore

Eqs. (2) and (6).

minu

XN

t1

g1 ut; xt; wt p xN 1

s:t: xt1 f xt; ut; wt t 1;. . .

; N 2

g2 ut; xt; wt 0 t 1; . . . ; N 3

ut 2 U t 1; . . . ; N 4

minu

maxt2 1...N

g1 ut; xt; wt p xN 5

s:t: xt1 f xt; ut; wt t 1; . . . ; N 6

g2 ut; xt; wt 0 t 1; . . . ; N 7

ut 2 U t 1; . . . ; N 8

An important aspect of the MPC optimization problem is that

each problem faced is quite similar to the problem at the previoustime-step. And other earlier time-steps may have had similar

conditions to the current one. This feature of the MPC optimization

problem turns out to be quite useful in generating good

optimization starting points, although it is often overlooked, and

to the authors knowledge it has not yet been taken advantage of in

previous buildings research. One must be careful to avoid getting

stuck in local minima when using this idea, but this concern can be

overcome in a number of ways, one of which is to use a multi-start

optimization algorithm, as used in the example below.

3.2. Framework overview

Within the software framework, the problem is divided into

three layers. The first layer consists of the simulation software thatis being used for the on-line model. The second layer is the

optimization layer, which runs one of many possible algorithms to

try to solve the optimization problem for a given time-step. The

third layer is an organization layer, which interfaces with the

building central control system, sets up the optimization problem

at each time-step, and performs a number of other organizational

and learning tasks. Text files are used to pass information between

layers. The basic structure is shown in Fig. 2, along with how it

interfaces with the buildings energy management system and

with a prediction module (which is considered as a separate

problem from theoptimization problem itself, andis notdealtwith

in detail here).

The simulation layer of the software framework can use any

energy simulation program, as long as it reads and writes to textfiles and can be called from the command line. The optimization

layer uses GenOpt as the interface between the optimization

algorithms and the simulation program. The organization layer

uses a java program named SimCon, which was written to meet the

requirements of this layer. For a given time-step, SimCon begins

the computation process by reading the text files for the current

conditions and the predicted future conditions, and it ends by

writing the decisions text file. So from the point of view of a central

control system, its use requires just that it write some of its sensor

information to text files, call SimCon, wait a pre-determined

amount of time, and then read a decision text file which tells it

what set-points to use. Details of the text file configurations,

syntax, source code and example files are included with the beta

version download [2].Fig. 1. Receding horizon control.

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3.3. The organizational layer

Aside from its roles of interfacing and overall coordination, the

organizational layer does two important things: (1) it stores the

results from previous time-steps; and (2) it writes an optimization

instructions file which gets read by the optimization algorithm

within the optimization layer. Similar to how GenOpt has an

extendable library of optimization algorithms, SimCon has been

developed with an extendable library of optimization instruction

algorithms, from which the user can select (or develop) the

algorithm that will write the optimization instructions file. Since

this file must be read by the optimization algorithm in GenOpt,

these two algorithms must be coordinated. In the case study

considered below, the optimization instructions file is used to

specify starting points and constraints for the optimizationalgorithm. (Other uses are possible, as discussed in Section 6.)

In particular, the optimization instruction algorithms used here

specify optimization starting points based on the results from the

previous time-step, and starting points and constraints based on

knowledge-based rules.

3.4. Virtual testing environment

A single run of SimCon is just for one time-step. To test its

performance, it needs to be used within a real-time environment,

with a central controller sending it conditions and predictions at

each time-step, and then acting on its decisions. This can be an

actual buildings control system, or it can be connected to the

control system of a virtual building. This link between SimCon andanother building model can be done a number of different ways.

The Building Controls Virtual Test Bed, recently developed at LBNL

[29] provides a good framework for this. In the case study

considered below,the virtual building is a copy of theonline model

in the controller, but slowed down to real-time (through the

addition of a TRNSYS object that causes the model to sleep for a

specified time period at each time-step), and with the addition of a

supervisory control object in TRNSYS that writes conditions files,

calls SimCon and reads the decisions file. This two-model virtual

testing arrangement allows for easier testing of SimCon than

would be possible through an actual supervisory controller

implementation in a real building. But as importantly, it also

allows one to test various MPC configurations under identical

conditions, and allows one to systematically consider the impacts

of various model inaccuracies (by changing parameter values so

that they are different in the two models), improper initialization

of the online model, or prediction inaccuracies.

4. Example algorithm

An example optimization instructions algorithm and optimi-

zation algorithm pair was developed for this framework, based on

a genetic algorithm. Although genetic algorithms tend to have slow

convergence rates, it was used here because of interesting

possibilities for coupling with SimCon. In particular, a genetic

algorithm can be initialized with numerous starting points, so they

can use some rule-based or learning-based suggestions forstarting

points and still have other randomly generated starting points that

mayallowit to discover unexpected points that maybe betterthan

those around the given points.

4.1. Basic genetic algorithm description

Genetic algorithms (GAs) are inspired by biological evolution,

using concepts of mating, mutation and natural selection to

impel successive populations of individuals (with each individ-

ual representing a point in the search space) towards an

optimization of the objective function. An initial population ofpoints is chosen, usually at random from throughout the search

space, and as the population evolves from one generation to the

next new points emerge, with the evolutionary processes

favouring the emergence of points that are ever closer to

optimal. Their path through the search space is stochastic (there

is some randomness in the mutation and mating processes

through which new points are chosen), so they can sometimes be

less efficient as optimizers than other possible algorithms, but

their stochastic search path also makes them more able to avoid

being trapped in local minima. Genetic algorithms have been

used extensively in previous buildings research for design

optimization problems [3035], but their use in contr ol

optimization has been limited.

A genetic algorithm for GenOpt was written for this example,and is included in the SimCon beta download [2]. It uses one-point

crossover and uniform mutation, and allows the user to specify the

population size, the percentage elite to maintain, and the rates for

crossover and mutation. To avoid problems that may result in later

generations due to a depletion of diversity, the algorithm is

configured to test for stagnation and if necessary it increases the

mutation rate to 100% for a generation. It also allows the user to

stipulate the maximum numberof simulations to run (some sort of

time-limiting factor is necessary for use within control optimiza-

tion), and the user can choose to keep the values considered for

each variable to a desired level of precision by having theGA search

over points on a user-defined grid.

4.2. Using the optimization instructions file

The genetic algorithm in GenOpt is also configured to read and

use starting points and constraints from the optimization

instructions file. A companion optimization instructions algorithm

was written for the SimCon library which writes starting points

and constraints to the instructions file, based on the following

three considerations:

1. The values obtained in the previous optimization solution

(which are stored by SimCon) are transferred over to an initial

point in the current optimization by moving them all back one

time-step, and finding an arbitraryway of filling in thelast time-

step values for the current point (in the example case below, the

last time-step value is set equal to the second-last one).

Fig. 2. Structure overview.


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2. Using rules for suggesting starting points: When Henze et al.

performed their case study on thermal storage control using

model predictive control [7,8], they found a number of points

where the controller actually performed worse than the

standard heuristic controller they were comparing against, as

it was stuck in a local minimum. This situation of performing

worse than a heuristic controller can be avoided if the

knowledge embedded in the heuristic controller is also

embedded in the model predictive controller in the form of

optimization starting points. (Note that, however, with an

imperfect model or poor predictions, this knowledge is not

necessarily enough to keep MPC from performing worse than

the heuristic controller.)

3. Using rules to set search-space constraints: In order to make the

time-constrained optimization problem more tractable, it is

helpful to eliminateparts of the search space that areunlikely to

produce good control points. (In the case study below, for

example, it may be assumed that the optimal point does not

include set-points near the end of the trim that are less than

25 C, so the constraints for these variables can be modified to

25 < T< 26 C, rather than their original 22 < T< 26 C.)

5. Example application study

5.1. Demand response with zone temperature ramping

A number of previous studies [36,37] have shown that demand

response with zone temperature reset can be an effective demand

trimming strategy, helping to avoid blackouts or the need for new

electrical production capacity, by producing substantial decreases

in cooling demand over a critical period (usually in the range of 1

3 h) without causing too much occupant discomfort. Most of these

previous studies have considered very simple control strategies,

focusing on the demand response potential with strategies that

could easily be mass-deployed.

However, research by Lee and Braun [3841] has looked more

closely at the optimal control of this set-point modification to

minimize the peak demand over the trimming period. Their workhas been along two related tracks: (1) the development of an

inverse model of a small commercial building, and the use of this

model to determine optimal set-point trajectories [38,41]; and

(2) the development and evaluation of simple control rules that

can approximate optimal control [39,40]. In the first track, they

used the fact that the optimal set-point trajectory produces a flat

demand over the trimming period. They used the inverse model

to calculate, at any given point in time, what the set-point must

be to produce a particular demand level. They then iterated over

the demand level to find the minimum level possible within the

problem constraints, and the collection of set-points associated

with that level is thus the optimal set-point trajectory. This is a

clever approach to the problem. The implementation is only

slightly different than the model predictive control approachconsidered in this paper, in that it does not march along making

control decisions each time-step in real-time, but rather

determines the full trajectory before the trim. But it could easily

be made to march along and re-do the optimization at each time-

step as new information became available (as noted in [41]). The

use of the demand-target approach by backing out the set-point

values for a specific demand level was possible because they

were using a simplified inverse model, but it would be very

difficult with a more detailed model and a standard simulation

tool, as used in the example study below. The second track of Lee

and Brauns research in this area, that of developing and

evaluating near-optimal rule-based strategies for demand

response with zone temperature ramping, is what is used most

in this paper. In particular, they have determined that a very

effective strategy is to use a logarithmic set-point trajectory over

the trim period.

In general, the problem of optimizing demand response with

temperature ramping has been well covered by Lee and Braun, and

their simplified rule-based approaches are very effective. Having

such well-charted territory is useful for the case study, and their

insights and heuristic rules are used both as a starting point and as

a basis for comparison.

5.2. Case study description

The case study consideredis for optimal demand response using

zone temperature set-point ramping for an office space in Ottawa.

The office space considered is area 8B1 of Place-du-Portage, whichhas a fairly standard open plan configuration. It is the home of the

Innovations & Solutions Directorate of Public Works and Govern-

ment Services Canada, and it has been outfitted with a highly

instrumented experimental personal environmental control (PEC)

system that gives occupants control over their lighting and over a

jet-diffuser that provides conditioned air to their workspace. The

substantial data availability with this experimental system makes it

amenable to the creation and calibration of a detailed thermal

model,2 whichwas donein TRNSYS. This modelwasusedbothas the

online model within the controller, and also to act as the actual

building for the virtual tests. In the case study, the personal air-

conditioning controls are over-ridden in favour of a demand

response action, for one particularly hot afternoon in July. The goal

of the demand responseaction is to minimize the maximum15-mincoolingdemandbetween 1:00and 4:00 p.m., withthe controlaction

allowed to begin at 12:30 p.m., and the zone temperature set-point

constrained to remain between 22 and 26 C. Fig. 3 shows the base

case with no action.

5.3. Results

Some heuristic controls were considered for comparison with

MPC. Fig. 4 (jump trim) shows the effect of simply increasing the

set-point to 26 C immediately and leaving it at that level

throughout the demand response period (this is the most common

simple strategy used in applications). Fig. 5 (linear trim) shows

Fig. 3. No trim.

2

Model details are available in [42].


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the effect of increasing the set-point linearly over the demand

response period. Fig. 6 (log trim) shows the effect of increasing

the set-point logarithmically over the demand response period, as

suggested by Lee and Braun. (The log trim requires the setting of a

parameter to determine the steepness of the curve. For this study,

that parameter was selected by an iterative search, simulating

possible values before using the best one.) It should be noted here

that these heuristic controls were also implemented with a 15-min

control time-stepin thevirtual tests (aswere theMPC cases), butin

reality such simple control strategies could be implemented on a

much shorter time-step and thus may perform slightly better than

shown here, but the improvement would be minor.

TheMPC cases were split into twotypes: ideal cases,wherethe

online model exactly matched the virtual test simulation model,the model was initialized perfectly and the prediction was perfect;

and non-ideal cases, considering the effects of model mismatch,

imperfect initialization and imperfect prediction. The case shown

in Fig. 7 is an ideal case with the computation time constraint

removed so that the model predictive controller can be used to

more closely approximate optimal control (the computation was

allowed to run over three nights rather than being constrained to

the 3-h window it would have in a real-time application). Note

that, intuitively and supported by [38,41], the optimum should

produce a horizontal line in the load during the trim period. This

case comes closer to that optimum than do any of the heuristic

cases, but it is still not quite optimal.

The results of the heuristic control cases and some of the MPC

cases considered are shown in Table 1. It was found that the

logarithmic trim was nearly ideal in this case, and should be

recommended for use in other similar cases. The optimal set-point

configuration, however, is actually quite complex and likely highlycase-dependent, and it would be difficult to imagine a rule-based

approach that would capture it. The logarithmic approach

produced a 28.0% trim, while the optimal was estimated to be

Fig. 4. Jump trim.

Fig. 5. Linear trim.

Fig. 6. Log trim.

Fig. 7. MPC trim with loosened time constraints.


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slightly greater than the 30.1% produced by the ideal non-time-

constrained MPC. The application of MPC in the ideal case and with

the real-time computation constraints produced a 29.5% trim.

Without rule-based initial suggestions or previous-time-step

learning, MPC (as configured with the genetic algorithm) does

not perform nearly as well, because it does not converge quickly

enough towards the optimum. And the performance of the

controller drops off as circumstances move away from the ideal:

with imperfect model calibration but perfect initialization and

prediction, MPC performed slightly worse than the logarithmic

approach, producing a 27.1% trim; and with perfect modelcalibration but imperfect initialization and prediction, the MPC

results became more sporadic and much further from the optimal.

(It should be noted that since the genetic algorithm is stochastic,

the results can vary from test to test. But in the ideal cases with

logarithmic starting points, MPC always performs somewhere

between the log trim and the optimal.)

6. Discussion

The software framework presented here opens up a variety of

possibilities for further research.

6.1. Appropriate complexity level for application studies

In the case study presented above, heuristic control was

shown to perform nearly as well as MPC (or possibly better, if one

considers model mismatch and imperfections in initialization

and prediction). But if the scenario were more complex, for

example if light dimming is being applied alongside the zone

temperature ramping or if more detailed consideration is to be

given of occupant comfort under these transient thermal

conditions [43], then MPC may be worth considering. And one

must consider other benefits of MPC as, such as ability to easily

adapt to changing electricity rate structures, and its links with

other model-based building operations improvements as dis-

cussed below. But in general, the relative performance of

heuristic control and MPC in this case study suggests that there

might be a certain level of problem complexity below which MPCis simply not appropriate. It is difficult to assess what this level

might be, but future research should be considering more

complex problems (with more control variables and/or more

complex control objectives), if we are to test practical applica-

tions of MPC in buildings.

6.2. Improving optimization results

Genetic algorithms have the benefit of allowing multiple

starting-point suggestions alongside other random starting points

and thus can more easily avoid local minima, but they are perhaps

not ideal for this control-optimization application because they do

not converge to solutions very quickly. Other optimization

algorithms should be developed for use within this supervisory

control framework. (For example, the generalized pattern search

algorithms available in the standard GenOpt library should be

explored for use in this context.) Hybrid algorithms are also likely

worth developing for this application, with different approaches

used for a global search phase and for a local search phase, and the

optimization algorithm could be made to switch from one to the

other after a certain number of simulations.

And there could be more advanced ways of using the

organizational layer to inform the optimization algorithm.

The organizational layer could search for more complex patterns

in the previous results and pass these on to the optimization

algorithms: it couldfind correlation strengths between variables in

optimization outputs, noting conditions where variables should

take on similar values (e.g. if in previous time-step optimizations

the variable values tend to change very little over the time horizon,

then the optimization layer could restrict its search); and the

organizational layer could perform sensitivity analyses on the

previous results to determine which variables have the greatest

effect on the objective function, then tell the optimization

algorithm to focus on these variables first before tweaking the

other variable values. It is worth noting that with an increased use

of such techniques, SimConalgorithms could begin to take on some

of the characteristics and benefits of learning-algorithm (e.g.

neural network) approaches. Other possible improvements to theuse of organization-layer information include finding ways of

treating future time-steps differently the further into the future

they are (e.g. to decrease their relative precision or constrain their

search ranges as a way of placing more focus on the more-

immediately upcoming time-steps), and developing or refining

heuristic starting point rules based on results from previous

optimizations.

All of these changes could significantly improve the efficacy of

the optimization. However, they all still walk around the

simulation program, treating it essentially as a black box,

generating and testing possible points. If simulation tools were

todevelop in such a way as to provide the optimizer more access to

the problem equations and/or to ensure differentiability, the

optimizer could use this to parse the problem into sub-regions orto analytically derive gradients, both of which could dramatically

improve computational efficiency. Such development could also

allow for the backing-out of set-point values given a desired

objective, as was used in the inverse-model studies of Lee and

Braun [38,41].

6.3. Imperfect models, initializations and predictions

The case study results have highlighted the need for more

consideration of model accuracy, initial conditions and predictions.

If not dealt with effectively, these aspects could undermine the

performance of any practical or theoretical application of MPC.

More research is required in these areas, but the following are

some good starting points.

1. Continuous model calibration: The automated error minimiza-

tion approach to model calibration [10,44,45] allows for the

model to be continuously tuned to become more accurate over

time. The conditions and optimization results database in

SimCon could be used for this.

2. Initialization: As noted earlier, this is an inherent problem with

theuse of most building simulation tools, which do notallow for

explicit state initialization, but instead require a warm-up

period. Development of more controls-friendly building simu-

lation tools will help get around this. But in the meantime, it

would be helpful to devise ways of rewinding or copying the

simulation process such that the warm-up period only needs to

be run once per optimization.

Table 1

Summary of results: trim percentages.

Heuristic Base case

Jump trim 23.0%

Linear trim 13.7%

Log trim 28.0%

Model predictive Ideal, no time constraints 30.1%

I deal, with time con stra ints 2 9.5%

Ideal, no learning 28.0%

Ideal, no rule suggestions 5.9%

Imperfect calibration 27.1%

Imperfect initialization 10.1%


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6.4. Other potential research areas with SimCon

One of the most alluring aspects of simulation-based control is

that it overlaps well with a number of other possible applications

of simulation in building operations. A controllers well-tuned

physics-based model of the building could be of great use in

evaluatingpossible retrofit strategies. And the overlap between the

idea of a model-based controller with automated calibration and a

model-based diagnostics tool [46,47] is interesting. In the first case

you want an accurate model of how the building is actually

performing, but in the second case you want an accurate model of

howthe building should be performing. But the models must share

the same structure, and could be treated as two sides of the same

model within an integrated controls-and-diagnostics system,

differing only in terms of some parameter values.

Although this paper has focused on the study of real-time MPC,

it should be acknowledged that another possible use of SimCon

(and perhaps a much more practical use in the short and mid term,

and possibly even in the long term) is for the development and

evaluation of standard heuristic control sequences for complex

systems. By relaxing the computational time constraints and

providing ideal circumstances (perfect model calibration, initiali-

zation and prediction), SimCon could be used to approximate

optimal control for any given (simulated) set of conditions.Iterating over various sets of conditions and analyzing the SimCon

outputs could allow researchers to devise rules for near-optimal

control.

There is an R&D policy interest in knowing the technical energy

savings potential with near-optimal control of highly dynamic

integrated building systems, but there is currently only a modest

amount of literature available on the energy savings potential

through integrated systems control (e.g. [48,49]), and none of this

extends to full integration of HVAC, lighting and dynamic facades.

SimCon could be used to provide an approximation of optimal

control for any type of complex idealized building system, and so

could be usefulin estimating an upper bound on theenergy savings

potential.

Personal control tends to lead to better occupant satisfactionand can also lead to decreased energy use in some cases [50,51],

but not all. Perhaps the best configuration would involve some

combination of automated control and occupant control. SimCon

could be used to determine appropriate control for the automated

parts of a building given stochastic occupant control of other parts

of it. Or it could be used to determine optimal configurations and

suggest these to the occupant to accept or ignore. Or it could be

used to determine when to allow occupant control with a red-

green-light system.

7. Conclusions

The example application study and example algorithm have

provided an illustration and test of the software framework. Andthe study has supported the findings of Lee and Braun that a

logarithmic trim is near optimal for demand response by zone

temperature reset. The framework should be used for more

complex application studies in the future, and more optimization

and organization-layer algorithms should be developed.

Model predictive control holds promise for energy efficiency

and demand response in integrated supervisory building control

systems. It is hoped that the framework presented herein will help

to facilitate further research and development in this field.

Acknowledgement

The authors gratefully acknowledge the support of Public

Works and Government Services Canada for this research.

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