Lecture 9

Pr inc ip les of Model ing for Cyber-Phys ica l Systems

Instructor: Madhur Behl

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 1

Model Predictive Control

Slides adapted from: Mark Canon (U. of Oxford)Manfred Morari (ETH, UPenn)Alberto Bemporad (IMT Lucca)

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 2

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MPC: Mathematical formulation

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 46

MPC: Mathematical formulation

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 47

Receding horizon philosophy

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 48

MPC: Mathematical formulation

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 49

Receding horizon philosophy

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 50

Energy Efficient Building Control

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 51

Energy Efficient Building Control

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 52

Energy Efficient Building Control

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Constraints

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 54

Constrained Infinite Time Optimal Control

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 55

Constrained Finite Time Optimal Control (CFTOC)

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 56

On-line Receding Horizon Control

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 57

On-line Receding Horizon Control

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 58

Unconstrained problem

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Unconstrained problem

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Unconstrained problem

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Unconstrained problem

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 62

Unconstrained problem

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Unconstrained problem

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Unconstrained problem

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 65

Unconstrained problem

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 66

Example

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Example

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Example

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Example

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 71

Example

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MPC challenges

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 74

Literature

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 75

MPC for buildings

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 76

MPC for buildings

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Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 78

Disturbances

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 79

Controlled variables

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 80

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 81

MLE+

MLE+ Overview

2. The scientific computational capability of Matlab/Simulink:I.Matlab Toolboxes

II.Matlab Built-in Functions.

Matlab

1. High-Fidelity Physical models of the whole-building Energy Simulator EnergyPlus.

E+

BACnet

3. Control Synthesis - Building Control Deployment.

82Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

EnergyPlus Building Model 1 System Identification2

Control Deployment54 Simulation ResultsControl Design inMatlab

3

From Control/Scheduling Algorithmsto Synthesis and Deployment in Real Buildings

MLE+ Workflow

83Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

EnergyPlus Building Modelü Small office building with 3 zonesü Chicago weather file during winterü Model Predictive Control:

o Minimize the power consumption of the radiant heatero Maintain thermal comfort (22°C - 24°C)

Advanced Controls: Model Predictive Control (MPC)

84Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Inputs to EnergyPlus

Outputs from EnergyPlus

Variable Configuration Screen1. Parses E+ File to abstract IN/OUT2. Selects Inputs/Outputs3. Writes Configuration File Automatically

Advanced Controls: Variable Configuration

85Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Inputs to EnergyPlus

Outputs from EnergyPlus

Configuration File1. .xml file contains Co-Simulation Exchange Variables2. Inputs to E+

• Power of radiant heating system3. Outputs from E+

• Room temperatures• Radiant heating system power

Advanced Controls: Input/Output Configuration

86Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

System Identification1. Random Signal Generator2. IDINPUT (Matlab Built-in

function)3. Package Data: IDDATA

(Matlab Built-in type)4. Import to System

Identification Toolbox (IDENT)

Advanced Controls: System Identification

87Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

System Identification (2)1. Estimate Model According

(IDENT)2. Inputs:

• Radiant Power• Outside Temp• Solar Radiation

3. Outputs:• Room Temp

Advanced Controls: System Identification (2)

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu 88

ü Use template script to specify controllerü Easily integrate with Matlab’s Model Predictive Control toolbox.ü MPC:

ü Prediction Horizon: 2ü Control Horizon: 9ü Minimize Total Power Consumption

Advanced Controls: Control Design

89Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Simulation Resultsü Displays and save results in Matlab

8 am 6 pm

Advanced Controls: Simulation Results

90Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Simulink Example: Co-Design & Controlsü 5 Zone Buildingü California Weather Fileü July 1st – 7th (Summer Time)ü VAV System

Integrated Modeling: MLE+ Simulink

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HVAC

E+ Building

Integrated Modelingü E+ Buildingü VAV model in Simulinkü Inputs to E+:

ü Heat Flowü Outputs from E+

ü Room Tempü Outdoor Temp

Integrated Modeling: Simulation Overview

92Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

HVAC System• Temperature Setpoints according to

Schedule• Central HVAC Model• VAV Boxes

CentralHVAC

VAV BoxesOccupancy Setpoints

Integrated Modeling: HVAC System

93Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

VAV Model1. Thermostat2. Reheat Coil

VAV Box

Integrated Modeling: VAV boxes

94Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Thermostat

Reheat Coilü VAV Boxü Inputs:

ü Setpointsü Room Tempü Supply Air Temp

ü Outputs:ü Mass Flow Rate

ü Thermostat Room Levelü Heat/FreeCool/Mec

hanicalCoolü Reheat Coil

Integrated Modeling: VAV Box

95Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

MLE+ is a featured third party tool recognized by DoE

96Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Campus-Wide Simulation

Supply SideEPlus LoadProfilerobject

Demand SideEPlus TemperatureSource object

MLE+ S function block in Simulink

97Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

MLE+ Over 400+

users

98Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

How are building models obtained today ?

White Box

1/Ugw

1/Ugi

1/Ugo

Cgo

Cgi

Tgo

Tg

Tgi

Tz

Q.rad,e

1/Uei1/Uew1/Ueo

Ceo Cei

TaTeo Tei

Q.sol,eQ.solt/2

1/Uci

1/Ucw

1/UcoCci

Cci

Ta

Q.sol,c

Q.rad,c

TaQ.conv + Q.sens

1/Uii 1/Uiw 1/Uio

Cii Cio

Tci

Tco

1/Uwin Tii Tio

Q.solt/2

Q.rad,g

[ExternalWalls]

Ti

[Ceiling]

[Floor]

[InternalWalls]

[Windows]

Grey Box

Black Box

99Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

How are building models obtained today ?

White Box

Grey Box

Black Box

100Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

White-Box Modeling

Hire building modeling experts

Set parametersFloor by floorZone by zoneWall by wall

Layer by layerEquipment by

equipmentTransfer geometry

Floor PlanHVAC layout

Not always

available

Guess nominalparameter

values

First principles basedHigh fidelity

Building energy simulation

Model TuningData

Sensor retrofits

101Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

White-Box Modeling

Hire building modeling experts

Set parametersFloor by floorZone by zoneWall by wall

Layer by layerEquipment by

equipmentTransfer geometry

Floor PlanHVAC layout

Not always

available

Guess nominalparameter

values

First principles basedHigh fidelity

Building energy simulation

Model TuningData

Sensor retrofits

Cost and time prohibitive(sensor installation, commissioning & expertise)

Not suitable for model-based controlModel complexity and uncertainty, (1000’s parameters and states)

102Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

How are building models obtained today ?

White Box

1/Ugw

1/Ugi

1/Ugo

Cgo

Cgi

Tgo

Tg

Tgi

Tz

Q.rad,e

1/Uei1/Uew1/Ueo

Ceo Cei

TaTeo Tei

Q.sol,eQ.solt/2

1/Uci

1/Ucw

1/UcoCci

Cci

Ta

Q.sol,c

Q.rad,c

TaQ.conv + Q.sens

1/Uii 1/Uiw 1/Uio

Cii Cio

Tci

Tco

1/Uwin Tii Tio

Q.solt/2

Q.rad,g

[ExternalWalls]

Ti

[Ceiling]

[Floor]

[InternalWalls]

[Windows]

Grey Box

Black Box

103Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Grey-Box [Inverse] Modeling

Hire building modeling experts

Set parametersFloor by floorZone by zoneWall by wall

Layer by layerEquipment by

equipmentTransfer geometry

Floor PlanHVAC layout

Not always

available

Guess nominalparameter

values

Parameter Estimation

DataSensor retrofits

Lumped Parameter‘RC’ model 104Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Grey-Box Modeling

Hire building modeling experts

Set parametersFloor by floorZone by zoneWall by wall

Layer by layerEquipment by

equipmentTransfer geometry

Floor PlanHVAC layout

Not always

available

Guess nominalparameter

values

Parameter Estimation

DataSensor retrofits

Lumped Parameter‘RC’ model

Promising but still cost and time prohibitive(sensor installation, commissioning & expertise

Modeling uncertainty,Time-varying parameters)

Suitable for model-based control(10-100’s parameters and states)

105Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Cost and Time prohibitive modeling

Project duration: May 2007 – March 2015

Phase 1: EnergyPlus model (white-box), RC model (grey box), MPC development and evaluation. [Only simulated studies]

Phase 2: Retrofitted building with sensors, commercial MPC software, demand response, peak reduction, uncertain models..

“..the biggest hurdle to mass adoption of intelligent building control is the cost and effort required to capture accurate dynamical models of

the buildings.”

Sturzenegger, D.; Gyalistras, D.; Morari, M.; Smith, R.S., "Model Predictive Climate Control of

a Swiss Office Building: Implementation, Results, and Cost-Benefit Analysis," Control Systems

Technology, IEEE Transactions on , vol.PP, no.99, pp.1,1, March 2015

106Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

How are building models obtained today ?

White Box

Grey Box

Black Box

107Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Black-Box Modeling

Data

Could beautomated

Feature engineering

Not well aligned with control synthesis

Coarse grained predictions

Non-physical parameters

108Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Too many sub-systemsNon-linear interactions

Modeling using first principles is hard !

Each building design is different.Must be uniquely modeled

Long operational lifetimes~50-100 years

109Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Energy Systems Modeling

Suitability for control

Mod

elin

g Di

fficu

lty

(cos

t)

UnsuitableSuitable

High

Lo

w

White Box

Grey Box

Black Box

110Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Foundations of Data Predictive Control for CPS

mbCRT DPC-RT Ensemble-DPC

Single-step look ahead[with single reg. trees]

Finite receding horizon[with single reg. trees]

Finite receding horizon[with ensemble models]

111Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Foundations of Data Predictive Control for CPS

mbCRT DPC-RT Ensemble-DPC

Single-step look ahead[with single reg. trees]

Finite receding horizon[with single reg. trees]

Finite receding horizon[with ensemble models]

112

- ICCPS ‘16, BuildSys 15, CISBAT 15, Journal of Applied Energy- Best Paper Award (SRC TECHCON-IoT): ‘Sometimes, Money Does Grow on Trees’-Ph.D. Dissertation: Madhur Behl, UPenn(2016)

- ACM BuildSys 16 (Best Presentation Award )

- ACM Transactions of Cyber Physical Systems.

- American Control Conference 17 (Best Energy Systems Paper Award )

Principles of Modeling for CPS – Fall 2018 Madhur Behl madhur.behl@virginia.edu

Energy CPS Module RecapReview of ODEs and dynamical systems.State-Space modeling and implementation

in MATLAB, LTI models.First principles – Generalized systems

theory.Heat transfer basics.HVAC systems and electricity markets

overview.Introduction to EnergyPlus.‘RC’ network based state-space thermal

modeling.

Nominal values of parameters from IDF file.Parameter estimation optimizationNon-linear least squares.Model evaluation and goodness of fit.Model sensitivity analysis and experiment

designModel predictive control basicsCodebase to learn a state-space model from

any data-set.

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