Online Simultaneous State Estimation and ... - Semantic Scholar
Online Simultaneous State Estimation and Parameter Adaptation for Building Predictive Control Mehdi Maasoumy, Barzin Moridian, Meysam Razmara, Mahdi Shahbakhti, Alberto Sangiovanni-Vincentelli 2013 ASME Dynamic Systems and Control Conference (DSCC’13) Stanford University October 21-23, 2013
Mehdi Maasoumy PhD Candidate University of California, Berkeley October 21, 2013 Sponsored by CREST, iCyPhy, and TerraSwarm Research Consortiums. A collaboration of UC Berkeley, and Michigan Technological University.
1
What’s the biggest energy consumer sector? Buildings Consume Significant Energy: • • • • •
40% of total US energy consumption 72% of total US electricity consumption 55% of total US natural gas consumption $ 370 Billion: Total US annual energy cost 200%: Increase in US electricity cons. since 1990.
Source: Buildings Energy Data Book 2006
Directly related to HVAC
Mehdi Maasoumy
University of California, Berkeley
2
Existing HVAC Control Logic
Lack of Integrated System Dynamics Model PID
On-Off
On-Off
On-Off UC Berkeley, Cory Hall
Mehdi Maasoumy
University of California, Berkeley
3
Previous works
2008 DB Crawley, (Simulation)
2010 - Y. Ma, (MPC) - F. Oldewurtel, (SMPC) - K Deng, (Model Reduction) - C Liao, (Occupancy Modeling) - Rasmussen (Gain Schedule Ctrl)
2009 M. Wetter, (modeling and simulation)
2012 - B. Hencey, (Estimation) - B. Rasmussen (Vapor Comp. Sys.) - M. Maasoumy (RMPC) - Y. Yang (BAS)
2011 - Y. Ma, (DMPC) - M. Maasoumy, (Hierarchical) - TX Nghiem, (Scheduling)
2013 - Alleyne (Optimal Partitioning)
Less Work on Improving the Quality of Building Dynamic Models Mehdi Maasoumy
University of California, Berkeley
4
Energy Savings of MPC Compared to RBC 60 Building Type I
Energy Saving Compared to Rule Based Control [%]
41 40
Building Type V
24 16
20
7
12
Model uncertainty [%]
0 0
25
50
75
100
-20 -23
-26
-40 -60
-38
High fidelity models -70
-80
-93
-100
Mehdi Maasoumy
University of California, Berkeley
5
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
6
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
7
Architecture of the proposed PAB model Proposed Architecture
Problem Statement • Highly time varying, and nonlinear nature of building dynamics. (e.g. Time-varying convective heat transfer coefficient of outside air). • Model-based controllers often need accurate estimate of all states, but not all the states of building model are measurable
Joint parameter-state estimation
PAB Model: Parameter Adaptive Building Model Mehdi Maasoumy
“On-line estimation” of states and unknown parameters of buildings… … leading to the: Parameter-Adaptive Building (PAB) model.
University of California, Berkeley
8
Proposed Architecture
Mehdi Maasoumy
University of California, Berkeley
9
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
10
Test-bed: Berkeley
Mehdi Maasoumy
University of California, Berkeley
11
Plant Modeling
Unmodeled dynamics
• Energy balance for a room node:
Thermal and circuit model of a wall with window Mehdi Maasoumy
University of California, Berkeley
12
Plant Modeling: Unmodeled Dynamics •
External heat gain
•
Internal heat gain
Disturbance:
which results to:
Leading to the LTI system:
Mehdi Maasoumy
University of California, Berkeley
13
Proposed Architecture
Mehdi Maasoumy
University of California, Berkeley
14
Offline Calibration: Berkeley Test-bed Mathematical Model
Scale-up to Building Level
Room Temperature [oC]
Data-Driven Predictive Model
Disturbance [oC/hr]
Time [hr]
Mehdi Maasoumy
Time [hr]
University of California, Berkeley
15
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
16
Test-bed at Different Climates
Mehdi Maasoumy
University of California, Berkeley
17
Lakeshore Center: Michigan Test-bed
Front View
Top View
Mehdi Maasoumy
University of California, Berkeley
18
Test bed: Office Space
Mehdi Maasoumy
University of California, Berkeley
19
Lakeshore Building HVAC System AHU
VAV
GSHP
Mehdi Maasoumy
University of California, Berkeley
20
Schematic of the Room
Mehdi Maasoumy
University of California, Berkeley
21
Proposed Architecture
Mehdi Maasoumy
University of California, Berkeley
22
Sensor Readings (Michigan test bed) Lakeshore building at Michigan Technological University
Mehdi Maasoumy
University of California, Berkeley
23
Offline Calibration (Michigan test bed)
!!! Mehdi Maasoumy
University of California, Berkeley
24
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
25
Proposed Architecture
Kalman Filter
Mehdi Maasoumy
University of California, Berkeley
26
Room Temperature Dynamics 𝒙𝟏 = 𝑥6 − 𝑥7 − 𝑥8 − 𝑥9 − 𝑥10 𝑥15 − 𝑥10 𝑢2 𝑐𝑎 𝑥1 +𝑥6 𝑥2 + 𝑥7 𝑥3 + 𝑥8 𝑥4 + 𝑥9 𝑥5 + 𝑐𝑎 𝑢1 𝑢2 + 𝑇5 𝑥15 + 𝐴𝑤𝑖𝑛 𝜏 𝑄𝑟𝑎𝑑 + 𝑄𝑖𝑛𝑡 . 𝑥10 𝒙𝟐 = 𝑥1 − 2𝑥2 + 𝑇2 . 𝑥11
𝒙𝟑 = 𝑥1 − 2𝑥3 + 𝑇3 . 𝑥11 𝒙𝟒 = 𝑥1 − 2𝑥4 + 𝑇4 . 𝑥11
States: 𝒙𝟏 = 𝑇𝑟1 𝒙𝟐 = 𝑇𝑤1,2 𝒙𝟑 = 𝑇𝑤1,3 𝒙𝟒 = 𝑇𝑤1,4 𝒙𝟓 = 𝑇𝑤1,5
𝒙𝟓 = 𝑥1 𝑥12 − 𝑥12 + 𝑥13 𝑥5 + 𝑇5 𝑥13 + 𝐴𝑤 51 𝑥14 𝑄𝑟𝑎𝑑 𝒙𝒊 = 0
∀𝑖 = 6, 7, … , 15.
Parameters: 1
1
𝑥6 = 𝐶 𝑟 𝑅
𝑥7 = 𝐶 𝑟 𝑅
1
𝑥9 = 𝐶 𝑟 𝑅
1 121
𝑥𝑡 = 𝑓 𝑥𝑡 , 𝑢𝑡 , 𝑑𝑡 , 𝑡
1
𝑥8 = 𝐶 𝑟 𝑅
𝑦𝑡 = 𝐶𝑥𝑡
1 141
1
where:
𝒙 = 𝒙𝟏 , 𝒙𝟐 , … , 𝒙𝟓 , 𝒙𝟔 , 𝒙𝟕 , … , 𝒙𝟏𝟓
States and:
𝑇 𝑢 = 𝑠1 𝑚𝑟1
Parameters
𝑇
1 151
1 𝑤 𝑅𝑤
𝑥10 = 𝐶 𝑟
𝑥11 = 𝐶
1
1
𝑥12 = 𝐶 𝑤 𝑅
51 511
α
𝑥14 = 𝐶 𝑤
1 131
51
1
𝑥13 = 𝐶 𝑤 𝑅
51 515
𝑥15 =
1 𝑤𝑖𝑛 𝑅15
27
UKF and EKF Algorithms Used to update the current estimate of state and parameters as new measurements arrive…
Mehdi Maasoumy
University of California, Berkeley
28
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
29
Offline v.s. Online Parameter Identification w/o parameter update Calibration period
Prediction period
Online Parameter Adaptation using EKF
Online Parameter Adaptation using UKF Mehdi Maasoumy
University of California, Berkeley
30
Summary
Developed a framework for simultaneous state estimation and parameter adaptation of building predictive models. Developed a Parameter-Adaptive Building (PAB) model
Applied Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) for simultaneous state estimation and parameter adaptation of the model.
Mehdi Maasoumy
University of California, Berkeley
31
Future Work Proposed Architecture
Utilize the PAB model for adaptive model predictive control of buildings*.
* Mehdi Maasoumy, Meysam Razmara, Mahdi Shahbakhti, Alberto Sangiovanni-Vincentelli “Handling Model Uncertainties in Model Predictive Control for Energy Efficient Buildings”, International Journal of Energy and Buildings. Submitted. (Journal Submission based on the extension of this work) 32
Thanks for your attention!!!
Thanks for your attention!!! Questions…?
Mehdi Maasoumy
University of California, Berkeley
33
Mehdi Maasoumy PhD Candidate University of California, Berkeley October 21, 2013 Sponsored by CREST, iCyPhy, and TerraSwarm Research Consortiums. A collaboration of UC Berkeley, and Michigan Technological University.
1
What’s the biggest energy consumer sector? Buildings Consume Significant Energy: • • • • •
40% of total US energy consumption 72% of total US electricity consumption 55% of total US natural gas consumption $ 370 Billion: Total US annual energy cost 200%: Increase in US electricity cons. since 1990.
Source: Buildings Energy Data Book 2006
Directly related to HVAC
Mehdi Maasoumy
University of California, Berkeley
2
Existing HVAC Control Logic
Lack of Integrated System Dynamics Model PID
On-Off
On-Off
On-Off UC Berkeley, Cory Hall
Mehdi Maasoumy
University of California, Berkeley
3
Previous works
2008 DB Crawley, (Simulation)
2010 - Y. Ma, (MPC) - F. Oldewurtel, (SMPC) - K Deng, (Model Reduction) - C Liao, (Occupancy Modeling) - Rasmussen (Gain Schedule Ctrl)
2009 M. Wetter, (modeling and simulation)
2012 - B. Hencey, (Estimation) - B. Rasmussen (Vapor Comp. Sys.) - M. Maasoumy (RMPC) - Y. Yang (BAS)
2011 - Y. Ma, (DMPC) - M. Maasoumy, (Hierarchical) - TX Nghiem, (Scheduling)
2013 - Alleyne (Optimal Partitioning)
Less Work on Improving the Quality of Building Dynamic Models Mehdi Maasoumy
University of California, Berkeley
4
Energy Savings of MPC Compared to RBC 60 Building Type I
Energy Saving Compared to Rule Based Control [%]
41 40
Building Type V
24 16
20
7
12
Model uncertainty [%]
0 0
25
50
75
100
-20 -23
-26
-40 -60
-38
High fidelity models -70
-80
-93
-100
Mehdi Maasoumy
University of California, Berkeley
5
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
6
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
7
Architecture of the proposed PAB model Proposed Architecture
Problem Statement • Highly time varying, and nonlinear nature of building dynamics. (e.g. Time-varying convective heat transfer coefficient of outside air). • Model-based controllers often need accurate estimate of all states, but not all the states of building model are measurable
Joint parameter-state estimation
PAB Model: Parameter Adaptive Building Model Mehdi Maasoumy
“On-line estimation” of states and unknown parameters of buildings… … leading to the: Parameter-Adaptive Building (PAB) model.
University of California, Berkeley
8
Proposed Architecture
Mehdi Maasoumy
University of California, Berkeley
9
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
10
Test-bed: Berkeley
Mehdi Maasoumy
University of California, Berkeley
11
Plant Modeling
Unmodeled dynamics
• Energy balance for a room node:
Thermal and circuit model of a wall with window Mehdi Maasoumy
University of California, Berkeley
12
Plant Modeling: Unmodeled Dynamics •
External heat gain
•
Internal heat gain
Disturbance:
which results to:
Leading to the LTI system:
Mehdi Maasoumy
University of California, Berkeley
13
Proposed Architecture
Mehdi Maasoumy
University of California, Berkeley
14
Offline Calibration: Berkeley Test-bed Mathematical Model
Scale-up to Building Level
Room Temperature [oC]
Data-Driven Predictive Model
Disturbance [oC/hr]
Time [hr]
Mehdi Maasoumy
Time [hr]
University of California, Berkeley
15
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
16
Test-bed at Different Climates
Mehdi Maasoumy
University of California, Berkeley
17
Lakeshore Center: Michigan Test-bed
Front View
Top View
Mehdi Maasoumy
University of California, Berkeley
18
Test bed: Office Space
Mehdi Maasoumy
University of California, Berkeley
19
Lakeshore Building HVAC System AHU
VAV
GSHP
Mehdi Maasoumy
University of California, Berkeley
20
Schematic of the Room
Mehdi Maasoumy
University of California, Berkeley
21
Proposed Architecture
Mehdi Maasoumy
University of California, Berkeley
22
Sensor Readings (Michigan test bed) Lakeshore building at Michigan Technological University
Mehdi Maasoumy
University of California, Berkeley
23
Offline Calibration (Michigan test bed)
!!! Mehdi Maasoumy
University of California, Berkeley
24
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
25
Proposed Architecture
Kalman Filter
Mehdi Maasoumy
University of California, Berkeley
26
Room Temperature Dynamics 𝒙𝟏 = 𝑥6 − 𝑥7 − 𝑥8 − 𝑥9 − 𝑥10 𝑥15 − 𝑥10 𝑢2 𝑐𝑎 𝑥1 +𝑥6 𝑥2 + 𝑥7 𝑥3 + 𝑥8 𝑥4 + 𝑥9 𝑥5 + 𝑐𝑎 𝑢1 𝑢2 + 𝑇5 𝑥15 + 𝐴𝑤𝑖𝑛 𝜏 𝑄𝑟𝑎𝑑 + 𝑄𝑖𝑛𝑡 . 𝑥10 𝒙𝟐 = 𝑥1 − 2𝑥2 + 𝑇2 . 𝑥11
𝒙𝟑 = 𝑥1 − 2𝑥3 + 𝑇3 . 𝑥11 𝒙𝟒 = 𝑥1 − 2𝑥4 + 𝑇4 . 𝑥11
States: 𝒙𝟏 = 𝑇𝑟1 𝒙𝟐 = 𝑇𝑤1,2 𝒙𝟑 = 𝑇𝑤1,3 𝒙𝟒 = 𝑇𝑤1,4 𝒙𝟓 = 𝑇𝑤1,5
𝒙𝟓 = 𝑥1 𝑥12 − 𝑥12 + 𝑥13 𝑥5 + 𝑇5 𝑥13 + 𝐴𝑤 51 𝑥14 𝑄𝑟𝑎𝑑 𝒙𝒊 = 0
∀𝑖 = 6, 7, … , 15.
Parameters: 1
1
𝑥6 = 𝐶 𝑟 𝑅
𝑥7 = 𝐶 𝑟 𝑅
1
𝑥9 = 𝐶 𝑟 𝑅
1 121
𝑥𝑡 = 𝑓 𝑥𝑡 , 𝑢𝑡 , 𝑑𝑡 , 𝑡
1
𝑥8 = 𝐶 𝑟 𝑅
𝑦𝑡 = 𝐶𝑥𝑡
1 141
1
where:
𝒙 = 𝒙𝟏 , 𝒙𝟐 , … , 𝒙𝟓 , 𝒙𝟔 , 𝒙𝟕 , … , 𝒙𝟏𝟓
States and:
𝑇 𝑢 = 𝑠1 𝑚𝑟1
Parameters
𝑇
1 151
1 𝑤 𝑅𝑤
𝑥10 = 𝐶 𝑟
𝑥11 = 𝐶
1
1
𝑥12 = 𝐶 𝑤 𝑅
51 511
α
𝑥14 = 𝐶 𝑤
1 131
51
1
𝑥13 = 𝐶 𝑤 𝑅
51 515
𝑥15 =
1 𝑤𝑖𝑛 𝑅15
27
UKF and EKF Algorithms Used to update the current estimate of state and parameters as new measurements arrive…
Mehdi Maasoumy
University of California, Berkeley
28
Outline • Parameter Adaptive Building (PAB) Model Architecture • Berkeley Test Bed o Mathematical Model o Offline Calibration Results • Michigan Test-bed o Mathematical Model o Offline Calibration Results • EKF / UKF Formulations • Results Mehdi Maasoumy
University of California, Berkeley
29
Offline v.s. Online Parameter Identification w/o parameter update Calibration period
Prediction period
Online Parameter Adaptation using EKF
Online Parameter Adaptation using UKF Mehdi Maasoumy
University of California, Berkeley
30
Summary
Developed a framework for simultaneous state estimation and parameter adaptation of building predictive models. Developed a Parameter-Adaptive Building (PAB) model
Applied Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) for simultaneous state estimation and parameter adaptation of the model.
Mehdi Maasoumy
University of California, Berkeley
31
Future Work Proposed Architecture
Utilize the PAB model for adaptive model predictive control of buildings*.
* Mehdi Maasoumy, Meysam Razmara, Mahdi Shahbakhti, Alberto Sangiovanni-Vincentelli “Handling Model Uncertainties in Model Predictive Control for Energy Efficient Buildings”, International Journal of Energy and Buildings. Submitted. (Journal Submission based on the extension of this work) 32
Thanks for your attention!!!
Thanks for your attention!!! Questions…?
Mehdi Maasoumy
University of California, Berkeley
33
