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Advances in Process Automation and Control 201712–14 June 2017, Birmingham, UK
Allocating automation functions within an IIoT architecture
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Traditional Purdue Reference Architecture IIoT Architecture
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Edge computing architecture
• Security
• Scalabilityo Flexible ‘plug and play’ design
• Open Standardso Interoperabilityo Portability
• Programmability
• Reliability, Availability, and Serviceability
Client Server Publish Subscribe
Communication Standards
• OPC-UA
• MQTT / AMQP
Programming Standards
• IEC61131-3
• PLCopen
Edge computing architecture
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• Large scale systems consist of complex networks of interconnected and interacting subsystems
• Examples:• Integrated process plants
• Utility networks (Electrical, Gas, Water)
• Buildings
• There is often significant benefit to be gained through optimisation of the complete system rather than treating it as series of distributed subsystems
• IIoT architectures provide an opportunity to better control larger and more geographically dispersed systems
Using IIoT to control large scale systems
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• Single centralized MPC
• Global objective function
• Stable for any interacting systems
• Complex & Inflexible
• Pareto optimal
• Benchmark solution
MPCmin V (u1, u2, …)
Centralised control
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• Each subsystem is controlled by a separate independent MPC
• Each MPC solves a local objective function
• No inter-controller communication
• MPC’s should be large enough to account for strong system interactions
• Not stable for strongly interacting subsystems
• Not globally optimal
MPC 1min V1 (u1)
MPC 3min V3 (u3)
MPC 5min V5 (u5)
MPC 2min V2 (u2)
MPC 4min V4 (u4)
Decentralised control
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• Each subsystem is controlled by a separate independent MPC
• Each MPC solves a local objective function
• Each MPC shares its move plan with other MPC’s
• A centralised coordinator may be used to coordinate steady state objectives
• MPC’s should be large enough to account for strong system interactions
• Not stable for strongly interacting subsystems
• Nash equilibrium
MPC 1min V1 (u1,u2..)
MPC 3min V3 (u1,u2..)
MPC 5min V5 (u1,u2..)
MPC 2min V2 (u1,u2..)
MPC 4min V4 (u1,u2..)
Centralised Coordinator (SS Optimizer)
Decentralised control with centralised coordinator
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• Each subsystem is controlled by a separate independent MPC
• All controllers share a common objective function
• Each MPC shares its move plan with other controllers
• Stable for strongly interacting subsystems
• Stability is independent of MPC size and design
• High flexibility
• MPC’s can have different execution frequencies
• Pareto optimal (with sufficient iterations)
MPC 1min V (u1,u2..)
MPC 3min V (u1,u2..)
MPC 5min V (u1,u2..)
MPC 2min V (u1,u2..)
MPC 4min V (u1,u2..)
Message Broker
Cooperative control
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• Each subsystem is controlled by a separate independent MPC
• All controllers share a common objective function
• Each MPC shares its move plan with other controllers
• Stable for strongly interacting subsystems
• Stability is independent of MPC size and design
• High flexibility
• MPC’s can have different execution frequencies
• Pareto optimal (with sufficient iterations)
MPC 1min V (u1,u2..)
MPC 3min V (u1,u2..)
MPC 5min V (u1,u2..)
MPC 2min V (u1,u2..)
MPC 4min V (u1,u2..)
Message Broker
Cooperative control
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Consider a simple plant with two subsystems:
𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 =
𝑖=1
𝑁−11
2[𝑥𝑖 , 𝑢𝑖]𝑖
𝑇𝐻𝑖[𝑥𝑖 , 𝑢𝑖]𝑖 + 𝑓𝑖𝑇[𝑥𝑖 , 𝑢𝑖]𝑖 + [𝑥𝑖 , 𝑢𝑖]𝑁
𝑇𝐻𝑁[𝑥𝑖 , 𝑢𝑖]𝑁
𝑃𝑖[𝑥𝑖 , 𝑢𝑖] ≤ 𝑏𝑖𝑥𝑖+1 = 𝐴𝑥𝑖 + 𝐵1𝑢𝑖 + 𝐵2𝑢2
𝑇ℎ𝑖𝑠 𝑐𝑎𝑛 𝑏𝑒 𝑠𝑜𝑙𝑣𝑒𝑑 𝑏𝑦 𝑖𝑡𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑜𝑣𝑒𝑟 𝑡ℎ𝑒 𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔 𝑠𝑡𝑒𝑝𝑠:
Step 1. 𝑆𝑒𝑡 𝑢2 = 𝑢2𝑝
: min𝑢1
𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 → 𝑢1∗, 𝑢2
𝑝
Step 2. 𝑆𝑒𝑡 𝑢1 = 𝑢1𝑝
: min𝑢2
𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 → 𝑢2∗ , 𝑢1
𝑝
𝑢i𝑝+1
= 𝛼 𝑢i𝑝
+ (1 − α) 𝑢i∗
MPC 1
MPC 2
U2*U1*
Step 3:
𝑝 = 𝑝 + 1
Cooperative Model Predictive Control
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MPC1𝐼𝑛𝑖𝑡𝑖𝑙𝑖𝑠𝑒 𝑚𝑜𝑣𝑒 𝑝𝑙𝑎𝑛 𝑢1
0
MPC2𝐼𝑛𝑖𝑡𝑖𝑙𝑖𝑠𝑒 𝑚𝑜𝑣𝑒 𝑝𝑙𝑎𝑛 𝑢2
0
Cooperative Model Predictive Control
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𝑢1∗, 𝑢2
𝑝
MPC1𝑆𝑒𝑡 𝑢2 = 𝑢2
0
min𝑢1
𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 → 𝑢1∗, 𝑢2
0
MPC2
𝑢20
Cooperative Model Predictive Control
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𝑢2∗ , 𝑢1
𝑝
𝑢1∗, 𝑢2
𝑝
MPC21. 𝑆𝑒𝑡 𝑢1 = 𝑢1
0
2. min𝑢2
𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 → 𝑢2∗ , 𝑢1
0
MPC1
𝑢10
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Cooperative Model Predictive Control
𝑢10, 𝑢2
∗
𝑢1∗, 𝑢2
0
𝑢i𝑝+1
= 𝛼 𝑢i𝑝
+ (1 − α) 𝑢i∗
MPC1𝑢11 = 𝛼 𝑢1
0 + (1 − α) 𝑢1∗
MPC2𝑢21 = 𝛼 𝑢2
0 + (1 − α) 𝑢2∗
Cooperative Model Predictive Control
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𝑢1∗, 𝑢2
𝑝
(𝑢1𝑝, 𝑢2
𝑝)
MPC1𝑆𝑒𝑡 𝑢2 = 𝑢2
1
min𝑢1
𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 → 𝑢1∗, 𝑢2
1
MPC2
𝑢21
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Cooperative Model Predictive Control
𝑢1𝑝, 𝑢2
∗
𝑢1∗, 𝑢2
𝑝
(𝑢1𝑝, 𝑢2
𝑝)MPC2
𝑆𝑒𝑡 𝑢1 = 𝑢11
min𝑢2
𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 → 𝑢2∗ , 𝑢1
1
MPC1
𝑢11
Cooperative Model Predictive Control
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𝑢2∗ , 𝑢1
𝑝
𝑢1∗, 𝑢2
𝑝
𝑢i𝑝+1
= 𝛼 𝑢i𝑝
+ (1 − α) 𝑢i∗
MPC1𝑢12 = 𝛼 𝑢1
1 + (1 − α) 𝑢1∗
MPC2𝑢22 = 𝛼 𝑢2
1 + (1 − α) 𝑢2∗
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Cooperative Model Predictive Control
Cost
u2
u1
• Iterating to convergence gives optimal plant-wide control
• Early termination of the optimization gives stable, suboptimal plant-wide control
• Stability can be proved using sub-optimal MPC theory
Iteration
u 4
Cooperative Model Predictive Control
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Flare
XB
XD
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LV control of distillation column
Cost Performance loss (%)
Centralized MPC 75.8 0
Cooperative MPC (10 iterates) 76.1 0.388
Cooperative MPC (1 iterate) 87.5 15.4
Non-cooperative MPC 382 404
Decentralized MPC 364 380
Rawlings and Stewart 2010
LV control of distillation column
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IIoT (Message Broker)
Ethylene Plant C2 Feed = f(Gas Plant Demethaniser Duty)
min𝑑𝑒𝑚𝑒𝑡ℎ
𝑉 𝐺𝑎𝑠 𝑃𝑙𝑎𝑛𝑡, 𝑁𝐺𝐿 𝑃𝑙𝑎𝑛𝑡, 𝐸𝑡ℎ𝑦𝑙𝑒𝑛𝑒 𝑃𝑙𝑎𝑛𝑡
100 km
DemethaniserDebutaniser
Deethaniser
Condensate
Flare
Gas Plant NGL Plant Ethylene Plant
FI
Ethylene Plant Ethane Feed
• Eliminates the requirement for a central optimiser or coordinator
• Can incorporate mixed dynamics
• Expandable and flexible -> plug and play design
• Stability is independent of the strength of process interactions or of individual controller design
• Systems can be geographically dispersed
• Suited to distributed hardware with limited processing capacity (such as embedded systems and edge devices)
• Ideally suited to an IIoT architecture
Advantages of Distributed Cooperative Control
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• J.B. Rawlings and D.Q.Mayne, “Model Predictive Control: Theory and Design,” Nob Hill Publishing, 2013.
• Stewart, Venkat, Rawlings, Wright and Pannocchia, “Cooperative distributed model predictive control,” Systems & Control Letters 59 (2010) 460-469.
• Christofides, Scattolini, Muñoz de la Peña and Liu, “Distributed model predictive control: A tutorial review and future research directions,” Computers & Chemical Engineering, Volume 51, April 2013.
• Shaoyuan Li and Yi Zheng, "Distributed Model Predictive Control for Plant-Wide Systems," Wiley, 2015.
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References
Get in touch
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