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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


Edge computing architecture

• Security

• Scalabilityo Flexible ‘plug and play’ design

• Open Standardso Interoperabilityo Portability

• Programmability

• Reliability, Availability, and Serviceability

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Communication Standards

• OPC-UA

• MQTT / AMQP

Programming Standards

• IEC61131-3

• PLCopen

Edge computing architecture


• 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


• Single centralized MPC

• Global objective function

• Stable for any interacting systems

• Complex & Inflexible

• Pareto optimal

• Benchmark solution

MPCmin V (u1, u2, …)

Centralised control


• 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



• 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..)





Centralised Coordinator (SS Optimizer)

Decentralised control with centralised coordinator



• 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..)





Message Broker

Cooperative control


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


MPC1𝐼𝑛𝑖𝑡𝑖𝑙𝑖𝑠𝑒 𝑚𝑜𝑣𝑒 𝑝𝑙𝑎𝑛 𝑢1

0

MPC2𝐼𝑛𝑖𝑡𝑖𝑙𝑖𝑠𝑒 𝑚𝑜𝑣𝑒 𝑝𝑙𝑎𝑛 𝑢2

0



𝑢1∗, 𝑢2

𝑝

MPC1𝑆𝑒𝑡 𝑢2 = 𝑢2

0

min𝑢1

𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 → 𝑢1∗, 𝑢2

0

MPC2

𝑢20



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



𝑢10, 𝑢2

∗

𝑢1∗, 𝑢2

0

𝑢i𝑝+1

= 𝛼 𝑢i𝑝

+ (1 − α) 𝑢i∗

MPC1𝑢11 = 𝛼 𝑢1

0 + (1 − α) 𝑢1∗


0 + (1 − α) 𝑢2∗



𝑢1∗, 𝑢2

𝑝

(𝑢1𝑝, 𝑢2

𝑝)

MPC1𝑆𝑒𝑡 𝑢2 = 𝑢2

1

min𝑢1

𝑉 𝑥1 0 , 𝑥2 0 , 𝑢1, 𝑢2 → 𝑢1∗, 𝑢2

1

MPC2

𝑢21



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



𝑢2∗ , 𝑢1

𝑝

𝑢1∗, 𝑢2

𝑝

𝑢i𝑝+1

= 𝛼 𝑢i𝑝

+ (1 − α) 𝑢i∗


1 + (1 − α) 𝑢1∗


1 + (1 − α) 𝑢2∗



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



Flare

XB

XD


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


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


• 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.


References

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