Integrating Scheduling and Control for Optimal Process ...egon.cheme.cmu.edu/ewo/docs/EWO_Seminar_02_03_2016.pdf · Process and Energy Systems Engineering. Smart Manufacturing and

Integrating Scheduling and Control forOptimal Process Operations in Fast-Changing Markets

Michael BaldeaMcKetta Department of Chemical Engineering &

Institute for Computational Engineering and SciencesThe University of Texas at Austin

Contributors: Dr. Juan Du (UT, now at PPG), Cara R. Touretzky (UT), Richard C. Pattison (UT), Jungup Park (UT), Ted Johansson (KTH/UT), Dr. Iiro Harjunkoski (ABB)

Enterprise-Wide Optimization Seminar Carnegie Mellon University, February 3, 2016

Process and Energy Systems Engineering

Outline

Background and Motivation

EWO Challenges

Integrating Scheduling and Control• Scale-bridging Principle• Model Predictive Control• Data-driven Models

Case Study

Conclusions and Perspective


Background and Motivation

3

• Significant expansion of renewable generation- GWh-scale wind generation www.awea.org

- >1GWh of PV solar installed in 2014 www.seia.org

• Increased capacity exacerbates variability issues

5 10 15 202

4

6

8

Win

d ge

nera

tion,

GW

1 2 3 4 5 6 7 8 9 101112131415161718192021222330

40

50

60

Gri

d de

man

d, G

WHour ending

Data: www.ercot.com Ondeck, Edgar, Baldea, Applied Energy, 593-606, 2015

http://www.awea.org/

http://www.seia.org/


Demand Variability

• Grid demand desynchronized from renewables• Peak demand → fast changing, high cost

$0.00

$0.10

$0.20

$0.30

$0.40

$0.50

$0.60

$0.70

0

10

20

30

40

50

60

70

0:00 3:00 6:00 9:00 12:00 15:00 18:00 21:00 0:00

Elec

tric

ity P

rice

($/k

Wh)

Pow

er D

eman

d (G

W)

Time

Energy DemandElectricity Price

ERCOT demand and day ahead settlement point prices for June 25, 2012 from www.ercot.com

4


The Peak Demand Problem

• Residential buildings are the primary culprits• Industry could help - how?

0

10

20

30

40

50

60

70

80

Moderate Day Peak Day

Pow

er D

eman

d (G

W)

Residential

Commercial

Industrial

Wattles, ERCOT Demand Response Overview & Status Report, 2011

5


Grid-Dependent Industries

Demand response: lower production during peak timePotential benefits for industry• Reduce production cost / generate profit from price incentives• Improve environmental performance• Improve grid operations

Soroush and Chmielewski, Comput. Chem. Eng., 51, 86-95, 2013; Paulus and Borggrefe, Applied Energy, 88, 432-441, 2011

6


Industrial Demand Response

• Reduce production rate (vs. nominal) during peak time• Increase production rate at off-peak hours • Excess capacity and product storage must be available

(or installed at reasonable cost)7


Example: DR Operation of Air Separation Unit

Production scheduled on an hourly basis to account for real-time energy pricing• Production levels• Liquid vs. gas products

Process dynamics evolve in a comparable time scale

Ierapetritou et al., Ind. Eng. Chem. Res., 41, 5262-5277, 2002; Miller et al., Ind. Eng. Chem. Res., 47, 1132-1139, 2008; Cao, Swartz, Baldea, Blouin, J. Proc. Contr., 54 (24), 6355–6361, 2015

8


Industrial Demand Response

• Frequent production rate (schedule) changes: process dynamics must be accounted for in production scheduling:

9


Broader Challenge of Flexible Production

• Rapid response to market conditions: transitions occur in the same time scale as scheduled production changes

• Customizable products• Specialty chemicals, pharma, etc.

10


Smart Manufacturing and EWO

11

“a design and operational paradigm involving the integration of measurement and actuation; environment, safety and environmental protection, regulatory control, high fidelity modeling, real-time optimization and modeling, and planning and scheduling.” (Edgar and Davis, 2009)


Hierarchy of Process Operation Decisions

12

Production management• Assume steady-state operation• Typically carried out off-line

Control • Account for dynamics• Online, in real-time

Different time horizons, objectives, personnel: production management and control carried out independently

Seborg et al., Wiley, 2010, Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014, Shobrys and White, Comput. Chem. Eng, 26, 149—160, 2002

PROCESS

Regulatory control(seconds – minutes)

Multivariable and constraint control (minutes – hours)

Scheduling(hours – days)

Planning (weeks – months)


PROCESS






13

Mezoscale interactions

Overlap in the time scales of production management and process control motivates considering the integrated problem

Seborg et al., Wiley, 2010, Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014, Shobrys and White, Comput. Chem. Eng, 26, 149—160, 2002


PROCESS






14

Mezoscale interactions

Goal: Mechanism for synchronizing production scheduling with the control system and accounting for the dynamic nature of transitions


Smart(er) Manufacturing

Scheduling- become aware of process

state/dynamics- rescheduling

ProcessSupervisory

controller

Scheduling

outputs

yinputs

u

setpoints/

targets

ysp

+

-

process state for rescheduling

schedule for predicting

Supervisory Control- become aware of future

changes in production; improved response

- dynamic models are large and cumbersome

- some details may not be necessary for scheduling

- disturbance rejection- fast/short horizon execution

needed; cannot make scheduling decisions

BUT

Baldea and Harjunkoski, Comput. Chem. Eng., 71, 377-390, 2014

15


', 1 , ', ,1 ' 1

τ−= =

= + +∑∑p pN N

f s ps s i s i s i i i s

i it t z z t

Slot-Based Scheduling: Conventional

16

static schedulingdemand

price

sequence zi,s

production time tps

Mixed integer program

Static:• Transition time is a pre-

-determined constant;• Agnostic to process

dynamics.

MIP• Sequence zi,s ∈{0,1}• Production time ∈R+

( ), ,1 1 1

1 p p sN N Nf

scheduling i i i s storage i m s ii i sm

J z c T tT

π ω ω= = =

= − −

∑ ∑∑

1 1s fs st t s−= ∀ ≠

,1

1, sN

i ss

z i=

= ∀∑ ,1

1, pN

i si

z s=

= ∀∑

, , max ,≤ ∀p pi s i st z T i s

,1

, > T sN

pi s i s i i m

sq t iω ω δ

=

= ∀∑

Pinto and Grossmann, Comput. Chem. Eng. 18 (9), 797-816, 1994


,1

τ=

= + + ∀∑pN

f s ps s s i s

it t t s

Scheduling and Control: Full Dynamic Approach

17

Scheduling + Control

(Solve simultaneously)

demand

price

control action u

process output y

Embed dynamic process model in scheduling calculation

Disadvantages:• Detailed dynamics: large-

scale, computational difficulties

• Open-loop (optimal) control

MIDO:• Sequence zi,s ∈{0,1}• Production time ∈R+• u ∈ U ⊂ R+

( ), ,1 1 1

1 p p sN N Nf

scheduling i i i s storage i m s ii i sm

J z c T tT

π ω ω= = =

= − −

∑ ∑∑

1 1s fs st t s−= ∀ ≠

,1

1, sN

i ss

z i=

= ∀∑ ,1

1, pN

i si

z s=

= ∀∑( ) ( )= +x f x G x u

( )=y h x ( ) ,τ = ∑ sss i s i

izy y

,1

, > T sN

pi s i s i i m

sq t iω ω δ

=

= ∀∑

, , max ,≤ ∀p pi s i st z T i s


Baldea, Harjunkoski, Park, Du., AIChE J., 2015; Du, Park, Harjunkoski, Baldea. Comput. Chem. Eng., 79, 59-69, 2015

setpoints/

targets

ysp

Concept: Scale-Bridging Model

Scale-Bridging Model: • Capture closed-loop input-output dynamics• Embed in scheduling calculation

ProcessSupervisory

controller

Scheduling

outputs

yinputs

u

setpoints/

targets

ysp

+

-




18

Scale-Bridging Model

Scheduling

outputs

y

Process and Energy Systems Engineering 19

Scale-Bridging Model: Concept• SBM is the explicit form of the closed-loop dynamics of

process with its supervisory controller

• Low dimensional:

• Dynamics of process systems at scheduling-relevant time scales

y xn n

• Process operates in closed-loop:

• stability guarantees

• robustness to modeling error

setpoints/

targets

ysp


Scheduling

outputs

y

Process and Energy Systems EngineeringSeborg, Edgar, Mellichamp, Doyle, Process Dynamics and Control (3rd Ed.), Wiley, 2011

Concept: Scale-Bridging Model

Capture closed-loop input-output dynamics• Not a trivial task for a general nonlinear

system• Historically, research has focused on stability

and speed of response, rather than the trajectory itself

ProcessSupervisory

controller

Scheduling

outputs

yinputs

u

setpoints/

targets

ysp

+

-




20


Scale-Bridging Model Approaches

Capture closed-loop input-output dynamics1. Scale bridging via input-output linearization2. Scale bridging and model predictive control (MPC)3. Scale bridging using empirical models

ProcessSupervisory

controller

Scheduling

outputs

yinputs

u

setpoints/

targets

ysp

+

-




21

synopsis


Scale-Bridging via Input-Output Linearization• SBM is the explicit form of the closed-loop dynamics of

process with its supervisory controller

• Use feedback linearization to design a control law that imposes a closed-loop behavior of the type:

0

τ=

=∑ir

j spi ji

i

d yy

dt

ProcessSupervisory

controller

outputs

yinputs

u

+

-

setpoints/

targets

ysp

• Input u calculated from inverse of process model (Hirschorn, 1979)

11

( )

( )

rr

sp i fir

r g f

y y L h xu

L L h x

τ

τ=−

− −=

∑( ) ( )= +x f x g x u

( )=y h x

• Decoupled response for MIMO systems, integral action can be added to deal with disturbances and plant-model mismatch

Kravaris and Kantor, Ind. Eng. Chem. Res., 29, 2295-2310, 1990; Daoutidis and Kravaris, Chem. Eng. Sci., 49, 433—447, 1994


Example: Multi-Product Reactor• Exothermal reactor with coolant flow rate as control variable.• Four products (A,B,C,D), concentration depends on operating

conditions• C,D: open-loop unstable states

23

Flores-Tlacuahuac and Grossmann, Ind. Eng. Chem. Res., 45, 6698–6712, 2006


• Integral action on 𝑦𝑦1,𝑠𝑠𝑠𝑠→ 𝑣𝑣


24

( )

2

2

-N y1 110 1

2 -N y210 1 2

dy 1-y= -k e ydt

ydy = +k e y - αF y -Tdt

θ

θ−f

c c

T

• Process model

• SBM: relative order 𝑟𝑟 = 2

• Impose critically damped second-order I/O behavior

• Controlled variable: 𝒚𝒚 = 𝑦𝑦1

• Manipulated variable: 𝒖𝒖 = 𝐹𝐹𝐹𝐹

Dimensionless concentration

Dimensionless temperature

22 1 1

12 2 ; 4.3β β β+ + = =d y dy y v hdt dt


Problem Formulation

25

• Objective function

• Cyclical production timing and sequencing:

• Demand satisfaction:

• Dynamic model discretization (Radau IIA); smoothness of u:

,1

1, pN

i si

z s=

= ∀∑ ,1

1, sN

i ss

z i=

= ∀∑

1 1s fs st t s−= ∀ ≠ s

s m st T s N≤ =

/ 1.1 , i i m iTδ ω δ≤ ≤ ,1

, ω=

= ∀∑sN

pi s i s

sq t i

, , 0, , , , ,1

+ ; ,τ=

= ∀ ∈ ∀∑

cpns

j k s k s m j m k sme

x x W x x k sn

x

0, , 0, 1, , , 1,1

+ ; 1;τ− −

=

= ∀ ∈ ∀ > ∀∑

cp

cp

ns

k s k s m n m k sme

x x W x x k sn

x

j, , 1, , 1 ; 1; ;ρ−− ≤ ∀ ∈ ∀ > ∀ ∀k s j k su u u j k su

1, , , 1, 2 ; 1;cpk s n k su u u k sρ−− ≤ ∀ ∈ ∀ > ∀u

( ), ,1 1 1

1 π ω ω= = =

= − −

∑ ∑∑

p p sN N Nf

scheduling i i i s storage i m si i sm

J c T tT

,1

τ=

= + + ∀∑pN

f s ps s s i s

it t t s , , max ,≤ ∀p p

i s i st z T i s

0,1, , 1 ;−= ∀ ∈ ∀sss i s ix z x x sx j,k, , ; 18;= ∀ ∈ ∀ > ∀ss

s i s ix z x x k sx

, , max ,ω ≤ ∀i s i sz W i s , max ,(1 ) ,ω ω≤ − − ∀i s i i sW z i s

Pinto and Grossmann, Comput. Chem. Eng., 18, 797-816, 1994; Flores-Tlacuahuac and Grossmann, IECR, 45, 6698–6712, 2006

Similar to “delta U” formulation in MPC


Full Dynamic Optimization

26

B DCA

Cycle time: 84.45h

Profit: $5,656


Schedule Based on SBM

27

• Integrated Scheduling and Control using second-order linear SBM

• Implemented in GAMS, solved using SBB/CONOPT3

• Full order: 5.2s; SBM-based: 1.7s

Production sequence and

cycle time are very similar


Closed-loop Implementation of Schedule

28

B DCA Cycle time: 84.45h

Profit: $5,190

• Excellent approximation of results derived using full-order model


Integration of Scheduling and MPC

• I/O linearization typically limited to unconstrained square systems with stable zero dynamics

• MPC: deal with constraints, non-square systems widely accepted in industry

29

• No explicit description of input-output behavior = NO SBM?

Seborg et al.,, 3rd Ed., Wiley, 2011

Qin and Badgwell, Contr. Eng. Prac., 11, 733-764, 2003, Kolavennu, Palanki, Cockburn, Chem. Eng. Sci., 56, 2103-2110, 2001,


Scheduling-Oriented MPC

ProcessScheduling

Oriented Model Predictive Control

Scheduling

outputs

y

inputs

u

setpoints/

targets

ysp

+

-

• Scheduling-oriented MPC that is based on a SBM

Replace tracking objective with SBM as a hard constraint

Scale Bridging Model

Baldea, Harjunkoski, Park, Du, AIChE J., 2015

30


• First-order response for temperature

Case Study: Scale-Bridging Model

31

( )

2

2

-N y1 110 1

2 -N y210 1 2

dy 1-y= -k e ydt

ydy = +k e y - αF y -Tdt

θ

θ−f

c c

T

• Process model

• SBM:

• Impose second-order I/O behavior for concentraiton

• Controlled variables: 𝒚𝒚 = 𝑦𝑦1,𝑦𝑦2

• Manipulated variables: 𝒖𝒖 = 𝜃𝜃,𝐹𝐹𝐹𝐹

Dimensionless concentration

Dimensionless temperature

22 1 1

1 1 1 1, 12 2 ; 3.7spd y dy y y hdt dt

β β β+ + = =

22 2 2, 2; 3.7sp

dy y y hdt

β β+ = =

Shorter time constant

due to MIMO control


MPC Problem Formulation

32

Solution strategy

• Convert to NLP by discretizing process model (implicit Euler)

• Implemented in MATLAB with IPOPT

s.t. Process model equations

2252 2 1

1 , , 1 2 1 3 1, 4 2, , 2,1 2

1( ) ( ) ( )control c a c a a a a sp a aa a a

dy dTJ w F F w w y w y y dtdt dt

θ θβ− −

=

= − + − + − + − −

∑

1

2 11 1 1 1,2 y sp

dy y y ydt

β β+ + =

/c dc dt=

Constraint softening


Closed-loop implementation with MPC

33

• MPC tracks setpoint, imposes second-order input-output behavior

Cycle time ~81h

(compare with 84.45h

for SISO control)

Profit $5,786 (compare to $5,656)


Data-Driven Scale Bridging Models

Industrial Processes• MPC rarely used for transitions in practice

- Linear models- Vendor software difficult to modify

• High complexity: large scale, interactions, noise, unmeasured disturbances

• Analytical model and SBM may be very difficult to obtain

• Data driven modeling of closed-loop behavior

34


Data-Driven Scale Bridging Models

Industrial Processes• Increased complexity: large scale, interactions,

noise, unmeasured disturbances• Usable data sets are likely available from

process operation history

• Multi-product transitions resemble system identification experiments

35


Case Study: DR of Air Separation Unit

36

Separate components of air via cryogenic distillation: high purity (>99%) Refrigeration via thermal expansion and energy recovery Large energy consumers: 19.4 TWh in US in 2010 Store energy as liquefied molecules: potential to shift grid load

Johansson, MSc thesis, KTH/UT Austin, 2015


Interaction with Electric Grid

37

Optimal process operation: Overproduce, store liquid

nitrogen off-peak Reduce production and gasify

stored product at peak periods

Challenges: Scheduled production changes

occur over time frames much shorter than the longest time constant of the process

Must ensure that sequence of production rate targets is feasible (product quality and process operation constraints)

ERCOT prices, September 2013


Product Quality Constraints (QCs):- Product purity (99.8%)- Production flowrate (20 mol/s)

Process Constraints (PCs):- Prevent tray flooding in the

column- Liquid level in the reboiler

does not deplete- All streams in the first zone of the PHX are in the gas phase- All streams exiting the second zone of the PHX are in the liquid phase- The temperature driving force in the reboiler/condenser is above the

lower limit

Product and Process Constraints

38


ASU Production Scheduling

39

Static formulation

𝐉𝐉 = �𝟎𝟎

𝑻𝑻𝒑𝒑 𝒕𝒕 𝑾𝑾 𝒕𝒕 𝒅𝒅𝒕𝒕min

s.t.

𝒚𝒚𝒔𝒔𝒑𝒑 (t)

Production quality and demand constraints

Rate of change constraints

Steady-state correlation between power consumption

and production rate

Inventory model


Implementing the Schedule: System Dynamics

40

Production rate changes are

NOT instantaneous

Schedule computed using

STATIC formulation :

Potentially severe quality violations

Pattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, submitted


ASU Scheduling Under (Dynamic) Constraints

41

Full-order dynamic model (P1)

𝐉𝐉 = �𝟎𝟎


s.t.



Inventory constraints

Full-order process model (DAE System with

6094 eqns, 430 state variables)

Process operating constraints

Inventory model

Static formulation

𝐉𝐉 = �𝟎𝟎


s.t.





and production rate

Inventory model


ASU Scheduling Under (Dynamic) Constraints

42


𝐉𝐉 = �𝟎𝟎


s.t.







Inventory model

Scheduling-oriented low-order dynamic model (P2)

𝐉𝐉 = �𝟎𝟎


s.t.




Low-order dynamic process model

Reduced set of process operating constraints

Inventory model

Static formulation

𝐉𝐉 = �𝟎𝟎


s.t.





and production rate

Inventory model


Scheduling-Oriented Low-Order Dynamic Models

43

SBMsProduction targets (desired product quality, flow rate)


Production output (quality, quantity)

In an industrial process

Must select judiciously the variables to model


Proposition (Pattison et al.)

“In a complex process with multiple operating constraints related to the process performance, efficiency, and safety, the constraints relevant to the scheduling calculation […] closely approach or reach their bounds during steady state operation and/or during transitions between operating points.”

• SBM: capture response of process variables involved in this subset of constraints


44


Model Identification

45

Training data: implementation of static scheduling result• Similar to historic data

collected during process operations

• Eight scheduling-relevant states (out of >400)

Identification challenges (Hammerstein-Wiener models):

• Multiple time scale response• High nonlinearity

Constraint

violations


Scheduling Results

46


𝐉𝐉 = �𝟎𝟎


s.t.







Inventory model

Scheduling-oriented low-order dynamic model (P2)

𝐉𝐉 = �𝟎𝟎


s.t.




Low-order dynamic process model:

51 differential variables

Reduced set of process operating constraints

Inventory model

Static formulation

𝐉𝐉 = �𝟎𝟎


s.t.





and production rate

Inventory model


Production Target

47

• Static formulation predictably yields most aggressive schedule• Embedding dynamics has a smoothing effect



Production Target

48

• Production rate scheduled to increase at off-peak timesPattison, Touretzky, Johansson, Harjunkoski, Baldea, IECR, in prep.


Production Rates

49

• Reduced-order model closely resembles the results derived using full-order model



Inventory Levels

50

• Synchronized with energy prices (rise off-peak, deplete at peak time)

•H

oldu

p (k

mol

)


Product Quality (Impurity Levels)

51

• Reduced-order model closely resembles the results derived using full-order model


Impu

rity

in N

2 st

ream

, ppm


Economics and Computational Statistics

52

*gPROMS ProcessBuilder 1.0, Intel Core i7 @3.40GHz, 16GB RAM, Windows 7 x64

Problem Variables Operating cost ($) CPU time (h)

Constant production rate

- 22,187 -

P1 (full-order model)

430 differential5,764 algebraic

21,520 (-3.0%) 97*

P2 (SBM) 51 differential 21,584 (-2.7%) 1.2*

• Exploiting energy price variability (vs. operating at constant production rate): significant savings

• Must account for dynamics to ensure quality and process constraints are met

• Scheduling-oriented low-order data-driven model: order-of-magnitude improvement in computation time – real time implementation possible


Process Constraints

53

• Condenser temperature gradient: ensure driving force for column operation



Process Constraints

54

• Reboiler holdup: ensure internal refrigeration is not depleted


=


Conclusions and Perspective

• Integrated scheduling and control- Required when frequency of scheduling decisions

overlaps with dynamic modes of the plant- Scale-bridging model: Low-order schedule-relevant

model of closed-loop dynamics- Closed-loop implementation: stability, robustness- Computational efficiency, scalability: SBM size

unlikely to increase significantly for large plants, real-time calculations

• Smarter operations- Chemical and petrochemical processes- Electric grid- Other players (e.g., buildings)

55


Quo Vadis, Integrated Scheduling and Control?

56

• Feedback: moving horizon implementation- Define rescheduling triggers (cf. Touretzky et al.,

AIChE Annual Meeting, AIChE J., in prep). - Define state observation/estimation strategy, “integral

action”- Extension to batch processes

• Applications: - Interaction of industrial energy users with the grid:

optimal plan operation from the user perspective != optimal operation from the grid perspective

- Cooperative approaches


Selected Publications

57

• M. Baldea, J. Du, J. Park, I. Harjunkoski, Integrated Production Scheduling and Model Predictive Control of Continuous Processes, AIChE J., 61(12), 4179–4190, 2015 http://dx.doi.org/10.1002/aic.14951

• J. Du, J. Park, I. Harjunkoski, M. Baldea, A Time Scale Bridging Approach for Integrating Production Scheduling and Process Control, Comput. Chem. Eng., 79, 59-69, 2015 http://dx.doi.org/10.1016/j.compchemeng.2015.04.026

• M. Baldea, I. Harjunkoski, Integrated Production Scheduling and Process Control: A Systematic Review, Comput. Chem. Eng., 71, 377-390, 2014, http://dx.doi.org/10.1016/j.compchemeng.2014.09.002

• C.R. Touretzky, M. Baldea, A Hierarchical Scheduling and Control Strategy for Thermal Energy Storage Systems, Energy and Buildings, 110, 94-107, 2015 http://dx.doi.org/10.1016/j.enbuild.2015.09.049

• R.C. Pattison+, C.R. Touretzky+, T. Johansson, M. Baldea, I. Harjunkoski, Optimal Process Operations in Fast-Changing Energy Markets: Framework for Scheduling with Low-Order Dynamic Models and an Air Separation Application, Ind. Eng. Chem. Res., submitted

•

http://dx.doi.org/10.1002/aic.14951

http://dx.doi.org/10.1016/j.compchemeng.2015.04.026

http://dx.doi.org/10.1016/j.compchemeng.2014.09.002

http://dx.doi.org/10.1016/j.enbuild.2015.09.049


Acknowledgements

• Dr. Juan Du, Cara R. Touretzky, Richard C. Pattison, Ted Johansson, Jungup Park

• Drs. Iiro Harjunkoski, Alf Isaksson, Michael Lundh and Per-Erik Modén

• ABB Corporate Research, NSF CAREER Award 1454433, NSF CBET-1512379, DOE DE-EE0005763, NSF I/UCRC IIP-1134849, Moncrief Grand Challenges Award, EPA STAR Fellowship (CRT), Engineering Doctoral Fellowship (RCP), KTH support (TJ)

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Integrating Scheduling and Control for Optimal Process ...egon.cheme.cmu.edu/ewo/docs/EWO_Seminar_02_03_2016.pdf · Process and Energy Systems Engineering. Smart Manufacturing and