Loading in 5 sec....

G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin aPowerPoint Presentation

G.A. Bunin a , Z. Wuillemin b , G. François a , S. Diethelm b , A. Nakajo b , and D. Bonvin a

- 59 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about '' - tarik-baldwin

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Model-Predictive Control (MPC) of an Experimental SOFC Stack:A Robust and Simple Controller for Safer Load Tracking

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

The HC-MPC Formulation Stack:

### Thank You! Stack:

### Extra Slides Stack:

G.A. Bunina, Z. Wuilleminb, G. Françoisa,

S. Diethelmb, A. Nakajob, and D. Bonvina

a Laboratoire d’Automatique, EPFL

b Laboratoire d’Énergétique Industrielle, EPFL

The Goal of This Talk Stack:

To demonstrate that the transient SOFC control problem can be handled very simply, yet robustly, while requiring littlecontrolknowledge and only a very basic model of the process.

The Goal of This Talk Stack:

To demonstrate that the transient SOFC control problem can be handled very simply, yet robustly, while requiring little control knowledge and only a very basic model of the process.

Outline of the Talk Stack:

- The System
- Basic MPC Theory
- Our “HC-MPC” Formulation
- Experimental Validation
- Concluding Remarks

The System Stack:

79% N2 21% O2

97% H2 3% H2O

Air

Fuel

- Inputs
- nH2: H2 flux
- nO2: O2 flux
- I: current

- Safety Constraints
- Ucell: cellpotential
- ν: fuel utilization
- λ: air excess ratio

- Performance
- πel: power demand
- η: electrical efficiency

Control Objective

Track the specified power demand while maximizing the efficiency and honoring the safety constraints.

6-cell

SOFC

Stack

Power

Furnace

Current

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency

Outline of the Talk Stack:

- The System
- Basic MPC Theory
- Our “HC-MPC” Formulation
- Experimental Validation
- Concluding Remarks

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency

Basic MPC Principles Stack:

B = f(a1,…,ap)

πel(new)

a5

a6

a7

a8

ap

a4

a3

a2

a1

πel(old)

t0+pΔt

t0

I = 30 A

I = 0A

t0

Δt

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Basic MPC Principles Stack:

πel=πel ,0 + BΔI + d

B = f(a1,…,ap)

πel(new)

d

πel,0

πel(old)

t0+pΔt

t0

I = 30 A

implement! (…then do it all again)

I = 0A

t0+mΔt

t0

Δt

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

MPC with Optimization Stack:

- MPC objective function
- Constraints: Ucell ≥ 0.79V, ν≤ 0.75, 4 ≤ λ ≤ 7

QP Transformation

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

MPC with Optimization Stack:

- MPC objective function
- Constraints: Ucell ≥ 0.79V, ν≤ 0.75, 4 ≤ λ ≤ 7

πel(high)

efficiency limited by Ucell

πel(mid)

efficiency limited by ν

πel(low)

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Outline of the Talk Stack:

- The System
- Basic MPC Theory
- Our “HC-MPC” Formulation
- Experimental Validation
- Concluding Remarks

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

- HC = “Hard Constraint”

nH2= 3.14mL

nH2= 10.0mL

ν= 0.75

I

Ucell= 0.79V

I = 30A

0

nH2

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

ν=0.75

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

The HC-MPC Formulation Stack:

ν=0.75

Ucell=0.79V

λ =4

λ =7

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Side-by-Side Stack:

- HC-MPC Solutions
- Weight Tuning
- Completely intuitive
- Practically no tuning
- Minimal validation

- Active Constraint?
- ν kept active
- Degradation?
- Doesn’t matter

- Violations
- Inequalities have direction
- Constraints are “hard”

- Weight Tuning

- Standard MPC Issues
- Weight Tuning
- Only partially intuitive
- Requires a good model
- Need validation

- Active Constraint?
- Must know πel(mid)
- Degradation!
- πel(mid) changes

- Violations
- Norms are directionless
- Constraints are “soft”

- Weight Tuning

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Intuitive Weight Scheme Stack:

- Bias Filter α

- Sufficient to normalize weights into 3 categories
- High Priority (w = 10)
- e.g.: power demand

- Standard Priority (w = 1.0)
- e.g.: efficiency (tracking active constraint)

- Low Priority (w = 0.1)
- e.g.: penalties on input moves (controller behavior)

- High Priority (w = 10)

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Side-by-Side Stack:

- HC-MPC Solutions
- Weight Tuning
- Completely intuitive
- Practically no tuning
- Minimal validation

- Active Constraint?
- ν kept active
- Degradation?
- Doesn’t matter

- Violations
- Inequalities have direction
- Constraints are “hard”

- Weight Tuning

- Standard MPC Issues
- Weight Tuning
- Only partially intuitive
- Requires a good model
- Need validation

- Active Constraint?
- Must know πel(mid)
- Degradation!
- πel(mid) changes

- Violations
- Norms are directionless
- Constraints are “soft”

- Weight Tuning

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Outline of the Talk Stack:

- The System
- Basic MPC Theory
- Our “HC-MPC” Formulation
- Experimental Validation
- Concluding Remarks

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Experimental Validation Stack:

Standard MPC

HC-MPC

η≈ 38%

η≈ 42%

η≈ 42%

standard

HC

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Standard MPC Stack:

HC-MPC

η≈ 38%

η≈ 42%

η≈ 42%

standard

input region

expansion

input region

contraction

HC

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Outline of the Talk Stack:

- The System
- Basic MPC Theory
- Our “HC-MPC” Formulation
- Experimental Validation
- Concluding Remarks

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Concluding Remarks Stack:

- The proposed HC-MPC is very effective as it:
- does NOT require a good model
- only four experimental step responses were used here

- has only one decision variable for tuning
- which is very intuitive

- minimizes oscillatory behavior and overshoot

- does NOT require a good model
- Potential Applications
- The above should hold for more complex systems
- + gas turbine
- + steam reforming
- + heat-load following

- The above should hold for more complex systems

Questions?

Experimental Validation Stack:

nH2: H2 flux nO2: O2 flux I: current Ucell: potentialν: fuel utilization λ: air ratio

πel: power demand η: efficiency p: pred. horizon m: cont. horizon B: dyn. matrix

Download Presentation

Connecting to Server..