Multiple Model Predictive Control (MMPC) for Nonlinear Systems and - - PowerPoint PPT Presentation

Multiple Model Predictive Control (MMPC) for Nonlinear Systems and Improved Disturbance Rejection

• B. Wayne Bequette
• Motivation & Tutorial Overview
• Multiple Model Predictive Control
• Nonlinear Processes
• Disturbance Rejection
• Summary

Chemical and Biological Engineering

Nonlinear Behavior: Steady-state

Input Multiplicity

10 20 30 40 50 60 70 80 50 60 70 80 90 100 110 120 130 140 150

Output Multiplicity (hysteresis)

T Fj

1 2 3 4 5 0.2 0.4 0.6 0.8 1 1.2 Van de Vuuse Reactor, Figure M5-2, page 609 dilution rate, 1/min

• conc. B, mol/liter

Two different input values yield the same output One input can yield three different output values

t k

current step

setpoint

y

actual outputs (past)

P

Prediction Horizon past control moves

u

max min

M

Control Horizon

past future model prediction

t k+1

current step

setpoint

y

actual outputs (past)

P

Prediction Horizon past control moves

u

max min

M

Control Horizon

model prediction from k new model prediction

• Constraints
• Multivariable
• Time-delays
• Objective function?
• Optimization technique?
• Model type?
• Disturbances/mismatch?
• Current and Future
• Initial cond./state est.?

MPC

“hidden slide” provided for additional background

Our Approaches to Nonlinear MPC

• Quadratic Objective Function
• Models

– Fundamental: numerical integration or collocation – Fundamental with linearization at each time step – Multiple model – Artificial neural network

• State Estimates/Initial Conditions

– Additive output disturbance (e.g. DMC) – Estimation horizon (optimization) – Extended/appended state Kalman Filter

• Importance of stochastic states

Intuitive Nonlinear Model-based Strategy

( ) ( )

x g y u x f x = = , 

( ) ( )

k k k k k t k

x g y u x F x

s

ˆ ˆ , ˆ ˆ

1 | 1 1

= =

− − −

Integrate model from time step k-1 to k Model equations Obtain plant measurement

k

y

1 |

ˆ

−

− =

k k k k

y y d

( ) ( )

k P k k P k P k P k t P k

d x g y u x F x

s

+ = =

+ + − + − + +

ˆ ˆ , ˆ ˆ

| 1 1

Integrate model from time step k to k +P (based on hypothetical control moves)

( ) ( )

k k k k k k t k

d x g y u x F x

s

+ = =

+ + + 1 | 1 1

ˆ ˆ , ˆ ˆ

to Choose hypothetical set of current and future control moves

1 1

, , ,

− + + P k k k

u u u 

Evaluate objective function and repeat until optimum is obtained Calculate model error (additive output disturbance)

Additive Disturbance Assumption

Model converges to different steady-state than plant (compensated by additive disturbance term)

Non-Convex Problem

Sistu and Bequette, 1992 ACC

M = 1, different values of P

EKF-based NMPC (Lee & Ricker, 1994)

• Nonlinear Model, integrate from step k-1 to k
• State Estimation: Extended Kalman Filter

– Linearized at each time step – Find best state estimate at time step k

• Prediction

– One integration of NL ODEs based on set of control moves (unforced or “free response”) from step k to k+P – Perturbation (linear) model - effect of changes in control moves (forced)

• Optimization

– QP, since linear model is used

Can use linear state- space KF-MPC code!

Motivation for Multiple Linear Models

• Development time for fundamental models

– Difficulty with physiological systems

• Much data required for artificial neural

networks

– Problems with “overfitting” and extrapolation

• At particular operating points, linear models

are often a good description

– How to switch between models?

Multiple Model-based Control

Multiple Model Adaptive Control (MMAC)

Athans et al. (1977) – LQG, Jet aircraft control Roy, Kaufman - Drug infusion control Schott, Bequette (1997) – PI, CSTR

Multiple Model Predictive Control (MMPC)

Rao et al. (2001, 2003) Drug Infusion Control Aufderheide & Bequette (2003) Nonlinear CSTR

First, a Concise Review of Linear MPC

“hidden slide” provided for additional background

Step Response & Additive Output

1 |

ˆ

−

− =

k k k k

y y d

Correction term

k k k k k

d y y + =

−1 | |

ˆ ˆ

The “corrected prediction” is set equal to the measured output The “corrected prediction” for jth future step is (step response form)

k k k

y y =

|

ˆ

“deadbeat” observer



term correction moves control past

• f

effect 1 1 moves control future

• f

effect 1 |

ˆ ˆ

j k j N k N N j i j i k i j i j i k i k j k

d u s u s u s y

+ + − − + = + − = + − +

+ + Δ + Δ =

∑ ∑

             

1 | 1

ˆ ˆ ˆ

− − + +

− = = = =

k k k k j k j k

y y d d d 

constant additive disturbance measured output model predicted output free response forced response

“hidden slide” provided for additional background

Problems with “Classical MPC” (e.g. DMC)

• Finite Step/Impulse Models Limited

– Many parameters (~50 for each input-output relationship) – Limited to open-loop stable processes (there is no corrective feedback to model states)

• Additive Output Disturbance Assumption

– Poor performance for input step disturbances – No explicit measurement noise trade-off

The most common criticism of MPC (Shinskey, 2002)

“hidden slide” provided for additional background

State Space Models & State Estimation





[ ]



a k a a a k a a k

x k k C k k Γ x k k Φ d x k k

d x C y u Γ d x I Γ Φ d x ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

+

+ +

          

1

1 1

k k k d k k k

x C y d u x x

1

= Γ + Γ + Φ =

+

Appended state formulation

Γ = Γd

For perturbations to manipulated inputs

Assume disturbance propagation

k k

d d =

+1 “hidden slide” provided for additional background

State Estimation Problem





[ ]



k x k k C k k Γ w k Γ x k k Φ d x k k

v d x C y w Γ u Γ d x I Γ Φ d x

a k a w,a a a k a a k

+ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

+

+ +

             

1

1 1

Random walk

( )

a k|k a k k a k|k a k|k k a a |k k a a k|k

x C y L x x u Γ x Φ x

1 1 1 1 1 1

ˆ ˆ ˆ ˆ ˆ

− − − − − −

− + = + =

Kalman Filter

k k k

w d d + =

+1 Prediction Correction

“hidden slide” provided for additional background

Offset-Free Performance

• Next few slides present conditions for offset-free

performance

• Unmeasured disturbances estimated as either state
• r output disturbances
• State observer techniques can then be used

Ref: Muske & Badgwell, J. Proc. Cont., 12: 617-632 (2002)

“hidden slide” provided for additional background

Disturbance Models





[ ]



a k a a a k a a k

x k k C k k x k k d x k k

d x C y u d x I d x ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡Γ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Γ Φ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

Γ Φ + +

+

          

1

1 1





[ ]



a k a a a k a a k

x k k C p k k x k k x k k

p x G C y u p x I p x ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡Γ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡Φ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

Γ Φ + +

+

            

1

1 1

Additive Output Disturbance State or Input Disturbance

I G p =

DMC:

“hidden slide” provided for additional background

Disturbance Models



[ ]

⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡Γ + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ Γ Φ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡

Γ Φ + + + k k k C p k k k k k d k k k

p d x G C y u p d x I I p d x

a a a

       

1 1 1

General Input and Output Disturbances

Ref: Muske & Badgwell, J. Proc. Cont., 12: 617-632 (2002)

“hidden slide” provided for additional background

State Estimator



⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ − ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡Γ + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ Γ Φ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡

− − − − − − − Γ − − − − − − Φ − − − 1 | 1 | 1 | 1 | 1 | 1 | | | | 1 1 | 1 1 | 1 1 : 1 1 | 1 | 1 |

ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ

k k k k k k a k p d x k k k k k k k k k k k k k k k k k k k d k k k k k k

p d x C y L L L p d x p d x u p d x I I p d x

a a

    

Ref: Muske & Badgwell, J. Proc. Cont., 12: 617-632 (2002)

For offset-free performance: # disturbances = # outputs, and augmented system must be detectable

Deterministic or stochastic

• bserver design

“hidden slide” provided for additional background

Problem: Unmeasured Step Input Disturbance

5 10 15 20

• 0.1

0.1 0.2 0.3 y time DMC vs. KF-MPC DMC KF-MPC 5 10 15 20

• 1.5
• 1
• 0.5

0.5 u time DMC KF-MPC

DMC: additive output disturbance assumption (bias) KF-MPC: appended state, estimated step input disturbance

“hidden slide” provided for additional background

MPC Plant Weight Calcs

Setpoints Inputs Outputs wk (weights)

Model Bank State Estimation

rk yk uk

1 |

ˆ

− k k i y

a k k ix |

ˆ

k k i y |

ˆ

Structure of MMPC

1 − k

u

1 | 1 ˆ − k k

y

1 | 2 ˆ − k k

y

1 |

ˆ

− k k n y

1 | 2 2 1 | 2 1 2 1 | 1 2 2 1 | 2

ˆ ˆ ˆ ˆ

− − − − − −

= Γ + Φ =

k k k k k k k k k

x C y u x x

• Each of the n linear models represents the system at a specified
• perating condition
• A model predicted output is calculated for each model using the

current manipulated input Model Bank Details

1 | 1 1 1 | 1 1 1 1 | 1 2 1 1 | 1

ˆ ˆ ˆ ˆ

− − − − − −

= Γ + Φ =

k k k k k k k k k

x C y u x x

1 | 1 | 1 1 | 1 1 |

ˆ ˆ ˆ ˆ

− − − − − −

= Γ + Φ =

k k n n k k n k n k k n n k k n

x C y u x x

• Need a way to account for model uncertainty and mismatch.

Step input disturbance

State Estimation

k i k i i k i k i k i k i k i i k i

d x C y d d u x x + = = Γ + Φ =

+ + 1 1

k i i k i k i k i i k i

x C y u x x = Γ + Φ =

+1

k i i k i k i k i k i d i k i k i i k i

x C y d d d u x x = = Γ + Γ + Φ =

+ + 1 1

Additive output disturbance

[ ]

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Γ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Φ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

+ + k i k i y i k i k i k i k i x i k i k i

d x G C y u d x I G d x

1 1

= Γ =

x d i x

G G

Step input Additive output

I G G

y y

= = 0

Step input Additive output

• Kalman predictor/corrector equations

State Estimation

Prediction Correction Updated output prediction

k a k i a i k i k i w i k a i a k i a i a k i

v x C y w u x x + = Γ + Γ + Φ =

+ , 1 1

ˆ

[ ]

k k i k i y i k i k i w i k i k i k i x i k i k i

v d x G C y w u d x I G d x + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Γ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Γ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Φ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

+ + 1 1

( )

a k k i a i k k i a k k i a i i a k k i a k k i k a i a k k i a i a k k i

x C y x C y L x x u x x

| | 1 | 1 | | 1 1 | 1 1 |

ˆ ˆ ˆ ˆ ˆ ˆ ˆ = − + = Γ + Φ =

− − − − − −

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = I L

i

gain Kalman L

i

=

Step input Additive output

Weight Calculation Model residual Bayesian probability, ith model

k k i k k i

y y

|

ˆ − = ε

( ) ( )

∑

= − −

Λ − Λ − =

n j k j k j i T k j k i k i i T k i k i

p p p

1 1 1

5 . exp 5 . exp ε ε ε ε

⎪ ⎪ ⎭ ⎪ ⎪ ⎬ ⎫ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≤ > = ∑

=

δ δ

k i k i n j k j k i k i

p p p p w

1

Weight, ith model

Model Predictive Control

• “Model average” for the output prediction

∑

= + +

=

n i k j k i k i k j k

y w y

1 | |

ˆ

• Quadratic objective function

( ) ( )

U W U Y R W Y R

u T y T

Δ Δ + − − = Φ min

• Constraints on inputs and outputs

Analytical Solution Quadratic Program (QP)

Van de vuuse isothermal reactor A B C A+A D CAin F CB F

Constant V,T, ρ Region with RHP zeros (nonminimum phase behavior) Connection between IM and RHP zeros: Sistu & Bequette, Chem. Eng. Sci. (1996)

Feed Concentration Disturbance

MMPC (u) EKF- based NL-MPC (u) CB (y)

Disturbances & Propagation Into Future

• Output step

– Generally poor assumption for chemical processes

• Input step

– Improved performance for many processes

• Input ramp

– Motivated by experience with diabetes problems

• Pulse

– Duties performed infrequently (shift change, etc.)

• Periodic

– Poorly tuned upstream controllers, diurnal variations

Step, Ramp, Generic





[ ]



k x k k C k k Γ w k Γ x k k Φ d x k k

v d x C y w Γ u Γ d x Γ Φ d x

a k a w,a a a k a a k

+ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

+

+ +

              1

1

1 1

[ ]

k x k k k C k k Γ k Γ x k k k Φ d x k k k

v d d x C y w u Γ d d x Γ Φ d d x

a k a w,a a a k a a k

+ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Δ

+

+ + +

                               1 1 1 1

1

1 1 1







[ ]



k x k k C k k Γ w k Γ x k k Φ w d x k k

v d x C y w u Γ d x Γ Φ d x

a k a w,a a a k a a k

+ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Γ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Φ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

+

+ +

          

1

1 1

Ramp Disturbance

5 10 15 20

• 0.02

0.02 0.04 0.06 0.08

time y DMC vs. KF-MPC (ramp) (Q=100,R=1), ramp disturbance

5 10 15 20

• 3
• 2
• 1

time u

DMC KF-MPC DMC KF-MPC

deviation variables

Unmeasured Feed Concentration

5 10 15 20 2 4 6 8 10 12 14 16 18 20

feed conc, actual & estimated, KF (Q=100,R=1) time Caf

deviation variables

Periodic Disturbance

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

Af B A B A

C V F C C C C 117 . 1 5714 . 7 2381 . 2 8333 . 4048 . 2   ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ d C C C C

Af Af Af Af

1

2

    ω

Poles on imaginary axis

Results in sin variation in feed concentration

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − + ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − = ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ d V F C C C C C C C C

Af Af B A Af Af B A

1 117 . 1 7 1 2381 . 2 8333 . 5714 . 4048 . 2

2

      ω

Appended state form

DMC vs. KF-MPC

5 10 15 20

• 0.04
• 0.02

0.02 0.04 0.06 time y DMC vs. KF-MPC (Q=100,R=1), actual plant outputs DMC KF-MPC 5 10 15 20

• 0.2
• 0.15
• 0.1
• 0.05

time u DMC KF-MPC

deviation variables

Feed Concentration Estimate

5 10 15 20

• 0.2

0.2 0.4 0.6 0.8 1 1.2 1.4 feed conc, actual & estimated, KF (Q=100,R=1) time Caf

deviation variables

Estimate Actual

Numerous Potential Disturbances

• Current Practice

– Choose most important disturbance(s) to estimate & reject (number of disturbances = number of measurements)

• Model Bank

– Each model associated with a different type of disturbance – Weighting/Blending or Switching between models

Disturbance Estimation - Framework

MPC Plant Weight Calcs

Setpoints Inputs Outputs wk (weights)

Dist. Bank State Estimation

rk yk uk

1 |

ˆ

− k k i y

a k k ix |

ˆ

k k i y |

ˆ

Primary difference is in the “disturbance bank”

Disturbance Bank Structure

1 − k

u

1 | 1 ˆ − k k

y

1 | 2 ˆ − k k

y

1 | 4 ˆ − k k

y

Model 1, Add Output Model 1, Step Input Model 1, Periodic Model 1, Ramp Input

1 | 3 ˆ − k k

y



[ ]

                  

a k k a a a k k a a k k

x k k k k C k k k Γ x k k k k Φ w d x k k k k

d x C y u Γ d x Γ Φ d x

1 | 1 | 1 | 1

| 1 | 1 1 | 1 ˆ 1 | 1 1 | 1 ˆ 1 | 1 |

ˆ ˆ ˆ ˆ ˆ ˆ ˆ

− − − +

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ Φ = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡

− − − − − − − − − −

Setpoint Tracking (No Disturbances)

Additive Output Disturbance

Measured

• utput

Weights

Step Input Disturbance

Measured

• utput

Weights

Ramp Input Disturbance

Measured

• utput

Weights

Periodic Input Disturbance

Measured

• utput

Weights

Step + Periodic Input Disturbances

Measured

• utput

Weights

Presentation Summary

• Nonlinear Model Predictive Control

– Limitations to DMC formulation – State estimation-based approaches – Multiple linear model-based approaches – Formulation for different disturbances

Acknowledgments

• Jing Sun (2011)

– China

• Matthew Kuure-Kinsey (2008)

– Cargill

• Brian Aufderheide (2002)

– University of Trinidad and Tobago

• Ramesh Rao (2000)

– ASPENTECH

• Clem Yu (1992)

– Baxter

Recent Applications of MMPC

• Integrated Gasification Combined Cycle

(IGCC) Power Plants

– Carbon Capture case

• ICU Blood Glucose Control

IGCC

• IGCC Power Plant is a complex system to simulate

– Significant reworking of steady-state flowsheet required adding plant details and dynamic behavior – 300 Units & 450 Streams – 80,000 equations solved – dynamic simulations

• Linear MPC is a powerful tool to control complex plants

– Hierarchical Control Structure Design – Load Following / Disturbance Rejection – Centralized Approach is better suited for following load-demand – Negative effect on controllability and robustness w/ increasing level of interactions

• Limitations of this research

– Simplifying assumptions on some units – Proprietary equipment details/ lack of validation data – Workaround for software bugs/limitations

IGCC Summary

Priyadarshi Mahapatra Ph.D., 2010; NETL

Fuel Cell Systems

– Combined heat & power – Nonlinear dynamics & control – Stack condition monitoring – Real-time optimization – Nature-inspired membrane and catalyst design (Marc-Olivier Coppens)

Electric power Matthew Kuure-Kinsey (Dec ‘08) Judy O’Rourke (Dec 2008) Jeff Marquis (w/Coppens) Matt Titus

Closed-loop Artificial Pancreas

Controller Sensor pump subject Glucose setpoint

u y r

Meal knowledge: Feedforward Feedback Insulin infusion rate Glucose sensor signal

Hyunjin Lee Now at Shell Development Jing Sun Ruben Rojas Fulbright Scholar Venezuela Fraser Cameron