Group of Process Optimization Institute for Automation and Systems Engineering

Technische Universität Ilmenau

Systems Optimization

Chapter 1: Introduction

Pu Li

pu.li@tu-ilmenau.de www.tu-ilmenau.de/prozessoptimierung

Modeling Simulation Control Optimization

Decision Support

Complex System

Process systems engineering

• Process modeling:

> Complex large-scale processes > Economic and information aspects > Nano-, bio- and molecular systems • Process optimization: > Dynamic optimization of large-scale systems > Optimization under uncertainty > Real-time optimization

• New application fields:

> Energy systems engineering > Water resources management > Biological (cellular and organ) systems > Mechatronic systems

Research incentives Challenges in process systems engineering

4

Cocks-oven-gas purification plant

What is the optimal operations strategy, so that the product specifications will be satisfied and meanwhile the operating costs minimized?

5

What is the optimal operating strategy, so that the environmental constrains will be satisfied and meanwhile the operating costs minimized?

Waste water treatment plant

6 Power plant

What is the optimal operating strategy, so that the power demand will be satisfied and meanwhile operating costs minimized?

7

8

Reactor- system

raw materials

stirred tank fixed-bed isotherm adiabat

Powerplant

fuels air water

Separation system

Distillationeextraction adsorption desorption

products by-products

Heat exchanger system

Process analysis:

9 Decisions: • Which units (colomns, reactors etc.) should be selected?

• How should these units be connected?

• How large should these units be?

• What should be the opertating point (pressure, temperature, etc.)?

Decision criteria: • Capital investment

• Costs of raw materials

• Safty issues

• Energy consumption

• Environmental impact

10 Heat exchanger design: cost minimization Flow A (high temperature TH) should exchange a certain amount of heat with flow B (low temperature TL). How large should the exchange area be?

On the other hand

According to Carnot:

Total costs = Equippment const + operating cost

Energy loss at the operation:

TU

11 Challenges (difficulties):

• Large-scale

• Nonlinear

• Combinatorial

• Dynamic

• Uncertain

Solution approaches: • Empiric / heuristic

• Thermodynamic principles

• Simulation

• Model-based mathematical / numerical optimization

Properties of the optimization problems in the process industry:

12

Optimization of the operating strategy of a batch reactor

13 Optimization of the operating strategy for a batch reactor

The chemical reaction:

A B C

Problem formulation:

mit

14 Solusion of the optimization problem:

Implementation of the results through the process control system.

0 0,2 0,4 0,6 0,8 1300

320

340

360

380

400

0 0,2 0,4 0,6 0,8 10

0,2

0,4

0,6

0,8

1

C(t)A

C(t) B

Optimal temperature strategy Trajectories of concentrations

The model and the model parameter should be verified!

15

• Process analysis Definition of the optimization task, analysis of optimization potentials,

and the degree of freedom

• Modeling Definition of the modeling spaces and assumptions, establishment of

model equations, simulation, model validation

• Problem formulation Definition of optimization variables, mathematical formulation of the objective function, equality and inequality constraints

• Solution with optimization approaches / software Adaptation to the approach / software, initialization, scaling and

fine tuning

• Implementation of the optimization results Result analysis, off-line or on-line realization

Steps to carry out process optimization

16 On-line Process Optimization The operating point should be adaptively changed due to changes of demand, feedstock, prises etc.)

Process management (Computer-Network)

Process optimization (PC oder Workstation)

Production planning Information from the plants

Process control (Process control system)

Optimal setpoints Process information

Prozess Disturbances

Process measurement

Manipulated variables

Market conditions

Plant

Sensor

Control System

Model Based Optimization

Process Model

Process Disturbances

Model Uncertainties,

Setpoint Changes

Parameter Estimation Database

Data Reconciliation

Measurement Errors

s y

θ ŷ

Changes in Prices/ Process Objectives

u

On-line process optimization

Farbe, Li, et al., Ind. Eng. Chem. Res., 2003

Stochastic Optimization under Uncertainty

20 4 6 8 10 12 14 16 18 22 24Look-ahead time [Hours]

2

2.5

3

3.5

Mea

sure

d va

lue

[MW

]

20

4

σ

PrL0

In process design and operation uncertainty has to be taken into account:

Uncertain conditions: • market • raw material • atmosphere • demand

Uncertain model parameters: • tray efficiency • activity of catalyst • kinetic parameters • heat transfer coefficients

Under the uncertainties an optimal and reliable solution is to be developed.

Chance Constrained Optimization • The decision should be

neither conservative nor aggressive.

• The restrictions will be satisfied with a desired probability (confidence) level.

• The expected value of the objective function will be optimized.

• A robust decision is to be achieved (not depending on the realization of the uncertain variables).

20 Mathematical solution approaches:

Applications:

Part 1: Steady-state optimization

•Linear programming (LP) •Mixed-Integer linear programming (MILP) •Nonlinear programming (NLP)

Part 2: Dynamic optimization

•Indirect methods •Direct methods Part 3: Stochastic optimization under uncertainty

•Chance constrained optimization

• Chemical engineering • Energy engineering • Water systems engineering • Systems biology

21 Lectures (40 hours):

Projects (5 hours):

• Problem formulation

• Solution approaches

• Application examples

(Topics will be distributed)

• Learning by doing

• Software (GAMS)

• Solution of practical problems

22 References: L. T. Biegler Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes SIAM, 2010

T. F. Edgar, D. M. Himmelblau Optimization of Chemical Processes McGraw-Hill, New York, 1989

Teo, K. L., Goh, C. J., Wong, K. H A Unified Computational Approach to Optimal Control Problems John Wiley & Sons, New York, 1991

C. A. Floudas Nonlinear and Mixed-Integer Optimization Oxford University Press, 1995

L. T. Biegler, I. E. Grossmann, A. W. Westerberg Systematic Methods of Chemical Processes Design Prentice Hall, New Jersey, 1997

J. Nocedal, S. J. Wright Numerical Optimization Springer, 2006