Perspective on Process Control James J. Downs Advanced Controls Technology Eastman Chemical Company.

Perspective on Process Control

James J. DownsAdvanced Controls TechnologyEastman Chemical Company

Early History

Ktesibios (270 BC)

Water Clock

Early History

Edmund Lee (1745)

Windmill Fantail

Industrial Age

James Watt (1788) Centrifugal governor patented for the steam engine

Mathematical Age

James Clerk Maxwell (1831-1879)

On Governors. Proc. Roy. Soc. 16 (1868) 270-283.

• Stability Concept• Simple Mathematical Models• Importance of integral action• Linearization

Mathematical AgeStability Concept

"It will be seen that the motion of a machine with its governor consist in general of a uniform motion, combined with a disturbance which may be expressed as the sum of several component motions. These components may be of four different kinds:

1. The disturbance may continually increase. 2. It may continually diminish. 3. It may be an oscillation of continually increasing amplitude. 4. It may be an oscillation of continually decreasing amplitude.

The first and third cases are evidently inconsistent with the stability of the motion: and the second and fourth alone are admissible in a good governor. This condition is mathematically equivalent to the condition that all the possible roots, and all the possible parts of the impossible roots of a certain equation shall be negative."

Mathematical Age

Proportional Action Concept

"Most governors depend on the centrifugal force of a piece connected with a shaft of the machine. When the velocity increases, this force increases, and either increases the pressure of the piece against a surface or moves the piece, and so acts on a break or a valve.

In one class of regulators of machinery, which we may call moderators, the resistance is increased by a quantity depending on the velocity."

Mathematical Age

Integral Action Concept

"But if the part acted on by centrifugal force, instead of acting directly on the machine, sets in motion a contrivance which continually increases the resistance as long as the velocity is above its normal value, and reverses its action when the velocity is below that value, the governor will bring the velocity to the same normal value whatever variation (within the working limits of the machine) be made in the driving-power or the resistance."

Mathematical Age

1877 Vishnegradsky – stability1893 Lyaponov – stability of nonlinear differential equations1895 Heaviside – transient behavior of systems

1927 Black – negative feedback1932 Nyquist – design of stable amplifiers1938 Bode – frequency response

(Bell Telephone Laboratories)

Time Domain 𝑑𝑥𝑑𝑡

= 𝑓 (𝑥 ,𝑡 )

Frequency Domain L [𝑦 (𝑡 ) ]=𝑌 (𝑠)

Hardware Age

Hardware Age

Control Implementation Technology

• Pneumatic single loop controllers (3-15 psig standard)

• Electronic controllers (4-20 ma standard)

Hardware Age

Control Implementation Technology

• Pneumatic ingenuity

7216 Variable Ratio Regulators are used with nozzle-mix burners to achieve temperature uniformity while using minimum excess air. … A high quality stainless steel spring is used to bias 7216 Regulator air/gas ratio. As air rate is turned down towards low fire, gas rate drops faster, giving increasing percentages of excess air …

Migration to the Computer Age

Control Implementation Technology

• Block logic (PID, summer, selectors, digital points, ratio, cascade, etc.

• Control logic programs

• Distributed vs. Centralized Architecture

Computer Age

Control Strategy Technology

• What should be controlled ?• Simple variables, measurements• Computed combinations of measurements• Inferred measurements• Laboratory measurements

• How to control process variables• Single loop control• Cascade, override, multivariable, feedforward, etc.• Tuning, performance considerations

• Control Objectives• Migration from "hold constant" to "find optimum"

Today's Age

Control to Maximize Profit

• Control Objectives• Measures of profit• Real time changes to the profit function (pricing, demand, etc.)

• Process Constraints• Measureable/predictable, unpredictable• Current time or future time• Operation at process constraints

• Changing Targets• Maintaining good control when the target is always moving• Interface with supply chain management

• Managing Process Variability• Control strategy design

Today's Age

Models

A model in this context is a mathematical description of a process

• Linear / Nonlinear• Continuous / Discrete• Deterministic / Stochastic• First principle / Empirical

ProcessModel

Inputs: valve positions flow rates energy inputs

Outputs: temperature composition properties

Parameters

Today's Age

Models

Example: ( linear, no dynamics, continuous )

Process y = au + b

Inputs: u

Outputs: y

Parameters:a, b

b

Today's Age

Models

Example: ( linear, dynamic, continuous )

ProcessInputs:

Outputs:

Parameters: A, B, C

𝑑𝒙𝑑𝑡

=𝐴 𝒙+𝐵𝒖

𝒚=𝐶 𝒙

Today's Age

Models

Example: ( linear, dynamic, continuous, uncertainty descriptions )

ProcessInputs:

Outputs:

Parameters:A, B, C, N(µ, σ)

𝑑𝒙𝑑𝑡

=𝐴 𝒙+𝐵𝒖+𝐺𝒘

+

Coming Age

Models

Example: ( nonlinear, dynamic, continuous, known uncertainty description )

ProcessInputs:

Outputs:

Parameters: a, b, c, …

𝑑𝒙𝑑𝑡

= 𝑓 (𝒙 ,𝒖 ,𝒘 )

𝒚=𝑔 (𝒙 ,𝒗 )

Coming Age

Control of Uncertain Processes

Characterization of Uncertainty

• Mean, standard deviation (normal distribution)• Other distributions• Non stationary distributions

Characterization of Risk

• Determination of the cost of risk• Deciding the risk/reward tradeoff point

Coming Age

The PSUADE Uncertainty Quantification Project

Uncertainty quantification is defined as the

• identification (Where are the uncertainties?), • characterization (What form they are in?), • propagation (How they evolve during the simulation?), • analysis (What are their impacts?), and • reduction of ALL uncertainties in simulation models.

Coming AgeModels

Current research:

• Improved, more accurate models• System identification methods to develop models• Model reduction techniques• Mathematical methods to drive models to optimum points in an

optimum manner (given a mathematical description of 'optimum').

Optimizers exploit model weaknesses and can find poor,

undesirable answers

As solution techniques get

stronger we need better models

Coming Age

Process Uncertainty

• Models provide a template upon which to overlay process data

• Uncertainty descriptions coupled with models can suggest "best" answers in a probabilistic sense.

• Techniques for handling model size, complexity, unknown parameters, probability distributions, initialization, etc. are barriers

DeterministicWorld

ProbabilisticWorld

Coming Age

Process

ModelStructure

Extracted DataFit to Model

Structure

Uncharacterized Process

Information

Coming Age

Process Inputs

RefineParameterize

AnalyzeOptimize

Strategize InvertFilter

Add LogicClampLimit

etc., etc.

Coming Age

How should we describe the remainder of the process information ?Other process

information/behavior we don't know about

… 0100101110100110 …

µ,σ

∑𝑛=1

∞

( 𝑎𝑛 cos 𝑛𝜋 𝑥𝐿 +𝑏

𝑛 sin 𝑛𝜋 𝑥𝐿 )

Process information we

are not measuring.

Coming Age

• Measure of risk• Probabilistic answers• Stochastic/chaotic• Random behavior

Process Inputs

Other process information/behavior we don't know about

Final Thoughts

ComputeModel

InverseProcess

Model

DesiredState

ProcessOutput

Inputs: Outputs:

Estimate

Applications

Biological Systems• Diabetes• Drug dosing strategies• Virus spread• Predator/prey dynamics• Population demographics

Economics• Stock market• Fiscal policy• Supply/demand• Financial modeling

Questions ?

Final Thoughts

ComputeProcessInputs

ProcessDesiredState

ProcessOutput

Inputs: Outputs:

Final Thoughts

ComputeModel

InverseProcess

Model

DesiredState

ProcessOutput

Inputs: Outputs:

Estimate

Final Thoughts

ComputeModel

InverseProcess

Model

DesiredState

ProcessOutput

Inputs: Outputs:

Estimate

Final Thoughts

ComputeModel

InverseProcess

Model

DesiredState

ProcessOutput

Inputs: Outputs:

Estimate