SIMULATION MODELLING OF THE DECISION-MAKING ACTIVITY OF THE AUTOMATED CONTROL SYSTEMS OPERATORS USING NONLINEAR ELEMENTS

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Nina Rizun Yurii Taranenko

Alfred Nobel University, Dnipropetrovsk

SIMULATION MODELLING

OF THE DECISION-MAKING ACTIVITY

OF THE AUTOMATED CONTROL SYSTEMS OPERATORS USING NONLINEAR ELEMENTS

Introduction

The development of modern automated control systems, the complication of systems and technology of hardware components, the extensive usage of computer technology in the organization and management of production process lead to an increased human’s role in management and restructuring of his activity [Timo07, Pavl07].

Thus, on the one hand, the following is still typical for automated control systems operators:

– efficient type of thinking, acquiring extended number of specific characteris- tics (indicators), which describe the particular conditions for the implementa- tion of the thought process;

– methods that are involved in the process of thinking and interpretation of op- erator’s choice (the decision), the main of which are the following: the close, actually transforming into unity, connection between perception and compre- hension of the rapidly changing information and conditions of the situation;

decision often merges with the process of its implementation;

– decision-making process is increasingly fraught with a stressful situation, characterized by unstructured, incomplete and at the same time congestive contradictory initial information coming;

– decision-making process is increasingly associated with rules of strictly lim- ited time.

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Nina Rizun, Yurii Taranenko 158

On the other hand, primary modes of work of the automated control systems operators are still the following [Stre01]:

– normal conditions (the operator only monitors the technological process, without interfering in it);

– emergency conditions (operator works in semiautomatic or mechanized mode, much depends on the accuracy of its sensorimotor actions and ability to assess the situation);

– boundary conditions – technological process still goes on within the pre- scribed limits, but is already close to its borders (problem statement – keep the process within required parameters of the technology);

– “free” conditions – the operator constructs new mode of working (task – the empowerment of operating system, saving of the material part, energy and own forces).

Balance and order in the above-mentioned provisions can make a modern decision-making theory, which divides the situations that require decisions into two categories: programmed and unprogrammed:

1. Programmed situations – are associated with the solving of routine, repeti- tive and well-structured problems, based on pre-established rules, regula- tions, as well as on operator’s experience and technical knowledge.

2. Non-programmed situations – are associated with the occurrence of uncer- tainty. They are characterized by semi-structured and unstructured problems.

Solutions, which have been received in the non-programmed situations, con- tain the risk. These solutions require specific personal and professional quali- ties and creativity.

In this case the automated control systems operator, depending on interpretation of the current situation, can prefer one of the following models of decision-making: rational; bounded rationality; intuitive [Kahn94, StWe99].

Rational decision-making model defines the solution as a result of an or- dered thought process and based on the notion of discretionarity. Discretionary actions of a person are those [Kahn94] based on deliberation, which includes comparison of the available alternatives to these actions explicitly. In this case the selection’s criteria of the preferred embodiment are usually set in advance, and the solution (the chosen alternative) is the most competitive (optimal) for specific circumstances.

The bounded rationality decision-making model was proposed by Herbert Simon. Instead of discretionary it is presupposed to use the heuristics, which could be described as follows: a set of prescriptions connected with desired (for- bidden) patterns of behavior, that emerged as a result of personal professional

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SIMULATION MODELLING OF THE DECISION-MAKING… 159

experience and practical skills of problems solving, and which have the similar initial conditions and prerequisites, and which are used in situations, when the rational decision-making model cannot be used as a „soft” option of rationality in a situation of individual choice.

Thus, bounded rationality is an information behavioral prerequisite for modeling for individual solutions. However, if the time selected for a decision- making is not enough to perform the comparison or none of the template situa- tions are suitable to describe the real situation, it is possible to use the intuitive decision-making model.

Intuitive decision-making model is based on the usage of “internal intui- tion”, common sense, associative and logical thinking, professional and emotional experience, impressions. The decision-making is equally (or differently) influenced by the knowledge, experience, motivational structure, purpose, life principles and values of the decision, and by the limited timeframe decision.

The taxonomy of the specific operational thinking, depending on the deci- sion-making models [Beac78, Chri09] and the main conditions of automated control systems operators, is formulated and presented by the author in Table 1.

Table 1 Indicators of Operational Thinking

Depending on Decision-Making Models

Indicators

Conditions of Operator’s Activity

Normal Conditions

Boundary Conditions

Emergency Condi- tions

“Free” Conditions Decision-Making Models Absolutely Rational Bounded

Rationality Intuitive

1 2 3 4

Capacities Completeness of infor-

mation Complete Incomplete Arguable

Structuring of the prob-

lem Structured Semi-Structural Nonstructural

Speed Deliberate Rapid Instant

Goal Clear Fuzzy Competing

Indeterminacy Certainty Risk Uncertainty

Techniques

Problem Processing Problem Solving Problem Resolution Problem Finding

Accuracy High Sufficient Low

Tools Value Heuristic Judgment

Options Difference Weighted Acceptable Indistinguishable

Situational Awareness Details Patterns, Clusters Big Picture

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Table 1 cont.

1 2 3 4

Accountability Statistics, Analytical

Tools Pre-Formulated Rules

Perception, Mental simulations,

Feelings

Experience Not necessarily Embedded in Direct

Habit

Embedded in Direct Experience

Emotional Level Emotion Free Legitimate Role

for Emotions

Emotionally Associative

Effort Requires Cognitive

Effort

Requires Developed a Range of Successful Adaptive Strategies

Appears Effortless

Choice

Metrics Numerative Good enough Failure or Success

Time Horizon Present The Near Future Future

Level of Detail Detailed Grouped Aggregate

Decisions Formulation Prescriptive Suggested Descriptive

Nature Objective Subjective “Gut Feeling” Based

Conscious Level Conscious Traditional Unconscious

Creativity Creativity Free Creativity Free Creative

Decisions Optimal Satisfied More Relevant

1. Problem Statement

High demands to the operator’s efficiency and reliability as elements of a closed loop of the automated control systems bring to the fore the problem of investigation of human intellectual activity with the purpose of enabling clarifi- cation of the main behavioral characteristics of an operator in the decision- making process and making recommendations on the classification and identification of operators based on degree of their compliance to certain required procedures/methods of decision-making.

It is obvious that the most objective results of evaluation of the human intellectual processes can be obtained on the basis of experimental studies of their activity directly at the workplace. However, such research is almost impossible due to high economic expenditures.

Development of analytical models of operator’s intellectual activity is often difficult due to the lack of adequate methods for formalized description (strict algorithm) of this processes and the inability to take into account all the factors influencing the process.

Authors [Pavl05, Zhab07, Pupk74, Youn79, Korm01, Rizu12, Rizu2013a, Rizu13] carried out a general analysis of human behavior as an element of information and technical systems with the use of Automatic Control Theory:

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The main tool for the study of operator’s behavior as a closed-loop subsystem is its description by means of the transfer function, described in the research results of the following scientists: L. Russell, 1960; J. Elkind, 1964; Anastin, 1960; D. Makruera, E. Krendel, 1959; M.Silvestrov, 1984 [Korm11]. The most widely used are the following quasilinear models: J. Henderson model

s 2

2

1 e

s ) Ts 2 s T (

) s ) T

s (

W ⁻^τ

ξ +

= k(1+

, D. Makruera and E. Krendel model

s 2 1

3 e

) s T 1 )(

s T 1 (

) s ) T

s (

W ⁻^τ

+ +

= k(1+

, and also the extended and transformed model of the automated control systems’ operator, based on the previous models.

However, from the author’s point of view, unresolved problems in parts of these models are as follows:

1. During the development of these models authors take the preconditions of good structuring and definition of human-machine systems as the basis and tend to ignore the leading role of a human in situations of uncertainty, as well as the elements of subjectivity, which are added to output and input of sys- tem.

2. The object of operator’s activity analysis, which is taken into account during mathematical modeling, is the dynamics of operator’s behavior as a closed- loop subsystem: the average time of free-error operation, failure frequency, mean time to repair, availability factor, the probability of timely fulfillment of tasks (in the stages of input perception and decision-making) as well as the inertia of its neuromuscular mechanism (in the stages of his activity). But the emphasis on the specificity of the operator’s intellectual activity processes is in different situations absent, leading to the making and implementation of concrete solutions for transforming the input information signal.

In order to analyze the possibility of using the mentioned quasilinear models of operator’s behavior for interpreting the features of his intellectual activity processes, a simulation model was developed by authors with the use of the MathCad. For these purposes it was suggested that: the simulation of Rational Decision-Making Model as a process of performing a certain number of stages of logical analysis of the problem by decomposing the original problem into simpler components and gradual approximation to the desired solution could be accomplished by using harmonic exponentially damped cosine signal

) t cos(

e A ) t (

x = ⋅

⁻^γ^⋅^t

⋅ λ ⋅

_.

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1

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(8)

In the view of the analysis of the subjective influence of the operator to input signals the main results are expressed in the phase and amplitude of the signal shift (delay). It may correspond to different degrees of decision-making success from the given (optimal) time as well as from the degree of processing (analyzing) of the possible alternatives.

The advantage of J. Henderson operator’s behavior model with relation to con- trol quality is the presence of an ideal integrator term. Due to this fact with minimal lag (instant response to an input signal) and with certain values of the time-constants it is possible to provide the fairly accurate reproduction of input cosine signal.

1.3. Simulation of the Operator’s Making-Decision Activity as a PID Controller

Basic operator’s behavior model as an element of a closed-loop system is the so-called accompanying tracking, in which he sees an input signal and a sig- nal about the current condition of a managed object. The operator’s purpose in this situation is to keep the difference between these signals close to zero.

The authors suggest the concept of interpretation of “automated control systems operator’s intellectual activity within the decision-making as a process of correspondence (maintenance) to the adjusted (required) setpoint level of the set problem solving (optimal, sufficient solution”) [Rizu13, p. 13-15].

In this view the authors propose the hypothesis that: basic processes of the operator’s decision-making activity could be adequately simulated and identified by the transient processes of the proportional-integral-derivative (PID) controller.

Mathematical form of the PID-algorithm is:

⎟⎟⎠

⎞

⎜⎜⎝

⎛ + ⋅ +

⋅

=^K ^e⁽^t⁾ _K¹

∫

^e⁽^t⁾^dt ^K ^de_dt⁽^t⁾

) t (

u _d

t

I o P

(1)

Authors propose the following interpretation of the PID-controller transfer function coefficients: Kp – the level of operator’s personal characteristics, which are necessary for solving this type of problem (confidence, endurance, stamina, ability to control the situation, persistence); KI – the problem domain awareness level; Kd – speed of logical operations performance.

Taking into account the main purpose of PID-controller – operator’s activities for keeping the setpoint measured parameter – these analogies similarly allow us to identify the main stages of decision-making in accordance with the given instruc- tions and algorithms in the standard (programmed) conditions with a clearly defined only one correct (optimal) solution. This concept corresponds to the inter- pretation of the automated control systems operator’s intellectual activity as a PID- controller in the conditions of using the rational decision-making model.

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t p

F

m p

−

− tual pon

W5 H(t

. t) + Fig.

Fig.

mak pare

− a f o

− p b t t d g s t

λ:

R l ac nent

5 s( ) t)=W

+0.0 5. S

6. T d

Th king ed w acc fect of r pres ble ters tive dec gor sien the

=

esu ctivi tiall

:=

W5(t 0015 Simu

Tran diffe

he g pr with oun t, b rece sen and s, w e (p cisio rithm

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0.05

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Td Kp t)^.W 5615 ulati

T nsien feren

adv roc h pr ntin but a

eipt nce d g whic prof on), m o char gnal

5

S

of as a dam

d:=

+T W6(s)

52 ion m

Td:=

nt ch nt va

van ess rev ng th

also t of

of grad

ch c fess , bu of d ract l to

SIM

the a PI mped

= T1 Td s⋅

)^. in

mod

=1 T harac alues

ntag es o iou he a o pr

the sop dual cou sion ut n deci teri

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e sim ID- d co

Ti:=

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Ti:=3 a) cteri s of

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2 x(

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ctua

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co d P 1-4 lity on- n;

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OF T

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wn

t ( ):=

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al ac

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THE

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in F

= K s+ λ

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cont acte Fig

Kp e⋅ ⁻ λ

λ + )

05t.

ty m

lectu

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the e pr g p mode

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utom de n th

CISI

trol eris gure

λ

− t⋅

)² cos(

mode

T ual a

an olle e fol rese proc el m

on on o king

mat elay he a

ION

l sy stic es 5

t⋅cos

Δ (2.0

el as

d:=1 activ

n an er tr llow ence

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N-MA

ystem usi , 6.

s(ω

Δ( )t

. t)

s PID

1 Ti vity

nalo rans win e no s w nag e ch a hi havi repe rom mpt

AKIN

ms ing

⋅ )t

:=

– 1.

D-co

:=8 b) mod

ogy sien ng:

ot o with

em han ghe ing etit m th

toti NG…

op inp

0 .937

ontro

Kp:

del a

be nt’s

only res

ent ngin er d the ion he v

c a

…

era put

7539

oller

:=5

as PI

etwe pro

y of spec

an ng o degr eir n of

view appr

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9^.e^-0.

r

ID-c

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f the ct t

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roxi

’s in rmo

5 t .

cont

n de sse

e de to th

mor ts p

of wn s

e gi of th

ima nte onic

sin(

trolle

ecis s, c

elay he t

re fl para sub styl iven he t atio

16

llec c ex

2.0

er fo

sion com

y ef tim

flexi ame bjec le o n al tran on o 65

c- x-

.

or

n- m-

f- me

i- e- c- of

l- n- of

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However, the unresolved part of the problem in this solution is the absence of interpretation and analysis of the divergent PID-controller transient process, which could be interpreted as a lack of ability to make a decision using well- known logic algorithms – as a result of a high degree of uncertainty of the prob- lem and/or lack of information, time constraints.

According to the above-mentioned analysis results (Table 1), decision- making in non-programmed situations requires form the operator the nonstan- dard decision-making methods, based not only on logic, but on intuition, professional experience and “gut feeling”.

Thus, the problem of identifying the decision-making process and studying the dynamic behavior of the automated control systems operator in the conditions of uncertainty and risk is a topical scientific problem, allowing, on the one hand, to as- sess the reliability and stability of the management system, on the other – to formal- ize a set of qualitative and quantitative requirements for professional operator skills.

Continuing the analogy between human intellectual activity and the Auto- matic Control Theory, the authors proposed the following required analysis and verification of the preconditions and hypothesis:

Precondition:

On the one hand, from the Automatic Control Theory it is well-known that the signal passing through the nonlinear elements, is “enriched” by additional harmonic components defined by the parameters of this elements.

On the other hand, operators, using their own experience and intuition (subjective vision, feeling of the current and future situation) for decision-making in non-programmed, precarious and often stressful situation, alter input information, “enrich” it by new subjectively formed components (decision) on the basis of their own knowledge, professional experience (skills) of the decisions adop- tion and implementation and the current state of psycho-physical activity.

Hypothesis:

Basic conditions, methods and results of the operative type of operator’s thinking in non-programmed situations (boundary, emergency, “free”) can be adequately simulated and identified by the transient processes of the nonlinear elements.

Thus, the purpose of this paper is to develop a simulation model to perform the identification and classification of automated control systems operators by the characteristics of nonlinear elements’ behavior, using the criteria the different decision- making models, which operators apply in the conditions of uncertainty and risk.

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2. Identification of the Operator’s Decision-Making Activity Models Using Nonlinear Elements

The main result, obtained by authors during the simulation experiment, is the Nonlinear Element’s Taxonomy in terms of the decision-making models used by the operator under conditions of uncertainty and risk (Table2).

Table 2 The Taxonomy of the Nonlinear Elements

Depending on the Decision-Making Models

Nonlinear Element’s Type and There Transient

Characteristics

Decision-Making Models Absolutely

Rational Bounded

Rationality Intuitive The Conditions of Operator’s Activity Normal

Conditions

Boundary Conditions

Emergency Conditions

“Free” Conditions

1 2 3 4 5

Two-position relay - x(t) > 0, b

x(t) < 0, −b -

Saturation

−a < x(t) < a x(t) < −a x(t) > a

-

Backlash

−a < x(t) < a x (t) < ⏐a⏐

Deadband

- x(t) < −a

x(t) > a −a < x(t) < a

Deadband with saturation

−b < x(t) < −a

a < x(t) < b x(t) < −b

x(t) > b −a < x(t) < a

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Table 2 cont.

1 2 3 4 5

Three-position relay without deadband

- x(t) < −a

x(t) > a −a < x(t) < a

Two-position relay with deadband

- x(t) > 0, b

x(t) < 0, −b x (t) < ⏐a⏐

Author’s nonlinear element

−b < x(t) < b - x(t) < −b x(t) > b

Authors’ interpretation of the main characteristics of nonlinear elements, presented in Table 2, allows to perform qualitative identification of the specifics of the operator’s decision-making activity under conditions of uncertainty and risk, as follows:

1. The simplest nonlinear elements perform static (instantaneous) nonlin- earity. Their output variable y(t) depends only on the input value x(t), and this dependence is strictly unambiguous.

1.1. Nonlinear element “Saturation” − in terms of basic characteristics (its amplitude and phase) of a signal being input – accu-

rately tracks the phase change, limiting the amplitude at the output beyond value ⏐−a⏐ (Figure 7). This type of nonlinearity is proposed by the authors to interpret (at a certain ratio of the amplitude values of the pa- rameters A and parameters value – b and c) as a follow- ing type of operator’s decision-making activity:

– using the bounded rationality model with limited amplitude in situations, where conditions do not meet (greater than x(t) < ⏐a⏐) the conditions of ap- plication of the rational decision-making model;

– transition to the rational decision-making model with decreasing (in terms of the operator) degree of non-programmed (uncertainty) tasks.

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