introduction to systems instructor dr. hanafy omar ge 605: modeling and simulation of engineering...

Introduction to Systems

InstructorDr. Hanafy Omar

GE 605: Modeling and Simulation of Engineering Systems

System: Entities, interactions, and boundary

Definition: A system is defined to be a collection of components (or entities) that act and interact together toward the accomplishment of some logical end.

A number of terms need to be defined to understand and analyse a system, which are:• Entity: Used to denote an object of

interest in the system.• Attribute: Denote a property of an

entity.• Activity: A function to be performed by

an entity.• State: A collection of variables

necessary to describe the system at a particular instant of time, with respect to the objectives of the study.

• Event: An instantaneous occurrence that may change the system state.

System: Entities, interactions, and boundary

Example of a system: A banking system in which customers arriving at a bank to be served by a teller. In this example, the system entities are Customer-queue and Tellers, for them the attributes are Balances, Account Number, Data Access, etc. The activities are Deposit or Money-Withdraw, etc. The system events are Customer-Arrival and Customer-Departure. The system states, which are changed by these events, are Number-of-Customers-in-the-Queue (an integer from 0 to n) and Teller-Status (busy or idle). A banking system is an event-based system in which system state changes at events occurring at particular time instants. Other systems are systems in which system states updated according to the set of activities happening in each time interval.

System: Entities, interactions, and boundary

Remark: According to the objectives of the particular study, a system may contains other entities of interest. For example, in the previous example of banking system, if the loan and credit card services are to be included, the system must be more inclusive accordingly.

Statement to be kept in mind: A system must be defined depending on the objectives of a particular study.

System: Entities, interactions, and boundary

A system is characterized by the following attributes:• System components (or entities)

and their interactions• System boundary• Environment or surroundings

System: Entities, interactions, and boundary

System components and their interactions:Components can be of different types and their interactions  refer to the influence of one component of a system on the performance of the other components as well as the system as a whole.

System boundary:• The boundary of a system

determines what falls inside and what falls outside the system.

• The system boundaries are observer-dependent, time-dependent, and most importantly system-dependent.

System: Entities, interactions, and boundary

System boundary: (Continued)• This boundary might be material

boundary (like the skin of a human body) or immaterial boundary (like the membership to a certain social group).

• The interaction between a system and its environment takes place mainly at the boundaries. It determines what can enter or leave a system (input and output).

• System boundary may be crisp (clearly defined) or fuzzy (ill defined).

System: Entities, interactions, and boundary

Environment:• The environment represents

everything that is important to understand the functioning of the system, but is not a part of the system.

• The environment is that part of the world that can be ignored in the analysis except for its interaction with the system.

• It includes competition, people, technology, capital, raw materials, data, regulation, and opportunities.

• Interaction between system and its environment has two components: input, that is, what enters the system from the environment through its boundary, and output, that is, what leaves the system boundary to the environment.

System: Entities, interactions, and boundary

Environment: (Continued)According to the type of interaction between a system and its environment, a system may be open system or closed system. An open system exchanges matter, information, and energy with its environment, whereas a closed system exchanges only energy.• A living organism is an open

system; it cannot survive without consuming oxygen, water, and food from its environment, while discharging urine, excrements, and carbon dioxide to the environment. It also exchanges information with its environment.

• Most systems are open systems.

System: Entities, interactions, and boundary

Environment: (Continued)Input-output relationship of a system is determined according to two views: black-box view and white-box view.• A black-box view is when we are

concerned only with the input and corresponding output of a system without looking at what happens inside the system during process. For example, when we consider the city as pollution production system, we may safely measure the total fuel consumption (input) of the city and the level of emissions (output) out of such consumptions without actually bothering about trivial details like who/what consumed more and who/what emitted or polluted the most. Such point of view considers the system as a black-box system.

System: Entities, interactions, and boundary

Environment: (Continued)A white-box view is when we are equally concerned about the internal details of the system and its processes besides the input and output variable. In the example of a city as pollution production system, we are now concern of computing how much pollution is produced by every single building of the city to determine the overall pollution levels.

Statement: The black-box view of the city will be much simpler andeasier to use for the calculation of overall pollution levels than the more detailed white-box view, but it is less accurate.

Classifications of systems

Systems can be classified on the basis of time frame, type of measurements taken, type of interactions, nature, type of components, etc.

According to the time frameSystems can be classified on the basis of time frame as Discrete-time Continuous-time Hybrid

Classifications of systems

According to the Complexity of the SystemSystems can be classified on the basis of complexity Physical systems Conceptual systems Esoteric systems

Classifications of systemsAccording to the complexity of the system (Continued)• Physical systems can be defined as systems whose

variables can be measured with physical devices that are quantitative such as electrical systems, mechanical systems, computer systems, hydraulic systems, thermal systems, or a combination of these systems.

• Conceptual systems are systems that are composed of non-physical objects, i.e. ideas or concepts. Variables of such systems cannot be measured directly with physical devices; all the measurements are conceptual or imaginary and in qualitative form. psychological systems, social systems, health care systems, economic systems, and transportation systems are all conceptual systems.

Classifications of systems

According to the complexity of the system (Continued)

Esoteric systems are the systems in which the measurements are not possible with physical measuring devices, such as solar systems, religions, philosophies, etc.

Classifications of systemsAccording to the degree of interconnection of events. Independent—If the events have no effect upon one another, then the system is classified as independent.Cascaded—If the effects of the events are unilateral (that is, part A affects part B, B affects C, C affects D, and not vice versa), the system is classified as cascaded.Coupled—If the events mutually affect each other, the system is classified as coupled.

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Classifications of systems

According to the nature and type of components Static or dynamic components Linear or nonlinear components Time-invariant or time-variant

components Deterministic or stochastic components Lumped parametric component or

distributed parametric component Continuous-time and discrete-time

systems

Classifications of systemsAccording to the uncertainties involved Deterministic systems Stochastic systems Fuzzy systems

Classifications of systems

Static vs. dynamic systems A static system or a memoryless system is when

the output at a given time depends on the input at that time but not on the past values of output and input. Therefore, the output reaches its steady-state value instantaneously. An example is an electric resistor.

A dynamic system or memory system is when the output at a given time depends on the input at that time and the past values of output and input. Therefore, the output experiences a transient response before reaching its steady-state value. An example is an electric capacitor.

Classifications of systems

Linear vs. nonlinear systemsLinear systems obeys superposition and homogeneity principles. Otherwise, systems are nonlinear.

Classifications of systemsLinear vs. nonlinear systemsSuperposition: If

then

Homogeneity: If

then

Classifications of systems

Linear vs. nonlinear systemsThe study of linear systems is important for two reasons:1. Even though most physical systems are nonlinear,

majority of engineering situations are linear at least within specified ranges of input. For example, the Ohm’s law states that the relation between the voltage across and the current through a resistor is linear. Unfortunately, this linear relationship does not hold good for all conditions.

2. Exact solutions of behaviour of linear systems can usually be found by standard techniques.

3. There are no standard methods for analysing nonlinear systems and solutions can only be found numerically.

Classifications of systems

Time-invariant vs. time-variant systemsA system whose parameters do not change with time is called time-invariant system. Otherwise, the system is time-variant. For a time-invariant system with input and output if

then

That is, the output of time-invariant system depends upon the shape and magnitude of the input and not on the instant at which the input is applied.

Classifications of systemsTime-invariant vs. time-variant systemsFigures below show a time-invariant system.

Classifications of systemsTime-invariant vs. time-variant systemsFigures below show a time-variant system.

Classifications of systemsLumped vs. distributed parameter systems A lumped parameter (or component or element)

system is one in which the components are considered to be concentrated at a point in space. An example is an electric circuit, where electric components are lumped. In a lumped parameter system, dependent variables of interest are functions of time alone.

Classifications of systemsLumped vs. distributed parameter systems A distributed parameter system however has its

components distributed continuously in space. An example is the power transmission line, where electric components are distributed. In a distributed parameter system, dependent variables on interest are functions of time and one or more spatial variables.

Classifications of systemsContinuous-time and discrete-time systemsSystems whose inputs and outputs are defined over a continuous interval of time (i.e., continuous-time signals) are continuous-time systems. On the other hand, systems whose inputs and outputs are signals defined only at discrete instants of time are called discrete-time systems.

Classifications of systemsContinuous-time and discrete-time systemsThe terms discrete and continuous qualify the nature of signal along the time axis as well as the signal amplitude axis. Signals in figure below, (a) continuous-time and continuous-amplitude, (b) continuous-time discrete-amplitude (or quantized), (c) discrete-time and continuous-amplitude, and (d) discrete-time and discrete-amplitude (digital).

Classifications of systemsContinuous-time and discrete-time systems• The discrete-time signals may arise naturally in situations

which are inherently discrete-time such as population in a particular town and number of customers served at an ATM counter.

• In addition, discrete-time signals are found by discretization (or sampling) processes. Indeed, in digital control, continuous-time signals are converted to discrete-time signals, using analog-to-digital converters (ADC), and then processed by the digital computer. The output of the digital computer is again converted back into continuous-time signals, using digital-to-analog converters (DAC).

Classifications of systems

Continuous-time and discrete-time systems An example of continuous-time systems in

which the state variables change continuously with respect to time is an airplane moving through the air, since dependent variables such as position and velocity can change continuously with respect to time.

Examples of discrete-time systems include microprocessors, semiconductor memories, shift registers, banking systems, etc.

Classifications of systemsDeterministic, stochastic , and fuzzy systemsA deterministic system will always produce the same output for a given input (or initial condition). In a deterministic system, there are no uncertainty in any variables. Example of deterministic systems is classic physics.

Classifications of systemsDeterministic, stochastic, and fuzzy systemsA stochastic (or random or probabilistic) system will produce different outputs for a given input (uncertainty). A stochastic system contains some random variables. A classical example of this is medicine: a doctor can administer the same treatment to multiple patients suffering from the same symptoms, however, the patients may not all react to the treatment the same way. This makes medicine a stochastic system.Remark: A random variable is a variable whose values are subject to variations due to chance. As opposed to other mathematical variables, a random variable conceptually does not have a single, fixed value (even if unknown); rather, it can take on a set of possible different values, each with an associated probability.

Classifications of systemsDeterministic, stochastic, and fuzzy systemsIn deterministic systems, If the input is known exactly, then the output could theoretically be predicted. However, in practice, for some of these systems, outputs are hard to predict. These are fuzzy systems. Some facts on fuzzy systems are in order:• Fuzzy logic; variables are between 0 and 1.• Analysis by fuzzy logic is useful when a mathematical model

of the system may not exist, or may be too "expensive" in terms of computer processing power and memory allocation.

• solution to the problem can be cast in terms that human operators can understand.

• Fuzzy variables are represented by fuzzy sets that map into truth values by membership functions.

• Deterministic (or crisp) systems could be analysed as fuzzy systems by using fuzzification and defuzzification techniques.

Classifications of systemsDeterministic, stochastic, and fuzzy systemsAn important type of stochastic systems is the discrete-event system in which system state evolves in accordance with the occurrence of physical events. Each event occurs at a particular instant in time and marks a change of state in the system. A common example of discrete-event systems is a banking system in which customers arriving at a bank to be served by tellers. In this example, the system entities are Customer-Queue and Tellers. The system events are Customer-Arrival and Customer-Departure. The system states, which are changed by these events, are Number-of-Customers-in-the-Queue (an integer from 0 to n) and Teller-Status (busy or idle). The random variables that need to be characterized to model this system stochastically are Customer-Interarrival-Time and Teller-Service-Time.