System dynamics
(MED 221)
Chapter One: Introduction to System Dynamics
Level 4
Mechatronics Department
Course instructor
Assos .Prof. Mohamed Abdelrahman
2022
Course content
Weeks
Topics
1
Introduction to system dynamic
2
Mathematical Modelling
3
Linear Mechanical System
4
Rotational Mechanical System
5
Electrical System
6
System Analogy
7
Transfer Functions
8
Mid-Term Exam
9
Electronic System
10
Electromechanical Systems
11
Electromechanical Systems
12
Application and course Project
13
Application and course Project
14
Revision
15
Final Exam
References
• Ogata, K. Modern Control Engineering, 5th ed . Prentice Hall, Upper
Saddle River, NJ, 2010.
• Ogata, K. system dynamics, fourth edition
• Nise, N. S. Control System Engineering, 6th ed. John Wiley & Sons
Ltd., UK, 2011.
3
Scientific Understanding
THEORY
MODELING &
SIMULATION
EXPERIMENTATION
➢ Mathematical modeling
o Mathematical modeling can be broadly defined as a formulation or equation that expresses the essential
features of a physical system or process in mathematical terms.
Physical system
Analysis
(mathematical modeling)
Equations
• Equation on motion (Newton ) Laws
• Mechanical
• Ohm & Kirchhoff laws
• Electrical
• continuity & momentum
• Hydraulic &
• Energy equation
Pneumatic
• Thermal
Differential equations
• Electromechanical
Difference equations
• Chemical
Input / output relations
Simulation
Tools
Introduction to
system
What is systems?
Most systems that surround us are :
• Multidimensional
• Extremely complex
• Time varying
• Nonlinear in nature
As they are comprised of large varieties of actively or
passively interacting sub-systems
Multidimensional
Complex
systems
Linear and Nonlinear
Superposition Rules
• If a X = a Y , b X = b Y
Input (X)
• a X + b X = a Y + b Y , linear system
• a X + b X≠a Y + b Y , Nonlinear system
System
Output (Y)
Time varying system
What is systems?
➢System is derived from the Greek word systema , which means an
organized relationship among units or components.
• System : a collection of entities (people or machines) that act and
interact together toward the accomplishment of some logical end.
• System is a collection of interconnected components.
What is systems?
System as collection of
interconnected components.
What is systems?
Some examples of the systems are:
• Medical / biological systems
• Socioeconomic systems
• Communication and information systems
• Planning systems
• Solar system
• Environmental systems
• Manufacturing systems
• Transportation systems
• Physical systems – electrical , mechanical , thermal , hydraulic systems , and
combination of them
What is systems?
Every system consists of subsystem or components at lower levels and supersystems at
higher levels.
What is systems?
• A system is characterized by the following
attributes:
1.
System boundary
2.
System components and their interactions
3.
Environments
• System boundary
To study a given system, it is necessary to determine
what comprises (falls inside and what falls outside)
a system
Environment
What is the systems?
System
boundary
System
It is partitioning line between the environment and the system.
System is inside the boundary and environment is outside the system.
A real or imaginary boundary separates the system from the rest of the
universe, which is referred to as the environment or surroundings.
System exchanges input-output from its environment.
This boundary might be material boundary (like the skin of a human body)
or immaterial boundary (like the membership to a certain social group).
What is the systems?
System Boundary
• It helps in identifying the system and its components.
• 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).
➢ In crisp boundaries , it is quite clear that what is inside the boundary (i.e. Part of system) and what is
outside the boundary (i.e. Part of environment).
➢ In fuzzy boundaries , it is not very clear whether a particular component belongs to the environment or the
system.
What is systems?
System components and their interaction
• System component is a fundamental building block.
• It is quite easy to find the input – output relations for the system components using
fundamental laws of physics, which is called the mathematical model for
components.
• It may be written in the form of difference or differential equations.
What is systems?
Business System
Inputs
•
•
•
•
Materials Services
New Equipment's
New Employees
Facilities
Customers
+
Suppliers
+
Other industries
+
Government
Ouputs
• Product
• Waste Materials
• Money
System components and their interactions
• It is static or dynamically changing with time , input , or state
of the system.
What is the
system?
• Interaction may be constrained or non-constrained type.
• The component interaction may be unidirectional or
bidirectional.
• Interaction strength may be 0 , 1 , or between 0 and 1.
What is the system?
Environment
• It represents everything that is important to understand the functioning
of the system but is not a part of the system.
• It is that part of the world that can be ignored in the analysis except for
its interaction with the system
Black Box System
White Box System
Classification of systems
❑ System can be classified on the basis of :
➢Time frame ,
➢Type of measurements taken ,
➢Type of interactions ,
➢Nature,
➢Type of components.
Classification of systems
According to the Time Frame
❖
Systems can be categorized on the basis of time frame as
➢Discrete
➢Continuous
➢Hybrid
Classification of systems
➢ Discrete system : in which the state variables change instantaneously at separated points in time .
❖
Ex. queuing system (bank , telephone network m traffic lights).
❖In a bank system , state variable are the number of customers in the bank , whose value changes only when
a customer arrives or when a customer finishes being served and departs.
Classification of systems
➢ Continuous system : in which the state variables change continuously with respect to time .
❖
Ex. Solar system , spread of pollutants , charging a battery .
❖
Ex. An airplane moving through the air , since state variable such as position and velocity
can change continuously with respect to time.
➢ Hybrid system : is a combination of and discrete dynamic system behavior .
➢ Hybrid system has the benefit of encompassing a larger class of systems within its structure ,
allowing more flexibility in modeling continuous and discrete dynamic phenomena.
Classification of systems
❑According to the complexity of the system.
System can be classified on the basis of complexity
➢ physical systems
➢Conceptual systems
➢Esoteric systems
Classification of systems
➢Physical system ; variables can be measured with physical devices
Ex. Electrical system , mechanical systems , computer systems , hydraulic systems , thermal
systems , or a combination of theses systems.
Physical system is a collection of components , in which each component has its own
behavior , used for some purpose .
These systems are relatively less complex.
Classification of systems
Conceptual systems : in which all the measurements are conceptual or
imaginary.
Ex. Psychological systems , social systems , health care systems , and
economic systems.
Conceptual systems are those systems in which the quantity of interest
cannot be measured directly with physical devices.
These are complex system
Classification of systems
Esoteric systems : in which all the measurements are not possible
with physical measuring devices.
The complexity of these systems is of highest order. (Black box)
Classification of systems
❑According to the Interactions , may be ;
▪ Unidirectional or bidirectional ,
▪ Crisp or fuzzy ,
▪ Static or dynamic
➢ System will be divided into three classes according to the degree of interaction of events ,
✓ Independent – systems
✓ Cascade – systems
✓ Couples – systems
Classification of systems
➢Independent – if the events have no effect upon one another.,
➢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 ).
➢Coupled – if the events mutually affect each other.
Classification 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.
Classification of systems
❑According to the Uncertainties Involved
➢Deterministic No uncertainty in any variables (model of pendulum).
✓System that will always produce the same output for a given input.
➢Stochastic : some variables are random , (airplane in flight with random wind gusts ,
mineral – processing and phone network with random arrival and call lengths).
✓System that will produce different outputs for a given input