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Definition of System “An object or collection of objects whose properties we would like to study” It contains of interacting components connected together in such away that the variation in one component affects the other components
Definition of System System and Surroundings We scope a system by defining its boundary; this means choosing which entities are inside the system and which are outside the boundary - part of the environment.
Definition of System input output SystemThe environment affects the system through the input (cause)and system responds (effect) due to the input.
Definition of System Way to structure a system • what belongs to the system, and what does not • inputs, outputs and internal dynamics Example: System’s view of cruise control in a car
System Classifications Static vs. Dynamic Systems Static System The output of the system depends only on the current input. The output does not change with the time if the input is held constant (time-invariant). Dynamic System The output of the system depends on the current and the previous input. The output changes with the time even if the input is constant (time varying).
System ClassificationsDynamic systems are found in all majorengineering areas. Mechanical Systems Electrical Systems Thermal Systems Fluid Systems Mixed Systems
Mechanical Systems What is mechanical system? Mechanical systems are concerned with the behavior of matter under the action of forces/torques. Governed by Newton’s 2nd Law
Electrical Systems What is electrical system?Electrical systems are concerned with the behavior ofthree fundamental quantities: charge, current and voltage.Two Kirchoff’s laws are used to model the electricalsystem:1. ?2. ?
Thermal Systems What is thermal system?Thermal systems involves heating of objects andtransports of thermal energy.Example of thermal system ?
Fluid Systems What is fluid system?Fluid system involves connection of fluid flows in tube andtank.Example of fluid systems ?
Mixed Systems What is mixed system?System which consists of two or more of previouslymentioned systems.Electro-mechanical systemFluid-mechanical systemThermo-mechanicalElectro-thermalMechatronics system !
Definition of System DynamicsSystem dynamics is the study of the time-behavior of a systemand includes the followings: System definition System boundaries, input and output variables Modeling of the system Usually in the form of mathematical or graphical relationship determined analytically or empirically Determination of the behavior of the system (i.e. Analytical/Simulation) Effect of the inputs to the system outputs Formulation of recommendation To improve system performance through modification of the system structure or parameter values
Definition of System Dynamics System Definition Modeling Simulation RecommendationSystem dynamics
System Dynamics Actual System System Definition Modeler’s Perception Modeling Mathematical Simulation Representation ValidationRecommendations
What is model? The word “model” is derived from a Latin word which originally means pattern or mold. Model of a system is basically a tool to study the behavior of a system without having experiment on the real system. Model can be: physical model, mental model, verbal model and also mathematical model. We concern ONLY mathematical model.
What is mathematical model?Model is a collection of mathematical equations whichrepresent behavior/characteristic of real system & x, x f m1 T = fr (m1 + m2 )&& + m2l (θ& cosθ − θ& 2 sin θ + 2ml&θ& cosθ + m&&sin θ ) = x & l f θ l lθ& + 2l&θ + && cos θ + g sin θ = 0 & & x m2
Why do we need mathematical model?• To avoid physical system – Can treat new designs/technologies without physical prototype – Do not disturb operation of existing system• Easier to work with than real world – Easy to check many approaches, parameter values,… – Flexible to time-scales – Can access immeasurable quantities• Support safety – Experiments may be dangerous – Operators need to train for extreme situations• Help to gain insight and understanding
Why do we need mathematical model?The first step in understanding aproblem is to model itsbehavior.“If it works on paper, it willwork in real life” <Susan Koerner Wright> mother to Wright ‘s brothersModel can be simulatedFast-time simulation save time.
Model CharacteristicsA model captures only some aspects of a system Important to know which aspects are modeled and which are not. Make sure that model is valid for intended purposeAll-encompassing models often a bad idea Large and complex – hard to gain insight Cumbersome and slow to manipulateGood models are simple, yet capture the essentials!
Simulation Model can be used to compute how the system would react upon certain inputs. This can be done mathematically solve the equations that describe the system and study the answer. OR With the power of computer we can perform a numerical computation to solve the equations.
Simulation Simulation is derived from Latin world simulare which means pretend. We may define simulation as a process of imitation the dynamic system using a computer in order to evaluate and/or improve the system performance.