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Simulation and Modelling

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Introduction


WHAT IS A SYSTEM

System modeling and computer simulation, recently has become one of the premier subject in the industry as well as Defence. It helps an engineer or a scientist to study a system with the help of mathematical models and computers. In other words, one can say, system simulation is nothing but an experiment with the help of computers, without performing actual experiment. It saves lot of money which is required, if we actually perform experiments with the real system.

Present book, “System Modeling and Simulation” has been written by keeping engineering students as well as scientists especially defence scientists in mind. Earlier this manuscript was prepared only for the use of defence scientists which has now been extended to other engineering applications. Modeling of a weapon system is just an application of basic techniques of modeling and simulation, which are being discussed in chapter two and four. After my superannuation from Defence Research & Development Organisation, briefly called DRDO in 2000, when I joined the Punjab Technical University, and taught this subject to B. Tech and M. Tech students, the manuscript was rewritten, so that it should be useful to engineering students too. Although many of the examples have been taken from target damage, yet care has been taken to include other examples, from marketing, and mechanical engineering and other related subjects. My intentions are that this book should prove itself as a complete manual for system simulation and modeling. That is the reason, that basic subjects required for modeling and simulation, such as probability theory, numerical methods and C++ have also been included and discussed wherever required. Wherever possible, computer programmes have been given with the output.

First question the user of this book can raise is, after all what is a system1 ? We give here a popular definition of what a system is? A broader definition of a system is, “Any object which has some action to perform and is dependent on number of objects called entities, is a system”. For example a class room, a college, or a university is a system. University consists of number of colleges (which are entities of the system called university) and a college has class rooms, students, laboratories and lot many other objects, as entities. Each entity has its own attributes or properties. For example attribute of a student is to study and work hard. Each college in itself can be treated as a complete system. If we combine few of these objects, joined in some regular interactions or inter-dependence, then this becomes a large system. Thus we can say university is a large system whereas college is a system. This means, each system can be divided into blocks, where each block is in itself a complete and independently working system (Fig. 0.1). When these blocks are combined, depending on some interdependence, they become entities of a larger system. An aircraft for example, is another example of a system. It consists of a cockpit, pilot, airframes, control system, fuel tank, engines etc. Each of these blocks can in itself be treated as a system and aircraft consisting of these interdependent blocks is a large system. Table 0.1 gives components of a system (say college) for illustrations purpose.

Does a system also has some attributes? I will say yes. Systems broadly can be divided into two types, static system and dynamic system. If a system does not change with time, it is called a Static System and if changes with time, it is called a Dynamic System. Study of such a system is called System Analysis. How this word originated is of interest to know.



While looking at these systems, we see that there are certain distinct objects, each of which possesses some properties of interest. There are also certain interactions occurring in the system that cause changes in the system. A term entity will be used to denote an object of interest in a system and the term attributes denotes its properties. A function to be performed by the entity is called its activity. For example, if system is a class in a school, then students are entities, books are their attributes and to study is their activity. In case of the autopilot aircraft discussed below, entities of the system are gyroscope, airframe and control surfaces. Attributes respectively are gyroscope setting, speed and control surface angles. Activity of the aircraft is to fly. Banks et al., (2002) has defined state variables and events as components of a system. The state is defined as collection of variables necessary to describe the system at any time, relative to the objectives of the study. An event is defined as an instantaneous occurrences that may change the state of the system. But it is felt, entities are nothing but state variables and activity and event are similar. Thus there is no need of further bifurcation.

Sometimes the system is effected by the environment. Such a system is called exogenous. If it is not effected by the environment, it is called endogenous. For example, the economic model of a country is effected by the world economic conditions, and is exogenous model. Aircraft flight is exogenous, as flight profile is effected by the weather conditions, but static model of the aircraft is endogenous. A class room in the absence of students, is endogenous. As mentioned earlier study of a system is called System Analysis. How this word “System Analysis” has cropped up? There is an interesting history behind this.

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