Modeling is the process of identifying the principal physical dynamic effects to be considered in analyzing a system, writing the differential and algebraic equations from the conservation and property laws, and reducing the equations to a convenient differential equation form.

System
A system is a combination of elements intended to act together to accomplish an objective. For example, an electrical resistor is an element for impeding the flow of current, and it is usually not considered to be a system in the sense of the definition. However, when it is used in a network with other resistors, capacitors, inductors, etc., it becomes part of a system.
The word system is used to define abstractly a relatively complex assembly (or arrangement) of physical elements characterized by measurable parameters.

To model the system:
The system’s boundaries or constraints must be defined.
The system behavior in response to excitations or disturbances from the environment must be predictable through its parameters.

Engineering System
Engineering system is a term referred to a product or device that may contain mechanical, electrical, fluid, and/or thermal components. An engineering system can therefore be interdisciplinary, and require a designer to have knowledge of many engineering fields.

Engineering is the application of physics and other branches of science to the creation of products and services that make the world a (hopefully) better place. Your success in engineering will likely be closely related to how well you can create products and services that your organization’s customers need and want. Unfortunately, it is found that creating new products and services is a lot more difficult than analyzing or criticizing those that already exist. Modeling is the creative side of engineering, and analyzing is the critical side.

The System Approach
The black-box concept is essential to what has been called the “system approach” to problem solving. With this approach, each element in the system is treated as a black box, and the analysis focuses on how connections between the elements influence the overall behavior of the system.
The behavior of a black-box element is specified by its input-output relation. An input is a cause; an output is an effect due to the input. Thus the input-output relation expresses the cause-and-effect behavior of the element. For example, a voltage v applied to a resistor R causes a current i to flow. The input-output or causal relation is i=v/R. Its input is v, its output is i, and its input-output relation is the preceding equation.

Block Diagrams
The black-box treatment of an element can be expressed graphically. The box represents the element. Inside the box, we place the mathematical expression that relates the output to the input. This graphical representation is a block diagram.
Not all black-box representations must refer to actual physical elements. Since they express cause-and-effect relations they can be used to display processes as well as components.

Integral Causality
Whenever an output is the time integral of the input, the element is said to exhibit integral causality.
The input-output relations for each element provide a means of specifying the connections between the elements. When connected together to form a system, the inputs to some elements will be the outputs from other elements.
The system itself can have inputs and outputs. These are determined by the selection of the system’s boundary. Any causes acting on the system from the world external to this boundary are considered to be system inputs. Similarly, a system’s outputs can be the outputs from any one or more of the elements, viewed in particular from outside the system’s boundary.

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