Modeling Systems

Traditional systems engineering methods include some combination of models, inputs, outputs and functional transforms.  A simple system diagram is illustrated in Figure 1.

 

Figure 1: Closed-loop feedback system

Inputs are transformed by the system into outputs.  In a feedback system some outputs are "fed backwards" to become new inputs to be transformed by the system at a future time.  

The theory of "systems engineering" is summarized at Dr Bahill's University of Arizona webpage; systems engineering is the methodical study of complex systems.  

http://sysengr.engr.arizona.edu/whatis/whatis.html

Models of systems are often created to investigate existing system and also to explore alternate designs.  

Figure 2: Controlled Closed-loop Feedback System

Figure 2 illustrates a simplified system that includes a controlled feedback loop.  Although also a simplified system, a decomposition of the complete system would reveal a set of coupled systems wherein inputs are transformed to outputs and those outputs become inputs to adjacent systems.

From left to right a "disturbance" presumably environmentally caused is part of set of inputs that becomes transformed by the "System" block.  In the illustrated system, "status" variables are emitted as outputs from the system block.  These "status" variables are utilized as inputs to a "measuring element" whereby "values" are emitted as outputs.   These "values" are compared to "set points" that can indicate "errors".  The "errors" become inputs to a "Controller" and in turn the "Controller" commands the "Effector" to generate "feedback" values that modifies inputs at the next time delta.  

Physically realized systems that utilize feedback control loops with set point values are not instantaneously successful in reaching the "set point / target" because physical systems contain inertia in mass based systems, resistance in electrical systems or attenuation in optics systems.  Disturbances might include externally induced vibrations like seismic waves, heat caused by adjacent systems and mismatches in optical coupling between fibers.