Overview of the Fundamentals of Control Systems
This chapter provides a fundamental and basic introduction to most popular control systems implemented in our current world. In fact, all control systems in our world belong to nonlinear time-variant systems (NLTV), which mean that the outputs of all systems are always changed and varied with the time period and different outputs can be achieved at different time moments. Also the input–output relationship is not linear. Therefore, it is very difficult or even challenging to analyze and study this kind of NLTV because of their nonlinear and time-variant properties, sometimes, it may be impossible to do this kind of analysis if multiple different voltage sources (DC and AC) are included in that system. In order to reduce this difficulty and make our analysis simple, in most cases, we need to simplify this kind of NLTV systems to approximate them to linear time-invariant (LTI) systems. The advantage of this simplification is by approximating the NLTV systems to the LTI systems, we can use superposition principle to divide our analysis into two separate parts: DC analysis and AC analysis. Eventually, we can combine these two analyses together to get the final results. The superposition principle only works for the LTI systems.