As we mentioned in the previous section the first step in designing a control system is to understand the original system you have at hand. You have to first analyze your original system to see how it behaves without a control system, and then be able to design the correct control system to augment the original system with.
In order to analyze your overall original system (plant) you basically need equations which describe the mechanics of the different parts. The equations for the mechanics of the different parts come from the physics behind them. As we previously said the parts can be either mechanical or electrical or a combination of both. Therefore, using knowledge we have from physics, like mass-spring relations, circuit analysis, motor dynamics, etc we can derive mathematical equations for each part of our system.
We then combine all these equations into a single equation which describes how the system acts from the input to the output. Basically, this equation will be a differential equation and will relate the input to the output.
This differential equation is the center of all our future analyses. We will be using it to examine the different outputs of the plant (without a control system) to different inputs we give it. We can then determine its current performance parameters of stability, transient response, and steady-state response. By knowing this information we will be able to design the correct control system.
In the next two sections we will be talking about different types of inputs and outputs of a system.
