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Bode plot is a very important tool in control system.  Let's have a short look on history of Bode Plot so that it sets the plot for the concept. Bode plot was was developed by Hendrik Wade Bode in the 1930's while he was designing feedback for use in telephone networks which showed the gain and phase margins required to maintain stability in a Linear Time invariant systems.  So what is a Bode Plot?  It is a graph of response of a Linear Time-Invariant system to sinusoidal inputs in the frequency domain.   It is a powerful tool for carrying out characterizing an LTI system or designing  a controller. An LTI system responds to a sinusoidal input in a very similar manner. The output of a LTI system sinusoid is also a sinusoid with different amplitude and phase. But THE FREQUENCY OF THE SIGNAL REMAINS SAME. Magnitude F or a given frequency ( ω ) we define the magnitude of an LTI system as the ratio of the magnitude of the sinusoidal output (y) to the magnitud...

Who on earth was this Laplace and why did he invent Laplace Transform? Well, the story goes like The life of Pierre-Simon, Marquis de Laplace is only tangentially related to the topic of Control systems. Though after the development of Laplace transform it allowed Linear Differential Equations which approximate the behavior of the system. His method changed how we see control systems. By doing Laplace transformations we could get a system into algebraic equations which is easier to solve.  What does Laplace Transform do??? Let me tell you this in a very raw manner, It solves very complex problems in a very simple manner hence it is a key element to control systems. Block Diagram is very useful to be able to represent a system as a series of blocks with discrete inputs and outputs. In order for a model of a system to work, we must be able to express the behavior of a system mathematically and to represent the output of a system as a functio...

What is Control System?   Is it like a system which can be controlled? Yes, Right. That it is. A system in which the output is controlled by varying the input. The first control system device was James Watt's Flyball governor, which was invented in 1767. The aim of inventing Flyball governor was to keep the speed of the engine constant by regulating the supply of the steam to the engine. As above shown system, change in input will bring changes in output.   Terminology in control system: State: The state of a system is the set of parameters that describe it at a given point in time. Model: A set of expressions which represent the behavior of the system.   There are two types of control system. 1) Open loop control system An open-loop control system is a system in which the control action is independent of the desired output signal. In this system, the output signal is not compared with the input signal which means there is no feedback signal in this ...

Control Systems is classified into the following categories: Linear & Non-Linear Systems Static & Dynamic Time invariant & Time  variant Causal & non-Causal Difference between Linear and Non-linear systems Linear Non-Linear The relationship of output with the input is linear . The relationship of output with the input is non-linear. Satisfy Homogeneity & Superposition theorems. Doesn’t satisfy Homogeneity & Superposition Example : Register R= V/I Example: Diode : I = I 0 ( e v/t -1)     Difference between Static system and Dynamic system Static systems Dynamic systems At any time output of the systems depends only on the present input of the systems. At any time output of the systems depends only on the present as well as the past input of the systems. Memory less systems Presence of Memory Element Y(t) = f (u(t)) This f...