Sometimes all the information in time domain is not sufficient. This makes us to move to frequency domain of the signal for extracting more information about the signal. This movement from one domain to other domain is known as transformation. For changing the domain of signal from time to frequency we have many tools. Fourier Series and Fourier Transform are two of the tools in which we decompose the signal into harmonically related sinusoids. With such decomposition, a signal is said to be rep

In a control system, there may be some energy storing elements attached to it. Energy storing elements are generally inductors and capacitors in case of an electrical system. Due to the presence of these energy storing elements, if the energy state of the system is disturbed, it will take a certain time to change from one energy state to another. The exact time taken by the system for changing one energy state to another is known as transient time and the value and pattern voltages and currents

What is a Nichols Chart?A Nichols Chart (also known as a Nichols Plot) is a plot used in signal processing and control system design to determine the stability and closed-loop frequency response of a feedback system. The Nichols chart is named after its founder, Nathaniel B. Nichols.How Does A Nichols Chart Work?Constant magnitude loci that are M-circles and constant phase angle loci that are N-circles are the fundamental components in designing the Nichols chart.The constant M and constant N ci

Laplace transformation is a technique for solving differential equations. Here differential equation of time domain form is first transformed to algebraic equation of frequency domain form. After solving the algebraic equation in frequency domain, the result then is finally transformed to time domain form to achieve the ultimate solution of the differential equation. In other words it can be said that the Laplace transformation is nothing but a shortcut method of solving differential equation.In

What is a Nyquist Plot?A Nyquist plot (or Nyquist Diagram) is a frequency response plot used in control engineering and signal processing. Nyquist plots are commonly used to assess the stability of a control system with feedback. In Cartesian coordinates, the real part of the transfer function is plotted on the X-axis, and the imaginary part is plotted on the Y-axis.The frequency is swept as a parameter, resulting in a plot based on frequency. The same Nyquist plot can be described using polar c

A transfer functionrepresents the relationship between the output signal of a control system and the input signal, for all possible input values. A block diagram is a visualization of the control system which uses blocks to represent the transfer function, and arrows which represent the various input and output signals.For any control system, there exists a reference input known as excitation or cause which operates through a transfer operation (i.e. the transfer function) to produce an effect r

In the solution of Networks, Transient, and Systems sometimes we may not be interested in finding out the entire function of time f(t) from it’s Laplace Transform F(s), which is available for the solution. It is very interesting to find that we can find the first value or last value of f(t) or it’s derivatives without having to find out the entire function f(t). We will be interested in finding out final values and it’s derivatives in this article.For the sake of example:If F(s) is given, we wou

Initial Value Theorem is one of the basic properties of Laplace transform. It was given by prominent French Mathematical Physicist Pierre Simon Marquis De Laplace. He made crucial contributions in the area of planetary motion by applying Newton’s theory of Gravitation. His work regarding the theory of probability and statistics is considered pioneering and this influenced a whole new generation of Mathematician. Laplace is one among the 72 people to have their name engraved on the Eiffel Tower.I

The order of a control system is determined by the power of ‘s’ in the denominator of its transfer function.If the power of s in the denominator of the transfer function of a control system is 2, then the system is said to be second order control system.The general expression of the transfer function of a second order control system is given asHere, ζ and ωn are the damping ratio and natural frequency of the system, respectively (we will learn about these two terms in detail later on).Rearrangin

After reading the theory of network synthesis, we can easily say that any pole of the system lies on the right hand side of the origin of the s plane, it makes the system unstable. On the basis of this condition A. Hurwitz and E.J.Routh started investigating the necessary and sufficient conditions of stability of a system. We will discuss two criteria for stability of the system. A first criterion is given by A. Hurwitz and this criterion is also known as Hurwitz Criterion for stability or Routh