Network Synthesis | Hurwitz Polynomial | Positive Real Functions

Theory of Network Synthesis Network Functions Network synthesis theory involves the synthesis of networks made up of both active components (like resistors) and passive components (like inductors and capacitors). Let’s start with the basics: what is a network function? In the frequency domain, network functions are defined as the quotient obtained by dividing the phasor … Read more

Mathematical Modelling of Control System | Mechanical Electrical

Mathematical Modelling of Control System There are various types of physical systems, namely we have: Mechanical systems Electrical systems Electronic systems Thermal systems Hydraulic systems Chemical systems First off we need to understand – why do we need to model these systems in the first place? Mathematical modeling of a control system is the process … Read more

Bode Plot Gain Margin and Phase Margin

Bode plots were first introduced by H.W. Bode, when he was working at Bell labs in the United States. Now before I describe what are this plots it is very essential here to discuss a few advantages over other stability criteria. Some of the advantages of this plot are written below: Advantages of Bode Plot … Read more

Transient State and Steady State Response of Control System

When we study the analysis of the transient state and steady state response of control system it is very essential to know a few basic terms and these are described below. Standard Input Signals : These are also known as test input signals. The input signal is very complex in nature, it is complex because … Read more

State Space Analysis of Control System

Before I introduce you about the concept of state space analysis of control system, it is very important to discuss here the differences between the conventional theory of control system and modern theory of control system. The conventional control theory is completely based on the frequency domain approach while the modern control system theory is … Read more

Root Locus Technique in Control System | Root Locus Plot

The root locus technique in control system was first introduced in the year 1948 by Evans. Any physical system is represented by a transfer function in the form of We can find poles and zeros from G(s). The location of poles and zeros are crucial keeping view stability, relative stability, transient response and error analysis. … Read more

Routh Hurwitz Stability Criterion

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 … Read more

Time Response of Second-Order Control System

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 transfer function of a control system is 2, then the system is said to be second-order control system. The general expression of transfer function of a … Read more

Initial Value Theorem of Laplace Transform

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 … Read more

Final Value Theorem

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 … Read more