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

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 ofWe 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. When the system is put to service stray inductance and capacitance get into the system, thus changes the location of poles and zeros. In root locus technique in control sy

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 based on time domain approach. In the conventional theory of control system we have linear and time invariant single input single output (SISO) syste

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 it may be a combination of various other signals. Thus it is very difficult to analyze characteristic performance of any system by applying these signals. So we use test signals or standard inpu

What is a Bode Plot?A Bode plot is a graph commonly used in control system engineering to determine the stability of a control system. A Bode plot maps the frequency response of the system through two graphs – the Bode magnitude plot (expressing the magnitude in decibels) and the Bode phase plot (expressing the phase shift in degrees).Bode plots were first introduced in the 1930s by Hendrik Wade Bode while he was working at Bell Labs in the United States. Although Bode plots offer a relatively s

Mathematical Modelling of Control SystemThere are various types of physical systems, namely we have: Mechanical systems Electrical systems Electronic systems Thermal systems Hydraulic systems Chemical systemsFirst 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 of drawing the block diagrams for these types of systems in order to determine their performance and transfer functions.Now let us describe the

Theory of Network SynthesisNetwork FunctionsNetwork 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 corresponding to the circuit output by the phasor corresponding to the circuit input.In simple words, network functions are the ra

What is Settling Time?The settling time of a dynamic system is defined as the time required for the output to reach and steady within a given tolerance band. It is denoted as Ts. Settling time comprises propagation delay and time required to reach the region of its final value. It includes the time to recover the overload condition incorporated with slew and steady near to the tolerance band.The tolerance band is a maximum allowable range in which the output can be settle. Generally, the toleran