In this topic, we will find out how to calculate inverse Laplace of a transfer function using Matlab. Let’s find out Inverse Laplace of the following function \[X(s)\frac{10{{s}^{2}}+20s+40}{{{s}^{3}}+12{{s}^{2}}+47s+60}=\frac{Numerator}{Denumerator}\] Let’s write a little code in Matlab now: Results: Here, we get the following results: Residue = 95.0000 -120.0000 35.0000 …

Read More »## Fourier series of a Square Wave using Matlab

In this tutorial, we will write Fourier series of a simple function using Matlab. Let’s assume we have a square wave with following characteristics: $\begin{align} & Period=2ms \\ & Peak-to-Peak\text{ }Value=2\text{ }V \\ & Average\text{ }Value=0\text{ }V \\\end{align}$ So, we can express it as: \[\begin{align} & x(t)=\frac{4}{\pi }\sum\limits_{n=1}^{\infty }{\frac{1}{(2n-1)}\sin \left[ (2n-1)2\pi {{f}_{o}}t …

Read More »## Ladder Diagram | Schematic Diagram | Wiring Diagram

Wiring Diagram Definition Wiring diagrams tend to show a close representation of the interior position of electrical components in a control cabinet and/or circuit. Sometimes wire diagrams can closely represent a picture. The only difference is components are represented by electrical symbols whether they are NEMA standard or IEC standard …

Read More »## Bode Plot Example | Bode Diagram Example MATLAB

Bode Plot Example of First Order System using Matlab In this article, Bode Plot of Simple Phase-Lag Network (First Order System) is obtained using Matlab. In order to draw Bode Plot, we need transfer function from which we deduce the equations for Magnitude and Phase. \[G(s)=\frac{1}{2s+1}\] Function in the frequency …

Read More »## Bode Plot MATLAB | Bode Plot Transfer Function

Bode Plot Definition H.W. Bode introduced a method to present the information of a polar plot of a transfer function GH(s), actually the frequency response GH (jω), as two plots with the angular frequency were at the common axis. The first plot shows the magnitude of the transfer function as …

Read More »## State Space Representation and Example

The state space models derivation is not contrary to that of transfer functions in that the differential equations are written first in order to express the system dynamics.Generally, In transfer function models, these differential equations are transformed and variables are carried off between them in order to achieve the relation …

Read More »## Root Locus Method | Root Locus Matlab

what is Root Locus Consider as a standard form for root locus construction, the open-loop transfer function given by; \[GH(s)=K\frac{(s+{{z}_{1}})(s+{{z}_{2}})\cdots (s+{{z}_{z}})}{(s+{{p}_{1}})(s+{{p}_{2}})\cdots (s+{{p}_{p}})}\] Where there are z finite zeros and p finite poles of GH(s). We write the characteristic equation for the system given below; Fig.1: Closed-Loop System \[\frac{C(s)}{R(s)}=\frac{G(s)}{1+G(s)H(s)}\] The …

Read More »## Transient Response | First and Second Order System Transient Response

Transient Response Definition Damping Oscillation: A typical Transient Response Example For a system with transfer function G(s), whether open loop or closed loop and input R(s), the output is \[C\left( s \right)=\text{ }G\text{ }\left( s \right)\text{ }R\left( s \right)\] For distinct poles, whether real or complex, the partial fraction expansion …

Read More »## Physical Quantities and Units | Physical Quantity Definition

Physical Quantity Definition A physical quantity is characterized by defining how it is measured or by expressing how it is computed from other measurements. For instance, distance and time are expressed by defining methods for evaluating them, while we express average speed by stating that it is computed as distance …

Read More »## Nyquist Theorem | Nyquist Stability Criterion

Nyquist Criterion Definition The Nyquist criterion is a frequency domain tool which is used in the study of stability. To use this criterion, the frequency response data of a system must be presented as a polar plot in which the magnitude and the phase angle are expressed as a function …

Read More »## Signal Flow Graphs and Mason’s Gain Formula

Signal Flow Graph The application of mason’s gain formula to the signal flow graph corresponding to a given detailed block diagram is undoubtedly simplest operational procedure for obtaining the system transfer function. A signal flow graph is composed of various loops and one or more paths leading from an input …

Read More »## Block Diagram | Block Diagram in Control System

Block Diagram in Contol System By using block diagrams when examining larger systems, attention can be focused on a smaller number of elements or subsystems whose properties may already be known. By doing this, a set of individual blocks representing the various elements or subsystems is formed, and these blocks …

Read More »## First Order Control System | First Order System Example

First Order Control System First Order System is the one that has only one independent energy storage element. The mathematical expression of first order system can be written in terms of a single variable and its derivative as $a\frac{dy}{dt}+by=f(t)\text{ (a)}$ The natural or un-driven response for above equation is given as …

Read More »## Feedback Control System Advantages and Disadvantages

Depending upon the process to be controlled and technical and economical considerations, either an open-loop or closed loop design may be preferable. However, a feedback control system is generally considered superior to an open-loop system. The following advantages are the fundamental reasons for using feedback. Many unnecessary disturbances and noise …

Read More »## Lyapunov Stability Analysis with Solved Examples

Lyapunov’s stability analysis technique is very common and dominant. The main deficiency, which severely limits its utilization, in reality, is the complication linked with the development of the Lyapunov function which is needed by the technique. The system dynamics must be described by a state-space model. It is a description …

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