Control Systems

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 …

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 …

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 …

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 domain …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

Depending upon the process to be controlled and technical and economic 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 …

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 …