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 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 …

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 …

Read More »## Steady State Error | Feedback Systems

Steady State Error High loop gains were shown advantageous to reduce the sensitivity to modeling accuracy, parameter variations, and disturbance inputs. They will now prove equally desirable from the point of view of the reduction of steady-state errors in feedback systems. Consider the unity feedback system in Figure 1. The …

Read More »## Laplace Transform Properties in Signal and Systems

The Laplace transform fulfills a number of properties that are quite valuable in various applications. In particular, by using these properties, it is possible to derive many new transform pairs from a basic set of pairs. In this tutorial, we state most fundamental properties of the Laplace transform. Linearity If …

Read More »## Laplace Transform:Introduction and Example

Laplace Transform Definition The Laplace transform X(s) is a complex-valued function of the complex variable s. In other words, given a complex number s, the value X(s) of the transform at the point s is, in general, a complex number. Given a function x (t) of the continuous-time variable t, …

Read More »## Z Transform Introduction | Z Transform Properties

INTRODUCTION TO Z-TRANSFORM For the sake of analyzing continuous-time linear time-invariant (LTI) system, Laplace transformation is utilized. And z-transform is applied for the analysis of discrete-time LTI system. Z-transform is fundamentally a numerical tool applied for a transition of a time domain into frequency domain and is a mathematical function …

Read More »## Continuous Time Graphical Convolution Example

This is the continuation of the PREVIOUS TUTORIAL. Steps for Graphical Convolution First of all re-write the signals as functions of τ: x(τ) and h(τ) Flip one of the signals around t = 0 to get either x(-τ) or h(-τ) Best practice is to flip the signal with shorter interval …

Read More »## Continuous Time Convolution Properties | Continuous Time Signal

Continuous Time Convolution For linear time-invariant (LTI) systems, the convolution is being utilized in order to achieve output response from the knowledge of input and impulse response. Given two continuous-time signals x(t) and h(t), the convolution is defined as $y\left( t \right)=\sum\limits_{\tau =-\infty }^{\infty }{x\left( \tau \right)h\left( t-\tau \right)d\tau }~~~~~~~~~~~~~~~~~~~~~~~~\left( …

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