Chapter 5: Root Locus
Chapter 5: Root Locus
Contents5-1Introduction ofRootLocus5-2Properties ofRootLocus5-3RootLocus SketchingRules5-4Root Locus Based SystemAnalysis andDesign
Contents 5-1 Introduction of Root Locus 5-2 Properties of Root Locus 5-3 Root Locus Sketching Rules 5-4 Root Locus Based System Analysis and Design
5-1Introduction ofRootLocusWhat we have known?.We have had a quick look at modeling and analysis forspecifying system performance.(Time domain method for first and second order systems).We will now look at a graphical approach, knownas the root locus method, for analyzing and designingcontrol systems·As we will see, the root locations are important indetermining the nature of the system response
• We have had a quick look at modeling and analysis for specifying system performance. (Time domain method for first and second order systems) • We will now look at a graphical approach, known as the root locus method, for analyzing and designing control systems • As we will see, the root locations are important in determining the nature of the system response What we have known? 5-1 Introduction of Root Locus
Proportional controllerR(s)C(s)G(s)KH(s)WehaveseenhowthisformoffeedbackisabletominimizetheeffectofdisturbancesForinvestigatingtheperformanceofa system,wehaveto solvetheoutputresponseofthe system.Limitations:(l)It isdifficultto solvetheRoot Locusespecially for a higher ofas,stem's(2)Wecan'teasilyinvestigatekuenperformance from the time-domain--especiallywhenparametersofthesystemvaryinagivenrange,or,whendevicesareadded tothe system
We have seen how this form of feedback is able to minimize the effect of disturbances. For investigating the performance of a system, we have to solve the output response of the system. (1) It is difficult to solve the output response of a system – especially for a higher order system. (2) We can’t easily investigate the changes of a system’s performance from the time-domain -especially when parameters of the system vary in a given range, or, when devices are added to the system. Proportional controller G(s) R(s) C(s) - K H(s) Limitations: Root Locus