The root locus plot depicts the trajectories of closedloop poles when the feedbackgain k varies from 0 to infinity. Gain a better understanding of root locus plots using matlab. The root locus graphically displayed both transient response and stability information. A matlab commands commonly used for plotting root loci are rlocussys rlocus sys, k. Use the angle criteria to determine suitability of any questionable points. Root locus page 33 characteristic equation root locus is obtained by for a fixed k 0, finding roots of the characteristic equation, and sweeping k over real positive numbers. Specifying percent overshoot in the continuoustime root locus causes two rays, starting at the root locus origin, to appear. As the openloop gain, k, of a control system varies over a continuous range of values, the root locus diagram shows the trajectories of the closedloop poles of the feedback system. In the discretetime case, the constraint is a curved line. Root locus method is a widely used graphical technique to analyze how the system roots vary with variation in particular parametric quantity, generally a gain in a feedback control system. Section 5 root locus analysis college of engineering. Typically, the root locus method is used to tune the loop gain of a siso control system by specifying a designed set of closedloop pole locations. Using matlab r2007b, is it possible to get the asymptotic centroid, asymptotic angles and the break away and break in points for a root locus plot and its jw axis crossing.
Based on root locus graph we can choose the parameter for stability and the desired transient. Root locus plot of dynamic system matlab rlocus mathworks. How to plot the root locus of transfer function in matlab. Locus segments now, determine if point 6is on the root locus again angles from complex poles cancel always true for real. The poles on the root locus plot are denoted by x and the zeros are denoted by o. Pole zero plots for the system transfer function in eq.
Root locus method root locus matlab electrical academia. Specific points on the locus also can be found accurately to give quantitative design information. Root locus is a process practiced as a stability measure in classical control which can find out system stability by plotting closed loop transfer function poles as a function of a gain parameter in the. Plot root locus and return plot handle matlab rlocusplot. Evans, is widely used in control engineering for the design and analysis of control systems.
Root locus elec304alper erdogan 1 1 lecture 1 root locus. Root locus design is a common control system design technique in which you edit the compensator gain, poles, and zeros in the root locus diagram. A point s is on the root locus, if and only if ls evaluated for that s is a negative real number. This matlab function computes and plots the root locus of the singleinput, singleoutput lti model sys. For more info visit please feel free to write me your quarries suggestions email.
The locus can be sketched quickly to get a general idea of the changes in transient response generated by changes in gain. Goals introduction goals rationale howto examples this lecture will help you understand what a root locus is and how to create and use one. Pdf root locus design using matlab matlabassignment. In this video i go through various ways to use matlab to plot and visualize the root locus. In this method, the closedloop system poles are plotted against the value of a system parameter, typically the openloop transfer function gain.