Root Locus Matlab

The root locus plot depicts the trajectories of closed loop poles when the feedback gain k varies from 0 to infinity rlocus adaptively selects a set of positive gains k to produce a smooth plot.

Root locus matlab.

In this tutorial we will introduce the root locus show how to create it using matlab and demonstrate how to design feedback controllers that satisfy certain performance criteria through the use of the root locus. In the discrete time case the constraint is a curved line. As the open loop gain k of a control system varies over a continuous range of values the root locus diagram shows the trajectories of the closed loop poles of the feedback system. The poles on the root locus plot are denoted by x and the zeros are denoted by o.

The main idea of root locus design is to estimate the closed loop response from the open loop root locus plot. By adding zeros and or poles to the original system adding a compensator the root locus and thus the closed loop response will be modified. 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. We can use matlab and its control system toolbox to plot the root locus of a control system given its characteristic equation or its forward transfer function.

As the open loop gain k of a control system varies over a continuous range of values the root locus diagram shows the trajectories of the closed loop poles of the feedback system. Specifying percent overshoot in the continuous time root locus causes two rays starting at the root locus origin to appear. It takes a transfer function and applies the standard rules for sketching a root locus plot by hand. 1 as a first example consider the system which characteristic equation is as follows.

For example in. Rlocusgui is a graphical user interface written in the matlab programming language. Write a program to draw the root locus of a given transfer function. For example in.

Of course matlab can do this more accurately but it is important to know how pole and zero locations affect the final plot. Thus we are limited to those responses that exist along the root locus. Theory root locus in control theory the root locus is the locus of the poles and zeros of a transfer function as the system gain k is varied on some interval the root locus is a useful tool for analyzing single input single output siso linear dynamis systems. 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.

Plotting the root locus. Let s first view the root locus for the plant.