RLTOOL - Root Locus Design GUIRLTOOL - Root Locus Design GUIThe Root Locus Design GUI is an interactive graphical tool to design compensators usingthe root locus method. This GUI plots the locus of the closed-loop poles as a function of the compensator gains. You can use this GUI to add compensator poles and zeros and analyze how their location affects the root locus and various time and frequency domain responses. Click on the various controls on the GUI to see what they do.The loop structure diagram shows the current configuration of the closed-loop system, including the locations of :The Root Locus toolbar provides options for building and manipulating the compensator. The four buttons allow you to : - Drag compensator poles and zeros, or closed-loop poles (in essence, change the compensator gain) - Add compensator poles (shown as red X's) - Add compensator zeros (shown as red O's) - Erase compensator poles and zerosYou can enter in a value for the compensator gain and visualize how the closed-loop poles move along the locus. The red squares in the figure above indicate the location of the closed-loop poles for this gain. You can also drag the closed-loop poles along the root locus and watch how the gain changes in this box.The grid check box toggles a default grid of constant damping ratio and natural frequencyon and off. You can change the default grid type from one of the options in the Tools menu.The axes show the locus of the closed-loop poles for the current model and compensator. The various features include : 1. The model poles and zeros (blue X's and O's, respectively) 2. Compensator poles and zeros (red X's and O's, respectively) 3. Closed-loop pole locations for the current compensator gain (red squares) 4. The locus of the closed-loop poles (blue lines) You can interact with this diagram using the various functions available from the Root Locus Toolbar at the top left of the axes.The Status bar provides additional information about the current, or last, action you performed with the Root Locus Design GUI. For example, the Status bar shows that the compensator gain was changed to 10.Closed-loop time domain responses and open-loop frequency domain responses can be analyzed by checking the desired check box. As shown above, checking one of the boxes opens an LTI Viewer displaying the desired response. This LTI Viewer is dynamically linked to the Root Locus Design GUI. Any changes to the compensator that affect the open- or closed-loop response are automatically shown in any open LTI Viewers.You can use the Zoom buttons to navigate around specific portions of the root locus diagram. In order, from left to right, you can - Zoom along both the X- and Y-axis - Zoom along the X-axis only - Zoom along the Y-axis only - Rescale the axes to show the entire locus Above, an X-Y zoom is being performed.http://www.engin.umich.edu/group/ctm/examples/motor2/rlocus2.htmlExample: Root Locus Design Method for DC MotorPosition Control Drawing the open-loop root locus Integral Control Proportional plus Integral Control Proportional plus Integral plus Derivative Control Finding the gain using the rlocfind command and plotting the closed-loop response From the main problem, the dynamic equations in transfer function form are the following: and the system schematic looks like: For the original problem setup and the derivation of the above equations, please refer to the Modeling a DC Motor page. With a 1 rad/sec step reference, the design criteria are: - Settling time less than 0.04 seconds - Overshoot less than 16% - No steady-state error - No steady-state error due to a