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Left click on the blue dots, this will display the time-domain specifications shown in the Figure below. Right-click on the plot, and select Characteristics and then Rise Time and Peak Overshoot. In addition the Gain Margin and Phase Margin are displayed in the Bode plot area, i.e., GM = 17.9 db, and PM = From Tools Menu select Loop responses/close-loop Step to obtain the step response. The gain is found to be K 0 = Also one of the complex pole and the natural frequency are displayed in the bottom panel, i.e., s1 = j1.02 and ω n = 1.28 rad/s. Then zoom in and drag the pole until damping ratio is 0.6. c 7B.4ĥ (b) To find the gain for damping ratio of 0.6, drag the complex pole until the damping ratio displayed in the bottom panel is in the neighborhood of 0.6. The gain for marginal stability is found to be K = 70. When the mouse is released, root locus will zoom in on the selected region. Turn on the Mouse Zoom and drag the mouse to draw a box around the pole. (a) To find the value of K for marginal stability drag the closed-loop pole along the locus to the jω -axis intersect. Drag the closed loop pole to the desired location. Click on the Mouse Zoom icon (Zoom in XY), and then repeatedly click on the desired location on the root locus for the necessary zoom. Alternatively you can use the Mouse Zoom from the Zoom icons on the toolbar. To place the roots accurately in a desired location first, select Zoom XY from the right-click menu then select a region of the root locus, hold and place a small square in the desired region. Also, you can change the gain by grabbing the red squares (closed-loop poles) on the root locus plot and moving them along the curve to the desired location. Right-Click Menu on the Root Locus plot Right-click Menu on the Bode plot 7B.3Ĥ You can change the compensator gain by typing a value in the C(s) field. The SISO Design Tool has right-click menus available in the plot regions with many features. Also the gain margin and the phase margin for the default gain of C(s) = 1 are listed on the Bode plot. The red squares on the loci represents the closed-loop poles corresponding to gain set point (default value C(s) = 1). The root locus and open-loop Bode diagrams are displayed in the plot regions. 7B.2ģ The Other button toggles between the two configurations. Select Gp and click on the arrow button to place it in the G field. All the available models will appear in the Model Listbox: The Blocks are coded as F (A preamplifier), G (Plant model) H (Sensor), K (Compensator) with default values of 1. This opens the Import System Data dialog box, which is shown below. The FS button toggles between two configurations, placing the compensator in the feedback or forward path as shown above. 7B.1Ģ The SISO Design Tool by default assumes that the compensator is in the forward path.
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To make the plant model and start the SISO Design Tool, at the MATLAB prompt type > Gp = tf(1, ) > sisotool An empty SISO Design Tool opens as shown. Also obtain the step response and the time-domain specifications. For this value of K obtain the frequency response GM and PM. (b) Value of K for the complex dominant-poles damping ration of 0.6. R() s G () c s Gp () s = 1 ss ( + 2)( s+ 5) Cs () Using sisotool determine the following: (a) Range of K for system stability. Example 1 In the control system showng ( s c ) is a proportional controller, K. Following examples are used to demonstrate some of the features of the Root Locus Design. You can import SISO LTI model into the Root Locus Design as follows: Load a model from the MATLAB workspace Load a model from a MAT-file Load the model from the SIMULINK diagram Similarly, rltool opens SISO Design Tool with only the Root Locus View.
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Where Gp is the plant object model and Gc is the compensator object model. For example, sisotool(gp), or sisotool(gp, Gc). To load an empty SISO Design Tool at MATLAB prompt type > sisotool sisotool can also be called with additional arguments. These GUI allows you to design compensators by interacting with the root locus, Bode, and Nichols plots of the open-loop system. rltool opens the SISO Design Tool with only Root Locus view on. sisotool opens the SISO Design Tool with Root Locus View and Bode diagram. These are two interactive design tools for the analysis and design of the singleinput single-output (SISO) linear time-invariant (LTI) control systems. 1 MATLAB Control System Toolbox Root Locus Design GUI MATLAB Control System Toolbox contains two Root Locus design GUI, sisotool and rltool.