MATLAB Control System Toolbox Root Locus Design GUI
MATLAB Control System Toolbox contains two Root Locus design GUI, sisotool and rltool . The are two interactive design tools for the analysis and design of the single-input single-output (SISO) linear time-invariant (LTI) control systems. sisotool opens the SISO Design Tool with Root Locus View and Bode diagram. rltool opens the SISO Design Tool with only Root Locus view on. The GUI allows you to design
compensators by interacting with the root locus, Bode, and Nichols plots of the open-loop system. To load an empty SISO Design Tool at MATLAB prompt type
>> sisotool
sisotool can also be called with additional arguments. For example, sisotool(Gp), or sisotool(Gp, Gc). Where Gp is the plant object model and Gc is the compensator object model.小仲马作品
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
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• Load the model from the SIMULINK diagram韩束属于什么档次
Similarly, rltool opens SISO Design Tool with only the Root Locus View.
Following examples are ud to demonstrate some of the features of the Root Locus Design.
磨山景区Example 1
In the control system shown G is a proportional controller,.
()c s K
Using sisotool determine the following:
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(a) Range of for system stability.
K (b) Value of for the complex dominant-poles damping ration of 0.6. For this value of obtain the frequency respon GM and PM. Also obtain the step respon and the time-domain specifications.
K K
To make the plant model and start the SISO Design Tool, at the MATLAB prompt type
>> Gp = tf(1, [1 7 10 0])
>> sisotool
An empty SISO Design Tool opens as shown.
The SISO Design Tool by default assumes that the compensator is in the forward path. The FS button toggles between two configurations, placing the compensator in the feedback or forward path as shown above. Select Import Model under the File menu. This opens the Import System Data dialog box, which is shown below. 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.
Select Gp and click on the arrow button to place it in the G field.
海尔兄弟冰箱The Other button toggles between the two configurations. Click OK. The root locus and open-loop Bode diagrams are displayed in the plot regions. The red squares on the loci reprents the clod-loop poles corresponding to gain t point (default value C(s) = 1). Also the gain margin and the pha margin for the default gain of C(s) = 1 are listed on the Bode plot.
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The SISO Design Tool has right-click menus available in the plot regions with many features.
火爆行业Right-Click Menu on the Root Locus plot Right-click Menu on the Bode plot
You can change the compensator gain by typing a value in the C(s) field. Also, you can change the gain by grabbing the red squares (clod-loop poles) on the root locus plot and moving them along the curve to the desired location. To place the roots accurately in a desired location first, lect Zoom XY from the right-click menu; then lect a region of the root locus, hold and place a small square in the desired region. This will zoom in the desired region. Alternatively you can u the Mou Zoom from the Zoom icons on the toolbar. Click on the Mou Zoom icon (Zoom in XY), and then repeatedly click on the desired location on the root locus for the necessary zoom. Turn off the Mou Zoom. Drag the clod loop pole to the desired location.
(a) To find the value of for marginal stability drag the clod-loop pole along the locus to the K j ω-axis interct. Turn on the Mou Zoom and drag the mou to draw a box around the pole. When the mou is relead, root locus will zoom in on the lected region. Drag the pole to this accurate position. The gain for marginal stability is found to be . A zoom out result is as shown.
70c K =
(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. Then zoom in and drag the pole until damping ratio is 0.6. The result is as shown.
The gain is found to be . Also one of the complex pole and the natural frequency are displayed in the bottom panel, i.e., 08.89K =10.766 1.02s j =−+ and 1.28n ω= rad/s. In addition the Gain Margin and Pha Margin are displayed in the Bode plot area, i.e., dB, and .
17.9GM =58.6=D PM
From Tools Menu lect Loop respons/Clo-Loop Step to obtain the step respon. Right-click on the plot, and lect Characteristics and then Ri Time and Peak Overshoot. Left click on the blue dots, this will display the time-domain specifications shown in the Figure below.
