The Almighty1Control System ToolboxThe SISO Design Tool University of Mohaghegh ArdabiliIntLTIViewSisotool EX 1EX 2 Transfer Function =2 + 4

2+ 6 + 5 = ( 2 4 , 1 6 5 ) =( + )( + )( + ) = (, , ) =2( + 2)( +1)( + 5) = ( 2, 1 2 , ( 1 1 , 1 5 )) [ ] = (, , , ) sys= tf(n,p)A= B=

C=[2 4]D= 0 2Int LTIView Sisotool EX 1EX 2 The LTI Viewer can display up to Seven different plot types simultaneously, including step, impulse, Bode (magnitude and phase or magnitude only), Nyquist, Nichols, sigma, pole/zero, and I/O pole/zero LTI Viewer typing ltiview in the MATLAB Command Window Access the LTI Viewer 3Int LTIView Sisotool EX 1EX 2 LTI Viewer File --> Import whose responses you wish to display in the LTI Viewer sometime during your current session 4Int LTIView Sisotool EX 1EX 2 LTI Viewer Right Click 5Int LTIView Sisotool EX 1EX 2 SISO TOOLThe SISO Designanalyze and tuneSISOfeedback control systems Using the SISO Design Tool, you can graphically tune the gains and dynamics of the compensator (C) and prefilter (F) root locus view to stabilize the feedback loop Enforce some minimum damping andBode diagrams to adjust the bandwidth, check the gain and phase margins 6Int LTIView Sisotool EX 1EX 2 SISO TOOL Manipulate closed-loop dynamics using root locus techniques. Shape open-loop Bode responses. Add compensator poles and zeros. Add and tune lead/lag networks and notch filters. Inspect closed-loop responses (using the LTI Viewer). Adjust phase and gain margins. Convert models between discrete and continuous time. You can perform the following tasks: 7Int LTIView Sisotool EX 1EX 2 SISO TOOLAccess = ( , ) () = (1, 2 5 ) (, ) = ( 2 4 , 1 6 5 ) 8( ) Int LTIView Sisotool EX 1EX 2 SISO TOOLAdd/Delete Zero or Pole 9Int LTIView Sisotool EX 1EX 2 SISO TOOLPlant Sensor Prefilter Compensator10Int LTIView Sisotool EX 1EX 2 SISO TOOLFile --> Import 11Int LTIView Sisotool EX 1EX 2 SISO TOOL12Add/Delete Pole and ZeroChange (Pole and Zero) locationInt LTIView Sisotool EX 1EX 2 SISO TOOL13Int LTIView Sisotool EX 1EX 2 SISO TOOL14Int LTIView Sisotool EX 1EX 2 SISO TOOL15You can do so many features by right clicking oncorresponding plot windows Int LTIView Sisotool EX 1EX 2 SISO TOOL16To see closed-loop step-response,choose Responses Step Command from Analysis menu. Int LTIView Sisotool EX 1EX 2 SISO TOOL17To transfer the plots to another application such as WORD, choose Print to Figure from File menu and then Save it by an .emf type file so you can change some properties later even in Microsoft Word Int LTIView Sisotool EX 1EX 2 SISO TOOLTo transfer the data to SIMULINK, chooseDraw Simulink Diagram from the Tools menu Note that: plant and compensator data have already been exported to MATLAB workspace File --> ExportInt LTIView Sisotool EX 1EX 2 Example 1 >> G = tf(1,[1 7 10 0]) >> sisotool(G) Design in Time Domain Int LTIView Sisotool EX 1EX 2 Example 1 To find the value of K for marginal stabilitydrag the closed-loop pole along the locus to the jw-axis intersect And the value of Kwill change to 70 Int LTIView Sisotool EX 1EX 2 Example 1 To find the gain of damping ratio of 0.6 drag the complex poleUntil the Damping displayed in the bottom panel reach to that value And the value of Kwill change to 8.89 Int LTIView Sisotool EX 1EX 2 Example 1 Now, Lets Design a PD compensator C(s) = KP + KDS for the following case : Damping ratio = 0.707 Settling time of ts = 2s Int LTIView Sisotool EX 1EX 2 Example 1 To place a pair of complex poles on your diagram at a damping ratio of 0.707 You can do the same for settling time Int LTIView Sisotool EX 1EX 2 Example 1 To have a close loop pole at -2+j2, A zero must be addedto shift the lucitowards the left halfs plane Int LTIView Sisotool EX 1EX 2 Example 1 Zero at -2.397 K =24 Using in workspace File --> Export Response to Step Command From Analysis menu Int LTIView Sisotool EX 1EX 2 Example 2 Design in Frequency Domain 50 < c< 70 Minimum Phase Margin = 60 Int LTIView Sisotool EX 1EX 2 Example 2 But PM : Int LTIView Sisotool EX 1EX 2 Example 2 As we need Phase Margin to be more than 60 We have too use a compensatorHere we will use a Lead compensator m = 60 11.3 =48.7We choose 55 Int LTIView Sisotool EX 1EX 2 Example 2 To Find K : For K= 100 Thanks [1] Matlab Help on Control System Toolbox Root Locus Design GUI [2] Guidelines for MATLABs SISO Design Tool GUI , Dr. Farzad Pourboghrat [3] Linear Control Systems , Faculty of Electrical , Amirkabir University , fall 2009 ( In Persian )