Control System Toolbox

Transcription

1 The Almighty University of Mohaghegh Ardabili Control System Toolbox The SISO Design Tool 1

2 Transfer Function TF = 2s + 4 s 2 + 6s + 5 TF = TF = 2(s + 2) (s + 1)(s + 5) 2(s + 2) (s + 1)(s + 5) 0 1 A= 5 6 B= 0 1 C= [2 4] D= 0 sys = tf( 2 4, ) sys = zpk( 2, 1 5, 2) sys = tf(conv 2, 1 2, conv( 1 1, 1 5 )) [n p] = ss2tf(a, B, C, D) sys= tf(n,p) 2

3 LTI Viewer 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 Access the LTI Viewer typing ltiview in the MATLAB Command Window 3

4 LTI Viewer File --> Import 4 whose responses you wish to display in the LTI Viewer sometime during your current session

5 LTI Viewer Right Click 5

6 SISO TOOL The SISO Design analyze and tune SISO feedback 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 and Bode diagrams to adjust the bandwidth, check the gain and phase margins 6

7 SISO TOOL You can perform the following tasks: 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. 7

8 SISO TOOL Access sisotool G = tf( 2 4, ) sisotool(g) ( Open loop TF ) G = tf( 2 4, ) C = tf(1, 2 5 ) sisotool(g, C) 8

9 SISO TOOL Add/Delete Zero or Pole 9

10 SISO TOOL Compensator Plant Prefilter Sensor 10

11 SISO TOOL File --> Import 11

12 SISO TOOL Add/Delete Pole and Zero Change (Pole and Zero) location 12

13 SISO TOOL 13

14 SISO TOOL 14

15 SISO TOOL You can do so many features by right clicking on corresponding plot windows 15

16 SISO TOOL To see closed-loop step-response, choose Responses Step Command from Analysis menu. 16

17 SISO TOOL To 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 17

18 SISO TOOL To transfer the data to SIMULINK, choose Draw Simulink Diagram from the Tools menu Note that: plant and compensator data have already been exported to MATLAB workspace File --> Export

19 Example 1 Design in Time Domain >> G = tf(1,[ ]) >> sisotool(g)

20 Example 1 To find the value of K for marginal stability drag the closed-loop pole along the locus to the jw-axis intersect And the value of K will change to 70

21 Example 1 To find the gain of damping ratio of 0.6 drag the complex pole Until the Damping displayed in the bottom panel reach to that value And the value of K will change to 8.89

22 Example 1 Now, Let s Design a PD compensator C(s) = K P + K D S for the following case : Damping ratio ζ = Settling time of t s = 2s

23 Example 1 To place a pair of complex poles on your diagram at a damping ratio of You can do the same for settling time

24 Example 1 To have a close loop pole at -2+j2, A zero must be added to shift the luci towards the left half s plane

25 Example 1 Zero at K =24 Using in workspace File --> Export Response to Step Command From Analysis menu

26 Example 2 Design in Frequency Domain 50 < ω c < 70 Minimum Phase Margin = 60

27 Example 2 But PM :

28 Example 2 As we need Phase Margin to be more than 60 We have too use a compensator Here we will use a Lead compensator Φ m = =48.7 We choose 55

29 Example 2 To Find K : For K= 100

30 Thanks [1] Matlab Help on Control System Toolbox Root Locus Design GUI [2] Guidelines for MATLAB s SISO Design Tool GUI, Dr. Farzad Pourboghrat [3] Linear Control Systems, Faculty of Electrical, Amirkabir University, fall 2009 ( In Persian )