1. A Freq. Resp. Example Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design A Radar Tracking System  Design a unity DC gain phase lead compensator  Specs: o PM = 50  o T s < 4 sec Slide 1 of 8

2. A Freq. Resp. Example Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design A proportional gain controller:  The Bode diagram of the unity gain OL transfer fn GM = 3.5 dB (@1.4 rad/s) PM = 11  (@1.1 rad/s) Looks like we need to remove about 11 dB of gain 11 dB = 3.55 (gain) K = 1/3.55 = 0.282 11 dB Slide 2 of 8

3. A Freq. Resp. Example Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design A proportional gain controller:  The Bode diagram of the unity gain OL transfer fn GM = 14.5 dB (@1.4 rad/s) PM = 50  (@0.49 rad/s) Slide 3 of 8

4. A Freq. Resp. Example Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Closed Loop Step Response  The T s < 4 sec is NOT met  PO  19% Increasing the PM by reducing K  less PO, less CL BW, & slower T r K=0.455  PM of 35  K=0.158  PM of 65  Closed-Loop FR (magnitude) Slide 4 of 8

5. A Freq. Resp. Example Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Phase Lead Compensator  Design a unity gain (a 0 =1) phase lead comp  From the T s < 4 requirement (and PM (  m =50  ) Slide 5 of 8

6. A Freq. Resp. Example Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Phase Lead Compensator Slide 6 of 8

7. A Freq. Resp. Example Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Phase Lead Compensator  The OL Freq Resp GM = 23.8 dB (@ 8.8 rad/s) PM = 50  (@1.7 rad/s) Slide 7 of 8

8. A Freq. Resp. Example Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Phase Lead Compensator  The CL Unit Step Response:  Comparing Lead & Lag The Lead compensator design meets both the T s and PM requirements Slide 8 of 8