1. A Freq. Resp. Example (PID) Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design A Radar Tracking System  Design a PID controller  Specs: o PM = 50  o T s < 4 sec Slide 1 of 8

2. A Freq. Resp. Example (PID) Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design A proportional Derivative (PD) controller:  From T s  Now,  Also,  Now, K I = 0, hence

3. A Freq. Resp. Example (PID) Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Slide 3 of 8 A proportional Derivative (PD) controller:  The open loop frequency response PM = 50  (@1.68rad/s) Closed-Loop Step Response The closed-loop step response is very similar to the Lead Compensator

4. A Freq. Resp. Example (PID) Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Slide 4 of 8 A proportional, Integral, Derivative (PID) controller: Effectively a Lead-Lag controller  K P =1.1 remains unchanged  Lets try a range of integrator gains o Start “small” K I = 0.005, 0.05, and 0.5

5. A Freq. Resp. Example (PID) Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Slide 5 of 8 A PID controller: Closed-Loop Step Response Open-Loop Frequency Response

6. A Freq. Resp. Example (PID) Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Slide 6 of 8 A PID controller: Closed-Loop Step Response Open-Loop Frequency Response

7. A Freq. Resp. Example (PID) Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Slide 7 of 8 A PID controller: Closed-Loop Step Response Open-Loop Frequency Response

8. A Freq. Resp. Example (PID) Wednesday 25 Oct 2013 EE 401: Control Systems Analysis and Design Slide 8 of 8 A PID controller:  Closed-Loop pole locations