1. Modern Control System EKT 308 Root Locus and PID controllers

2. PID Controllers Proportional Controller

3. PID Controllers (contd…) Integral controller

4. Derivative controller PID controller

5. PID Controllers (contd…)

6. Effect of a PID controller on the system Fig 1: PID controller and the process

8. PID Controllers (contd…) Whereas the original system had two poles and no zeros, now the controller + system has three poles and two zeros. The root locus of the system is shown in figure 2 below. Fig 2: root locus of system + controller

9. PID Controllers (contd…) f) Angle of arrival at –z1 and –z2

10. The resulting PID+System has i) Percentage overshoot to step input, less than 2% ii) Steady state error for step input will be zero. iii) Settling time will be approax 1 sec. Lower settling time can be obtained by further adjusting Kd, Kp and KI

11. Frequency Response By the term frequency response, we mean the steady-state response of a system to sinusoidal input. In frequency response methods, we vary the frequency of the input signal over a certain range and study the resulting response.

18. Outline for Bode plot

24. Plot of tan(theta) versus theta Plot of atan(x) versus x

27. Step 1:

28. Step 2: Step 3:

29. Step 4: To be continued ….