Modern Control System EKT 308 Root Locus and PID controllers

PID Controllers Proportional Controller

PID Controllers (contd…) Integral controller

Derivative controller PID controller

PID Controllers (contd…)

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

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

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

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

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.

Outline for Bode plot

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

Step 1:

Step 2: Step 3:

Step 4: To be continued ….