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…)

PID Controllers (contd…) Effect of a PID controller on the system

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 1 below. Fig 1: 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