PID controller

Control engineering and signal processing

Michala Srnová2009/2010

Content Compensator P compensator PI compensator Lead compensator Lag compensator PID controller

PID controller Proportional + integral + derivative

Transfer function: KD – derivative gain Used in majority of closed-loop industrial processes

PID controller Step response

Rise time Overshoot Settling Time Steady state Error

Effect of increasing the parameters:

Tune Alter step response Find out parameter Kp, Ki, Kd Various methods

Manual Tuning Ziegler-Nichols Software Tools Cohen-Coon

Manual Tuning No math required On-line method

1. What in characteristic need to be improved2. Kp – decrease the rise time3. Kd – reduce overshoot and settling time4. Ki – eliminate steady state error

Does not work in every time

Ziegler-Nichols Rules for determine Kp, Ki, Kd Based on step response Proposed more methods First method – Step response method No integrators No dominant

complex-pairs Response:

s-shape, no overshoot Ʈ, a

Ziegler-Nichols Parameters Ʈ and a – calculating

Drawbacks: lack robustness Improvement : K, Ʈ, T in model

From step response

Ziegler Nichols Second method – frequency response

1. Ki and Kd =0, setting of Kp2. Starting of ocsillations → Kc, period – Tc3. These values used to calculate Kp,Ki,Kd

Software Tuning Modern industrial facilities Online, offline method Software will

Gather data Develop process model Suggest optimal tuning

Principle Mathematical loops Frequency response to impulse Design PID loop values

Thank you for your attention