pp2a_1

PID A-1 pole placement controller for second order processes.

Transfer function of the controlled system:

Vector of identification initial parameter estimations:

Controller specific parameters:

Parameter

Description

xi – damping factor

Dumping factor x specifying dynamic behaviour of closed loop. The dynamic behaviour of the closed-loop is similar to second order continuous system with characteristic polynomial .

omega - natural frequency

Natural frequency w specifying dynamic behaviour of closed loop. The dynamic behaviour of the closed-loop is similar to second order continuous system with characteristic polynomial .

Control law:

where ek is control error (  ) and controller parameters , ,  and  are calculated by solving following diophantine equation:

where polynomials are as follows:

for

 

for

 

 

Solving the diophantine equation leads to following relations for controller parameters:

where:

Source code:

sid

on-line identification s-function

pp2a_1

function for computation of controller parameters

scqp

controller s-function

See also:

On-line identification methods

List of common controllers parameters