PID A-1 pole placement controller for second order processes.
Transfer function of the controlled system:
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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:
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where ek is control error ( ) and controller parameters , , and are calculated by solving following diophantine equation:
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where polynomials are as follows:
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for |
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for |
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Solving the diophantine equation leads to following relations for controller parameters:
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where:
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Source code:
sid |
on-line identification s-function |
pp2a_1 |
function for computation of controller parameters |
scqp |
controller s-function |
See also: