How to Design Outer PID for Cascaded Control When Inner Loop Yields Imaginary Poles?

Hi,

I am implementing a Cascaded feeddback control (two PIDs, the inner being only an Integrator as the system is a PT1 and the outer WOULD be i guess a PID controller as i would be having a PT3 system then). Now when I want to parameterize my outer PID controller according to this table ( http://www.eal.ei.tum.de/fileadmin/tueieal/ww...utorial/WS1213/BDGEA_UE3_Handout_20130124.pdf ) , i m not able to find a correct Plant equation for it to relate to because when i get a complete plant equation from the inner loop for the outr loop, the plant has imaginery poles. And i guess the table above holds true only for Real poles. How do i proceed ?

Thankyou

Hi Adel,

Complex can be simplify that depends on the equation you have. You can denote as -1 sqrt or any setup that does not violate mathematical rules.

By the way, can you specify the table your are referring to or maybe I can't visualize it through the link you've provided because of its language. You may provide your plant Equation, so we'll try to comprehend the case you have. Thanks.

God Bless.

Best,
Neil

Hi Neil,

Sorry for the language of the table but i cannot seem to find an english version of it. I could try and make it simpler for u. below are some translations.
Strecke=Plant transfer function
Regler=Controller transfer function
Günstiger bereich=Valid area
Typ=Type(as in a P, I or PI etc.)
Einstellung=The values of Tn, Vr, Tv, Tg etc are defined here(which again are nothing but combinations of coefficients from the plant transfer function )
U can overlook the 'opt. krit' column.

The closed tranfer function for my inner loop(secondary) is attached.

T_w is the time constant ofcourse.

Regards