Tuning methods for fractional-order controllers

Details Tuning methods for fractional-order controllers Tuning methods for fractional-order controllers

2006-05-17

2009-10-06

Masinick, Michael D (Department: 2128)

Data processing: generic control systems or specific application

Generic control system, apparatus or process

Optimization or adaptive control

C700S028000

Reexamination Certificate

active

07599752

ABSTRACT:
A method for tuning a fractional-order proportional-integral (PI) controllerC⁡(s)=Kp⁡(1+Ki⁢1sα)includes deriving values for Kp, Ki, and α that satisfy a flat phase condition represented by∠⁢ⅆG⁡(s)ⅆs⁢s=jwc⁢=∠⁢⁢G⁡(s)s=jwc.Kpis derived to ensure that a sensitivity circle tangentially touches a Nyquist curve on a flat phase. Kiand α are derived to ensure that a slope of a Nyquist curve is approximately equal to the phase of an open loop system at a given frequency. A method for tuning a PI controllerC⁡(s)=Kp⁡(1+Ki⁢1sα)where the gain crossover frequency wcis known includes obtaining measurements of ∠P(jwc) and |P(jwc)| of an unknown, stable real plant P(s) using iterative relay feedback tests, and approximating the derivative of the plant phase, ∠P(jwc), provided by the relationshipsp⁡(wc)=wc⁢ⅆ∠⁢⁢P⁡(jw)ⅆw⁢❘wc⁢≈∠⁢⁢P⁡(jwc)+2π⁡[ln⁢Kg-ln⁢P⁡(jwc)],wherein |Kg|=P(0) is the static gain of the real plant P(s).

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