Patent ID: 7599752

Claim:
A method for tuning a fractional-order proportional-integral (PI) controller to control a process of an industrial plant, the method comprising: for a given fractional-order PI controller C(s) that is a function of proportional gain K p integral gain K p , K i , fractional integrator order α, and Laplace variable s, deriving values for controller parameters K p , K i , and α that satisfy a flat phase condition represented by ∠ ⁢ ⅆ G ⁡ ( s ) ⅆ s ⁢ | s = jw c ⁢ = ∠ ⁢ ⁢ G ⁡ ( s ) ⁢ | s = jw c . tuning the controller parameters K p , K i , and α based on iteratively testing the process of the industrial plant P(s) using a relay feedback approach; and controlling the process of the industrial plant P(s) by using the controller C(s), the controller C(s) comparing a measured value from the process with a reference setpoint value and calculating a new manipulated process output that brings the measured value of the process toward the reference setpoint value, wherein G(s) is the transfer function of the open loop system including the controller C(s) and the process of the industrial plant P(s) such that G(s)=C(s)P(s), and wherein w c is the gain crossover frequency at which the sensitivity circle tangentially touches the Nyquist curve.