Fractional-Order Feedback in Linear Systems

摘要

Three methods of producing the fractional derivative or integral of an input signal are investigated. The method selected employs a circuit developed at Trent University, Ontario, Canada for use in electrochemistry research. The results presented show the circuit accurately differentiates a sinusoidal input for a frequency range spanning 0.01 Hz to 10.0 Hz. The second-order differential equation above is simulated on an analog computer. An optimal u(t) is then used for feedback modification of the original open-loop system. Improved system performance resulted. A Laplace transform method and a Mittag-Leffler expansion provide analytical predictions of the system's response. The output of the two methods is identical. Comparison of the theoretical predictions with the experimental data shows the excellent agreement with respect to the initial transient behavior and asymptotic behavior of the steady-state response for both the open- and closed-loop systems. Keywords: Theses. (KR)