Design of Cascaded and Shifted Fractional-Order Lead Compensators for Plants with Monotonically Increasing Lags

Abstract

This paper concerns cascaded, shifted, fractional-order, lead compensators made by the serial connection of two stages introducing their respective phase leads in shifted adjacent frequency ranges. Adding up leads in these intervals gives a flat phase in a wide frequency range. Moreover, the simple elements of the cascade can be easily realized by rational transfer functions. On this basis, a method is proposed in order to design a robust controller for a class of benchmark plants that are difficult to compensate due to monotonically increasing lags. The simulation experiments show the efficiency, performance and robustness of the approach.

Analog Modeling of Fractional-Order Elements: A Classical Circuit Theory Approach

“…They are: the fractional order  (or equivalently the approximate phase angle i), the value Fo in (1), the frequency limits of the constant-phase bandwidth (CPB) L and H (or equivalently the specified bandwidth BW=H/L and the central frequency c), the phase deviation  (or Gmax/Gmin) representing the specified maximum allowable phase variation within the CPB limits as shown in Fig. 2, and the function order N (or approximation order n) 7 . The approximation methods used for the comparison are presented in chronological order.…”

“…This awareness has resulted in the increased development of fractional calculus applications in various fields of engineering and science. They include more efficient PI  D  controllers compared to conventional PID controllers [3]- [6], more precise lead/lag compensators [7] [8], a FO model that efficiently approximates the electroencephalographic measurement chain system [9], high-speed FO PLLs with broader capture range and bandwidth, lower phase error and shorter locking time [10], active-RC FO filters that allow for a fractional step in the stopband [11]- [15], FO resonators which can have infinite Q-factors [16], FO oscillators for very high or very low frequency signals [17], FO band-pass filters and resonators realized in integrated form allowing low frequency operation, huge inductance values and electronic tunability of order and other parameters [18] [19]. Besides, Westerlund has shown that capacitors with dielectric can only be modelled accurately with FO derivatives [20], because nature works with FO derivatives [21].…”

The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models

“…Example IV.1. The fractional lead (+α) compensator used in Control to increase the phase of a system around a chosen frequency and the lag (−α) compensator, used to increase the static gain of a plant, are defined by the TF [114], [23], [115] C(s) = τ s + a s + a (…”