Bode shaping-based design methods of a fractional order PID controller for uncertain systems

Abstract

This paper deals with robust fractional order PID controller design via numerical optimization. Three new frequency-domain design methods are proposed. They achieve good robustness to the variation of some parameters by maintaining the open-loop phase quasi-constant in a pre-specified frequency band, i.e., maintaining the iso-damping property of the controlled system. The two first methods are extensions of the well-known Monje-Vinagre et al. method for uncertain systems. They ameliorate the numerical optimization algorithm by imposing the open-loop phase to be flat in a frequency band not only around a single frequency. The third method is an interval-based design approach that simplifies the algorithm by reducing the constraints number and offers a more large frequency band with an iso-damping property. Several numerical examples are presented to show the efficiency of each proposed method and discuss the obtained results. Also, an application to the liquid carbon monoxide level control is presented.B. Saidi · M. Amairi (B) · S. Najar · M. Aoun Research Unit Modeling, Analysis and Control of Systems (MACS)06/UR/11-12, National Engineering

Review of fractional PID controller

“…The bode and bode envelope are shaping tuning methods presented in [107] . These methods, which are an extension of the Monje-Vinagre et al method, are based on numerical optimization and robustness.…”

Numerical study of optimized fractional-order controller for chaos control of nonlinear dynamical power system

“…While because of constant phase feature of FOPID, phase margin remains unchanged even if gain varies over a wide range (due to interlacing of poles and zeros in such a fashion so as to make phase plot a flat response). Details of interlacing and FOPID design are well documented in another study …”

“…Details of interlacing and FOPID design are well documented in another study. 14 This additional freedom of fractional order of integration (λ) and differentiation (μ) and its realization using desired Bode plot shaping, with K p , K I , and K D remaining the same, cause performance to be robust irrespective of gain variation of uncertain system gain.…”

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