Abstract
Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc. In the present paper a novel fractional order generalized optimum method for controller design using frequency domain is presented. The tuning rules are inspired from the symmetrical optimum principles of Kessler. In the first part of the paper are presented the generalized tuning rules of this method. Introducing the fractional order, one more degree of freedom is obtained in design, offering solution for practically any desired closed-loop performance measures. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, using simple tuning-friendly equations. It can be applied to a wide range of process models, from integer order models to fractional order models. Simulation results are given to highlight these advantages.
Highlights
Fractional calculus has become very useful over the last years due to its many applications in almost all applied sciences
Classical fractional order controller tuning techniques usually establish the parameters of the controller by solving a system of nonlinear equations resulted from the frequency domain specifications like phase margin, gain crossover frequency, iso-damping property, robustness to uncertainty, etc
The tuning rules are inspired from the symmetrical optimum principles of Kessler
Summary
Fractional calculus has become very useful over the last years due to its many applications in almost all applied sciences. The work of Podlubny [8] had a major impact in control engineering He proposed a generalization of the PID controller, namely the PIλ Dμ controller, involving an integrator of order λ and a differentiator of order μ and of Oustaloup [9], who introduced the CRONE approach for these systems. Several works approach the tuning of the fractional order PID controller through frequency domain specifications, firstly described by [12]. The frequency domain fractional-order controller design methods are generally based on the following design specifications [12]: 2. After this first, brief introductory part, the second section describes the proposed controller design method, followed by case studies for different process models, from integer order model to fractional order model.
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