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•Our paper introduces a controller design formulation for plants containing relay nonlinearity.•The controller produces ‘reduced’ amplitude sustained oscillations in the output along-with desirable loop performance.•Describing function of nonlinearity is utilized for shaping the limit cycles and controlling the transient behavior.•The methodology is illustrated by designing a fractional PI controller.
In this paper, a constrained optimization problem is formulated to tune the limit cycle minimizing controllers meeting additional loop-shaping performances such as phase margin and gain crossover frequency. A graphical approach is proposed so as to determine the superior controller in terms of better limit-cycle suppression. The framework is illustrated with a suitable case of elementary servo plant...
In this paper, we report an interesting superiority of fractional order controllers over conventional order controllers. It is found that the fractional order proportionalintegral controllers (PIα and [PI]α) designed for precision modular servo experimental setup to meet given loop shaping requirements outperform the correspondingly designed integer order PID in limit cycle suppression. More precisely,...
The cart-pendulum system is a typical benchmark problem for testing various control algorithms. Basically, it is a Single Input Multi Output (SIMO) system which has two output variables to be controlled (pendulum-angle and cart-position) using a single input (input voltage to power amplifier). This paper presents application of fractional calculus to the design of controllers for such a system. The...
In the existing literature, tuning methods of fractional order controllers are available for given structure of plant. Generalization of such methods is necessary while dealing with different class of plants so as to minimize the tuning efforts. This paper provides such generalization to tune PIα / PDβ controller for any class of plants satisfying given performance and robustness specifications. The...
The tuning methods of fractional order PIα / PDβ controllers are available in the literature for the given structure of plant. Generalization of these methods to deal with any generalized fractional order plant structure minimizes the tuning efforts significantly. This paper provides such generalization to meet the given performance and robustness specifications. With the help of typical plant cases...
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