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This paper deals with the design of fractional order PI l D m controllers, in which the orders of the integral and derivative parts, l and m, respectively, are fractional. The purpose is to take advantage of the introduction of these two parameters and fulfill additional specifications of design, ensuring a robust performance of the controlled system with respect to gain variations and noise. A method for tuning the PI l D m controller is proposed in this paper to fulfill five different design specifications. Experimental results show that the requirements are totally met for the platform to be controlled. Besides, this paper proposes an auto-tuning method for this kind of controller. Specifications of gain crossover frequency and phase margin are fulfilled, together with the iso-damping property of the time response of the system. Experimental results are given to illustrate the effectiveness of this method. r

The objective of this work is to find out optimum settings for a fractional PI λ controller in order to fulfill three different robustness specifications of design for the compensated system, taking advantage of the fractional order, λ. Since this fractional controller has one parameter more than the conventional PI controller, one more specification can be fulfilled, improving the performance of the system and making it more robust to plant uncertainties, such as gain and time constant changes. For the tuning of the controller an iterative optimization method has been used, based on a nonlinear function minimization. Two real examples of application are presented and simulation results are shown to illustrate the effectiveness of this kind of unconventional controllers.

In recent years the increasing amount of work related to the application of Fractional Calculus (FC) is remarkable in many areas of science and engineering. In relation to automatic control, the use of Fractional Order Control (FOC) needs, for real applications, to develop methods for controller design and parameter tuning, and efficient strategies for controller implementation. On the other hand, the Proportional Integral Derivative (PID) controller is currently by far the most widely used form of feedback controller in industrial applications. This paper, after an introduction to FC and FOC, briefly presents methods for fractional PID controller tuning, including auto-tuning, and some software and hardware strategies for efficient implementations of controllers in industrial applications.

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