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This paper deals with the design of fractional order PIlambdaDmu controllers, in which the orders of the integral and derivative parts, lambda and mu, 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 PIlambdaDmu 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.