Automation, Control and Intelligent Systems 2014; 2(4): 42-52 Published online September 10, 2014 (http://www.sciencepublishinggroup.com/j/acis) doi: 10.11648/j.acis.20140204.11 ISSN: 2328-5583 (Print); ISSN: 2328-5591 (Online) Differential flatness applications to industrial machine control Ejike C. Anene 1 , Ganesh K. Venayagamoorthy 2 1 Electrical Engineering Programme, Abubakar Tafawa Balewa University, PMB 0248, Bauchi, Nigeria 2 Real-Time Power and Intelligent Systems Laboratory, Clemson University, Clemson, USA Email address: ejikeanene@yahoo.com (E. C. Anene), gkumar@ieee.org (G. K. Venayagamoorthy) To cite this article: Ejike C. Anene, Ganesh K. Venayagamoorthy. Differential Flatness Applications to Industrial Machine Control. Automation, Control and Intelligent Systems. Vol. 2, No. 4, 2014, pp. 42-52. doi: 10.11648/j.acis.20140204.11 Abstract: In this article the applications of differential flatness to some industrial systems are presented. Computational methods of obtaining the flat output and the straight forward method of constructing the corresponding control law are given. Some theoretical and industrial systems are used as illustration including the third order synchronous machine model and the one degree of freedom magnetic levitation system model. Computations of the flat output are done using various approaches. The Levine’s approach is presented in such detail as to facilitate quick understanding. Computations for the synchronous machine model yielded a flat output that is a function of the load angle while the magnetic levitation model yielded a flat output that is a function of the objects’ position. Results showing the stabilization of the applied systems in fault and uncertain situations are discussed. Keywords: Magnetic Levitation, Flatness, Feedback Linearization, Synchronous Machine 1. Introduction THE concept of differential flatness proposed by Michel Fliess and co-workers [1],[2] about twenty years ago has evolved into a full-fledged field for the study of control systems in a practically new way. In this setting, controllability is linked with system flatness and controllable systems possess this flatness property [3],[4]. For such systems there is a solution set called flat output in the solution space consisting of a set of state variables that completely parameterize the system without the need for solving differential equations. Once this output is shown to be flat, it in effect implies that the system possesses a well characterized dynamics[5] . This is because all system parameters and control becomes a function of the linearizing output that can enable the generation of reference trajectories a-priori. The construction of the feedback law is done by a simple inversion of system equations with respect to the control. The scheme in derivation is an extension from the input- output linearization scheme with zero internal dynamics. Fliess et-al [1] proposed the notion of endogenous equivalence and defined a class of dynamic feedbacks for classification and linearization of systems in the form of Fliess’ differential algebraic forms. Such classes of systems are the so-called differentially flat systems. One of the main consequences of their result is a constructive method of computing the feedback that exactly linearizes a flat system. Accordingly a control system , MF is differentially flat around p if and only if it is equivalent to a trivial system in a neighborhood of p . A trivial system can be defined as one which is without dynamics described by a collection of independent variables or R F s s ∞ , where F yy y yy y s (, , , ..... ) (, , , ..... ) () () () () 1 2 1 2 = , with y R s ⊂ y [6]. It is said to be differentially flat if it is differentially flat around every p of an open dense subset of M . The set y y j s j = = { | , ..... ,} 1 is called a flat or linearizing output of M described by a collection of independent variables, the flat output having the same number of components as the number of control variables. The following deductions are shown with proofs in [1]. 1. The number of components of a flat output is equal to number of input channels. 2. A classic linear system is flat if and only if it is controllable. 3. The controllability of differentially flat systems is related to the well known strong accessibility