On Cauchy’s Interlacing Theorem and the Stability of a Class of Linear Discrete Aggregation Models Under Eventual Linear Output Feedback Controls

Real-Time Control for the EHU Stellarator

At present, two main magnetic confinement fusion devices exist: tokamaks and stellarators. Moreover, stellarators have been demonstrated to be a good alternative to tokamaks, due to their ability to operate in continuous mode, which eventually translates into a higher commercial profitability. In stellarators, the magnetic confinement of the plasma is achieved exclusively by the coils, thus no electric current through the plasma is needed. In particular, this article presents the Columbia Non-Neutral Torus stellarator that is located in the Automatic Control Group of Euskal Herriko Unibertsitatea (EHU). This EHU stellarator maintains symmetry in its structure due to the topology of the mesh that is formed by its coils. A cornerstone of future fusion reactors is to obtain real-time control that enables a sustained reaction. In this article, a control-oriented model for the installed magnetic confinement coils is presented. The model is based on matrices that preserve symmetry, which is defined from physical principles and then validated by different sets of experimental data. Then, based on this model, a novel predictive control suited to this particular model with symmetric objective function is implemented in the numerical simulations, and its response is compared to that of traditional controllers. Finally, this control is implemented in a real plant and the satisfactory experiment results provide validation of both the numerical model and proposed controller.

A New Stability Theory for Grünwald–Letnikov Inverse Model Control in the Multivariable LTI Fractional-Order Framework

The new general theory dedicated to the stability for LTI MIMO, in particular nonsquare, fractional-order systems described by the Grünwald–Letnikov discrete-time state–space domain is presented in this paper. Such systems under inverse model control, principally MV/perfect control, represent a real research challenge due to an infinite number of solutions to the underlying inverse problem for nonsquare matrices. Therefore, the paper presents a new algorithm for fractional-order perfect control with corresponding stability formula involving recently given H- and σ -inverse of nonsquare matrices, up to now applied solely to the integer-order plants. On such foundation a new set of stability-related tools is introduced, among them the key role played by so-called control zeros. Control zeros constitute an extension of transmission zeros for nonsquare fractional-order LTI MIMO systems under inverse model control. Based on the sets of stable control zeros a minimum-phase behavior is specified because of the stability of newly defined perfect control law described in the non-integer-order framework. The whole theory is complemented by pole-free fractional-order perfect control paradigm, a special case of fractional-order perfect control strategy. A significant number of simulation examples confirm the correctness and research potential proposed in the paper methodology.