This article describes a method for the active control of the deformations on a magnetically levitated moving-magnet planar motor. The planar motor under consideration is comprised of a stator on a double coil array configuration and a mover with permanent magnets, and it is designed to perform positioning tasks with nanometer level of accuracy. Due to the spatially asymmetric, nonuniform force distribution on the magnet plate, mechanical deformations are induced to the mover, which can severely hinder the desired positioning accuracy. The proposed method overcomes this challenge by properly shaping the force distribution on the moving magnet plate, which is enabled by the presence of multiple coils interacting with the mover, corresponding to an “overactuation” scheme. As a consequence, the independent control of elementary deformation shapes (modes) is achieved. The proposed overactuation scheme is experimentally validated on a planar motor prototype, proving the efficiency of the proposed method during both standstill and motion.

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, which are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for L ₂ -gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables.

We derive direct data-driven dissipativity analysis methods for Linear Parameter-Varying (LPV) systems using a single sequence of input-scheduling-output data. By means of constructing a semi-definite program subject to linear matrix inequality constraints based on this data-dictionary , direct data-driven verification of $(Q,S,R)$ -type of dissipativity properties of the data-generating LPV system is achieved. Multiple implementation methods are proposed to achieve efficient computational properties and to even exploit structural information on the scheduling, e.g., rate bounds. The effectiveness and trade-offs of the proposed methodologies are shown in simulation studies of academic and physically realistic examples.