Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

Abstract

Robust pole-placement based on convex DR-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is non-convex, having a “cardioid” shape. In this paper, we further develop our recent results on the inner convex approximations of the cardioid, present systematical analysis of its design parameters and their influence on the corresponding closed loop performance (measured by standard integral of absolute error (IAE) and Total Variance criteria). The application of a robust controller designed with the proposed convex approximation of the discrete-time pole region is illustrated and evaluated on a real laboratory magnetic levitation plant.

Comparison of Nonlinear and Linear Controllers for Magnetic Levitation System

“…This paper studies and compares control designs for Magnetic levitation laboratory plant (ML), Figure 1. Magnetic levitation is inherently unstable system with fast dynamics corresponding to electromagnetic forces [19,25]. In our laboratory plant, the aim is to position the levitating ferromagnetic ball (sphere) within the air-space between two electromagnets.…”

“…To guarantee stability around the working point, the resulting linearized model is then represented as a polytopic uncertain system. For such system model, we recall a robust pole region approach introduced in [9] and briefly summarize our recent results for a discrete-time domain [18,19]. Robust pole-placement control is designed directly in a discrete-time domain since control implementation uses digital controller.…”

“…The existing results in literature have been mostly proposed for continuous-time systems [10,14,15,17]. In our recent works [18][19][20] we developed specific D R regions for discrete-time systems, motivated by the fact that in real world application, mostly the digital controllers are implemented. In this paper we aim at the comparison of our recent results on robust poleplacement discrete-time state feedback control design with a nonlinear control developed for a laboratory magnetic levitation (ML) plant.…”

“…Most of them consider continuous-time control. In [18][19][20] we proposed D R region based discrete-time robust pole-placement controller for ML system. This paper is devoted to a study and comparison of two principal approaches applied on a laboratory Magnetic levitation system.…”

“…The first approach is based on feedback linearization [3,4,22], where an algebraic transformation is applied on nonlinear state space model together with a nonlinear control law to obtain the linearized closed-loop system. The second approach employs robust pole-placement controller design for a system linearized around the working point and described by an uncertain polytopic system [7,9,18,19]. The main contribution of the paper is in simplified development of nonlinear control law with novel approximation of nonlinear terms, developed robust pole-placement controller for different levitating balls, comparison and evaluation of the obtained results received with nonlinear continuous-time control and discrete-time linear one.…”