Active magnetic bearing (AMB) system has been recently employed widely as an ideal equipment for high-speed rotating machines. The inherent challenges to control the system include instability, nonlinearity and constricted range of operation. Therefore, advanced control technology is essential to optimize AMB system performance. This paper presents an application of model predictive control (MPC) based on linear parameter-varying (LPV) models to control an AMB system subject to input and state constraints. For this purpose, an LPV model representation is derived from the nonlinear dynamic model of the AMB system. In order to provide stability guarantees and since the obtained LPV model has a large number of scheduling parameters, the parameter set mapping (PSM) technique is used to reduce their number. Based on the reduced model, a terminal cost and an ellipsoidal terminal set are determined offline and included into the MPC optimization problem which are the essential ingredients for guaranteeing the closed-loop asymptotic stability. Moreover, for recursive feasibility of the MPC optimization problem, a slack variable is included into its cost function. The goal of the proposed feedback control system is twofold. First is to demonstrate high performance by achieving stable levitation of the rotor shaft as well as high capability of reference tracking without violating input and state constraints, which increases the overall safety of the system under disturbances effects. Second is to provide a computationally tractable LPVMPC algorithm, which is a substantial requirement in practice for operating the AMB system with high performance over its full range. Therefore, we propose an LPVMPC scheme with frozen scheduling parameter over the prediction horizon of the MPC. Furthermore, we demonstrate in simulation that such frozen LPVMPC can achieve comparable performance to a more sophisticated LPVMPC scheme developed recently and a standard NL MPC (NMPC) approach. Moreover, to verify the performance of the proposed frozen LPVMPC, a comparison with a classical controller, which is commonly applied to the system in practice, is provided.

This article introduces a systematic approach to synthesize linear parameter‐varying (LPV) representations of nonlinear (NL) systems which are described by input affine state‐space (SS) representations. The conversion approach results in LPV‐SS representations in the observable canonical form. Based on the relative degree concept, first the SS description of a given NL representation is transformed to a normal form. In the SISO case, all nonlinearities of the original system are embedded into one NL function, which is factorized, based on a proposed algorithm, to construct an LPV representation of the original NL system. The overall procedure yields an LPV model in which the scheduling variable depends on the inputs and outputs of the system and their derivatives, achieving a practically applicable transformation of the model in case of low order derivatives. In addition, if the states of the NL model can be measured or estimated, then a modified procedure is proposed to provide LPV models scheduled by these states. Examples are included to demonstrate both approaches.

A compact, reliable, and straightforward mathematical modeling of the eddy current (EC) braking torque is proposed in this article. First, the braking magnetic force, which curbs the movement of a rotating disk (RD), is evaluated using the basic laws of electromagnetism. Second, the braking torque is related to the braking force through a polynomial function model. The model parameters are evaluated by plugging in measurement samples in the equation of motion taking into account the nonlinear behavior of the aerodynamic drag forces. The proposed model neither has limitations on the braking system geometry nor the disk rotational speed as long as the measurement samples cover the whole speed range. Moreover, it is validated experimentally for constant and alternating magnetic flux profiles with best fit rates (BFRs) more than 85% and 93% for both rotational speed and braking torque, respectively. Furthermore, programmable braking application is demonstrated using the proposed approach and its applicability is verified experimentally.

In this paper, a practical model predictive control (MPC) for tracking desired reference trajectories is demonstrated for controlling a class of nonlinear systems subject to constraints, which comprises diverse mechanical applications. Owing to the linear parameter-varying (LPV) formulation of the associated nonlinear dynamics, the online MPC optimization problem is solvable as a single quadratic programming (QP) problem of complexity similar to that of LTI systems. For offset-free tracking, based on the notion of admissible reference, the controller ensures convergence to any admissible reference while its deviation from the desired reference is penalized in the stage cost of the optimization problem. This mechanism provides a safety feature under the physical limitations of the system. To guarantee stability and recursive feasibility, a terminal cost as a tracking error penalty term and a terminal constraint associated with both the terminal state and the admissible reference are included. We use tube-based concept to deal with the uncertainty of the scheduling parameter over the prediction horizon. Therefore, the online optimization problem is solved for only the nominal system corresponding to the current value of the scheduling parameter and subject to tightened constraint sets. The proposed approach has been implemented successfully in real-time onto a robotic manipulator, the experimental results illustrates its efficiency and practicality.