Model Predictive Control Based on Linear Parameter-Varying Models of Active Magnetic Bearing Systems

Abstract

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.INDEX TERMS Model predictive control, linear parameter-varying models, magnetic bearing systems, parameter set mapping, asymptotic stability.

Imbalance compensation of active magnetic bearing systems using model predictive control based on linear parameter-varying models

“…Following the same steps presented in (Morsi et al, 2021), the PSM technique is applied to the LPV model (5). Table 4 shows the values of v m % (approximating accuracy) corresponding to different values of n ξ ; here n ξ = 4 is selected indicating that 97.9% of the system information is captured.…”

“…In our previous work (Morsi et al, 2021), an LPV-MPC scheme has been proposed to control the AMB system taking into account stability and feasibility guarantees. The main control objective in (Morsi et al, 2021) was to achieve a stable levitation of the rotor shaft of the AMB system while the rotor is in a stationary case (not rotating). Therefore, the sinusoidal imbalance problem has not been discussed, as it exists while the AMB system is rotating.…”

“…To achieve that, first, we adopt an AMB system based on the experimental setup of (Morse et al, 1996), see Figure 1. Then, a more detailed non-linear model of the AMB system, compared with the one presented in (Morsi et al, 2021), is considered which is embedded in an LPV representation. Next, to deal with the large number of the scheduling parameters of the obtained LPV model, the parameter set mapping (PSM) technique of (Kwiatkowski and Werner, 2008) is used.…”

Suspension Strategy of Maglev Vertical Axis Wind Turbine Based on Sliding Mode Adaptive Neural Network Predictive Control

“…And for the MVAWT studied in this paper, reliability, robustness and rapidity are the most important performance indicators. Therefore, model predictive control (MPC) with constraint optimization, simple structure and multi-objective optimization becomes an ideal suspension strategy, especially it has been widely employed in the field of power electronics in recent years [23][24][25][26][27][28][29]. In [27], the MPC based on two-level state feedback was designed to ensure the safe and reliable operation of MS.…”

“…In [28], the generalized MPC method based on input and output data was proposed to adjust the parameters of the controller and ensure the system stability while suppressing the vibration caused by the elastic track. In [29], an application of MPC based on linear parameter-varying model is presented to control the active magnetic bearing subject to input and state constraints. The simulation analysis verifies the effectiveness of the proposed control method, but the application of this method requires linearization of the magnetic levitation system.…”