The performance of the fuzzy controllers depends highly on the proper selection of some design parameters which is usually tuned iteratively via a trial and error process based primarily on engineering intuition. With the recent developments in the area of global optimization, it has been made possible to obtain the optimal values of the design parameters systematically. Nevertheless, it is well known that unless a priori knowledge is available about the optimization search-domain, most of the available time-domain objective functions may result in undesirable solutions. It is consequently important to provide guidelines on how these parameters affect the closedloop behavior. As a result, some alternative objective functions are presented for the time-domain optimization of the fuzzy controllers, and the design parameters of a PID-type fuzzy controller are tuned by using the proposed time-domain objective functions. Finally, the real-time application of the optimal PID-type fuzzy controller is investigated on the robust stabilization of a laboratory active magnetic bearing system. The experimental results show that the designed PID-type fuzzy controllers provide much superior performances than the linear on-board controllers while retaining lower profiles of control signals.

Abstract-This paper studies the system identification and robust control of a multi-input multi-output (MIMO) active magnetic bearing (AMB) system. The AMB system under study is open-loop unstable, and the presence of right-half plane zeros and the rotor flexible modes bring additional degrees of difficulty to the control design of such a system. Firstly, a closed-loop system identification is performed by using frequency-domain response data of the system. Genetic Algorithm-based Weighted Least Squares method is employed to obtain the best frequencyweighted model of the system. As the cross-coupling channels have negligible gains in the low-frequency region, it is assumed that the system can be diagonalized. This allows the analysis of the system as a family of low-order single-input single-output (SISO) subsystems. On the other hand, the effects caused by the coupling channels become more significant at higher frequencies. Therefore, a similar method is used to obtain a high-order MIMO model of the system by including the cross-coupling effects. Next, SISO H∞ controllers and lead-lag type compensators are designed on the basis of the SISO models of the systems. To strive for a better performance, MIMO H2 and H∞ optimal controllers are synthesized on the basis of the MIMO model of the system. Extensive experimental studies are conducted on the performance of the designed SISO and MIMO controllers in real-time by taking into consideration both constant disturbances while the rotor is stationary, as well as sinusoidal disturbances caused by the centrifugal forces and the rotor mass-imbalance while the rotor is in rotation. Unlike the recently published works, it is shown that the accurate modeling of the system being controlled is the key to successful design of high-performance stable controllers that not only guarantee the internal stability of the system-controller interconnection, but also no further modifications are required before the real-time implementation of the designed controllers.

Active magnetic bearing systems (AMBs) have many potential industrial applications where extremely fast and accurate operations are required. However, AMBs are often subject to disturbances in the form of synchronous vibrations due to unmodeled dynamics such as the rotor mass-imbalance and centrifugal forces while the rotor is in rotation. Several methods such as variable notch filters, gain scheduling controllers, and linear parameter varying controllers have been proposed recently to reject the disturbances while the system is operating at high rotational speeds. These methods are practical only if the frequencies of these sinusoidal-like disturbances are directly measurable or accurately known in advance. In this paper, a hybrid control scheme comprised of a feedback H∞ controller and an inner-loop disturbance observer-based control is proposed. The effectiveness of this control scheme is verified by simulation and real-time experiments on an AMB system. Both constant and sinusoidal disturbances are taken into consideration while the rotor is stationary as well as while it is rotating at different speeds. The results demonstrate that the proposed hybrid control scheme exhibits significantly improved performance in comparison to single-loop controllers in the presence of unknown but bounded disturbances.

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