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This paper deals with optimal controller design for active magnetic bearing (AMB) systems for which nonlinear rotordynamic behavior is evident, and so vibration predicted by operating point linearization differs from that which occurs in actuality. Nonlinear H-infinity control theory is applied with a rotordynamic model involving nonlinear stiffness and/or damping terms. The associated Hamilton-Jacobi-Isaacs (HJI) equation is formulated and solved to obtain a state feedback control law achieving specified vibration attenuation performance in terms of the peak L 2 gain of the nonlinear system. The method is applied in case study to a flexible rotor/AMB system that exhibits nonlinear stiffness properties owing to rotor interaction with a clearance bearing. Simulations are performed to quantify RMS vibration due to harmonic disturbances and the results compared with the norm-bound values embedded in the HJI equations. A feedback controller design method is then presented that is similar in approach to the standard loop-shaping/mixed-sensitivity methods used for linear systems, and involves augmenting the system model with weighting transfer functions. Experiments are undertaken to compare controller performance for designs based on nonlinear and linearized models. The results highlight the shortcomings of applying linear optimal control methods with rotor systems exhibiting nonlinear stiffness properties as large amplitude vibration and loss of rotordynamic stability can occur. Application of the described nonlinear H-infinity control method is shown to overcome these problems, albeit at the expense of vibration attenuation performance for operation in linear regimes.

This paper considers the problem of controlling the vibration of a lightweight thin-walled rotor with a distributed actuation magnetic bearing (DAMB). A theoretical flexible rotor model is developed that shows how multiharmonic vibration arises due to small noncircularity of the rotor cross section. This model predicts a series of resonance conditions that occur when the rotational frequency matches a subharmonic of a system natural frequency. Rotor noncircularity can be measured offline, and the measurement data used to cancel its effect on the position sensor signals used for feedback control. A drawback of this approach is that noncircularity is difficult to measure exactly and may vary over time due to changing thermal or elastic state of the rotor. Moreover, any additional multiharmonic excitation effects will not be compensated. To overcome these issues, a harmonic vibration control algorithm is applied that adaptively modifies the harmonic components of the actuator control currents to match a target vibration control performance, but without affecting the stabilizing feedback control loops. Experimental results for a short thin-walled rotor with a single DAMB are presented, which show the effectiveness of the techniques in preventing resonance during operation. By combining sensor-based noncircularity compensation with harmonic vibration control, a reduction in vibration levels can be achieved without precise knowledge of the rotor shape and with minimal bearing forces.

Study aim: Evaluation of dynamic balance is inferred to be compulsory for fall prevention in the elderly. Therefore, this study aimed to develop a modified digital functional reach test device using an ultrasonic sensor for balance assessment and to test validity and reliability of the newly developed tool to qualify psychometric properties. Material and methods: This study was a cross-sectional study of a convenient sample including 50 participants both males and females. Mean age of the participants was 51.20 ± 19.30 years. Reliability of the newly developed device was analysed using the intraclass correlation coefficient (ICC) and standard error of measurement (SEM). The criterion validity was also investigated using a yardstick mounted on the wall at a level of shoulder together with the MaxTraq® 2D motion analysis software. The modified digital functional reach test device using an ultrasonic sensor was correlated with the conventional FRT and the MaxTraq® 2D motion analysis. Results: The results presented that test-retest reliability of the modified digital functional reach test device was good reliability (ICC = 0.76) and low standard error of measurement (1.41) was found for test-retest reliability. The degree of agreement between the modified device, the conventional FRT, and the MaxTraq® 2D motion analysis was high (r = 0.71 and 0.77 respectively). Conclusions: The findings suggested that the modified digital functional reach test device using an ultrasonic sensor was a valid and reliable instrument for fall risk screening towards functional reach distance.

This paper describes an exact linearizing control approach for a distributed actuation magnetic bearing (DAMB) supporting a thin-walled rotor. The radial DAMB design incorporates a circular array of compact electromagnetic actuators with multi-coil winding scheme optimized for supporting thin-walled rotors. A distinguishing feature is that both the x and y components of the radial bearing force are coupled with all four of the supplied coil currents and so a closed form solution for the linearizing equations cannot be obtained. To overcome this issue, a gradient-based root-finding algorithm is proposed to solve the linearizing equations numerically in real-time. The proposed method can be applied with any chosen constraints on current values to achieve low RMS values while avoiding zero-current operating points. The approach is implemented and tested experimentally on a rotor system comprising two radial DAMBs and a uniform cylindrical shell rotor. The results show that the method achieves more accurate reproduction of demanded bearing forces, thereby simplifying the rotor suspension control design and providing improved stability and vibration control performance compared with implementations based on operating point linearization.