Truncated Predictor Feedback Control for Active Magnetic Bearing Systems With Input Delay

One of the performance-limiting factors in the design of robust controllers for active magnetic bearing systems is the fact that the controller needs to be robust to the gyroscopic effects, that is rotational speed-dependent dynamics of the system. Studies in the literature show that better performance and stability can be achieved when gyroscopic effects are explicitly handled by a cross-feedback control for rigid rotor-active magnetic bearing systems. For flexible rotor-active magnetic bearing systems, gyroscopic effects are mainly dealt by defining the rotational speed as an uncertain parameter of the model or with linear parameter-varying controllers. This study explores the novel idea of compensating gyroscopic effects of a flexible rotor-active magnetic bearing system with an add-on controller and investigates its effects on the achieved performance of μ-controllers. The study is carried out on an experimental active magnetic bearing test rig with relatively high gyroscopic effects. An add-on controller is designed to compensate the gyroscopic effects of the first and second flexible modes of the rotor. Two μ-controllers are designed for the system: (1) benchmark controller that is designed using a standard control approach for active magnetic bearing systems and (2) controller designed with a modified model of the system in which the gyroscopic effects for the first and second flexible modes are reduced because of the presence of the add-on controller. Both controllers are implemented, and their performances are compared for initial levitation, run-up test from 0 to 10,000 r/min, orbit sizes at various speeds, and the computational cost of implementing each controller. The results suggest that better performance is potentially possible at the cost of significant increase in the computational complexity of the controller.

A successful industrial application of flexible rotors supported on active magnetic bearings (AMBs) requires careful attention not only to rotordynamic design aspects but also to electromagnetic and feedback control design aspects. Model-based control design provides the framework to ensure efficient, reliable, and safe operation of turbomachinery on AMBs. This paper describes in detail the design, construction, and modeling process for a high performance AMB test rig which typifies a small industrial super-critical centrifugal compressor. A unique aspect of the design are the two additional radial AMBs to allow the application of simulated destabilizing fluid or electromagnetic forces to the rotor. These forces are difficult to predict and can lead to rotordynamic instability of industrial machinery if not properly accounted for. This test rig provides a realistic platform to evaluate stabilizing control algorithms for high performance turbomachinery. A complete model of rotor, AMB actuators and accompanying electronics, is constructed from individually verified component models. Model validation is confirmed through the successful design and implementation of a μ-synthesis controller.

Magnetic levitation rotating machinery has been widely used in industrial applications. Odd harmonic currents in the active magnetic bearing coils, which are caused by rotor mass unbalance and sensor runout, increase the power consumption and the base vibration. Repetitive control has recently been used to suppress harmonic currents in magnetic bearing systems. However, repetitive control needs the rotor rotational speed information and has some limitations without a speed sensor. In this paper, an adaptive odd repetitive control which does not need the speed sensors is proposed to suppress the active magnetic bearing odd harmonic currents. Compared to the conventional repetitive control, the second-order generalized integral frequency-locked loop is applied in adaptive odd repetitive control to estimate the rotor speed in real time without additional speed sensors. The magnetically suspended rotor with harmonic disturbances is modeled. The work principle, structure, and design of the adaptive odd repetitive control are addressed. The simulation and experiments are carried out on a rotor active magnetic bearing test rig to validate the effectiveness of the proposed adaptive odd repetitive control, and the results show that the active magnetic bearing odd harmonic currents are well suppressed.

Active magnetic bearing (AMB) with power electronics drive is an important technology for high-speed rotational machinery suspension. There were seldom literatures concerning the common mode (CM) electromagnetic interference (EMI) problems of the AMB system. In this article, we found that the power electronic converter used for AMB control will not only bring EMI to the devices but also influence the performance of the levitation control. To cope with this problem, the parasitic paths of the leakage currents in the five-degrees-of-freedom AMB system were analyzed. The control principle and the novel zero CM PWM (ZCMPWM) strategy for the AMB driven by a four-leg converter were presented to suppress the CM EMI. Experiment has been done on an AMB-based compressor. The proposed method can significantly reduce the CM EMI caused by the AMB controller and improve the performance of levitation.

This article aims at proposing an adaptive neural control strategy for a class of nonlinear time-delay systems with input delays and unknown control directions. Different from previous researches that investigated delays and constraints separately, the novelty of this article lies in that it simultaneously considers delays (state and input delays) and input constraints (magnitude and rate constraints) for a class of uncertain nonlinear systems. In this article, the uncertain states and input delays are handled by integrating a constructed auxiliary system that functions as an observer with neural networks (NNs), with which the adverse effects caused by the uncertain states and input delays can be approximated and compensated. By involving smooth hyperbolic tangent functions in the designed auxiliary system, the problem of magnitude and rate constraints of the control input is fully addressed. Then, the backstepping technique runs through the entire control designing process, which allows the designed adaptive neural control strategy to handle the input constraints and delays at the same time. Furthermore, Nussbaum functions are employed to resolve the problem of unknown control directions. Due to the introduction of an input-driven filter, only the output of the system is required to be measured as the control feedback, which promotes the applicability of the designed controller. Under the proposed control scheme, semiglobal, uniform, and ultimate boundedness of all signals of the closed-loop system is realized with uncertain control directions, input and state delays, and guaranteed magnitude and rate constraints of control inputs. Finally, simulation results are illustrated to verify the effectiveness of the presented control method.

As with a continuous-time linear system, the predictor state feedback law for a discrete-time linear system with input delay is the product of a feedback gain matrix with the predicted state at a future time instant ahead of the current time instant by the amount of the delay, which is the sum of the zero input solution and the zero state solution of the system. The zero state solution for a discrete-time system is a finite summation that involves past input. The zero input solution is the product of the transition matrix and the initial state. The truncated predictor feedback (TPF), which results from discarding the finite summation part of the predictor feedback law, reduces implementation complexity. The delay independent TPF law further discards the delay-dependent transition matrix in the TPF law and is thus robust to unknown delays. It was pointed out in Lin (Commun. Inf. Syst. 7(3), 227–264 (2007)) and Zhou and Lin (IEEE Trans. Circuits Syst. I Regular Papers 58(11), 2741–2754 (2011)) that such a delay independent TPF law stabilizes a discrete-time linear system with all its poles at z = 1 or inside the unit circle no matter how large the delay is.

This paper introduces the applied AMB(Active Magnetic Bearing) System supported by magnetic bearing which is controlled. The system needs component design technique for develop AMB System. Magnetic field analysis, PID control and 3D rotordynamic analysis of AMB is performed. The required performance of motor is a 220 kW, 30 krpm high speed motor. The 3D rotordynamic analysis considering magnetic bearings are simulated to find the critical speed of rotor by Cambpell diagram. The analysis shows that the critical speed of the rotor is higher than operating speed with sufficient separation margin. All the performances of the AMB high speed motor prototype are verified successfully

In this paper, a nonlinear modeling and control method for magnetic bearings is designed, considering the core material nonlinear high flux behavior for the first time. A combination of the generalized Lur'e method and linear matrix inequalities is used during the modeling and control design process. It is common to include a margin of safety in amplifiers and other active magnetic bearing (AMB) components. The nonlinear modeling makes it possible to operate an existing industrial AMB system with larger electric currents and thus achieve a larger maximum load capacity than existing AMB modeling and control practices allow. As a result, existing industrial AMB's can be tuned to become more resilient in dealing with external disturbances. In addition, smaller and lighter AMBs can be designed by using the proposed method, which enables achievement of the same maximum force requirement of present-day larger AMB systems.

An active magnetic bearing (AMB) is a kind of high-performance bearing that uses controllable electromagnetic force to levitate the rotor. Its control performance directly affects the operation characteristics of high-speed motors and other electromechanical products. The magnetic bearing control model is nonlinear and difficult to control. Sliding mode control algorithm can be used in the magnetic bearing control system, but the traditional sliding mode control has the problem of high-frequency chattering, which affects the operation stability of magnetic bearings. Based on the second-order sliding mode control algorithm, a new second-order sliding mode controller for active magnetic bearing control was designed, and the stability of the designed sliding mode control law was proven by Lyapunov criterion. On the basis of the established active magnetic bearing control model, the numerical analysis of the designed controller was carried out, and the control effect was compared with that obtained by the exponential reaching law for the sliding mode control algorithm. The experimental results show that the designed sliding mode controller has better dynamic performance and stability than the exponential reaching law for the sliding mode controller.

In an effort for human colonization and exploration of the lunar surface there should be a way to store energy for when demand requires it. For energy storage a flywheel can provide a reliable, efficient and low-maintenance system for this need. This paper contains the description of a low-speed flywheel that includes an external rotor and hubless electrical machine. This allows for a high energy low loss machine. For the machine to be hubless it requires the use of active magnetic bearings. In this paper the system model and control algorithm for the active magnetic bearings for the flywheel energy storage system is presented. The simulation and validation of the model is shown.

This paper introduces a new method to improve the characteristic of an active magnetic bearing (AMB) control system by flux time derivative. The theoretical analysis and computer simulation results show that this method can improve the phase margin effectively, and simplify the design and realization of the compensation device. >

The stabilization of nonlinear stochastic systems with input and output delays is investigated in this article. First, an observer that includes input delay information is designed to estimate the state information after eliminating the effect of input delay. Second, a predictive scheme with delay information is utilized to predict the system state affected by output delay, and an event‐triggered predictive controller is established to eliminate the effects of input and output delays simultaneously. Subsequently, the convergence of the prediction error is analyzed by utilizing a recursive method, and a sufficient condition to ensure the global exponential stability is given by constructing a new closed‐loop system. Finally, numerical simulations of two nonlinear stochastic systems with different delay sizes are utilized to verify the impact of the event‐triggered predictive control in addressing the stabilization of nonlinear stochastic systems with time delays.

Many important industrial problems in the control of rotating machinery with active magnetic bearings concern the minimization of the rotor vibration response to poorly characterized disturbances at a single or several shaft locations, these typically not corresponding to those of a sensor or actuator. Herein, we examine experimental results of a multivariable controller obtained via μ synthesis with a laboratory test rig. These indicate that a significant improvement in performance can be obtained with a multivariable μ controller over that achieved with an optimal decentralized PD controller.

Sliding mode control for active magnetic bearing system with flexible rotor

In this paper, a voltage level adaptive controller for a single axis of the active magnetic bearing (AMB) system is designed using an integrator backstepping technique to deal with unknown sudden static load change and unbalance. The unbalanced rotor is controlled to rotate about its geometric axis. The proposed adaptive control guarantees zero steady state error of the rotor position in presence of static load change and unbalance. The estimated parameters converge to the true values. Simulation results show satisfactory performance.