A Second-Order Dual Mode Repetitive Control for Magnetically Suspended Rotor

In magnetically suspended rotor (MSR) system, harmonic vibration appears inevitably produced by mass imbalance of the rotor and sensor runout. Least mean square (LMS) is one method to reject the harmonic frequency component of the disturbance in a control system. Nevertheless, the performance of the conventional LMS is not optimal and the transient response is relatively slow. In this paper, the rotor dynamic model including mass imbalance and sensor runout is built, and the mechanism of vibration is analyzed. A harmonic vibration force suppression method based on frequency-domain adaptive LMS is proposed. Compared to the existing adaptive LMS methods, this article introduces a new convergence factor in frequency domain, which improves the updating strategy of the step size and the convergence rate of the algorithm. Simulation results demonstrate that the proposed method can effectively restrain the harmonic vibration force of magnetically suspended rotor system.

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.

The harmonic current in active magnetic bearing (AMB) system usually results from rotor unbalance and sensor runout. It not only causes considerable harmonic vibration, but also brings about the power saturation and the instability of AMB system especially for the high-speed rotor. Therefore, a novel parallel finite dimension repetitive controller (PFDRC) is proposed to restrain the harmonic current in this paper. Compared with the conventional repetitive controller (RC), PFDRC only introduces the limited imaginary poles, so that the problem that the infinite imaginary poles of RC endanger the stability and instantaneous characteristic of the closed-loop system is solved. In order to realize the harmonic current suppression, the power amplifier system is taken as the controlled object, and the proposed PFDRC is parallel with the original equivalent main controller. Then the root reclus method is adopted to design the parameters and to analyze the closed-loop system stability. Based on the phase-frequency characteristic of the system function, the compensators are introduced to improve the system stability margin. Meanwhile, the low-pass property of power amplifier system is sufficiently taken into consideration in the parameters design. Finally, the simulations and experiments are implemented to validate the effectiveness of the proposed PFDRC, and the results demonstrate that the harmonic current is dramatically restrained by the proposed method.

A repetitive control theory is proposed to solve the synchronization problem between the wafer stage and reticle stage. A macro-micro control method is used based on a macro-micro control structure in which a linear motor is combined with a voice coil motor. A synchronization controller of the reticle stage is added base on the conventional PID control system. The repetitive controller is designed based on the repeated movement of the reticle stage and the wafer stage during the scan and exposure period, and the effects of synchronization control system can be improved because of the repetitive control can effectively track and inhibit the periodicity excitation signal. The repetitive control system effectively reduces the synchronization error during the scan and exposure period，in the meanwhile keep the tracking accuracy and dynamic characters. Simulation results show that the synchronization error can be reduced effectively.

Two optimized control schemes of shunt active power filter (SAPF) in balanced three-phase three-wire system are proposed in this paper, including a fast fractional-order repetitive control (RC) strategy and a computation reduced harmonic detecting method. The improved RC is implemented in the synchronous reference frame (SRF) and based on the fractional-delayed-filter. Compared with the conventional RC (CRC), the proposed strategy can reduce the repetitive period from one fundamental cycle to one-sixth of the fundamental cycle, which results in the faster dynamic response. The fractional-delayed-filter, as the delay part of the proposed improved RC strategy, is used to achieve the high tracking accuracy of reference signals for control systems with different sampling rates. This paper also proposes a harmonic detecting method in the SRF based on the sliding Discrete Fourier transform (SDFT) with reduced computational burden, catering for selective harmonic elimination. Simulations and experiments show the validity of the proposed solutions.

A repetitive control method is presented that is implemented in real-time for periodic wind disturbance rejection for linear systems with multiple inputs and multiple outputs and with both repetitive and non-repetitive disturbance components. The novel repetitive controller can reject the periodic wind disturbances for fixed-speed wind turbines and variable-speed wind turbines operating above-rated and we will demonstrate this on an experimental “smart” rotor test section. The “smart” rotor is a rotor where the blades are equipped with a number of control devices that locally change the lift profile on the blade, combined with appropriate sensors and controllers. The rotational speed of wind turbines operating above-rated will vary around a defined reference speed, therefore methods are given to robustify the repetitive controllers for a mismatch in the period. The design of the repetitive controller is formulated as a lifted linear stochastic output-feedback problem on which the mature techniques of discrete linear control may be applied. For real-time implementation, the computational complexity can be reduced by exploiting the structure in the lifted state-space matrices. With relatively slow changing periodic disturbances it is shown that this repetitive control method can significantly reduce the structural vibrations of the “smart” rotor test section. The cost of additional wear and tear of the “smart” actuators are kept small, because a smooth control action is generated as the controller mainly focuses on the reduction of periodic disturbances.

Dear Editor, This letter presents an improved repetitive controller (IRC) that uses a complex-coefficient filter to enhance the tracking performance of a system for periodic signals. Compared with the low-pass filter used in the conventional repetitive controller (CRC), the complex-coefficient filter causes less change in the phase and amplitude of a signal at the frequencies of the periodic signal, especially at the fundamental frequency, when the two filters have the same cutoff-frequency. Thus, the IRC-based control system has better tracking performance than the CRC-based control system. Simulation results of a rotational control system demonstrate the superiority of the IRC.

The repetitive control technique is widely adopted in ac systems, because of its excellent steady‐state tracking performance and low total harmonic distortion. The repetitive control method with one‐sixth of the system fundamental period T0 as the delay time has been proposed to achieve fast transient response. In this study, an improved control scheme based on the T0/6 repetitive control is proposed for three‐phase grid‐connected inverters. The proposed scheme adopts T0/6 as the delay time in the positive‐rotating and negative‐rotating synchronous reference frames to suppress the 6n ± 1 harmonics. Meanwhile, the proportional‐integral regulator and the plug‐in repetitive controller are combined to reinforce the system performance. A new auxiliary function based on the linear interpolation is proposed to maintain the ideal repetitive control performance when one‐sixth of the ratio of the sampling frequency to the grid fundamental frequency is non‐integer. The effectiveness of the proposed scheme on improving the T0/6 repetitive control is confirmed by simulation and experimental results finally.

In this paper, a parallel structure repetitive control scheme is proposed for three-phase PWM inverters to compensate 6k ± 1th order harmonics. This new control scheme divides conventional repetitive control into two branches in parallel structure. By this design, it avoids using filters in series, thus achieving higher gains for targeted harmonic groups than other 6k±1 repetitive controllers. Besides, the proposed control scheme reduces the number of delay units required to one third of that in conventional repetitive control schemes, thereby offering faster convergence rate and better transient performance. Stability and convergence of this approach are proved mathematically. Experimental results are provided to show the effectiveness of the proposed control scheme.

It is well known that the speed control system, even though which is constructed with an excellent control method, has an unexpected steady speed error when it is suffered by a periodical load disturbance. As the method of eliminating the speed fluctuation caused by such kind of disturbance, a repetitive control is the most effective. But the repetitive control method is only adoptive for a constant speed control system.In this paper, a novel control system designing method which is effective to both the constant speed control system and variable speed driving system is shown. The fact that a periodical disturbance depends on time function and also rotational angle is utilized to design the control system. From the result, the numerical modeling of the controlled object is derived in the rotational angle function domain. For the obtained numerical model, an extended state variable equation based on the original system is presented by using the control technique named “Error System Technique”. And then the optimal feedback gains are decided by solving the optimal regulator problem for the extended state equation. Therefore, a stability of the system is ensured.The proposed control method is applied to DC motor variable speed control system and the experimental setup is constructed. Finally, the effectiveness of the proposed method is confirmed by the result of simulations and experiments.

This paper presents a general parallel structure repetitive control (PSRC) scheme for multiphase dc-ac pulse-width modulation (PWM) converters to cancel output total harmonic distortion more efficiently. With parallel structure, categorized harmonic frequency internal models are connected in parallel. Each categorized internal model has its own independent control gain and PSRC can optimize the total convergence rate by tuning the control gains independently according to the harmonic distribution. Compared with a multiresonant controller, PSRC has more compact structure and yields much less computation burden. Compared with conventional repetitive control (CRC), PSRC can achieve a much faster dynamic response without any loss of tracking accuracy or any added data memory. Moreover, PSRC is a general parallel structure RC for housing various existing RC, such as CRC, odd-harmonic RC, and dual-mode-structure RC. Experimental results of the PSRC-controlled three-phase dc-ac PWM converters show the validity and advantages of the proposed PSRC scheme.

The differential current in Modular Multilevel Converters (MMCs) is inherently subjected to even order harmonics, which are mainly caused by the voltage mismatch between phase legs and dc bus. This issue may exist in both single-phase and multi-phase MMC systems and can be eased by repetitive control based active harmonic suppression methods, which regulate the circulating current through legitimate adjustment of the voltage applied on the arm inductance. Nevertheless, conventional repetitive controllers have relatively slow dynamic response because of the presence of one fundamental period delay, and all the sampled errors in the past one cycle have to be stored for closed-loop control. This paper presents an improved even-harmonic repetitive control scheme that requires less data memory with faster dynamic response. The steady state performance can also be enhanced if system disturbances e.g. frequency deviation are considered. In order to verify its practicality and effectiveness, PLECS simulation and experimental results are presented to show the excellent dynamic response and disturbance rejection of the proposed even-harmonic elimination scheme.

Repetitive control (RC) presents an attractive solution to achieve low steady-state tracking error and total harmonic distortion for periodic signals. For the conventional RC (CRC), it requires the ratio of the reference signal period to the fixed sampling period to be an integer. Therefore, the reference signal with a variable frequency or a fractional period ratio will lead to severe performance degradation. Although existing hardware variable sampling (VS) rate methods enable the CRC to be frequency adaptive, the VS frequency will also influence the overall system stability, and they need that the CPU has the VS frequency ability. In this paper, a flexible and easy-to-implement method, virtual VS (VVS), is proposed to enable the RC to be frequency adaptive. The proposed VVS method that creates a virtual delay unit to approximate each VS delay achieves a flexible VS as similar to the hardware-based VS but it does not influence the overall system sampling frequency and stability. Experimental results of a single-phase dc/ac converter system are presented to demonstrate the effectiveness of the proposed VVS-RC.

In view of the surplus torque and complexity of controlled plant in passive electrical load system, a novel approach based on single neuron PID adaptive control and repetitive control for repetitive periodic load control system is proposed. Radial basis function (RBF) neural network is used to identify the system on-line for the single neuron PID controller to adjust its weights and PID parameters by self- learning and self-adapting based on the desired output. The dynamic state performance can be improved by the single neuron adaptive PID control and the steady state performance is also improved by modified repetitive control. Computer simulation results show that the force/position hybrid control system can effectively reduce the surplus torque and improve the loading precision, and also it has fine dynamic and steady state performance and good robustness. The reliability of whole system is further improved.

The tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.