Accurate tracking control of a limited angle torque motor

Comparison of control strategies for hysteresis attenuation in electromechanical actuators subject to dispersion

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.

This paper shows that design of a robustly stable repetitive control system is equivalent to that of a feedback control system for an uncertain linear time-invariant system satisfying the well-known robust performance condition. Once a feedback controller is designed to satisfy the robust performance condition, the feedback controller and the repetitive controller using the performance weighting function robustly stabilizes the repetitive control system. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. Moreover, using this result, a sufficient condition is provided, which ensures that the least upper bound of the steady-state tracking error generated by the repetitive control system is less than or equal to the least upper bound of the steady-state tracking error only by the feedback system

The modified repetitive control system is a type of servomechanism for periodic reference inputs. That is, the modified repetitive control system follows the periodic reference input with a small steady state error, even if a periodic disturbance or uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plant does not include time-delay, transfer functions from the periodic reference input to the output and from the disturbance to the output have infmite numbers of poles. To specify the input-output and the disturbance attenuation characteristic easily, Yamada et al. proposed the concept of a simple repetitive control system such that the controller works as a modified repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have fmite numbers of poles. In addition, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. Recently, the p...

We give a parameterization of all causal stabilizing repetitive learning controllers for single-input and single-output linear minimum phase systems. The past studies on the parameterization of a repetitive learning control system were to obtain the parameterization of all internally stabilizing controllers for the control system such that the plant is connected 1/(1-e/sup -sT/) in series. Since 1/(1-e/sup -sT/) has no zeros in the closed right half plane, also the serial connections of 1/(1-e/sup -sT/) and a minimum phase system have no zeros in the closed right half plane. That is, the parameterization of all stabilizing controllers for a repetitive learning control system may be obtained by using the parameterization for a minimum phase system in Glaria and Goodwin (1994). Using the above mentioned idea, at first, the parameterization of all stabilizing repetitive learning controllers for the biproper minimum phase system is carried out. Next, since the exact repetitive learning controllers to stabilize the strictly stable proper system do not exist, the parameterization of all modified repetitive learning controllers using a low-pass filter in the repetitive learning controller is given.

A new design method of the repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented, which can design a low-pass filter of the repetitive controller and a stabilizing controller simultaneously in the repetitive control system. Using a Lyapunov functional for the repetitive control system, sufficient conditions are derived in terms of a linear matrix inequality (LMI), which ensure robust stability of the repetitive control system and achieve the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance. Based on derived conditions, the problem of designing a stabilizing controller and finding the cut-off frequency of a low-pass filter is reformulated as an optimization problem with an LMI constraint of the free parameter. Then, an iterative algorithm is presented to calculate the largest cut-off frequency of a low-pass filter and design the corresponding state-feedback controller simultaneously. A numerical example is presented to illustrate the validity of the proposed method.

Effects of Non-Periodic Disturbances on Repetitive Control Systems

The problem of designing output error controllers to track periodic reference signals for a class of uncertain linear time-delay systems subject to periodic disturbances is addressed. A repetitive controller, which is a type of output error controller, is developed for these systems and a sufficient condition for stability of the closed-loop system is derived by applying the Lyapunov–Krasovskii functional and linear matrix inequalities (LMIs). In order to relax the stability condition, the theory of the modified repetitive control (RC) system is extended to the systems represented by irrational transfer functions. Based on the extended theory of the modified RC system, a modified repetitive controller, another type of output error controller, is developed for these systems and sufficient conditions for stability of the closed-loop system are derived in terms of a frequency-domain criterion and LMI. Numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.

Better torque performance and higher reliability have long been the focus of research for slotted limited-angle torque motors (LATMs), which are primarily used to position first-stage valves in electrohydraulic servosystems. This paper presents a high reliability axial-flux slotted LATM with quasi-Halbach array for torque performance improvement including constant torque range (CTR) and output torque. Firstly, the structure with two sets of windings and the operation principle of the proposed slotted LATM is analyzed. Secondly, a brief design procedure is presented, the structure selections of open slot and double-stator single-rotor (DSSR) interior rotor with surface mounted quasi-Halbach permanent magnet (PM) array are illustrated, and the geometric parameters are optimized to obtain the optimal design of the proposed slotted LATM. Then, 3-D finite-element method (FEM) is employed to compare the proposed slotted LATM with the conventional surface mounted PM slotted LATM in terms of cogging torque, no-load back EMF, and output torque, and the results show that the proposed LATM with quasi-Halbach array has a 10% improvement in output torque and a 25% improvement in CTR. Meanwhile, the flux linkages and torque performance of the two sets of windings under various conditions verify good magnetic isolation. Finally, prototypes of two different rotor types are manufactured and a series of experiments are performed to validate the analysis.

Feedback control systems can have reasonably good performance executing a desired trajectory, but only for frequencies up to the bandwidth of the control system. They never offer perfect tracking of an arbitrary desired trajectory. Repetitive control designs controllers to adjust the command to a feedback system aiming to converge to zero tracking error for any desired trajectory of a known period. It also aims to produce zero error in the presence of a periodic disturbance of known period. The ideal of zero tracking error is unusual in control and also challenging. This paper gives an overview of the methods preferred by the author to approach as closely as possible to this performance ideal.

The structured singular value method is applied to continuous-time SISO repetitive control systems in order to determine their stability and performance robustness in the presence of structured parametric modeling error in the plant. Performance measures for repetitive control systems are introduced and the robust performance analysis using structured singular values is modified, taking the alternating magnitude behaviour of the sensitivity function of a repetitive control system into account. The analysis procedure is simplified considerably in the case of large time delay by noting that the upper and lower envelopes of the structured singular value plots are obtained from corresponding finite dimensional systems without any time delay. The analysis procedures developed are applied to an example on repetitive control of an electrohydraulic material testing machine, available in the literature, to demonstrate their usefulness.

Compensation in Repetitive Control System for Aperiodic Disturbances and Input Dead Zone

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.

Induction motors are robust and inexpensive machines and are widely used for variable speed control because of recent development of electronic technique. In the case that loads of the motors are compressors, pumps, and so on, the constant V/F control of the induction motors is usually employed because it is difficult to install speed sensors and accurate speed control is not required. In such loads, the rotational speed of the motors is considerably fluctuated because the load torque is pulsated. When frequency of the torque pulsation is close to the resonant frequency of the mechanical system, large vibration and acoustic noise are produced especially in low frequency region.In this paper, authors propose a method to suppress the variation of the rotational speed of the V/F controlled induction motor with a fluctuated load by feedforward compensation using a timing sensor of 1 pulse/rev. considering that the load torque varies periodically. The feedforward data by a period for the compensation is obtained by the learning control based on the repetitive control in which the motor speed is controlled by periodically reflecting the past speed error on the present V/F input to the inverter. Effectiveness of the proposed method is confirmed by approximate analysis, simulations and experiments.

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.