The main objective of this paper is to solve the position tracking control problem for the permanent magnet linear motor by using the discrete-time fast terminal sliding mode control (SMC) method. Specifically, based on Euler's discretization technique, the approximate discrete-time model is first obtained and analyzed. Then, by introducing a new type of discrete-time fast terminal sliding surface, an improved discrete-time fast SMC method is developed and an equivalent-control-based fast terminal SMC law is subsequently designed. Rigorous analysis is provided to demonstrate that the fast terminal SMC law can offer a higher accuracy than the traditional linear SMC law. Numerical simulations and experimental results are finally performed to demonstrate the effectiveness of the proposed approach and show the advantages of the present discrete-time fast terminal SMC approach over some existing approaches, such as discrete-time linear sliding mode control approach and the PID control method.

Discrete-Time Fast Terminal Sliding Mode Control for Permanent Magnet Linear Motor

Precision positioning systems with large working stroke (millimeter or more) and micro/nano-scale positioning resolution are widely required in both scientific research and industries. For this kind of applications, piezoelectric materials based actuators show unique advantages and have been widely employed. To overcome the demerit of the limited working stroke for single piezoelectric element, various stepping motion principles have been proposed in the past years, and accordingly, stepping piezoelectric actuators with various structures have been designed and evaluated. This review is aimed to summarize the recent developments and achievements in stepping piezoelectric actuators with large working stroke. Especially, the emphasis is on three main types of stepping piezoelectric actuators, i.e., inchworm type, friction-inertia type, and parasitic type. The motion principles of these three types of piezoelectric actuators and the corresponding developments of various actuators are discussed respectively, followed by pointing out the existing problems in these three types of piezoelectric actuators and proposing some potential research directions in this topic. It is expected that this review is helpful for relevant researchers to understand stepping motion principles as well as piezoelectric actuators, and to successfully select and design stepping piezoelectric actuators for specific applications.

Stepping piezoelectric actuators with large working stroke for nano-positioning systems: A review

In this paper, we aim to study the observer design problem for polytopic linear-parameter-varying (LPV) systems with uncertain measurements on scheduling variables. Due to the uncertain measurements, the uncertainties are considered in the weighting factors. It is assumed that the vertices of polytope are the same when the measurements on scheduling variables are uncertain and perfect. Then, an LPV system with the uncertain weighting factors can be transferred to an LPV system with uncertainties. To deal with the uncertainties and unknown disturbance in the observer design problem, we propose a gain-scheduling sliding mode observer. Defining the estimation error as the state vector minus the estimated state vector, the estimation error dynamics is established. The sliding mode observer design method is developed based on analysis results of the established estimation error system. The proposed observer design method is then applied to an electric ground vehicle (EGV) in which the measurement of longitudinal velocity is assumed to be uncertain. Experimental tests and comparisons are given to show the advantages of the proposed design method and the designed observer.

$\mathcal{H}_{\infty}$ Observer Design for LPV Systems With Uncertain Measurements on Scheduling Variables: Application to an Electric Ground Vehicle

This paper presents a practical discrete-time fractional order terminal sliding mode (DFOTSM) control strategy for high-precision tracking tasks based on a linear motor. In particular, the practical parametric uncertainties involving sliding friction, uncertain payload, and disturbance in tracking tasks are considered in this paper. Combining Grunwald–Letnikov fractional order definition and terminal sliding mode technique, the proposed method synthesizes a novel DFOTSM control law to drive the sliding mode dynamics into the stable region in finite steps theoretically, even though the system is suffering from uncertainties and disturbances, and the motion on the surface can guarantee higher tracking precision than the conventional discrete-time terminal sliding surface by selecting suitable controller parameters. The theoretical analyses give out the guideline of parameter selection, and experiments are carried out on the linear-motor-based test platform to demonstrate that the proposed controller is easily implemented and can achieve high-precision tracking, fast response, and considerable robustness to uncertainties.

Discrete-Time Fractional Order Terminal Sliding Mode Tracking Control for Linear Motor

The aim of this study is to develop an adaptive fuzzy fractional-order sliding-mode control (AFFSMC) strategy to control the mover position of a permanent magnet linear synchronous motor (PMLSM) system. First, the mathematical model of the PMLSM is investigated by using the principle of field oriented control. Subsequently, a fractional-order sliding-mode control (FSMC) is designed by means of a new fractional-integral sliding surface. Because it is difficult to determine the hitting control gain for the FSMC in practice, the AFFSMC is further developed in which an uncertainty observer is developed to observe uncertainties while an adaptive fuzzy reaching regulator is designed to concurrently compensate for observation deviations and suppress the chattering phenomenon. The adaptive laws are derived to tune the control parameters online based on the Lyapunov stability theorem. Thus, the uncertainty bound information is not required while the chattering can be attenuated. Finally, experiments demonstrate that the proposed AFFSMC system performs the robust control performance and precise tracking response for the PMLSM drive system against the parameter variations and external disturbances.

Precision Motion Control of Permanent Magnet Linear Synchronous Motors Using Adaptive Fuzzy Fractional-Order Sliding-Mode Control

This paper presents a novel disturbance compensation scheme to attenuate periodic disturbances on repetitive motion using permanent magnet linear synchronous motors (PMLSMs), and this scheme is called the periodical adaptive disturbance observer. The scheme is based on assumptions that all measured states and disturbances are periodic and repetitive when the tasks executed by PMLSM motion systems have periodic and repetitive characteristics. In the proposed control scheme, a lumped disturbance is estimated by the classical linear disturbance observer (DOB) for the initial time period and stored in memory storages. It consists of parametric errors multiplied by states, friction force, and force ripple, and then, it is updated for each time period by the periodic adaptation law. This scheme requires no mathematical models of disturbances and adaptation laws of model parameters such as the mass of the mover and viscous friction coefficient. Also, it is possible to compensate for disturbances above as well as below the bandwidth of the Q-filter (LPF) of DOB. The effectiveness of the proposed control scheme is verified by various experiments that take into account varying frequency components of disturbances along the operating speed of a mover of PMLSM such as force ripple and friction force.

A High-Precision Motion Control Based on a Periodic Adaptive Disturbance Observer in a PMLSM

This paper proposes a new scaleless position estimation method. From the industrial perspective, the Hall sensor has several advantages: tiny size, light weight, extremely low cost, and insensitivity to environmental contamination and external disturbance. Compared to the square wave Hall sensor, the linear Hall sensor provides more detailed information along the position. However, for combining more than two linear Hall sensors, the sensor offset, the difference in scale, and the unwanted phase shift between them and the harmonics would decrease the validity and reliability of sensor measurement. The fast Fourier transform and the fixed point iteration method are applied to compensate for those issues without any low-pass filter or additional signal conditioning. The effectiveness of the proposed scheme is verified through a prototype permanent magnet linear synchronous motor system.

Position Estimation Using Linear Hall Sensors for Permanent Magnet Linear Motor Systems

In this paper, an extended Kalman filter is designed and applied to a feed-forward based lumped disturbance compensator which consists of position dependent functions for a permanent magnet linear synchronous motor system. In our previous research, a lumped disturbance model including the force ripple and the Coulomb friction force was developed and utilized as a feed-forward controller. To improve the performance of that model, following two studies are conducted. First, an initial position estimator is designed to create synchronization between the model and real disturbance. This step is necessary because almost all linear motor systems are equipped with an incremental encoder for position measurement. Second, to cancel out a slight variation in real disturbance, an adaptive controller in the form of coefficients adaptation is designed. These two studies are combined by a sixth order extended Kalman filter. To make a comparison, a recursive least squares filter and disturbance observer and its modified version are prepared. The effectiveness of the proposed scheme is verified by the overall disturbance shape, RMS position error and FFT analysis on the position error.

Lumped disturbance compensation using extended Kalman filter for permanent magnet linear motor system

Linear motor system has been developed to achieve high speed and high precision motion control in linear motion system, since rotary type motor has backlash and hysteresis due to mechanical parts like chain, belt or screw. However, paradoxically, linear motor system becomes more sensitive to the external disturbance, because it doesn't have such transmission mechanism. Many studies have been focused on detent force which have dominant and position dependant non-linear properties among the external disturbances. But the solutions suggested by them are mostly complicated and dificult to apply due to the non-linear property of detent force. In this paper, a novel method to analyze the disturbance magnitude related to the harmonics order is introduced. It is based on a disturbance observer that is famous for its simple but robust and powerful scheme to eliminate disturbance. Nevertheless, from the implementation perspective, there exists a limitation with direct feedback of the disturbance observer output. It is because the bandwidth of disturbance observer is limited by measurement noise, while the disturbance gets higher frequency with the speed due to the position dependant property of detent force. To resolve this problem, feed-forward controller with a function of position is suggested. Through experimental results, the suggested method was verified to have much better performance compared to direct feedback of disturbance observer.

A Novel Method on Disturbance Analysis and Feed-Forward Compensation in Permanent Magnet Linear Motor System

In many industrial fields, the mass information of a moving system is important and necessary to prevent undesired motion or failure and to control the system in its desired trajectory. One simple solution could be direct measurement of the mass using a sensor such as force sensor and accelerometer. However, it requires additional cost increase. In addition, it is not easy to measure the mass of a moving part in many cases. For those reasons, in this research, an online varying mass estimation algorithm is designed using an Extended Kalman Filter (EKF) without any additional sensors. Furthermore, the lumped disturbance compensating algorithm, which was designed by the authors in the previous research using EKF, is combined to obtain further position tracking performance. The effectiveness of the suggested method is validated through simulations. Additional verification with experiments is planned for future work.

Jonghwa Kim

Papers

A High-Precision Motion Control Based on a Periodic Adaptive Disturbance Observer in a PMLSM

Position Estimation Using Linear Hall Sensors for Permanent Magnet Linear Motor Systems

Lumped disturbance compensation using extended Kalman filter for permanent magnet linear motor system

A Novel Method on Disturbance Analysis and Feed-Forward Compensation in Permanent Magnet Linear Motor System

Varying mass estimation and force ripple compensation using Extended Kalman Filter for linear motor systems