Qi Wu,Li Yu,,Yao-Wei Wang,and Wen-An Zhang,

Abstract—The position synchronization control(PSC) problem is studied for networked multi-axis servo systems(NMASSs) with time-varying delay that is smaller than one sampling period. To improve the control performance of the system, time-varying delays,modeling uncertainties,and external disturbances are first modeled as a lumped disturbance.Then,a linear extended state observer(LESO) is devised to estimate the system state and the lumped disturbance,and a linear feedback controller with disturbance compensation is designed to perform individual-axis tracking control. After that,a cross-coupled control approach is used to further improve synchronization performance.The bounded-input-bounded-output(BIBO)stability of the closedloop control system is analyzed. Finally, both simulation and experiment are carried out to demonstrate the effectiveness of the proposed method.

I.Introduction

POSITION synchronization control(PSC)for multi-axis servo systems is a crucial part in manufacturing industry,which is used to ensure that all machine shafts move synchronously and coordinately according to a certain proportion during the motion.with the rapid development of network communication technologies, both academia and industry have attempted to implement the PSC for networked motion control systems(NMCSs),for example,the computer numerical control(CNC)systems[1]–[3],the surface mount systems[4],the electric multiple units[5],and the robotic arms[6]–[8].Although the application of the NMCS brings many benefits,such as simplified wiring, powerful extensibility and easy maintenance,it also raises several new challenging issues.One of them is the network-induced delay,which may seriously degrade system performances.

In the past few decades,most studies on multi-axis synchronization control methods have been summarized into the following two categories,namely,the coupled method and uncoupled method.Compared with the uncoupled methods[9],[10],the coupled methods have some advantages,such as high precision,fast response,and easy implementation.Therefore,coupled control(especially the cross-coupling control(CCC)) methods have been widely used in multi-axis motion control systems[11]–[13]and achieved good synchronization performance.Most existing literatures only consider the effects of coupling between multiple axes[14],non-linear friction [15]–[17]and system uncertainty[18]–[21],while the time-varying delays caused by the communication network are not taken into account.Thus synchronization performance will degrade due to the effect of netwok-induce delay.Aiming at this issue,several advanced control methods have been proposed to deal with the time delay,such as the Smith predictor[22],switched system control[23],[24],and robust control[25],etc.Laiet al.[22]developed an adaptive Smith predictor with an online timedelay estimator and validated its feasibility on an AC 400W servo system.Zhanget al.[23]analyzed the stability of the networked control system(NCS)under the switched system control,in which the time-varying delay was assumed to be smaller than one sampling period.Furthermore,a quantitative relation between the stability of the closed-loop NCS and the parameters of short time-varying delay can be found in[25].Although the aforementioned methods have made a great progress in dealing with the network-induced problems for the NCS,several critical issues need further investigation,for example,how to reduce online computation burden and the number of undetermined parameters.

The disturbance-observer-based approach that treats the time delay as a network disturbance has received increasing attention due to its simplified structure and strong capacity of disturbance rejection.Over the past few decades,several disturbance-estimation techniques have been presented,for example,the unknown input observer(UIO)[26],the disturbance observer(DOB)[27],the equivalent input disturbance(EID)[28]and the extended state observer(ESO)[29].Among them,the ESO is able to estimate plant dynamics and requires the least amount of plant information,which has been substantially developed[30]–[33].In[30],an intuitive modification of the regular ESO was analyzed, where a time delay block was added to synchronize the signals entering the ESO.To obtain the prediction of the system state,a method combining the Smith predictor(SP)with ESO was presented in[31],where the input of the ESO was replaced by predicted outputs.In addition,an extended state predictor observer(ESPO)[32] was proposed for a class of nonlinear systems with output delays.However,the aforementioned methods also have some limitations, which can be found in a recent overview[33].For example,the time delay block based ESO has limitations with respect to the size of the time delay and the SP based ESO is hard to handle unstable nominal models.In application,ESO based methods are effective ways in controlling uncertain systems with time delays.

As a typical NMCS,the networked multi-axis servo system(NMASS)is suffered from both network-induced delay and disturbances caused by unmodeled dynamics.It is an unresolved problem how to carry out high-precision PSC for such an NMASS.This motivates us to carry out this study.In this paper,an integrated synchronization controller that combines the linear extended state observer(LESO)approach and the CCC strategy is proposed to guarantee both high tracking and synchronization performance of the NMASS.

The main contributions of this paper are as follows:1)The network-induced time delay,system uncertainties,and external disturbances are regarded as the lumped disturbance of the NMASS.Then,an LESO is applied to estimate the lumped disturbances and a linear state feedback control law is designed to eliminate it.2)It is rigorously proved that the closed-loop control system under the proposed controller is bounded-input-bounded-output (BIBO)stable.3)The bandwidth-based parameterization method [34]is employed to simplify the parameter tuning of both observer and controller,which is easy to be used in engineering practice.4)Compared with the improved PID-based PSC method in[11], the proposed LESO-based PSC method is more superior in both tracking and synchronization performance.

The rest of the paper is organized as follows.The problem statement and the system model are given in Section II.In Section III,an integrated synchronization controller is proposed to minimize both the position and synchronization error of the NMASS.In addition, the stability analysis is also given in this section.The simulations and experiments on a networked four-axis motion control platform are provided in Section IV and Section V,respectively.Finally,the paper is concluded in Section VI.

II.Problem Formulation

An experimental NMASS(Fig.1)consists of two parts:machinery and monitoring.The machinery part contains four identical motion units and each unit includes an ECMA-106RS04 servomotor and an ASDA-A2 communication servo controller.As a universal servo controller,the ASDA-A2 provides several control modes to meet different requirements,and its built-in encoders are able to collect the motion states including displacement,speed,and torque in a constant sampling frequency.In the part of monitoring,a PC is connected to the interface board through an Ethernet,and is employed for both data monitoring and algorithm implementation.The communication between the PC and interface board is implemented by TCP/IP protocol,while the data interaction between interface board and servo controller is accomplished by CANopen protocol.The task is to synchronize four motion units so as to obtain both high tracking and synchronization performance of the NMASS.

Fig.1.Experimental setup of the NMASS.

III.Main Resu l ts

In this section,an integrated synchronization controller is proposed to improve both the tracking and synchronization performance of the NMASS.Furthermore,the stability analysis of the closed-loop system under the proposed controller is provided.

A.Composite Control Design

As shown in Fig.3,an integrated synchronization controller is designed with two parts.The PartA(shaded area with blue)is the CCC strategy to solve the synchronization problem between the multiple axes.The PartB(shaded area with red)represents the LADRC method to improve the tracking control

B.Stability Analysis

IV.Simulation

In order to verify the effectiveness of the proposed controller,extensive simulations were performed on MATLAB R2016b/Simulink.Based on our previous work[36],the input-output model of the experimental platform was obtained by the system identification method,and the parameter matricesa0=diag{?129.8,?128.6,?130.2,?130.5},b0=diag{10.5,10.2,9.5,9.8}.The controller bandwidth and observer bandwidth were designed by (18)and(24),whereωc=diag{76.40,76.1,76,76.6}andωo=diag{100,100,100,100}.The network-induced delay was set to τ(t)∈[2 ms,3 ms], the external disturbancew(t)=0.01s in( 5πt).Then,the quantitative evaluation was given by using the integral criterion,and is given as follows

First,the set-point position synchronization control for the system with four motors was examined.To show the effectiveness of the time-delay compensation,the LESObased PSC without disturbance compensation was also presented to provide a comparison study.The simulation result is shown in Fig.4,where two approaches have the same designed gains.The three small diagrams in Fig.4(a)represent the position error,synchronization error,and the disturbance estimation of the system under the proposed LESO-based PSC,respectively.Obviously, the proposed approach exhibits the better convergence of the position errors and the superiority performance of the position synchronization.The comparison results of the steady-state errors and control inputs are shown in Fig.4(b).Compared with the method without time-delay compensation,the proposed method ensures that the system has the smaller steady-state errors.

Then, the effect of synchronization control gain α on the control performance was analyzed.Table I presents the results of α from 0.1to 1.0.To be more intuitive,the relationship between the performance of the third servo subsystem and the parameter α is described in Fig.5(a).It can be seen that the synchronization error decreases as α increases.On the other hand, both position and synchronization errors increase if the value of α is too large. As a result,a moderate value of α=0.1should be selected.

Finally,the robustness of the proposed approach against model uncertainty was tested.The aging and wear of the equipment will lead to the perturbation of system parameters.Table II and Fig.5(b)also show the results of different values of the control gainb0.It can be seen that the choice ofb0will affect the performance of the system.Whenb0is selected near the true value,there is no obvious difference in the position synchronization.On the other hand,the ITAE(integral of time-weighted absolute error)scores of all the position error,synchronization error and coupled position error increase ifb0is far from the true value.Then,we can conclude that the proposed approach is robust to the perturbation of the parameterb0within a certain range.

V.Experimental Verification

VI.Conclusion

Fig.6.Comparison between the LESO-based PSC and the improved PIDbased PSC.

Fig.7.The estimated disturbance and the measured time-varying delays.

This paper has presented an effective stabilizing synchronization controller design approach for the NMASS with short time-delays.It is demonstrated that the proposed approach can deal with the effects of system uncertainty,external disturbance,and short time-varying for the NMASS.The bandwidth-parameterization tuning method is applied in both controller design and observer design,so that the number of parameters that need to be adjusted is greatly reduced.Numerical simulation and experimental results are carried out to verify the effectiveness and superiority of the proposed approach.