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PMSM is an important category of the electric machines, in which the rotor magnetization is created by permanent magnets attached to the rotor. Many mathematical models have been proposed for different applications, such as the abc-model and the two axis dq-model. Due to the simplicity of the two axis dq-model, it becomes the most widely used model in PMSM engineering controller design. The dq-model offers significant convenience for control system design by transforming stationary symmetrical AC variables to DC ones in a rotating reference frame. Based on the dq reference frame theory, the mathematical model of the PMSM can be expressed as the following equations: 1) Circuit equation )(qqrdsdddiLiRudtdiLω+−= (1) )(frddrqsqqqiLiRudtdiLΨ−−−=ωω (2) 2) Electromagnetic torque equation: ])([qdqdqfpeiiLLinT−−Ψ= (3) 3) Motion equation dLerTTTdtdJ−−=ω (4) Wheredi,qirepresent the current of the d-axis and q-axis;du,qurepresent the voltage of the d-axis and q-axis;dL,qL represent the inductance of the d-axis and q-axis;sRis the stator resistance; rωis the rotor speed; fΨis the magnitude of the permanent magnet flux linkage; pnis the number of pole pairs; J is the inertia of the rotor;eTis the electromagnetic torque,LTis the load torque of the motor anddTis the uncertain torque disturbance caused by the external and internal disturbance ; III.MATHEMATICAL MODEL OF THE ADRC An ADRC consists of three components, a tracking differentiator (TD), an extended state observer (ESO) and a nonlinear state error feedback (NLSEF)[9]The function of the n-order TD is to arrange the ideal transient process. It tracks the input )(tVwithout overshoot and provides the generalized derivatives of the input signal, 11,z,…n,z1. The function of (n+1)-order ESO is to observe the state variables12,z,…n,z2and estimate the total disturbances 12+n,z of the plant. ESO can compensate the entire uncertain external and internal disturbance in real time. The function of NLSEF is to level off the output of the controlled plant and expand the stability region of the whole closed-loop system. The control output of NLSEF can be mathematically described by ),,(),,()(110δεδεafalkafalktunn++=..(5) wherei,i,izz21−=ε(i=1,…n), a,δ, and ik(i=1,…n) are adjustable parameters. The nonlinear functionfal is defined by ⎪⎩⎪⎨⎧≤>=−δεδεδεεεδεiaiiiaiiafal1/)sgn(),,( (6) where sgn(x) is a sign function. Thus the actual control for the plant can be expressed as bztutun1,20)()(+−= (7) According to the equation 4, the rotor speedrωcan be described as: JTJTTdLer//)(−−=•ω(8is considered as the total unknown disturbance of the servo system, which might be estimated and compensated by the ESO. According to the above theory, the ADRC for rotator speed is designed as below. Design the one-order TD as ),,(00011δεafalkz−=• (9) wherrefnz−=11ε, 0a, 0δ, 0k are adjustable parameters. Then the ESO can be constructed as ⎪⎩⎪⎨⎧−=+−=••),,()(),,(1112222111212221δεδεafalkztbuafalkzz (10) where rzωε−=211,1a,1δ,21k, b,22kare adjustable parameters. In this paper, a conventional PI controller is used to replace the NLSEF of the ADRC in the Fig.1, which can enhance the calculating speed of the algorithm and maintain the disturbance rejection advantage of the ADRC. Where ⎪⎩⎪⎨⎧−=+=∫bzuudtkkuip/220220εε (11) where21112zz−=ε,pkand ikare the adjustable parameters of the PI controller. The structural expression of the system control law shows control doesn’t attach to the internal parameters of the system, but to the output and the reference input of the system VS Sewing Machines

SIMULATION RESULTS OF SERVO CONTROL OF THE INDUSTRIAL SEWING MACHINE SYSTEM The position control of the industrial sewing machine system based on the ADRC is shown in Fig.2. Proportional control is adopted to the position loop, and the PI control is adopted to the current loop. Simulation results have been done in the Matlab/simulink. The parameters of PMSM are as follows: np=2, Rs=3.4 Ω, Ld=8.317 mH, Lq=5 mH, J=0.8*10-3 kg.m2, ψf=0.175 Wb. The ADRC parameters are chosen as follows: 0k=10, pk=2.0, ik=6.6, 21k=1200,22k=15000, 5.010==aa, 05.010==δδ, b=10000, TL=5 N.m. Fig.3~ Fig.7 show the dynamic and steady state performance of the servo control of the industrial sewing machine based on the ADRC of the speed loop. The expected speed ismin)/(1300r=ω, and the stop position is 21000 rad. Fig.3 shows the speed curve of the rotor. From which we can see that the speed of the system has no overshoot, and the system has a good dynamic response. Fig.4 is the curve of rotor position, which shows that the ADRC control system has high precision in servo control. Fig.5 shows the electromagnetic torque of the PMSM. Fig.6 shows the transient process of the expected rotor speed arranged by the TD of ADRC. Fig.7 is the rotor speed estimated by the ESO of the ADRC. As load torque often changed dramatically in the industrial sewing machine system, such as the type or the thickness change of the fabric will cause the load torque disturbance. It is necessary to test the robustness of the ADRC and PI controller. Fig.11 shows the rotor speed response of the ADRC and PI controller when TLchanged suddenly from 5 N.m to 10 N.m at 0.06s. From the Fig.11 we can see that the rotor speed drop of the ADRC is less than the PI controller. And it shows that the ADRC has better dynamic response and robustness than the PI controllerIn this paper, servo control of the industrial sewing machine system based on the ADRC is proposed. Compared with the conventional PID control, it can estimate and compensate the uncertain load torque disturbance caused by the external and internal of the system, which can highly enhance the robustness of the system. Simulation results have proved the effectiveness and feasibility of the ADRC, and the control system has better dynamic performance and robustness. https://www.vssewingmachine.in/