Research on an Improved Method for Permanent Magnet Synchronous Motor

In permanent magnet synchronous motor (PMSM) traditional vector control system, PI regulator is used in the speed loop, but it has some defects. An improved method of PMSM vector control is proposed in the paper. The active-disturbance rejection control (ADRC) speed regulator is designed with the input signals of given speed and real speed and the output of given stator current q coordinate component. Then, in order to optimize ADRC controller, the least squares support vector machines (LSSVM) optimal regressionmodel is derived and successfully embedded in theADRCcontroller. ADRCobservation precision anddynamic response of the system are improved.The load disturbance effect on the system is reduced to a large extent.The system anti-interference ability is further improved. Finally, the current sensor CSNE151-100 is selected to sample PMSM stator currents.The voltage sensor JLBV1 is used to sample the stator voltage.The rotor speed of PMSM ismeasured bymechanical speed sensor, the type of which is BENTLY 330500. Experimental platform is constructed to verify the effectiveness of the proposed method.

PMSM is nonlinear and is strongly coupling.In order to achieve high performance operation, the uncertainties and nonlinear impact on the system must be overcome.In traditional vector control system, PI regulator is adopted in the speed loop.PI controller structure is simple; nevertheless, its parameter robustness is poor and there are contradictions between speed and overshoot.PI control is difficult to meet the requirements of high performance operation.
Based on the preliminary research results, an improved method of PMSM control is proposed in the paper.The active-disturbance rejection controller (ADRC) is designed for speed loop.Then, in order to optimize ADRC controller, the least squares support vector machines (LSSVM) optimal regression model is derived and successfully embedded in the ADRC controller.ADRC observation precision and dynamic response of the system are improved.The load disturbances effect on the system is reduced to a large extent.The system anti-interference ability is further improved.Finally, different sensors sampling current, voltage, and rotor speed are used to finish experimental validation.

PMSM Mathematical Model
- coordinate is chosen.The voltage equation of PMSM is as follows: where 2

Journal of Sensors
The electromagnetic torque equation of PMSM is shown as follows: For surface PMSM,   =   .Equation (3) can be derived from (2): The motion equation of PMSM is as follows: where  is rotational inertia;  is friction coefficient; and   is the load.

Design of ADRC Speed Regulator
3.1.ADRC Theory.ADRC controller is composed of tracking-differentiator (TD) and extended state observer (ESO) and nonlinear state error feedback control rate (NLSEF) [18,19].First-order system is assumed as follows: The TD model of the first-order system (5) is as follows: where fst(V 1 , , ) is defined as where V 1 is the tracking signal of V;  is the tracking speed factor; and  is the sample period.
The ESO model of first-order system (3) is as follows: where  1 is the tracking signal of ;  2 is the estimation value of disturbance;  1 ,  2 are nonlinear factors;  is filter factor;  01 ,  02 are the parameters; and fal(, , ) is nonlinear function: NLSEF model of system ( 3) is as follows: where  1 is filter factor and  3 is nonlinear factor.

Speed
Regulator Design.Equation ( 11) is obtained from (3) and ( 4): Based on ADRC theory,   , , and  are seen as disturbance velocity loop.The disturbance is denoted as (), () = −(    /) − (  /).Equation ( 12) is got as follows: The output of the speed loop is the given value of   , which is  *  .Then, ( 13) is got: Speed regulator based on ADRC with  *  and   as the input signals and  *  as the output signal is designed according to ( 6), (8), and (10).The diagram of speed regulator based on ADRC is shown in Figure 1.  ∈  is the output data.The goal of LSSVM is to construct a regression model as follows [20][21][22][23]:

Design of LSSVM-ADRC Controller
where  ∈   is weight vector;  ∈  is the offset; and () is the mapping function in kernel space.LSSVM regression algorithm is to calculate the optimum as follows: where  is the optimized objective function;  ∈  is the regularization parameter; and   ∈  is the relaxation factor of insensitive loss function.
The corresponding Lagrange function is shown as follows: where   ∈  is Lagrange factor.The partial derivation operation of  is made, and then make it to zero.Equation ( 17) is got: Thus, the optimization problem is transformed into solving the following linear equation: where  is a coefficient which decides the scaling extent of input variable in learning algorithm.Define M = Ω +  −1 I.The solution of ( 18) is expressed as follows: Therefore, the LSSVM approximation function is as follows:  In Figure 2, the LSSVM model can estimate part of system disturbance  LSSVM according to the input signal  1 . LSSVM and the other disturbance   2 estimated by ESO compose the total disturbance.Therefore, it can be seen that the ADRC disturbances estimation burden has reduced and system response has been improved.Furthermore, the system antiinterference ability is enhanced.The mathematical model of LSSVM-ADRC controller is obtained:

Simulation Result.
Based on Matlab/Simulink, the system simulation model is constructed to carry out simulation.LSSVM training is programed using m file in Matlab.The main parameters of PMSM are as follows:   = 13 Ω,   = 0.7 Wb, and   = 2.
(1) The given speed is 700 r/min; at 0.3 s load torque changes from 0 to 3 N⋅m.The speed waves are shown in Figures 3 and 4 under ADRC speed regulator and LSSVM-ADRC speed regulator, respectively.
From Figure 3, it can be seen that, based on ADRC speed controller, rotor speed instantly drops to 660 r/min when load suddenly changes, and then it reaches a steady state once again after 0.1 seconds.Contrastively, under LSSVM-ADRC speed controller in Figure 4, rotor speed drops to 695 r/min when load suddenly changes, and only after 0.06 s it reaches steady state again.The reason is LSSVM has reduced the burden on the ESO observation.The observation accuracy and system response speed have been improved under LSSVM-ADRC method.
(2) The given speed is 1500 r/min; at 0.25 s load torque changes from 3 N⋅m to 6 N⋅m.The speed waves are shown in Figures 5 and 6 under ADRC speed regulator and LSSVM-ADRC speed regulator, respectively.
From Figure 5, it can be seen that, based on ADRC speed controller, when load suddenly changes rotor speed drops from 1500 r/min to 1470 r/min, and after that it reaches a steady state after 0.07 seconds.Contrastively, under LSSVM-ADRC speed controller in Figure 6, rotor speed drops from 1500 r/min to 1497 r/min when load suddenly changes, and only after 0.03 s it reaches a steady state again.
Combining the above simulation results under conditions of low speed and high speed, it can be concluded that, based  on LSSVM-ADRC method, system responsiveness has been greatly improved; at the same time, system anti-interference ability has been improved to a large extent.

Experiment Result.
To validate the performance of the proposed method, experimental study is conducted on a PMSM turbine.The motor parameters are the same as the simulation motor.The chip TI DSP TMS320F2812 is chosen as the control core.The AC-DC-AC main circuit structure is   From Figures 7-10, it can be seen that, based on LSSVM-ADRC method, system responsiveness has been greatly improved; at the same time, system anti-interference ability has been improved to a large extent.It is consistent with the simulation results.

Conclusion
An improved method of PMSM vector control is proposed in the paper.The ADRC speed regulator is designed.Then, LSSVM optimal regression model is derived and embedded in the ADRC controller.ADRC observation precision and dynamic response of the system are improved.The system anti-interference ability is further improved.Finally, the current sensor, voltage sensor, and speed sensor are chosen to sample PMSM current, voltage, and speed.Experimental platform is constructed to verify the effectiveness of the proposed method.

Figure 1 :
Figure 1: Diagram of the speed regulator based on ADRC.

Figure 3 :
Figure 3: Simulation waves under ADRC method when given speed is 700 r/min and load changes from 0 to 3 N⋅m at 0.3 s.

Figure 4 :
Figure 4: Simulation waves under LSSVM-ADRC method when given speed is 700 r/min and load changes from 0 to 3 N⋅m at 0.3 s.

Figure 5 :
Figure 5: Simulation waves under ADRC method when given speed is 1500 r/min and load changes from 3 N⋅m to 6 N⋅m at 0.25 s.

Figure 6 :
Figure 6: Simulation waves under LSSVM-ADRC method when given speed is 1500 r/min and load changes from 3 N⋅m to 6 N⋅m at 0.25 s.

Figure 7 :
Figure 7: Experiment speed wave under ADRC method when given speed is 700 r/min and load changes from 0 to 3 N⋅m.

Figure 8 :
Figure 8: Experiment waves under LSSVM-ADRC method when given speed is 700 r/min and load changes from 0 to 3 N⋅m.

Figure 9 :
Figure 9: Experiment speed wave under ADRC method when given speed is 1500 r/min and load changes from 3 N⋅m to 6 N⋅m.

Figure 10 :
Figure 10: Experiment waves under LSSVM-ADRC method when given speed is 1500 r/min and load changes from 3 N⋅m to 6 N⋅m.