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A control strategy of permanent magnet synchronous motors (PMSMs), which is different from the traditional vector control (VC) and direct torque control (DTC), is proposed. Firstly, the circular rotating magnetic field is analyzed on the simplified model and discredited into stepping magnetic field. The stepping magnetomotive force will drive the rotor to run as the stepping motor. Secondly, the stator current orientation is used to build the control model instead of rotor flux orientation. Then, the discrete current control strategy is set and adopted in positioning control. Three methods of the strategy are simulated in computer and tested on the experiment platform of PMSM. The control precision is also verified through the experiment.

The permanent magnet synchronous motors (PMSMs) have become the popular AC motors and are used in various situations for their advantages of high efficiency, power factor, small size, and avoidance of exciting current. As servo motors, PMSMs are usually controlled with two methods, that is, vector control (VC) by flux orientation and direct torque control (DTC).

VC was put forward in 1971 for asynchronous motor by German engineer Blaschke [

DTC is proposed by Professor Depenbrock in 1985 [

Both methods are based on rotor flux which needs to be tested by an observer or to be controlled with other variables [

In PMSM, distributed winding, which is used in normal AC motor, is often coiled as shown in Figure

Distributed winding form.

Despite the differences of poles number, slots number, and the coiling form of the 3-phase AC motor, the physical model of stator can be described as in Figure

Simplified stator model of synchronic motor.

When powering the stator model with the 3-phase current as (

The composite MMF in the air gap will be expressed as

It is a rotating MMF vector, of which the amplitude is 1.5 times of each phase. The electric angle of the MMF rotating in the space corresponds to that of the current changing in the winding, which is

When the current changes by a cycle, the rotating MMF goes 2

The MMF

If the motor is powered with the currents described in

An example as

Each MMF will generate a positioning point, and the torque driving the rotor MMF to approach this point is defined as positioning torque. Here, the angle is calculated by electric angle; the actual step number

The stepping angle is determined by

Make the angular speed of the rotating frame equal to that of stator current vector in general frame of PMSM which is shown in Figure

The two components of

According to the mathematical expression of PMSM on rotating frame, the flux function can be rewritten as the following equation:

Substituting

Unlike the VC and DTC, in this control method, magnitude and phase of stator current are regulated dynamically for best torque responding, instead of keeping the amplitude of stator current and rotor flux or maintaining the angle

The structure of motor control system can be simplified as shown in Figure

The outer loop is the only one closed loop to control the speed or position. In the loop, the input is the rotor angle frequency difference or angle difference of preset and feedback, and the output is preset current vector including the magnitude and the rotation angle. To regulate the two variables, we give the motor the maximum current for maximum torque to start or brake and supply the rated current and adjust the

The inner loop is current loop, in which the three-phase stator current is transformed into current vector on

When the stator is powered with the discrete current as (

Stepping MMF of three-phase winding as

Vector diagram of stator current orientation.

Block diagram of stator current oriented control system PMSM.

Current vector regulation based on voltage space vector.

The angle between the two adjacent current vectors is defined as stepping angle just like the step motor, which is

Therefore, the torque of PMSM can be written as

This torque is also called reposition torque, impelling the rotor to run forward to catch up with the stator. Therefore, the stopping point of the stator current vector is the very positing point achieving incremental movement of a motor. Take

Positioning star diagram.

The proposed strategy of PMSM is called discrete current control, in which the main control variable is the torque angle between stator current vector and rotor flux vector, and the amplitude of stator current is the rating (except for starting and braking which is the maximum). It is different from VC and DTC, and the latter is to control the angle of flux of stator and rotor keeping the stator flux constant. The proposed strategy is more suitable for positioning because of the characteristic of positioning torque generated by discrete current and stepping motion, and the control process is also easier than the two classical methods.

To describe the proposed control strategy, two errors generated in the operation must be declared.

Static angle error: generated by load torque. It needs an electromagnetic torque to balance, so the torque angle cannot be decreased to zero which become an error for the control.

Dynamic angle error: the following process of rotor is not synchronous with stator current vector. The rotor will lag behind the vector when driving or go beyond the positioning point when braking. But the dynamic error will be disappeared when the rotor stops.

Pointing control is a typical discrete control method, controlling the motor to move a step forward every time. Only when the transient process of the first step is completely terminated, the second step begins.

The one-step torque

The greater the stepping angle, the more serious the oscillation phenomenon near the positing point, which needs to be avoided if possible. The simulation result is shown in Figure

Position and speed curve under point control.

The oscillation of pointing control is produced by

The time-optimal method is to brake at a proper time to remove the overshoot. As shown in Figure

Maximum torque control is to give the maximum torque at the accelerating stage and brake with the maximum negative torque when the position is vicinity to the stator current vector. The maximum torque is generated as

Position and speed curve under time optimization.

Position and speed curve under maximum torque.

Some motors need a constant frequency control method, which is only to change the step number in a constant frequency and to keep it not losing its steps. The angle frequency of motor

In the positioning control of this method, the motor responses will oscillate in starting and braking time. These oscillations can be eliminated by optimal controls as which is used in pointing control. The response curves generated by this method will be shown in the experiment in Section

It needs more time to accelerate or decelerate for the large-capacity motor, because the rotor could store more kinetic energy. If only give the motor a step change in constant frequency, the dynamic angle error may be over the maximum and lead to steps losing. It is necessary to preset an increment or decrement frequency of the motor to accelerate or decelerate.

The highest frequency is limited by the electromagnetic torque which is a function of angle frequency. A frequency of stator current vector, which is less than the jumping frequency, is given to accelerate at

Generally, to obtain a better result of control, this control is designed with closed loop to get an optimal up frequency curve. Moreover, the curve of frequency will be designed as two, three, or five segments according to the travel length. The experiment of three-segment curve is shown in Section

The experiments are based on a device of PMSM, which includes motor and transmission platform and digital driving controller. The platform is shown in Figure

Experiment platform.

The digital driving controller is composed of control unit and power amplifier shown in Figure

Digital driving controller.

The structure diagram of the control system is shown in Figure

The structure diagram of control system.

In the experiment, the motor is with 2 pairs of pole and the electric angle is 720° per revolution. We divided the cycle of stator current into 12 parts and the electric angle will be 30° per step. The number of positioning point will be

The stator current vector is given as formula (

Experiment curve of pointing control.

Current change of A phase

Position curve

Speed curve

In order to watch the control process, this experiment uses a frequency of 0.5 Hz. From Figure

Experiment curve of constant frequency control.

Current change of A phase

Position curve

Speed curve

Three-segment-speed curve of motor is used in rapid positioning, which only includes accelerating, constant speed, and decelerating. The experiment curve is shown in Figure

Experiment curve of up-down frequency control.

Position and speed curve

Current of A phase

Analyzing the error of stepping control of PMSM, we can gain the precision of it used in positioning. The steady error is less than one stepping angle which is 15° here. If we use the pulses of rotary encoder, of which 360° is corresponded to 4096 pulses, to stand for the absolute position, we can get a table of precision.

When driving the motor to run 160 revolutions, the emitting pulses and the operation time are shown in Tables

Experiment data of position precision incensement motion.

Given step | 1 | 12 | 24 | 100 | 500 | 1000 |

Pulse number | 181 | 2052 | 4224 | 17002 | 85452 | 170702 |

Rotating angle | 15.9° | 180.35° | 371.25° | 1494° | 7510.4° | 62464.02° |

Actual step | 1.1 | 12.02 | 12.7 | 99.6 | 500.7 | 1000.2 |

Experiment data of operating 160 revolutions.

No. | 1 | 2 | 3 | 4 | 5 |

Distance (pulse number) | 655202 | 655365 | 655369 | 655406 | 655485 |

Time (s) | 5.78 | 5.80 | 5.60 | 5.69 | 5.72 |

Error (pulses number) | 158 | 5 | 9 | 46 | 125 |

If use open loop control method and let the speed follow the three-segment curve, when the rotor moves 160 revolutions, then the number of pulses is 655360, and we get the result recorded in Table

It is proved that the discrete current vector method of PMSM has more advantages than existing methods. Firstly, the structure is simply just using single loop. Secondly, the control method with discrete MMF can generate the larger torque to start or drive the high inertia loads. Thirdly, positioning precision is determined by the stepping angle that can get higher accuracy. Moreover, the reliability and robustness of this method are better than those of the original driver which needs to often change its parameter especially for high inertia loads.

In this paper, a stepping control method of PMSM is presented. In the method, the circle of rotating MMF is discretized to regular polygon, and in this case, the positioning on stator current orientation has been discussed with the mechanism model of PMSM. The three methods of control are simulated and tested in experiment, which is available with a general DSP controller.

Although good performance is achieved, the method needs deeper studies in theory and applications, such as current responding, harmony wave analysis of discrete current, and influence of the method to grid. Our further works in this area will be oriented to implementation of this method in transmission technology of valve and artillery in order to improve the performance and efficiency and simplify structure.

This work is supported by the Natural Science Funds of Hebei Province (E2013202108) and by the National High Technology Research and Development Program of China (863 Program) (2006AA040306).