KR20150002919A - Apparatus and method for controlling position of permanent magnet stepper motors based on singular perturbation theory - Google Patents

Apparatus and method for controlling position of permanent magnet stepper motors based on singular perturbation theory Download PDF

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KR20150002919A
KR20150002919A KR1020130073740A KR20130073740A KR20150002919A KR 20150002919 A KR20150002919 A KR 20150002919A KR 1020130073740 A KR1020130073740 A KR 1020130073740A KR 20130073740 A KR20130073740 A KR 20130073740A KR 20150002919 A KR20150002919 A KR 20150002919A
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motor
target
permanent magnet
current
controller
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KR1020130073740A
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Korean (ko)
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정정주
김원희
신동훈
이영우
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한양대학교 산학협력단
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K37/00—Motors with rotor rotating step by step and without interrupter or commutator driven by the rotor, e.g. stepping motors
    • H02K37/10—Motors with rotor rotating step by step and without interrupter or commutator driven by the rotor, e.g. stepping motors of permanent magnet type
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P8/00—Arrangements for controlling dynamo-electric motors rotating step by step
    • H02P8/12—Control or stabilisation of current
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P8/00—Arrangements for controlling dynamo-electric motors rotating step by step
    • H02P8/14—Arrangements for controlling speed or speed and torque

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  • Power Engineering (AREA)
  • Control Of Stepping Motors (AREA)

Abstract

An apparatus and method for controlling the position of a permanent magnet type stepping motor based on the singular perturbation theory are disclosed. A position control method for a permanent magnet type stepping motor according to an example of the present invention is a method for controlling a position of a stepping motor by inputting a target position, a target speed and a target angular velocity to a step motor, - the differential controller, calculates the target torque through the feedforward controller and the proportional-integral-differential controller, calculates the target current using the calculated target torque, compensates the resistance component using the calculated target current , The position and speed of the stepper motor are measured to generate the motor input voltage including the counter electromotive force compensation, and the generated motor input voltage is applied to the stepper motor.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus and method for controlling a position of a permanent magnet type stepping motor based on a singular perturbation theory,

The present invention relates to a drive control technique for a stepper motor, and more particularly, to an apparatus and a method for controlling microstepping utilizing a peculiar perturbation theory in a permanent magnet type stepper motor.

In general, step motors (or stepping motors or stepper motors) are widely used in fields requiring precise position control such as robotic positioning systems. The stepper motor is the motor that is most commonly used for general position control, and it can be said that it is suitable for the position requiring the stopping accuracy of the position.

Permanent magnet stepper motors are utilized in a variety of positioning applications due to their power density as well as their high torque inertia ratio without durability, high efficiency and rotor winding. Another advantage of a permanent magnet type stepper motor is that it can operate in open-loop control, i.e., full stepping or half stepping. Although permanent magnet step motors were originally designed for open-loop operation, they are often also used in closed-loop systems.

In order to improve the position control of the permanent magnet type stepper motor, various feedback control methods have been studied as shown in the prior art documents cited below. Although these methods improve the position tracking performance of permanent magnet type step motors, there are two problems as follows.

First, in the position control of the permanent magnet stepper motor, the required bandwidth of the electrical dynamics for current follow-up is higher than the required bandwidth of the mechanical dynamics for position tracking. That is, the frequency of the required current is higher than the frequency of the required position. Thus, previous methods have been designed to maintain high frequency bandwidth for both position and current tracking. However, efforts to control the high frequency bandwidth required for current tracking sacrifice the control effort for tracking the position, so that the position tracking performance may deteriorate particularly in the acceleration and deceleration sections.

Second, another practical problem is that in the previous methods, the inductance is assumed to be a known constant. However, there is a mechanical error in the permanent magnet type stepper motor inductance, and in industry, the mechanical error of the inductance is generally ± 20%. Furthermore, the inductance can change during operation.

Therefore, it is required to provide a technical means for solving the above-mentioned problem in the permanent magnet type stepping motor.

 M. Zribi and J. Chiasson, " Position control of a PM stepper motor by exact linearization, " IEEE Trans. Automat. Contr., Vol. 36, no. 5, pp. 620-625, May 1991.  M. Bodson, J. Chiasson, R. Novotnak, and R. Rekowski, "Highperformance nonlinear feedback control of a permanent magnet stepper motor," IEEE Trans. Control Syst. Technol., Vol. 1, no. 1, pp. 5-14, March 1993.

SUMMARY OF THE INVENTION It is an object of the present invention to solve the problem that position tracking performance is deteriorated due to high frequency bandwidth control for current follow in the position control of a conventional permanent magnet type stepping motor, and when there is uncertainty of inductance, We want to overcome the limitation of vulnerability.

According to an aspect of the present invention, there is provided a position control method for a permanent magnet type stepping motor, the method comprising: receiving a target position, a target velocity, and a target angular velocity with respect to the stepping motor, FF) controller, measuring the position of the stepper motor and applying it to a proportional integral derivative (PID) controller; Calculating a target torque through the feedforward controller and the proportional-integral-derivative controller, and calculating a target current using the calculated target torque; Compensating a resistance component using the calculated target current and measuring a position and a speed of the step motor to generate a motor input voltage including counter electromotive force compensation; And applying the generated motor input voltage to the stepper motor.

In the position control method of the permanent magnet stepper motor according to an embodiment, the step of generating the motor input voltage may include the steps of: calculating a first voltage by compensating a resistance component to the calculated target current; Calculating a second voltage at which the counter electromotive force is compensated from the position and velocity measured from the step motor; And generating a motor input voltage from the first voltage and the second voltage.

In the position control method for a permanent magnet type stepping motor according to an embodiment, the step of generating the motor input voltage includes measuring the position and speed of the stepping motor without measuring a current, .

In the position control method for a permanent magnet type stepping motor according to an embodiment, the kinematics of the stepping motor is based on a singular perturbation theory, and the control of the high-frequency bandwidth for the current follow- The tracking error of the motor decreases exponentially to zero.

In the position control method of the permanent magnet type stepping motor according to the embodiment, the position measured from the stepping motor is fed back to the proportional-integral-derivative controller, the target current calculation step and the step of compensating the counter electromotive force , The speed measured from the stepper motor is fed back to the step of calculating the target current and the step of compensating the counter electromotive force.

According to an aspect of the present invention, there is provided a position control apparatus for a permanent magnet type stepping motor, including: a first controller for receiving a target position, a target speed, and a target angular velocity and performing feedforward control on the target position; A second controller for receiving the target position and measuring the position of the stepper motor to perform proportional-integral-derivative control based on the error of the target motor; An operation unit for calculating a target torque through the first control unit and the second control unit and calculating a target current using the calculated target torque; A controller for compensating a resistance component using the calculated target current and measuring a position and a speed of the stepper motor to generate a motor input voltage including a counter electromotive force compensation and applying the generated motor input voltage to the stepper motor, ; And a permanent magnet type step motor operated by the motor input voltage.

In the position control apparatus for a permanent magnet type stepping motor according to an embodiment, the control unit may include: a resistance component compensating unit for compensating a resistance component of the calculated target current to calculate a first voltage; And a counter electromotive force compensator for calculating a second voltage whose counter electromotive force is compensated from the position and the velocity measured from the step motor, wherein the motor input voltage is generated from the first voltage and the second voltage.

In the position control apparatus for a permanent magnet type stepping motor according to an embodiment, the control unit measures the position and speed of the stepping motor without measuring current, and uses only the resistance component compensation and the counter electromotive force compensation to measure the motor input voltage And a PWM driver for generating a PWM signal.

In the position control apparatus for a permanent magnet type stepping motor according to an embodiment, the kinematics of the stepping motor is in accordance with the singular perturbation theory, and the follow-up error of the stepping motor is controlled without control of the high-frequency bandwidth for the current follow- Exponentially decreasing to zero.

In the position controller of the permanent magnet stepper motor according to the embodiment, the position measured by the step motor is fed back to the second controller, the calculating unit and the control unit, And fed back to the control unit.

Embodiments of the present invention propose a nonlinear position controller based on the singular perturbation theory, so that the controller configuration can be simplified since a current controller or a current sensor having a high frequency bandwidth is not required in position control, and a permanent magnet type step motor Not only can the tracking error be exponentially reduced to zero, but also the problem of the position error of the transient state can be improved.

Figure 1 is a graph showing the position of the target reference position and open-loop microstepping.
2 is a graph showing the current of the open loop microstage.
3 is a flowchart illustrating a position control method of a permanent magnet type stepping motor based on the singular perturbation theory according to an embodiment of the present invention.
4 is a block diagram showing a position control apparatus for a permanent magnet type stepping motor based on the singular perturbation theory according to an embodiment of the present invention.
FIG. 5 is a view showing in detail each structure and calculated values of the position control apparatus of the permanent magnet type stepping motor of FIG. 4 according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

In the technical field in which the embodiments of the present invention are utilized, that is, the permanent magnet type step motor is constituted by a permanent magnet (permanent magnet) installed inside the case, and the magnetic flux generated by the current applied from the coil of the stator . The stator is a slotted stator, and the windings of the stator are located in two (of course, differently) windings and have two phases. A rotor made of a permanent magnet is installed on the rotating shaft and rotates together with the rotating shaft, and has N poles and S poles. In this way, a permanent magnet step motor (PMSM) is used as the permanent magnet.

As noted above, a current feedback controller can be used to ensure the desired current to improve the positional accuracy of the permanent magnet stepper motor. At this time, in order to follow a desired current having a higher high frequency bandwidth as compared with the bandwidth of mechanical dynamics, a current controller having a higher frequency bandwidth than the frequency of a desired current should be used. However, using a current controller having such a high frequency band may deteriorate the actual target position control performance. A separate current sensor for current controller configuration is also required.

To solve these problems, embodiments of the present invention to be described below propose a new approach to a position control method based on the singular perturbation theory. The dynamics of permanent magnet type step motors include slow and fast models. For this reason, the singular perturbation theory can be applied to the position tracking control of a permanent magnet type stepper motor, which has the advantage that the control design can be made very simple. Although the singular perturbation theory has been extensively developed in terms of control, there is still no practical application for a permanent magnet type step motor. Embodiments of the present invention will suggest how to utilize the singular perturbation theory in the position tracking control of a permanent magnet type stepper motor. Such an attempt would simplify the design process, such as a control algorithm suitable for real-time control. In other words, we design a position controller that does not need a current sensor and does not have a high-frequency bandwidth by generating desired torque using position feedback and using singular perturbation theory.

The features of the control method to be achieved through the technical means adopted by the embodiments of the present invention are as follows.

- Tracking error decreases exponentially to zero.

- The proposed control method is robust to the uncertainty of the inductance.

- No effort is required to control high frequency bandwidth for current tracking.

- The proposed control method requires no current measurement, but a position and velocity measurement is necessary.

In the following, the system model and the theory of the permanent magnet type step motor are introduced first.

(1) System model of permanent magnet type step motor

The mechanical / dynamic modeling for a permanent magnet type stepper motor can be expressed as the following equation (1).

Figure pat00001

Here, the symbols are as shown in Table 1 below.

Figure pat00002

In order to analyze the angular error of the microstepping drive from this, we first define the variables and symbols as shown in Table 2 below.

Figure pat00003

For all analytical purposes

Figure pat00004
The load torque perturbation expressed as < RTI ID = 0.0 > In a permanent magnet type stepper motor, detent torque can be neglected because it does not significantly affect the torque produced by the motor. In addition, the magnetic force formed between the phases can be ignored as well as the change of the inductance due to the magnetic saturation. The ideal sinusoidal flux distribution is assumed. The parameters of the permanent magnet type step motor are shown in Table 3 below.

Figure pat00005

In the position tracking control of a permanent magnet type stepper motor, the bandwidth required for electrical dynamics for current tracking is higher than the bandwidth required for mechanical dynamics for position tracking. That is, the frequency of the required current is higher than the frequency of the required position. This fact can be illustrated through simulation.

Figure 1 is a graph showing the position of the target reference position and the open-loop microstepping, and the target position, as shown in Figure 1, was used in this simulation. 2 is a graph showing the current of the open loop microstage.

In order to follow the target position, the open-loop micro stepping is used with reference to the following equation (2).

Figure pat00006

here,

Figure pat00007
Is a target position,
Figure pat00008
Is the amplitude of the input voltage. The position and current of the permanent magnet type stepping motor using the open loop micro stepping are as shown in FIGS. 1 and 2. FIG.

As described above, it can be confirmed that the frequency of the current is higher than the frequency of the position. In many prior art techniques, high frequency bandwidth control methods have been designed to follow both the target current and the target position. However, high-frequency bandwidth control for current tracking has the potential to sacrifice position tracking performance. Particularly, since the frequency of the current is high and rapidly changes between the acceleration and deceleration sections, the position tracking performance may deteriorate between these sections.

(2) Singular Perturbation Model singular perturbation model )

A typical standard specific perturbation system is shown in Equation 3 below.

Figure pat00009

here

Figure pat00010
Wow
Figure pat00011
Is continuously differentiable,
Figure pat00012
Is a state of a slow subsystem,
Figure pat00013
Is a state of fast subsystem,
Figure pat00014
Is a small amount of parameter. Now, to express the solution of the singular perturbation problem
Figure pat00015
And
Figure pat00016
Lt; / RTI > The main idea of the singular perturbation method is to separate the dynamics of the system into two separate time-scales, to change the design problem so that it is easier to solve than the design problem of the entire singular perturbation system.
Figure pat00017
Is assumed to have an isolated real root as shown in Equation 4 below.

Figure pat00018

The reduced-order system is then defined as: < EMI ID = 6.0 >

Figure pat00019

Figure pat00020
Is the solution of Equation (5), and the quasi-steady-state is expressed by the following Equation (6).

Figure pat00021

Figure pat00022
In order to move the quasi-steady state of the particle to its origin,
Figure pat00023
Is defined as the following Equation (7).

Figure pat00024

Now, the new time variable

Figure pat00025
, A boundary-layer system is obtained as shown in the following equation (8).

Figure pat00026

here,

Figure pat00027
And
Figure pat00028
Is treated as a fixed parameter. If the boundary layer model according to Equation 8 is exponentially stable and the reduced order system according to Equation 5 is also exponentially stable,
Figure pat00029
Positive constant that satisfies one condition
Figure pat00030
, And the system according to equation (3)
Figure pat00031
, And
Figure pat00032
The only thing about
Figure pat00033
,
Figure pat00034
And the second is the second. Also,
Figure pat00035
When given,
Figure pat00036
Uniformly
Figure pat00037
Maintained
Figure pat00038
Lt; / RTI >

In substantially well-designed permanent magnet type step motors,

Figure pat00039
Is a parameter
Figure pat00040
Can play a role. Therefore, the permanent magnet type step motor according to Equation (1) can be rewritten as Equation (9).

Figure pat00041

here

Figure pat00042
to be. In the permanent magnet type stepper motor according to Equation (9), fast kinetic can be expressed by electric dynamics, that is,
Figure pat00043
,
Figure pat00044
, And the slow kinetics is mechanical dynamics
Figure pat00045
,
Figure pat00046
to be. Therefore, the singular perturbation theory can be used to solve the position tracking problem. The permanent magnet type stepper motor according to Equation (9) can be rewritten as a form of the singular perturbation model as shown in the following Equation (10).

Figure pat00047

here

Figure pat00048
to be.

Lemma  One

Consider the singular perturbation problem of the permanent magnet type stepping motor according to Equation (1). In Equation (9), the origin of the boundary layer model is exponentially stable. To prove this, the following Equation (11) can be obtained with reference to Equation (1).

Figure pat00049

To move the equilibrium point to its origin,

Figure pat00050
,
Figure pat00051
As shown in the following Equation (12).

Figure pat00052

Therefore, the following equation (13) is obtained.

Figure pat00053

In addition,

Figure pat00054
, The boundary layer system is obtained as shown in the following Equation (14).

Figure pat00055

here,

Figure pat00056
Is always positive, the origin of the boundary layer system according to Equation (14) is exponentially stable. Furthermore, the region of attraction of the fast manifold covers the entire domain.

Remark  One

The eigenvalue of the fast model can be approximated as: < EMI ID = 15.0 >

Figure pat00057

Therefore,

Figure pat00058
And the inductance
Figure pat00059
, The fast model only performs a small role in the transient response. Thus, a larger resistance or a smaller inductance is expected. This limits the application of the singular perturbation theory to solve permanent magnet stepper motor applications. Although there are limitations mentioned above, in a substantially well-designed permanent magnet stepper motor
Figure pat00060
This theory can be exploited because it is small.

The reduced order model is obtained as: < EMI ID = 16.0 >

Figure pat00061

here

Figure pat00062
to be.

Remark  2

The control method utilizing the singular perturbation method provides the following advantages to the control method of the permanent magnet type step motor in which the embodiments of the present invention are implemented. First, there is no need to consider the uncertainty of the inductance often used for the design of a permanent magnet type stepper motor. That is, the controller using the singular perturbation method is robust against the uncertainty of the inductance.

(3) Controller design

Position tracking error

Figure pat00063
Is defined by the following equation (17).

Figure pat00064

here

Figure pat00065
Is the target reference position. Also
Figure pat00066
Is defined by the following equation (18).

Figure pat00067

Referring to Equations (16), (17) and (18) above, the reduced order model is changed as shown in Equation (19).

Figure pat00068

here

Figure pat00069
Is a positive constant. now,
Figure pat00070
Is defined as the following equation (20).

Figure pat00071

Then, the equation (19) is summarized as the following equation (21).

Figure pat00072

To design the control rule, a communication scheme such as the following Equation (22) is used.

Figure pat00073

Then, the control rule can be designed as shown in Equation 23 below.

Figure pat00074

Lemma  2

For a singular perturbation system according to equation (10), if

Figure pat00075
,
Figure pat00076
,
Figure pat00077
And their partial derivatives are sufficiently smooth functions and both the reduced order system and the boundary layer system are exponentially stable to a compact set,
Figure pat00078
≪ RTI ID = 0.0 > (10) < / RTI > is exponentially stable at the equilibrium point
Figure pat00079
Lt; / RTI >

Theorem  One

Consider the singular perturbation problem of the permanent magnet type stepping motor according to Equation (1). Suppose that the control rule given by equation (23) is applied to a permanent magnet type step motor. if

Figure pat00080
,
Figure pat00081
this
Figure pat00082
If the real part of the solution is designed to be negative,
Figure pat00083
A positive constant in which the positive follow-up error is exponentially decreasing
Figure pat00084
Lt; / RTI >

Equation (11) and Equation (23) can be proved as follows.

Figure pat00085

According to Lemma 1, the origin of the boundary layer model in equation (9) is exponentially stable. therefore,

Figure pat00086
And
Figure pat00087
Quasi-steady state
Figure pat00088
And
Figure pat00089
Hunting exponentially. Since the control rule according to Equation (23) is used, the reduced-order model according to Equation (21) is expressed as Equation (25).

Figure pat00090

Therefore,

Figure pat00091
If the real part of the root of the root is negative,
Figure pat00092
Converge to zero exponentially. Finally, we conclude that the origin of the boundary layer model and the reduced order model is exponentially stable. therefore,
Figure pat00093
A positive constant in which the positive follow-up error is exponentially decreasing
Figure pat00094
Lt; / RTI >

Remark  3

Goal location

Figure pat00095
Is a dynamic profile, the position follow-up error during the non-zero velocity interval is an order
Figure pat00096
, It is evident that a system having a sufficiently small inductance tracks the target position with a very small error. if
Figure pat00097
Which is the upper limit of the inductance which degrades the position tracking performance,
Figure pat00098
Lt; / RTI > However, this upper limit is usually much greater than the normal range of inductance that can be encountered in a real application.

To summarize, the proposed method using the singular perturbation theory is shown in Equation (26).

Figure pat00099

Hereinafter, embodiments of the present invention for solving the above-described technical problems will be described in detail based on the controller design model derived above. In the following description and the accompanying drawings, detailed description of well-known functions or constructions that may obscure the subject matter of the present invention will be omitted. It is to be noted that the same components are denoted by the same names and reference numerals as possible throughout the drawings.

FIG. 3 is a flowchart showing a position control method of a permanent magnet type stepping motor based on the singular perturbation theory according to an embodiment of the present invention, which includes the following steps that can be performed by the controller.

In step S310, the controller receives the target position, the target speed, and the target angular speed with respect to the stepping motor, applies the same to the feed forward (FF) controller, measures the position of the stepping motor and calculates proportional- integral derivative, PID) controller.

In step S320, the controller calculates the target torque through the feedforward controller and the proportional-integral-derivative controller, and calculates the target current using the calculated target torque.

In step S330, the controller compensates the resistance component using the target current calculated in step S320, and measures the position and speed of the stepper motor to generate a motor input voltage including counter electromotive force compensation. In the process of generating the motor input voltage, the first voltage is calculated by compensating the resistance component to the target current calculated in step S320, and the second voltage, which is obtained by compensating the counter electromotive force from the position and speed measured by the step motor, And generating the motor input voltage from the first voltage and the second voltage.

Particularly, it is preferable that the process of generating the motor input voltage is performed by using only the resistance component compensation and the counter electromotive force compensation, while measuring the position and speed of the step motor without measuring the current.

In step S340, the controller applies the motor input voltage generated in step S330 to the stepper motor.

On the other hand, the position measured by the step motor is fed back to the proportional-integral-derivative controller, the target current calculating step and the step of compensating the counter electromotive force, and the speed measured by the step motor is calculated And the step of compensating the counter electromotive force.

In the above-described series of steps, the dynamics of the stepping motor is based on the singular perturbation theory, and the tracking error of the stepping motor is exponentially set to 0 without control of the high-frequency bandwidth for the current follow- The effect of which is shown in Fig.

FIG. 4 is a block diagram illustrating a position control apparatus for a permanent magnet type stepping motor based on the singular perturbation theory according to an embodiment of the present invention, and includes a position control module 10 and a stepping motor 20.

More specifically, the first control unit 11 receives the target position, the target speed, and the target angular velocity, respectively, for feedforward control, the second control unit 13 receives the target position and measures the position of the step motor, Proportional-integral-derivative control.

The calculation unit 15 calculates the target torque through the first control unit 11 and the second control unit 13, and calculates the target current using the calculated target torque.

The controller 17 compensates the resistance component using the target current calculated through the calculator 15, measures the position and speed of the stepper motor to generate a motor input voltage including counter-electromotive force compensation, And the motor input voltage is applied to the step motor 20. Here, the control unit 17 includes a resistance component compensating unit (not shown) for calculating the first voltage by compensating the resistance component to the target current calculated through the calculating unit 15, and a resistance compensating unit And a counter electromotive force compensating unit (not shown) for calculating a second voltage compensated for the counter electromotive force from the speed, wherein the motor input voltage is generated from the first voltage and the second voltage.

The controller 17 may be implemented as a PWM driver that measures the position and speed of the stepper motor 20 without measuring the current and generates a motor input voltage using only the resistance component compensation and the counter electromotive force compensation .

Finally, the step motor 20 is operated by the motor input voltage applied from the control unit 17. [

In the position control apparatus as described above, the kinematics of the step motor is in accordance with the singular perturbation theory, and the follow-up error of the step motor is exponentially reduced to zero without control of the high-frequency bandwidth for current follow-up of the step motor.

Further, the position measured from the step motor 20 is fed back to the second controller 13, the arithmetic unit 15 and the control unit 17, and the speed measured by the step motor 20 is supplied to the arithmetic unit 15) and the control unit (17).

FIG. 5 is a view showing in detail each constitution and calculated values of the position control apparatus of the permanent magnet type stepping motor of FIG. 4 according to an embodiment of the present invention, wherein the same reference numerals denote the same components. Therefore, in order to avoid duplication of description, each configuration will be described with the flow of each signal as the center.

First, the next desired location (

Figure pat00100
), The desired speed (
Figure pat00101
), The desired angular velocity (
Figure pat00102
(FF) controller 11. The feedforward (FF) Further, from the step motor 20,
Figure pat00103
(PID) controller 13 and the feedforward controller 11 to determine the desired torque (< RTI ID = 0.0 >
Figure pat00104
).

Now, the calculating unit 15 calculates the desired current (< RTI ID = 0.0 >

Figure pat00105
,
Figure pat00106
). In this process, the process of calculating the desired current from the torque is according to Equation 26 given above.

The resistance component compensator 16 is constituted by using the desired current calculated from the calculating section 15 and the position of the step motor 20

Figure pat00107
) And speed
Figure pat00108
) Measurement is used to determine the motor input voltage (< RTI ID = 0.0 >
Figure pat00109
,
Figure pat00110
). Such a voltage input can be implemented through a PWM driver or the like. Here, the operation for compensating the counter electromotive force to generate the motor input voltage is also according to the above-described expression (26).

Finally, the motor input voltage is applied to the permanent magnet type stepping motor 20.

In the above, a nonlinear position controller based on singular perturbation theory is proposed. Since the dynamics of a permanent magnet type stepper motor include slow and fast models, we have explained that the singular perturbation theory can be applied. Thus, according to the above-described embodiments, since the non-linear position controller based on the singular perturbation theory is proposed, the current controller or the current sensor of the high frequency bandwidth is not required in the position control, so that the controller configuration can be simplified, Not only the magnet type step motor can be provided but also the problem of the position error of the transient state can be improved by decreasing the tracking error exponentially to zero.

The present invention has been described above with reference to various embodiments. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. Therefore, the disclosed embodiments should be considered in an illustrative rather than a restrictive sense. The scope of the present invention is defined by the appended claims rather than by the foregoing description, and all differences within the scope of equivalents thereof should be construed as being included in the present invention.

10: Position control device for permanent magnet type step motor
11: first control unit 13: second control unit
15: operation unit 16: resistance component compensating unit
17: control unit 18: counter-
20: Permanent magnet type stepping motor

Claims (10)

A position control method of a permanent magnet type stepping motor,
A target speed, and a target angular speed are input to the stepping motor and applied to a feed forward (FF) controller, and the position of the stepping motor is measured to obtain a proportional integral derivative (PID) Applying to the controller;
Calculating a target torque through the feedforward controller and the proportional-integral-derivative controller, and calculating a target current using the calculated target torque;
Compensating a resistance component using the calculated target current and measuring a position and a speed of the step motor to generate a motor input voltage including counter electromotive force compensation; And
And applying the generated motor input voltage to the stepper motor. The method according to claim 1,
Wherein generating the motor input voltage comprises:
Calculating a first voltage by compensating a resistance component of the calculated target current;
Calculating a second voltage at which the counter electromotive force is compensated from the position and velocity measured from the step motor; And
Generating a motor input voltage from the first voltage and the second voltage. The method according to claim 1,
Wherein generating the motor input voltage comprises:
Measuring a position and a speed of the stepper motor without measuring a current, and performing only by using the resistance component compensation and the counter electromotive force compensation. The method according to claim 1,
The kinematics of the stepper motors follow the singular perturbation theory,
Wherein the tracking error of the step motor is exponentially reduced to zero without controlling a high frequency bandwidth for current follow-up of the step motor. The method according to claim 1,
Wherein the position measured from the stepper motor is fed back to the proportional-integral-derivative controller, calculating the target current, and compensating the counter electromotive force,
Wherein the speed measured from the step motor is fed back to the step of calculating the target current and the step of compensating the counter electromotive force. A position control device for a permanent magnet type stepping motor,
A target position, a target velocity, and a target angular velocity;
A second controller for receiving the target position and measuring the position of the stepper motor to perform proportional-integral-derivative control based on the error of the target motor;
An operation unit for calculating a target torque through the first control unit and the second control unit and calculating a target current using the calculated target torque;
A controller for compensating a resistance component using the calculated target current and measuring a position and a speed of the stepper motor to generate a motor input voltage including a counter electromotive force compensation and applying the generated motor input voltage to the stepper motor, ; And
And a permanent magnet type step motor operated by the motor input voltage. The method according to claim 6,
Wherein,
A resistance component compensating unit for compensating the resistance component to the calculated target current to calculate a first voltage; And
And a counter electromotive force compensating unit for calculating a second voltage to which the counter electromotive force is compensated based on the position and the velocity measured from the step motor,
And generates a motor input voltage from the first voltage and the second voltage. The method according to claim 6,
Wherein,
Wherein the driver is a PWM driver that measures the position and speed of the stepper motor without measuring a current and generates a motor input voltage using only the resistance component compensation and the counter electromotive force compensation. The method according to claim 6,
The kinematics of the stepper motors are in accordance with the singular perturbation theory,
Wherein the tracking error of the step motor is exponentially reduced to zero without controlling the high-frequency bandwidth for the current follow-up of the step motor. The method according to claim 6,
The position measured by the step motor is fed back to the second controller, the arithmetic unit and the control unit,
And the speed measured by the step motor is fed back to the operation unit and the control unit.
KR1020130073740A 2013-06-26 2013-06-26 Apparatus and method for controlling position of permanent magnet stepper motors based on singular perturbation theory KR20150002919A (en)

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WO2019125734A1 (en) * 2017-12-20 2019-06-27 Microsemi Soc Corp. Apparatus and method for sensorless detection of load torque of a stepper motor and for optimizing drive current for efficient operation
CN110011583A (en) * 2019-04-12 2019-07-12 中国矿业大学 Permanent magnet synchronous motor System with Sliding Mode Controller and modeling method based on singular perturbation theory
CN113193594A (en) * 2021-04-29 2021-07-30 华中科技大学 Reduced order modeling method of doubly-fed wind generator in fault ride-through period under weak grid

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2019125734A1 (en) * 2017-12-20 2019-06-27 Microsemi Soc Corp. Apparatus and method for sensorless detection of load torque of a stepper motor and for optimizing drive current for efficient operation
US10511245B2 (en) 2017-12-20 2019-12-17 Microsemi Soc Corp. Apparatus and method for sensorless detection of load torque of a stepper motor and for optimizing drive current for efficient operation
CN111543002A (en) * 2017-12-20 2020-08-14 美高森美SoC公司 Sensorless detection of load torque for stepper motors and apparatus and method for optimizing drive current for efficient operation
CN111543002B (en) * 2017-12-20 2023-11-03 美高森美SoC公司 Sensorless detection of load torque for stepper motors and apparatus and method for optimizing drive current for efficient operation
CN110011583A (en) * 2019-04-12 2019-07-12 中国矿业大学 Permanent magnet synchronous motor System with Sliding Mode Controller and modeling method based on singular perturbation theory
CN113193594A (en) * 2021-04-29 2021-07-30 华中科技大学 Reduced order modeling method of doubly-fed wind generator in fault ride-through period under weak grid

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