CN113193794A - Rapid tracking control system and method for permanent magnet brushless direct current motor servo system - Google Patents

Rapid tracking control system and method for permanent magnet brushless direct current motor servo system Download PDF

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CN113193794A
CN113193794A CN202110538824.4A CN202110538824A CN113193794A CN 113193794 A CN113193794 A CN 113193794A CN 202110538824 A CN202110538824 A CN 202110538824A CN 113193794 A CN113193794 A CN 113193794A
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permanent magnet
magnet brushless
tracking control
servo system
direct current
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CN113193794B (en
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袁雷
卿意
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Wuhan Haizhuotake Technology Co ltd
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    • 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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/08—Arrangements for controlling the speed or torque of a single motor
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P23/0009—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P23/0022—Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0077—Characterised by the use of a particular software algorithm
    • 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
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/04—Arrangements or methods for the control of AC motors characterised by a control method other than vector control specially adapted for damping motor oscillations, e.g. for reducing hunting
    • 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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/34—Modelling or simulation for control purposes

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Abstract

The invention provides a rapid tracking control system and a rapid tracking control method for a permanent magnet brushless direct current motor servo system. The control system is typically connected with a permanent magnet brushless direct current motor; the control system comprises a nonsingular terminal sliding mode surface function module, a self-adaptive variable speed approach law function module and a servo control system rapid tracking control module. Firstly, establishing a mathematical model of a permanent magnet brushless direct current motor servo system containing parameter uncertainty; and then designing a self-adaptive variable speed approach law algorithm, adaptively adjusting the approach law speed according to the distance between the system state quantity and a balance point, and combining the approach law algorithm with non-singular terminal sliding mode control to design a rapid tracking control method suitable for a permanent magnet brushless direct current motor servo system. The control method realizes high-precision tracking control of the permanent magnet brushless direct current motor servo system, reduces the buffeting problem of the sliding mode, and improves the control quality and the robustness of the servo control system.

Description

Rapid tracking control system and method for permanent magnet brushless direct current motor servo system
Technical Field
The invention relates to the technical field of permanent magnet synchronous motor control, in particular to a quick tracking control method for a permanent magnet brushless direct current motor servo system.
Background
The permanent magnet brushless direct current motor is widely applied to the fields of industry, aerospace and military due to the advantages of large starting torque, high power factor and the like. Although a brushless direct current motor servo control system based on the traditional PI control can obtain a satisfactory control effect to a certain extent, the PI control system is applied to the occasions with higher control performance requirements and is limited to the bandwidth of the PI controller, and the PI controller cannot meet the requirements of actual performance.
To solve this problem, a number of advanced control algorithms have been proposed. The sliding mode control is concerned with due to the advantages of simple controller design, strong robustness and the like, but the control performance of the traditional sliding mode control is easily interfered by sliding mode buffeting, so that the control error is large. In order to enable the sliding mode control to obtain better control performance, the optimization of the sliding mode control algorithm has important practical application significance.
The invention patent with publication number CN112180721A provides an adaptive sliding mode control method of an electromechanical servo system based on a variable speed approach law. The control method comprises the following steps: firstly, a hyperbolic tangent auxiliary function is constructed and a new speed change approaching law is designed to adjust the convergence speed of a sliding mode variable, so that the sliding mode variable has a higher convergence speed before reaching a speed reduction point, and buffeting can be effectively weakened after reaching the speed reduction point. On the basis, an adaptive sliding mode controller is constructed, and the system position output can be ensured to track the expected track quickly and stably. Meanwhile, the upper bound of the square of the uncertainty term is estimated by a design parameter updating law, so that the continuity of the control signal is ensured, and the buffeting of the control signal is reduced. Although the method can solve the sliding mode buffeting problem to a certain extent, the implementation mode of designing a new speed change approach law is too complex, and a controller designed based on a traditional linear sliding mode surface function cannot enable a control system to converge to an expected track within a limited time.
In view of the above, there is a need for an improved fast tracking control system and method for a servo system of a permanent magnet brushless dc motor to solve the above problems.
Disclosure of Invention
The invention aims to provide a quick tracking control system and a quick tracking control method for a permanent magnet brushless direct current motor servo system.
In order to achieve the purpose, the invention provides a rapid tracking control system of a permanent magnet brushless direct current motor servo system. A fast tracking control system of the permanent magnet brushless direct current motor servo system is typically connected with the permanent magnet brushless direct current motor; the fast tracking control system of the permanent magnet brushless direct current motor servo system comprises a nonsingular terminal sliding mode surface function module, a self-adaptive variable speed approaching law function module and a fast tracking control module of the servo control system;
the output end of the nonsingular terminal sliding mode surface function module is connected with the input end of the self-adaptive variable speed approximation law function module;
the output end of the nonsingular terminal sliding mode surface function module and the output end of the self-adaptive variable speed approach law function module are respectively connected with the input end of the servo control system quick tracking control module;
the fast tracking control system of the permanent magnet brushless direct current motor servo system firstly establishes a mathematical model of the permanent magnet brushless direct current motor servo system with uncertain parameters; and then combining the self-adaptive variable speed approximation rule function set in the self-adaptive variable speed approximation rule function module with the nonsingular terminal sliding mode surface function set in the nonsingular terminal sliding mode surface function digital module, thereby comprehensively obtaining the rapid tracking control algorithm of the permanent magnet brushless direct current motor servo system in the rapid tracking control module of the servo control system.
In order to achieve the above object, the present invention further provides a fast tracking control method for a permanent magnet brushless dc motor servo system, based on the tracking control system, including the following steps:
s1, establishing a mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty;
s2, designing a self-adaptive variable speed approach law algorithm, adaptively adjusting the approach law speed according to the distance between the state quantity of the system and the balance point, enabling the system to converge to a steady state value in a shorter time, and simultaneously reducing the buffeting problem of sliding mode control.
S3, designing a fast tracking control method of a permanent magnet brushless direct current motor servo system: the self-adaptive variable speed approaching law algorithm is combined with the nonsingular terminal sliding mode control, so that the control quality and the robustness of the servo control system are improved.
As a further improvement of the present invention, the mathematical model of the servo system of the permanent magnet brushless dc motor in step S1 is constructed as follows:
1) the electromagnetic torque equation of a permanent magnet brushless dc motor can be expressed as
Figure BDA0003070822190000031
Where ω is the mechanical angular velocity of the permanent magnet brushless DC motor, ea、eb、ecBack electromotive force, i, of ABC three-phase statora、ib、icRespectively three-phase stator phase current, TeIs an electromagnetic torque.
2) The equation of motion for a brushless dc motor can be expressed as:
Figure BDA0003070822190000032
wherein B is a damping coefficient, J is a rotational inertia of the motor, and TLIs the load torque, KTIs the torque coefficient, i is the torque current, θmIs a mechanical angle.
3) The mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty is as follows:
Figure BDA0003070822190000033
let g (t) be the total uncertainty, i.e.
Figure BDA0003070822190000034
Wherein,
Figure RE-GDA0003121733460000034
is a mechanical angle thetamThe second derivative of (a) is,
Figure RE-GDA0003121733460000035
is a mechanical angle thetamIs the uncertainty of the corresponding term and is bounded. Let g (t) be the total indeterminate quantity and satisfy | g (t) | < lg， lgIs a normal number.
As a further improvement of the present invention, the adaptive shift approach law designed in step S2 is as follows:
Figure BDA0003070822190000041
in the formula, k, mu, alpha and beta are all parameters to be designed which are more than 0, sgn (·) is a sign function, | (·) is an absolute value function, e(·)Is an exponential function.
The self-adaptive speed change approaching law can self-adaptively adjust the approaching speed of the approaching law along with the distance between the state quantity of the servo system and the balance point.
1) When | s | is large, e-βs|And e-α|s|Will gradually go to 0, when mu (1-e)-β|s|) The terms will gradually trend towards mu, k (1-e)-α|s|) Will gradually move towards-k, thereby retaining the excellent property of rapid convergence of the conventional exponential approximation law.
2) Conversely, when | s | → 0, e-β|s|And e-α|s|Will gradually tend to 1, when mu (1-e)-β|s|) The term gradually goes to 0, so that the influence of the system jitter matrix can be eliminated.
Thus, the approach law can adaptively adjust the parameters of the exponential approach law according to the position of the system state.
Defining Lyapunov functions
Figure BDA0003070822190000042
And the first derivative is calculated, and the adaptive variable speed approaching law is substituted to obtain
Figure BDA0003070822190000043
In the formula, V is a Lyapunov function, s is a sliding mode surface function,
Figure BDA0003070822190000044
is the first derivative of s.
Satisfying the Lyapunov theorem of stability.
As a further improvement of the present invention, the fast tracking control method for the permanent magnet brushless dc motor servo system designed in step S3 is as follows:
order to
Figure BDA0003070822190000045
In the formula, thetamIs the actual value of the mechanical angle of the motor, thetarIs a reference value of the mechanical angle of the motor, thetamIs a mechanical angle thetamThe first derivative of (a). x is the number of1As position error, x2Is a position error x1The first derivative of (a).
The mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty is obtained by derivation of the formula as follows:
Figure BDA0003070822190000051
in the formula,
Figure BDA0003070822190000052
is x1The first derivative of the signal is a derivative of,
Figure BDA0003070822190000053
is x2The first derivative.
Setting a nonsingular terminal sliding mode surface function as follows:
Figure BDA0003070822190000054
wherein λ >0, a >0 and a/b >1, q >0 and is odd, p >0 and is odd, and 2> p > q >1,
when the system works in a stable state, namely the system state quantity reaches the sliding mode surface and starts sliding mode movement, the requirement is met at the moment
Figure BDA0003070822190000055
Based on the adaptive variable speed approaching law, the expression of the fast tracking control algorithm of the permanent magnet brushless direct current motor servo system can be obtained as follows:
Figure BDA0003070822190000056
wherein D ═ k (1-e)-α|s|)s+μ(1-e-β|s|) sgn(s), and μ > lg。
Defining Lyapunov functions
Figure BDA0003070822190000057
And taking the first derivative thereof
Figure BDA0003070822190000058
In the formula, V is a Lyapunov function, s is a sliding mode surface function,
Figure BDA0003070822190000061
is the first derivative of s.
According to the sliding mode arrival condition, the controller is gradually stable, and the Lyapunov stability theorem is met.
After the syndrome is confirmed.
The invention has the beneficial effects that:
1. the invention provides a rapid tracking control method of a permanent magnet brushless direct current motor servo system, which designs a self-adaptive variable speed approach law algorithm, can self-adaptively adjust the approach law speed according to the distance between a system state quantity and a balance point, can enable the system to converge to a steady state value in a shorter time, and simultaneously reduces the buffeting problem of sliding mode control.
2. The invention provides a fast tracking control method of a permanent magnet brushless direct current motor servo system, which is designed to combine a self-adaptive variable speed approach law algorithm with non-singular terminal sliding mode control, realize high-precision tracking control of the permanent magnet brushless direct current motor servo system, reduce the buffeting problem of the sliding mode and improve the control quality and the robust performance of the servo control system.
Drawings
Fig. 1 is a schematic structural diagram of a fast tracking control system of a permanent magnet brushless dc motor servo system provided in the present invention.
Fig. 2 is a schematic flow chart of a fast tracking control method of a permanent magnet brushless dc motor servo system according to the present invention.
Reference numerals
10-a fast tracking control system of a permanent magnet brushless direct current motor servo system; 11-nonsingular terminal sliding mode surface function module; 12-an adaptive variable speed approach law function module; 13-servo control system fast tracking control module; 20-permanent magnet brushless dc motor.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the structures and/or processing steps closely related to the aspects of the present invention are shown in the drawings, and other details not closely related to the present invention are omitted.
Further, it is also noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Referring to fig. 1, the present invention provides a fast tracking control system 10 of a servo system of a permanent magnet brushless dc motor, which is typically connected to a permanent magnet brushless dc motor 20; the fast tracking control system 10 of the permanent magnet brushless direct current motor servo system comprises a nonsingular terminal sliding mode surface function module 11, a self-adaptive variable speed approaching law function module 12 and a fast tracking control module 13 of the servo control system;
the output end of the nonsingular terminal sliding mode surface function module 11 is connected with the input end of the adaptive variable speed approximation law function module 12;
the output end of the nonsingular terminal sliding mode surface function module 11 and the output end of the adaptive variable speed approach law function module 12 are respectively connected with the input end of the servo control system fast tracking control module 13;
the fast tracking control system 10 of the permanent magnet brushless direct current motor servo system firstly establishes a mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty; then, combining the adaptive variable speed approximation rule function set in the adaptive variable speed approximation rule function module 12 with the nonsingular terminal sliding mode surface function set in the nonsingular terminal sliding mode surface function digital module 11, thereby comprehensively obtaining the fast tracking control algorithm of the permanent magnet brushless direct current motor servo system in the servo control system fast tracking control module 13.
Example 1
Referring to fig. 2, embodiment 1 provides a fast tracking control method for a permanent magnet brushless dc motor servo system, and a fast tracking control system 10 based on the permanent magnet brushless dc motor servo system includes the following steps:
s1, establishing a mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty, and constructing as follows:
s11, the electromagnetic torque equation of the permanent magnet brushless DC motor can be expressed as
Te＝(eaia+ebib+ecic)/ω；
Where ω is the mechanical angular velocity of the permanent magnet brushless DC motor, ea、eb、ecBack electromotive force, i, of ABC three-phase statora、ib、icRespectively three-phase stator phase current, TeIs an electromagnetic torque.
S12, the equation of motion of the brushless dc motor can be expressed as:
Figure BDA0003070822190000081
wherein B is a damping coefficient, J is a rotational inertia of the motor, and TLIs the load torque, KTIs the torque coefficient, i is the torque current, θmIs a mechanical angle.
S13, the mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty is as follows:
Figure BDA0003070822190000082
let g (t) be the total uncertainty, i.e.
Figure BDA0003070822190000083
Wherein,
Figure RE-GDA0003121733460000084
is a mechanical angle thetamThe second derivative of (a) is,
Figure RE-GDA0003121733460000085
is a mechanical angle thetamFirst order ofThe numbers, delta a and delta b are respectively uncertain factors of corresponding items and are bounded. Let g (t) be the total indeterminate quantity and satisfy | g (t) | < lg， lgIs a normal number.
S2, designing a self-adaptive speed-changing approaching law algorithm based on the self-adaptive speed-changing approaching law function module 12, wherein the self-adaptive speed-changing approaching law algorithm can adaptively adjust the approaching law speed according to the distance between the system state quantity and a balance point, so that the system can converge to a steady-state value in a shorter time, and meanwhile, the buffeting problem of sliding mode control is reduced; the specific process is as follows:
s21, the adaptive variable speed approach law algorithm is as follows:
Figure BDA0003070822190000091
in the formula, k, mu, alpha and beta are all parameters to be designed which are more than 0, sgn (·) is a sign function, | (·) is an absolute value function, e(·)Is an exponential function.
The self-adaptive speed change approaching law can self-adaptively adjust the approaching speed of the approaching law along with the distance between the state quantity of the servo system and the balance point.
Specifically, in this embodiment, the adaptive variable approach law algorithm module 12 of the present invention utilizes a reference value θ of mechanical anglerWith the actual value thetamThe sliding mode surface function related to the difference value adaptively adjusts the approaching speed of the approaching law along with the distance between the state quantity of the servo system and the balance point.
When | s | is large, e-β|s|And e-α|s|Will gradually go to 0, when mu (1-e)-β|s|) The term will gradually trend towards mu, -k (1-e)-α|s|) Will gradually move towards-k, thereby preserving the excellent property of rapid convergence of the traditional exponential approximation law.
Conversely, when | s | → 0, e-β|s|And e-α|s|Will gradually tend to 1, when mu (1-e)-β|s|) The term gradually goes to 0, so that the influence of the system jitter matrix can be eliminated.
Thus, the approach law can adaptively adjust the parameters of the exponential approach law according to the position of the system state.
S22, defining Lyapunov function
Figure BDA0003070822190000092
And the first derivative is calculated, and the adaptive variable speed approximation law algorithm is substituted to obtain the self-adaptive variable speed approximation law
Figure BDA0003070822190000093
Satisfying the Lyapunov theorem of stability.
S3, designing a fast tracking control method of the permanent magnet brushless direct current motor servo system based on the fast tracking control module 13 of the permanent magnet brushless direct current motor servo system, which comprises the following steps: the self-adaptive variable speed approach law algorithm is combined with non-singular terminal sliding mode control, the control quality and the robust performance of a servo control system are improved, and the specific process is as follows:
s31, the fast tracking control method of the permanent magnet brushless direct current motor servo system is as follows:
order to
Figure BDA0003070822190000101
In the formula, thetamIs the actual value of the mechanical angle of the motor, thetarIs a reference value of the mechanical angle of the motor.
The mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty is obtained by derivation of the formula as follows:
Figure BDA0003070822190000102
s32, based on the nonsingular terminal sliding mode surface function module 11, setting the nonsingular terminal sliding mode surface function as:
Figure BDA0003070822190000103
wherein λ >0, a >0 and a/b >1, q >0 and is odd, p >0 and is odd, and 2> p > q >1,
s33, when the system works in a stable state, namely the system state quantity reaches the sliding mode surface and starts sliding mode movement, the requirement is met at the moment
Figure BDA0003070822190000104
Based on the adaptive variable speed approaching law, the expression of the fast tracking controller of the permanent magnet brushless direct current motor servo system can be obtained as follows:
Figure BDA0003070822190000105
wherein D ═ k (1-e)-α|s|)s+μ(1-e-β|s|) sgn(s), and μ > lg。
S34, defining Lyapunov function
Figure BDA0003070822190000106
And taking the first derivative thereof
Figure BDA0003070822190000111
According to the sliding mode arrival condition, the controller is gradually stable, and the Lyapunov stability theorem is met.
The self-adaptive variable speed approach law algorithm of the invention is related to a mechanical angle reference value thetarWith the actual value thetamThe sliding mode surface function related to the difference value between the two functions can self-adaptively adjust the approach speed of the approach law along with the distance between the state quantity of the servo system and the balance point, thereby avoiding the inherent buffeting problem of sliding mode control to a great extent, having good self-adaptive effect on parameter perturbation and external interference and improving the high-performance control of the control system of the permanent magnet brushless direct current motor 20.
In summary, the present invention provides a fast tracking control system and method for a servo system of a permanent magnet brushless dc motor. The control system is typically connected with a permanent magnet brushless direct current motor; the control system comprises a nonsingular terminal sliding mode surface function module, a self-adaptive variable speed approach law function module and a servo control system rapid tracking control module. The control method comprises the steps of firstly, establishing a mathematical model of a permanent magnet brushless direct current motor servo system containing parameter uncertainty; and secondly, designing a self-adaptive variable speed approach law algorithm, adaptively adjusting the approach law speed according to the distance between the state quantity of the servo system and a balance point, and combining the approach law algorithm with non-singular terminal sliding mode control to design a rapid tracking control method suitable for the permanent magnet brushless direct current motor servo system. The control method realizes high-precision tracking control of the permanent magnet brushless direct current motor servo system, reduces the buffeting problem of the sliding mode, and improves the control quality and robustness of the servo control system.
Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention.

Claims (7)

1. The utility model provides a quick tracking control system of permanent magnetism brushless DC motor servo which characterized in that: the fast tracking control system (10) of the permanent magnet brushless direct current motor servo system is typically connected with the permanent magnet brushless direct current motor (20); the fast tracking control system (10) of the permanent magnet brushless direct current motor servo system comprises a nonsingular terminal sliding mode surface function module (11), a self-adaptive variable speed approaching law function module (12) and a fast tracking control module (13) of the servo control system;
the output end of the nonsingular terminal sliding mode surface function module (11) is connected with the input end of the self-adaptive variable speed approximation law function module (12);
the output end of the nonsingular terminal sliding mode surface function module (11) and the output end of the self-adaptive variable speed approach law function module (12) are respectively connected with the input end of the servo control system fast tracking control module (13);
the fast tracking control system (10) of the permanent magnet brushless direct current motor servo system firstly establishes a mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty; and then combining the self-adaptive variable speed approximation rule function set in the self-adaptive variable speed approximation rule function module (12) with the nonsingular terminal sliding mode surface function set in the nonsingular terminal sliding mode surface function module (11), thereby comprehensively obtaining the rapid tracking control algorithm of the permanent magnet brushless direct current motor servo system in the rapid tracking control module (13) of the servo control system.
2. A fast tracking control method of a permanent magnet brushless direct current motor servo system is characterized in that: the fast tracking control system using the permanent magnet brushless dc motor servo system of claim 1 for fast tracking control, comprising the steps of:
s1, establishing a mathematical model of the permanent magnet brushless direct current motor servo system containing parameter uncertainty;
s2, designing a self-adaptive variable speed approach law algorithm, wherein the self-adaptive variable speed approach law algorithm can adaptively adjust the approach law speed according to the distance between the state quantity in the servo system and a balance point, so that the servo system converges to a steady-state value in a shorter time, and meanwhile, the buffeting problem of sliding mode control is reduced;
s3, combining the self-adaptive variable speed approach law algorithm with non-singular terminal sliding mode control to design a rapid tracking control method of the permanent magnet brushless direct current motor servo system.
3. The fast tracking control method of the permanent magnet brushless dc motor servo system according to claim 2, wherein: the mathematical model of the permanent magnet brushless dc motor servo system including the parameter uncertainty described in step S1 is constructed as follows:
Figure RE-FDA0003121733450000021
assuming g (t) as the total uncertainty, we obtain:
Figure RE-FDA0003121733450000022
wherein B is a damping coefficient, J is a rotational inertia of the motor, and TLIs the load torque, KTIs the torque coefficient, i is the torque current;
Figure RE-FDA0003121733450000023
is a mechanical angle thetamThe second derivative of (a) is,
Figure RE-FDA0003121733450000024
is a mechanical angle thetamThe first derivative of (1), delta a and delta b are uncertain factors of corresponding terms respectively and are bounded;
let g (t) be the total indeterminate quantity and satisfy | g (t) | < lg，lgIs a normal number;
order to
Figure RE-FDA0003121733450000025
In the formula, thetamIs the actual value of the mechanical angle of the motor,
Figure RE-FDA0003121733450000026
is thetamFirst derivative of, thetarIs a reference value of the mechanical angle of the motor,
Figure RE-FDA0003121733450000027
is thetarThe first derivative of (a);
the derivation is performed on the formula 2, and in combination with the formula 1, the mathematical model of the servo system of the permanent magnet brushless dc motor including the uncertainty of the parameters is as follows:
Figure RE-FDA0003121733450000028
in the formula,
Figure RE-FDA0003121733450000031
is x1The first derivative of the signal is a derivative of,
Figure RE-FDA0003121733450000032
is x2The first derivative.
4. The fast tracking control method of the permanent magnet brushless dc motor servo system according to claim 2, wherein: the adaptive shift approach law designed in step S2 is as follows:
Figure RE-FDA0003121733450000033
in the formula, k, mu, alpha and beta are all parameters to be designed which are more than 0, sgn (·) is a sign function, | (·) is an absolute value function, e(·)Is an exponential function;
the self-adaptive speed change approaching law can self-adaptively adjust the approaching speed of the approaching law along with the distance between the state quantity of the servo system and a balance point.
5. The fast tracking control method of the permanent magnet brushless DC motor servo system according to claim 4, characterized in that: in the formula 4, when | s | is large, e-β|s|And e-α|s|Will gradually go to 0, when mu (1-e)-β|s|) The term will gradually trend towards mu, -k (1-e)-α|s|) Will gradually move towards-k, thereby preserving the fast convergence property of the conventional exponential approximation law.
6. The fast tracking control method of the permanent magnet brushless DC motor servo system according to claim 4, characterized in that: in the formula 4, when | s | → 0, e-β|s|And e-α|s|Will be driven byGradually trend to 1, when mu (1-e)-β|s|) The term gradually goes towards 0 so that the effect of sliding mode buffeting can be eliminated.
7. The fast tracking control method of the permanent magnet brushless DC motor servo system according to claim 4, characterized in that: in step S3, the fast tracking control method of the permanent magnet brushless dc motor servo system is as follows:
setting a nonsingular terminal sliding mode surface function as follows:
Figure RE-FDA0003121733450000034
wherein λ >0, a >0 and a/b >1, q >0 and is odd, p >0 and is odd, and 2> p > q > 1;
when the system works in a stable state, the system state quantity reaches the sliding mode surface and starts sliding mode motion, and the requirement of sliding mode motion is met at the moment
Figure RE-FDA0003121733450000035
Based on the adaptive variable speed approach law in formula 4, the expression of the fast tracking control algorithm of the permanent magnet brushless dc motor servo system can be obtained as follows:
Figure RE-FDA0003121733450000041
wherein D ═ k (1-e)-α|s|)s+μ(1-e-β|s|) sgn(s), and μ > lg。
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