CN112769368B - Permanent magnet direct current motor control method and system based on fractional order sliding mode controller - Google Patents
Permanent magnet direct current motor control method and system based on fractional order sliding mode controller Download PDFInfo
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- H—ELECTRICITY
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- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
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- 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
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- H—ELECTRICITY
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- 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
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- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
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Abstract
The invention discloses a permanent magnet direct current motor control method and a permanent magnet direct current motor control system based on a fractional order sliding mode controller, wherein the permanent magnet direct current motor control method comprises the following steps: under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor; converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation; establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model; designing a control law of a fractional order terminal sliding mode function; correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting; and controlling the operation of the permanent magnet direct current motor to be controlled based on the control law corrected by the fractional order terminal sliding mode function.
Description
Technical Field
The application relates to the technical field of sliding mode control, in particular to a permanent magnet direct current motor control method and system based on a fractional order sliding mode controller.
Background
The statements in this section merely provide background information related to the present application and may not necessarily constitute prior art.
The Direct Current (DC) motor has the advantages of easy driving, high torque-weight ratio, lower maintenance cost and the like, so that the Direct Current (DC) motor is widely applied to the fields of intelligent home, wheeled robots, unmanned aerial vehicles and the like. For practical systems, the measurement of the status unit is hardly achieved due to the limitations of the sensor and economic reasons. In addition, since the mathematical model of the system is unknown, a state observer and model approximations are typically used to design the controller. The slip-mode controller has proven to be a robust advantage for application to dc motor control systems. Even if the sliding mode controller is robust, a state estimator must be built to respond faster to changing environmental disturbances, improving the control performance of the dc motor closed loop system.
In electromechanical systems, output feedback slip-mode controllers have been designed using dynamic models of continuous-time dc motors. Furthermore, in addition to discrete time domain or computer systems, the control problem of dc motors has become important in many industrial applications. Practical control schemes have been developed to control dc motors, such as proportional-integral-derivative (PID) fuzzy controllers, neural network control techniques, and robust controllers. However, the controller is designed. Some unknown uncertainty factors, such as dead bands, output constraints, back emf, etc., are often needed or estimated, and these nonlinear terms can affect the tracking effect of the control system.
Model-free adaptive control (MFAC) is one of the typical representatives of data-driven control, and has been widely used in many fields involving nonlinear system control. Fractional order sliding mode control (Fractional Order Sliding Model Control, fosc) has some unique features such as obvious physical meaning, global memory, slight jitter, etc. When a digital computer system is employed to implement its control strategy, the control accuracy is deteriorated by neglecting the influence of the sampling interval. Furthermore, if the Riemann-liooville type fractional order operator definition is employed, non-physical initial conditions exist in the experiment. Thus, the fractional calculus of Caputo is used to mathematically solve this problem, but in engineering applications, the definition of Caputo can only be implemented in approximation methods based on laplace transforms, which will introduce additional approximation errors in the control system.
Compared with FOSMC, the fractional terminal sliding mode control (Fractional Order Terminal Sliding Model Control, FOTSMC) can obtain higher control precision. However, most of the existing FOTSMC control techniques are model-based control methods, and in practice, accurate mathematical models of permanent magnet dc motors are often difficult to obtain. The MFAC technology establishes a dynamic linearized data model based on the input and output of a control system, the controller design is independent of model parameters of the controlled system, and parameters of the data model can be updated online. Therefore, in order to further improve the control precision of the permanent magnet direct current motor, the two methods are combined to perform control system design by utilizing the respective advantages of the MFAC method and the FOTSMC method, so that the control system is a current research hot spot.
Disclosure of Invention
In order to solve the defects in the prior art, the application provides a permanent magnet direct current motor control method and system based on a fractional order sliding mode controller;
in a first aspect, the present application provides a method for controlling a permanent magnet dc motor based on a fractional order sliding mode controller;
a permanent magnet direct current motor control method based on a fractional order sliding mode controller comprises the following steps:
under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor;
converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation;
establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model; designing a control law of a fractional order terminal sliding mode function;
correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting;
and controlling the operation of the permanent magnet direct current motor to be controlled based on the control law corrected by the fractional order terminal sliding mode function.
In a second aspect, the present application provides a permanent magnet direct current motor control system based on a fractional order slip mode controller;
a permanent magnet direct current motor control system based on a fractional order sliding mode controller comprises:
a model building module configured to: under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor;
a model conversion module configured to: converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation;
a fractional order terminal sliding mode function setup module configured to: establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model; designing a control law of a fractional order terminal sliding mode function;
a correction module configured to: correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting;
a control module configured to: and controlling the operation of the permanent magnet direct current motor to be controlled based on the control law corrected by the fractional order terminal sliding mode function.
In a third aspect, the present application further provides an electronic device, including: one or more processors, one or more memories, and one or more computer programs; wherein the processor is coupled to the memory, the one or more computer programs being stored in the memory, the processor executing the one or more computer programs stored in the memory when the electronic device is running, to cause the electronic device to perform the method of the first aspect.
In a fourth aspect, the present application also provides a computer readable storage medium storing computer instructions which, when executed by a processor, perform the method of the first aspect.
In a fifth aspect, the present application also provides a computer program (product) comprising a computer program for implementing the method of any of the preceding aspects when run on one or more processors.
Compared with the prior art, the beneficial effects of this application are:
aiming at the control problem of a permanent magnet direct current motor, the invention provides a fractional order terminal sliding mode control method based on data driving, which has the following specific advantages: firstly, under the condition that external disturbance exists in a permanent magnet direct current motor, the unknown disturbance of the system is estimated on line through a disturbance estimation algorithm, and the anti-interference capability of the control system is improved; compared with the existing processing method, the method has the advantages that the sliding mode surface near the origin of the phase plane has steeper slope due to the adoption of the fractional terminal sliding mode control method, so that the track tracking precision of the permanent magnet direct current motor is further improved; thirdly, the expected track of the system can be tracked rapidly and stably by adjusting design parameters; fourth, the designed controller only depends on the input and output measurement data of the permanent magnet direct current motor control system, and is irrelevant to the mathematical model parameters of the permanent magnet direct current motor.
Additional aspects of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute an undue limitation to the application.
FIG. 1 is a flow chart of a method of a first embodiment;
FIG. 2 is a comparative schematic diagram of tracking performance of the three methods of the first embodiment;
FIG. 3 is a schematic diagram of three method control inputs of the first embodiment;
FIG. 4 is a pseudo partial derivative update process for three methods of the first embodiment;
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, unless the context clearly indicates otherwise, the singular forms also are intended to include the plural forms, and furthermore, it is to be understood that the terms "comprises" and "comprising" and any variations thereof are intended to cover non-exclusive inclusions, such as, for example, processes, methods, systems, products or devices that comprise a series of steps or units, are not necessarily limited to those steps or units that are expressly listed, but may include other steps or units that are not expressly listed or inherent to such processes, methods, products or devices.
Embodiments of the invention and features of the embodiments may be combined with each other without conflict.
Example 1
The embodiment provides a permanent magnet direct current motor control method based on a fractional order sliding mode controller;
as shown in fig. 1, the permanent magnet direct current motor control method based on the fractional order sliding mode controller comprises the following steps:
s101: under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor;
s102: converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation;
s103: establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model; designing a control law of a fractional order terminal sliding mode function;
s104: correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting;
s105: and controlling the operation of the permanent magnet direct current motor to be controlled based on the control law corrected by the fractional order terminal sliding mode function.
As one or more embodiments, the S101: under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor; the method specifically comprises the following steps:
under the condition of uncertain parameters, load and friction, establishing a data driving model of the permanent magnet direct current motor to be controlled based on the output current and the input voltage of the permanent magnet direct current motor;
y(k+1)＝y(k)+φ(k)Δu(k)+Δd(k) (8)
wherein y (k) is the output current of the permanent magnet direct current motor at the moment k, y (k+1) is the output current of the permanent magnet direct current motor at the moment k+1, and Deltau (k) is the difference between the voltage of the input end of the permanent magnet direct current motor at the moment k and the voltage of the input end of the permanent magnet direct current motor at the moment k-1; Δd (k) =d (k) -D (k-1) represents the difference between the system disturbance at time k and the system disturbance at time k-1, defined herein as generalized disturbance, and |d (k) |d, D >0 is a positive constant; phi (k) represents a time-varying pseudo-partial derivative, and phi (k) is less than or equal to b, b being a positive constant.
As one or more embodiments, the S102: converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation; the new data driven model refers to:
wherein ,
delta (k) represents the pseudo partial derivative estimation error; />
Representing a pseudo partial derivative estimate; deltau (k) represents the difference between the voltage at the input end of the permanent magnet direct current motor at the moment k and the voltage at the input end of the permanent magnet direct current motor at the moment k-1;
an estimated value representing a difference between the system disturbance at time k and the system disturbance at time k-1; />
Is the disturbance estimation error.
As one or more embodiments, the step S103: establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model; the method comprises the following steps:
s(k)＝λ 1 e(k)+λ 2 Δ α-1 e ξ (k-1) (23)
wherein s (k) is as followsShowing a fractional order terminal sliding mode function; lambda (lambda) 1 and λ2 A non-zero positive constant; e (k) represents a tracking error of the output current at time k; e, e ξ (k-1) represents a tracking error of the output current at time k-1, ζ is a ratio of two odd integers, and 0<ξ<1；Δ α-1 Representing fractional order calculus operators, and alpha represents the order of the fractional order operators.
e(k)＝y(k)-y r (k) (22)
Wherein y (k) is the actual output current value of the permanent magnet direct current motor at the moment k, y r (k) Is the given output current value of the permanent magnet direct current motor at the moment k.
As one or more embodiments, the step S103: designing a control law of a fractional order terminal sliding mode function; the method comprises the following steps:
wherein Deltau (k) represents the difference between the voltage of the input end of the permanent magnet direct current motor at the moment k and the voltage of the input end of the permanent magnet direct current motor at the moment k-1;
an estimated value representing a difference between the system disturbance at time k and the system disturbance at time k-1; />
Representing a pseudo partial derivative estimate; y is r (k+1) is a given output current value of the permanent magnet direct current motor at time k+ 1; s (k) represents a fractional terminal sliding mode function; y (k) is the actual output current value of the permanent magnet direct current motor at the moment k; delta α-1 Representing a fractional order calculus operator, wherein alpha represents the order of the fractional order operator; e, e ξ (k) Represents the tracking error of the output current at time k, ζ is the ratio of two odd integers, and 0<ξ<1；λ s Is the switching control gain; sgn (s (k)) represents a sign function of s (k), i.e., when s (k) is a positive number, the sign of sgn (s (k)) is positive, and vice versa.
Delta (k) is pseudo partial derivative estimation error and is bounded for convenient controlSetting a maker, namely taking the value of delta (k) as a constant delta which is not more than M; when (when)
When small, the control input may become large or even unbounded, introducing a parameter estimation error δ as an estimate +.>
Is used to avoid this phenomenon.
As one or more embodiments, the step S104: correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting; the method specifically comprises the following steps:
the sign function of the control law of the fractional order terminal sliding mode function is replaced by:
wherein σ>0.
A fractional order Discrete time terminal sliding mode control (Data Driven Fractional-order Discrete-time Terminal Sliding Mode Control, DD-FODTSMC) method based on data driving. The method comprises the following steps:
step one: data driven modeling analysis
Where y (k+1), u (k) are the output of the system at time k+1 and the input at time k, respectively; d (k) represents a systematic perturbation or an unmodeled dynamics, defined herein as a generalized perturbation, and |d (k) |d, D>0 is a positive constant; n is n y and nu Is the unknown order of the system; f (·) is an unknown nonlinear function, let
From (1), it can be seen that
y(k+1)＝y m (k+1)+d(k) (3)
Suppose 1 that the input and output of the system (1) are observable and controllable, i.e. in the presence of generalized disturbances d (k) and the desired output signal y r In the case of (k+1) being bounded, there is a bounded control input signal, which makes the output of the system equal to the desired output of the system under the influence of this signal.
It is assumed that 2:f (·) is continuous with respect to the partial derivative of u (k).
Suppose 3 that the system (1) satisfies the generalized Lipschitz, i.e. there is an arbitrary k and |Deltau (k) |noteq0
And (d) deltay (k+1) deltau (k) 4 wherein deltay (k+1) =y (k+1) -y (k), deltau (k) =u (k) -u (k-1), and b is a positive constant.
When the linear system represented by the formula (2) satisfies the assumption condition 1-3, and |Δu (k) | is equal to 0, there must be an amount Φ (k) called pseudo-partial derivative, so that
Δy m (k+1)＝φ(k)Δu(k) (5)
And |phi (k) |is less than or equal to b, wherein b is a positive constant, Δy m (k+1)＝y(k+1)-y(k)，Δu(k)＝u(k)-u(k-1).
Rewriting (5) to
y m (k+1)＝y m (k)+φ(k)Δu(k) (6)
Can be pushed out
Δy(k+1)＝Δy m (k+1)+Δd(k) (7)
wherein Δym (k+1)＝y m (k+1)-y m (k)，Δy(k+1)＝y(k+1)-y(k)，Δd(k)＝d(k)-d(k-1).
Available under consideration of (5)
y(k+1)＝y(k)+φ(k)Δu(k)+Δd(k) (8)
Step two: disturbance estimation
Based on the disturbance estimation technique, the disturbance term Δd (k) in equation (8) can be estimated by the value of its one-step delay as follows:
then the formula (8) becomes
wherein 
Is a disturbance estimation error and is bounded, further denoted as
From the quotients 1, phi (k) is bounded, and y m (k) U (k) is bounded and is therefore considered to be represented by formula (11)
It is reasonable to be bounded.
Step three: pseudo partial derivative estimation
The unknown parameter phi (k) is estimated using the following criterion function
From the optimal conditions
Is available in the form of
When (when)
Or |Deltau (k-1) |ε, then ++>
Wherein mu>0；η∈(0，1]The method comprises the steps of carrying out a first treatment on the surface of the Epsilon is a sufficiently small positive constant ± the following>
Is->
Is the initial value of>
The writing of (10) can be performed as
wherein 
Representing parameter estimation errors.
Step four: grunwald-Letnikov fractional order function
The Grunwald-Letnikov fractional order difference with arbitrary order alpha.epsilon.R is described as follows:
where h denotes the sampling interval and the number of samples is denoted as k.
As a binomial coefficient, it can be calculated according to the following equation:
to save computational resources, the finite record number L is introduced into a given fractional order difference definition, then equation (16) becomes
In mathematical operation n-! Euler Gamma function Γ (q) obtained on the basis of allowing n to take a real number or even a complex number, in the specific form of
Where q takes on the right half plane of the complex plane, i.e., re (q) >0.
Wherein Γ (·) is calculated using formula (19).
Consider the bounded sequence y (k), k=0, 1,..and max { y (k-1) } ε. Ltoreq.gamma. y The corresponding fractional order difference is bounded as shown in the following formula
wherein 
Step five: designing a controller;
for the system shown in the formula (15), a sliding mode controller is designed, and the output tracking error is defined as follows:
e(k)＝y(k)-y r (k) (22)
where y (k) is the system output, y r (k) Is the desired output.
The discrete fractional order terminal sliding mode function is defined as follows:
s(k)＝λ 1 e(k)+λ 2 Δ α-1 e ξ (k-1) (23)
wherein λ1 >0，λ 2 >0, ζ is the ratio of two odd integers, and 0<ξ<1。
In order to force a sliding surface to be reached at one sampling instant, a DITSMC control strategy is designed based on the following approach law:
Δs(k)＝s(k+1)-s(k)＝0 (24)
substituting formula (15) into formula (24) yields:
ignoring interference estimation errors
Can obtain equivalent control delta u eq (k) Is that
Wherein the implementation of the controller requires a future reference position y r (k+1) in general, y in control system applications r (k+1) is predefined, therefore, y r (k+1) is known a priori.
Notably, given that interference can be accurately estimated, i.e
A control law of the formula (26) is available, but in practice +.>
Therefore, in order to improve the robustness of the controller, the switching control is designed as follows: />
Where sgn (·) represents the sign function, λ s Is a switching control gain and satisfies
Will control the equivalent Deltau eq (k) And switching control Deltau sw (k) The combination gives the overall control law:
Δu(k)＝Δu eq (k)+Δu sw (k) (28)
i.e.
Delta (k) is the PPD estimation error and is bounded, e.g., delta (k) is +.M, delta (k) is bounded, see the stability analysis section herein, delta (k) is not precisely obtained because phi (k) is unknown, delta (k) is taken to be a constant delta that is no greater than M for ease of controller tuning, additionally, when
When small, the control input may become large or even unbounded, introducing a parameter estimation error δ as an estimate +.>
Can avoid this phenomenon.
Step six: stability analysis
This step demonstrates the stability of the designed control system.
From equation (23), the one-step forward sliding mode function s (k+1) can be derived as follows:
s(k+1)＝λ 1 e(k+1)+λ 2 Δ α-1 e ξ (k) (30)
substituting formula (22) into formula (30) and taking into consideration formulas (15) and (29) to obtain
Is obtained by the formula (31)
Consider
Is available in the form of
Therefore, when s (k) >0, it can be obtained from the formula (32) and the formula (33)
When s (k) <0, can be obtained from the formulas (32) and (33)
Taking into account the formulae (34) and (35), it is possible to obtain
Equation (36) satisfies discrete sliding mode presence and arrival conditions
And equation (37) is a filling condition for the existence of discrete quasi-sliding mode states, and s (k) monotonically decreases, i.e., |s (k) | < s (k+1) |, meaning that under the action of equation (29), the system will reach quasi-sliding mode in a limited number of steps.
To mitigate buffeting, the sign function in equation (29) is replaced with
Where σ >0. In practice, the parameter σ is chosen as a compromise between robustness and suppression of jitter effects.
Step seven: simulation experiment verification
The correctness and validity of the proposed control scheme is verified by a SISO discrete time nonlinear system and compared with MFAC and neural network sliding mode control (Neural Networks Sliding mode control, NN-SMC) methods.
Consider a nonlinear system as follows
Wherein the disturbance is d (k) = [0.5,0.15sin (k/30)][y(k),y(k-1)] T Time-varying parameter a (k) =1+round (k/500). Obviously, the structure, parameters and orders of the controlled system are all time-varying.
The desired output signal is
In the three comparison methods, the initial conditions of the system are the same, u (1) =u (2) =0, y (1) =y (2) =0,
parameter estimation algorithm parameter is setLet η=μ=1. ρ=0.6 in the prototype MFAC method, λ=2.nn-SMC method q=0.6, c= [1,2]Sigma=3, epsilon=0.0002. Lambda in the proposed method 1 ＝λ 2 ＝0.1，α＝0.5，ξ＝9/11，λ s =0.002, h=0.002, l=10. The simulation results are shown in fig. 1-3. For quantizing the tracking results, mean Absolute Error (MAE) and Root Mean Square Error (RMSE) are defined as follows
Where k represents the number of sampled data.
From the quantization results of fig. 2 and table 1, it is clear that: 1) The DD-FODTSMC method obtains control effects superior to those of the prototype MFAC and NN-SMC on various performance indexes, and 2) the response speed and the control accuracy of the system of NN-SMC are slightly superior to those of the prototype MFAC, but the overshoot is larger. It should be noted that when k=500, i.e. when the system structure changes, it can be seen from the detailed diagrams that the NN-SMC method responds most rapidly, but the overshoot is larger in the three comparison methods. When k=855, as can be seen from the detailed diagram, the prototype MFAC method and the NN-SMC method both generate larger oscillations, and the proposed method has better effect. The control input amounts corresponding to the three control methods are shown in fig. 3. The parameter PPD updating procedure of the different control methods is shown in fig. 4.
Table 1 output error index
Step eight: end of design
The whole design process mainly considers the simplicity, stability and rapid accuracy of track tracking of the controller design. For the considered problem, firstly, determining a data model of the nonlinear system in the first step; the second step gives a disturbance estimation method; thirdly, an estimation method of pseudo partial derivatives in the data model is given; the fourth step gives a specific description of the Grunwald-Letnikov fractional order function; fifthly, designing a fractional order discrete terminal sliding mode controller based on a data driving model; the sixth step introduces closed loop system trajectory tracking stability analysis. After the steps, the design is finished.
Example two
The embodiment provides a permanent magnet direct current motor control system based on a fractional order sliding mode controller;
a permanent magnet direct current motor control system based on a fractional order sliding mode controller comprises:
a model building module configured to: under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor;
a model conversion module configured to: converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation;
a fractional order terminal sliding mode function setup module configured to: establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model; designing a control law of a fractional order terminal sliding mode function;
a correction module configured to: correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting;
a control module configured to: and controlling the operation of the permanent magnet direct current motor to be controlled based on the control law corrected by the fractional order terminal sliding mode function.
It should be noted that, the model building module, the model conversion module, the fractional terminal sliding mode function building module, the correction module and the control module correspond to steps S101 to S105 in the first embodiment, and the modules are the same as examples and application scenarios implemented by the corresponding steps, but are not limited to the disclosure of the first embodiment. It should be noted that the modules described above may be implemented as part of a system in a computer system, such as a set of computer-executable instructions.
The foregoing embodiments are directed to various embodiments, and details of one embodiment may be found in the related description of another embodiment.
The proposed system may be implemented in other ways. For example, the system embodiments described above are merely illustrative, such as the division of the modules described above, are merely a logical function division, and may be implemented in other manners, such as multiple modules may be combined or integrated into another system, or some features may be omitted, or not performed.
Example III
The embodiment also provides an electronic device, including: one or more processors, one or more memories, and one or more computer programs; wherein the processor is coupled to the memory, the one or more computer programs being stored in the memory, the processor executing the one or more computer programs stored in the memory when the electronic device is running, to cause the electronic device to perform the method of the first embodiment.
It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general purpose processors, digital signal processors DSP, application specific integrated circuits ASIC, off-the-shelf programmable gate array FPGA or other programmable logic device, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may include read only memory and random access memory and provide instructions and data to the processor, and a portion of the memory may also include non-volatile random access memory. For example, the memory may also store information of the device type.
In implementation, the steps of the above method may be performed by integrated logic circuits of hardware in a processor or by instructions in the form of software.
The method in the first embodiment may be directly implemented as a hardware processor executing or implemented by a combination of hardware and software modules in the processor. The software modules may be located in a random access memory, flash memory, read only memory, programmable read only memory, or electrically erasable programmable memory, registers, etc. as well known in the art. The storage medium is located in a memory, and the processor reads the information in the memory and, in combination with its hardware, performs the steps of the above method. To avoid repetition, a detailed description is not provided herein.
Those of ordinary skill in the art will appreciate that the elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
Example IV
The present embodiment also provides a computer-readable storage medium storing computer instructions that, when executed by a processor, perform the method of embodiment one.
The foregoing description is only of the preferred embodiments of the present application and is not intended to limit the same, but rather, various modifications and variations may be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.
Claims (4)
1. The permanent magnet direct current motor control method based on the fractional order sliding mode controller is characterized by comprising the following steps of:
under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor; the method specifically comprises the following steps:
under the condition of uncertain parameters, load and friction, establishing a data driving model of the permanent magnet direct current motor to be controlled based on the output current and the input voltage of the permanent magnet direct current motor;
y(k+1)＝y(k)+φ(k)Δu(k)+Δd(k) (8)
wherein y (k) is the output current of the permanent magnet direct current motor at the moment k, y (k+1) is the output current of the permanent magnet direct current motor at the moment k+1, and Deltau (k) is the difference between the voltage of the input end of the permanent magnet direct current motor at the moment k and the voltage of the input end of the permanent magnet direct current motor at the moment k-1; Δd (k) =d (k) -D (k-1) represents the difference between the system disturbance at time k and the system disturbance at time k-1, defined herein as generalized disturbance, and |d (k) |d, D >0 is a positive constant; phi (k) represents a time-varying pseudo-partial derivative, and phi (k) is less than or equal to b, b being a positive constant;
converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation; the new data driven model refers to:
wherein ,
delta (k) represents the pseudo partial derivative estimation error; />
Representing a pseudo partial derivative estimate; deltau (k) represents the difference between the voltage at the input end of the permanent magnet direct current motor at the moment k and the voltage at the input end of the permanent magnet direct current motor at the moment k-1; />
An estimated value representing a difference between the system disturbance at time k and the system disturbance at time k-1; />
Is a disturbance estimation error;
establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model; the method comprises the following steps:
s(k)＝λ 1 e(k)+λ 2 Δ α-1 e ξ (k-1) (23)
wherein s (k) represents a fractional terminal sliding mode function; lambda (lambda) 1 and λ2 A non-zero positive constant; e (k) represents a tracking error of the output current at time k; e, e ξ (k-1) represents a tracking error of the output current at time k-1, ζ is a ratio of two odd integers, and 0<ξ<1；Δ α-1 Representing a fractional order calculus operator, wherein alpha represents the order of the fractional order operator;
e(k)＝y(k)-y r (k) (22)
wherein y (k) is the actual output current value of the permanent magnet direct current motor at the moment k, y r (k) The given output current value of the permanent magnet direct current motor at the moment k;
designing a control law of a fractional order terminal sliding mode function;
correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting;
controlling the operation of the permanent magnet direct current motor to be controlled based on the control law corrected by the fractional order terminal sliding mode function;
designing a control law of a fractional order terminal sliding mode function; the method comprises the following steps:
wherein Deltau (k) represents the difference between the voltage of the input end of the permanent magnet direct current motor at the moment k and the voltage of the input end of the permanent magnet direct current motor at the moment k-1;
an estimated value representing a difference between the system disturbance at time k and the system disturbance at time k-1; />
Representing a pseudo partial derivative estimate; y is r (k+1) is a given output current value of the permanent magnet direct current motor at time k+1; s (k) represents a fractional terminal sliding mode function; y (k) is the actual output current value of the permanent magnet direct current motor at the moment k; delta α-1 Representing a fractional order calculus operator, wherein alpha represents the order of the fractional order operator; e, e ξ (k) Represents the tracking error of the output current at time k, ζ is the ratio of two odd integers, and 0<ξ<1；λ s Is the switching control gain; sgn (s (k)) represents a sign function of s (k), i.e., when s (k) is a positive number, the sign of sgn (s (k)) is positive, and vice versa;
delta (k) is a pseudo partial derivative estimation error and is bounded, and for the convenience of controller setting, the value of delta (k) is taken as a constant delta not greater than M; when (when)
When small, the control input may become large or even unbounded, introducing a parameter estimation error delta as an estimate
Is added to avoid this phenomenon;
correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting; the method specifically comprises the following steps:
the sign function of the control law of the fractional order terminal sliding mode function is replaced by:
wherein σ>0.
2. Permanent magnet direct current motor control system based on fractional order slipform controller, characterized by including:
a model building module configured to: under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor;
a model conversion module configured to: converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation;
a fractional order terminal sliding mode function setup module configured to: establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model;
designing a control law of a fractional order terminal sliding mode function;
a correction module configured to: correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting;
a control module configured to: controlling the operation of the permanent magnet direct current motor to be controlled based on the control law corrected by the fractional order terminal sliding mode function;
under the condition of external interference, a data driving model of the permanent magnet direct current motor to be controlled is established based on the output current and the input voltage of the permanent magnet direct current motor; the method specifically comprises the following steps:
under the condition of uncertain parameters, load and friction, establishing a data driving model of the permanent magnet direct current motor to be controlled based on the output current and the input voltage of the permanent magnet direct current motor;
y(k+1)＝y(k)+φ(k)Δu(k)+Δd(k) (8)
wherein y (k) is the output current of the permanent magnet direct current motor at the moment k, y (k+1) is the output current of the permanent magnet direct current motor at the moment k+1, and Deltau (k) is the difference between the voltage of the input end of the permanent magnet direct current motor at the moment k and the voltage of the input end of the permanent magnet direct current motor at the moment k-1; Δd (k) =d (k) -D (k-1) represents the difference between the system disturbance at time k and the system disturbance at time k-1, defined herein as generalized disturbance, and |d (k) |d, D >0 is a positive constant; phi (k) represents a time-varying pseudo-partial derivative, and phi (k) is less than or equal to b, b being a positive constant;
converting the data driving model into a new data driving model through disturbance estimation and partial derivative estimation; the new data driven model refers to:
wherein ,
delta (k) represents the pseudo partial derivative estimation error; />
Representing a pseudo partial derivative estimate; deltau (k) represents the difference between the voltage at the input end of the permanent magnet direct current motor at the moment k and the voltage at the input end of the permanent magnet direct current motor at the moment k-1; />
An estimated value representing a difference between the system disturbance at time k and the system disturbance at time k-1; />
Is a disturbance estimation error; />
Establishing a corresponding fractional order terminal sliding mode function aiming at the new data driving model; the method comprises the following steps:
s(k)＝λ 1 e(k)+λ 2 Δ α-1 e ξ (k-1) (23)
wherein s (k) represents a fractional terminal sliding mode function; lambda (lambda) 1 and λ2 A non-zero positive constant; e (k) represents a tracking error of the output current at time k; e, e ξ (k-1) represents a tracking error of the output current at time k-1, ζ is a ratio of two odd integers, and 0<ξ<1；Δα -1 Representing a fractional order calculus operator, wherein alpha represents the order of the fractional order operator;
e(k)＝y(k)-y r (k) (22)
wherein y (k) is the actual output current value of the permanent magnet direct current motor at the moment k, y r (k) The given output current value of the permanent magnet direct current motor at the moment k;
designing a control law of a fractional order terminal sliding mode function; the method comprises the following steps:
wherein Deltau (k) represents the difference between the voltage of the input end of the permanent magnet direct current motor at the moment k and the voltage of the input end of the permanent magnet direct current motor at the moment k-1;
an estimated value representing a difference between the system disturbance at time k and the system disturbance at time k-1; />
Representing a pseudo partial derivative estimate; y is r (k+1) is a given output current value of the permanent magnet direct current motor at time k+1; s (k) represents a fractional terminal sliding mode function; y (k) is the actual output current value of the permanent magnet direct current motor at the moment k; delta α-1 Representing a fractional order calculus operator, wherein alpha represents the order of the fractional order operator; e, e ξ (k) Represents the tracking error of the output current at time k, ζ is the ratio of two odd integers, and 0<ξ<1；λ s Is the switching control gain; sgn (s (k)) represents a sign function of s (k), i.e., when s (k) is a positive number, the sign of sgn (s (k)) is positive, and vice versa;
delta (k) is a pseudo partial derivative estimation error and is bounded, and for the convenience of controller setting, the value of delta (k) is taken as a constant delta not greater than M; when (when)
When small, the control input may become large or even unbounded, introducing a parameter estimation error δ as an estimate +.>
Is added to avoid this phenomenon;
correcting a symbol function in a control law of a fractional order terminal sliding mode function to relieve buffeting; the method specifically comprises the following steps:
the sign function of the control law of the fractional order terminal sliding mode function is replaced by:
wherein σ>0.
3. An electronic device, comprising: one or more processors, one or more memories, and one or more computer programs; wherein the processor is coupled to the memory, the one or more computer programs being stored in the memory, the processor executing the one or more computer programs stored in the memory when the electronic device is running, to cause the electronic device to perform the method of claim 1.
4. A computer readable storage medium storing computer instructions which, when executed by a processor, perform the method of claim 1.
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