Preset time control method of permanent magnet synchronous motor based on event triggering

Abstract

The present invention discloses a preset time control method for a permanent magnet synchronous motor based on event triggering, including designing a state observer, constructing a Lyapunov function, introducing a fuzzy logic system, a preset time filter, and event triggering to design a parameter adaptive law and a controller. The present invention is aimed at a permanent magnet synchronous motor system with an unmeasurable state, and studies a fuzzy adaptive preset time control method based on event triggering, and a state observer of a fuzzy logic system is used to estimate the unmeasurable state. An event triggering mechanism consisting of a controller to an actuator channel is constructed by using adaptive backstepping recursive technology, a preset time control scheme based on output feedback is proposed, and a preset time filter is designed, and Lyapunov theory and preset time stability theory are used. The present invention can verify the effectiveness and feasibility of the proposed adaptive preset time event triggering control method through simulation results.

Description

Technical Field

[0001] The present invention belongs to the field of permanent magnet synchronous motor control, and in particular relates to a permanent magnet synchronous motor preset time control method based on event triggering. Background Art

[0002] Permanent magnet synchronous motor systems are increasingly used in the manufacturing industry due to their energy-saving capabilities, simple structure, high efficiency, and reliable operation. Driven by the emergence and price decline of rare earth materials, since the 1980s, due to the rapid development of microcomputer technology, power electronics technology, and control theory, permanent magnet synchronous motors have gradually replaced DC motors and stepper motors and become a new development direction for servo drives. In theoretical analysis, design and control strategies emerge to further study new topics. Advanced control technologies such as direct torque control, adaptive control theory, robust control, and sliding mode variable structure control have been successfully applied to the control of PMSM. However, with the advancement of science and technology, the demand for motor systems continues to increase. The inherent complexity of PMSM, a multivariable, strongly coupled nonlinear system, makes it prone to parameter fluctuations and external load damage, rendering traditional control methods insufficient to meet the changing requirements.

[0003] Therefore, in order to obtain a high-performance permanent magnet synchronous motor system, it is necessary to conduct an in-depth analysis of the permanent magnet synchronous motor model and study advanced intelligent control methods to make the system have strong environmental adaptability and anti-interference ability. However, the existing technology still has the following problems:

[0004] First, existing finite-time fuzzy or neural network control schemes require that the state variables of the PMSM system must be measurable. Therefore, they cannot solve the problem of unmeasurable state involved in the present invention. Although neural network finite-time output feedback control methods have also been studied, they can only guarantee finite-time stability, not preset-time stability.

[0005] Second, although the existing invention proposes an event-triggered control scheme for the PMSM system, it requires that the state of the controlled system is completely measurable and does not consider the problem of preset time control. Summary of the invention

[0006] In order to solve the deficiencies in the prior art, the present invention designs a permanent magnet synchronous motor preset time control method based on event triggering for a permanent magnet synchronous motor system with an unmeasurable state.

[0007] In order to achieve the above-mentioned purpose, the technical scheme of the present invention is as follows: an event-triggered fuzzy adaptive preset time control method for an unmeasurable permanent magnet synchronous motor system, wherein the permanent magnet synchronous motor system research includes designing a state observer, constructing a Lyapunov function, introducing a fuzzy logic system, a preset time filter, and event triggering to design a parameter adaptive law and a controller, wherein the state observation module involves a fuzzy logic system to estimate unknown nonlinear dynamics, and the event triggering and preset time filter are based on adaptive backstepping recursive technology, constructing an event triggering mechanism consisting of a controller to actuator channel, and proposing a preset time control scheme.

[0008] The method for controlling a permanent magnet synchronous motor preset time based on event triggering of the present invention comprises the following steps:

[0009] Step 1, construct the permanent magnet motor dynamics model and write it into a state space expression;

[0010] Step 2: Introduce a state observer and use the estimated state variables Rewriting the spatial representation of the permanent magnet motor;

[0011] Step 3: preset the time filter and use coordinate transformation to convert the error to obtain the tracking error z i Expression;

[0012] Step 4: construct the Lyapunov function, design the virtual controller and parameter adaptation law; transform the dynamic surface error z i and the estimated state variables Input to the parameter adaptive law and virtual controller to obtain the intermediate control signal α i-1 ;

[0013] The intermediate control signal α i-1 Enter the preset time filter in step 3 and loop;

[0014] At the same time, the intermediate control signal α i-1 Input dynamic events trigger the controller to obtain control signals

[0015] Step 5: Calculate the output of the controller according to the event triggering mechanism.

[0016] Furthermore, the permanent magnet motor dynamics model constructed in step 1 is described by the following equation:

[0017]

[0018] In the dq coordinate rotating reference system of the permanent magnet synchronous motor, u d represents the d-axis component of the stator voltage in the rotating coordinate system, u qrepresents the q-axis component of the stator voltage in the rotating coordinate system; R s represents the armature resistance; i d represents the d-axis component of the stator current in the rotating coordinate system, i q represents the q-axis component of the stator current in the rotating coordinate system; L d represents the d-axis component of the stator inductance in the rotating coordinate system, L q represents the q-axis component of the stator inductance in the rotating coordinate system; ω represents the rotor angular velocity; Φ f represents the inertial flux link, θ represents the rotor angle, and p is the number of pole pairs;

[0019] In order to simplify the permanent magnet synchronous motor system model, let

[0020] x1=θ,x2=ω,x3=i q ,x4=i d

[0021]

[0022] Among them, x1 represents the rotor position, x2 represents the angular velocity, x3 represents the q-axis current, and x4 represents the d-axis current;

[0023] The state space expression of permanent magnet synchronous motor is:

[0024]

[0025] in f3(x)=b3x2+b1x3+b2x2x4, f4(x)=c1x4+c2x2x3, (x=[x1,x2,x3,x4] T );y is the output, d l (t) represents an unknown external disturbance, which exists satisfy u q ,u d The input voltage of the system, y represents the control system output, x represents the state vector of the system, and x = [x1, x2, x3, x4] T ;f i (x) represents the unknown nonlinear dynamics of the system and satisfies f i (x(0))=0, where i=2, 3 and 4.

[0026] Furthermore, for nonlinear dynamics f i (x), the FLSs nonlinear function approximator is designed as follows:

[0027]

[0028] is the ideal weight, φ i (·) is the fuzzy basis vector with x as input, ε i is the approximation error, which is caused by an unknown positive constant For the boundary, require

[0029] Permanent Magnet Synchronous Motor System Approximated by Fuzzy Logic System

[0030]

[0031] Furthermore, in step 2, a state observer is introduced to write the spatial expression of the permanent magnet motor as follows:

[0032] The model of the permanent magnet synchronous motor system after the state observer is introduced is as follows

[0033]

[0034] in Represents the estimated state variable is the estimated value of the output signal, for The estimated value of .

[0035] Further, in step 3, the filter is referenced and the error is converted using coordinate transformation to obtain the dynamic surface error z i The expression is as follows:

[0036]

[0037] where y d It represents the reference signal that the system output y is tracking. This is a smooth function. z1 is the tracking error. i is the dynamic surface error, α i-1 The intermediate control signal of the filter can be obtained by the preset time filter as follows:

[0038]

[0039] w i (0) = α i (0)

[0040] where γ = ρ / 2 1+η / 2 , ρ=[(4n+1)N] η / 2 , T d and η are key control design parameters; T d >0,η=η1 / η2,η1>0,η2>0 are even and odd numbers respectively, and satisfy η1<η2. Considering the preset time stability of the system, the design parameters also need to satisfy s i-1 =w i-1 -α i-1 is the filtering error, α i-1 is the intermediate control signal; i is the filter design parameter, satisfying Design parameters for the filter.

[0041] Furthermore, the Lyapunov function constructed in step 4 is:

[0042]

[0043] in,

[0044] Further, the virtual controller is:

[0045]

[0046] Furthermore, the parameter adaptation law is

[0047]

[0048] Furthermore, the dynamic event triggering controller is:

[0049]

[0050] Furthermore, the event triggering mechanism is:

[0051]

[0052] in Design constants, There exist parameters |r1|≤1,|r2|≤1, for We have controller

[0053]

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] First, existing finite-time fuzzy or neural network control schemes require that the state variables of the PMSM system must be measurable. Therefore, they cannot solve the problem of unmeasurable state involved in the present invention. Although neural network finite-time output feedback control methods have also been studied, they can only guarantee finite-time stability, not preset-time stability. The present invention has conducted a pioneering study on the design complexity of preset-time output feedback control of PMSM systems. A novel fuzzy adaptive preset-time output feedback control technology is introduced.

[0056] Second, although the existing inventions have proposed event-triggered control schemes for PMSM systems, they require that the state of the controlled system is fully measurable and do not consider the preset time control problem. The present invention proposes a novel event-triggered strategy, which consists of an event-triggered mechanism from the controller to the actuator channel. Based on the designed event-triggered mechanism and the introduction of a preset time filter in the backstepping control design process, the developed adaptive control scheme solves the computational complexity explosion at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the control flow of the permanent magnet synchronous motor system.

[0058] Figure 2 is the reference signal y d And output signal x1 measurement effect diagram.

[0059] Figure 3 is x1 and Curve effect diagram.

[0060] Figure 4 is x2 and Curve effect diagram.

[0061] Figure 5 is the control input u q Effect picture.

[0062] Figure 6 is the control input u d Effect picture.

[0063] Figure 7 This is the effect diagram of the tracking error trajectory z1,z2,z3,z4.

[0064] Figure 8 is u q and Curve effect diagram.

[0065] Fig. 9 is u d The trigger effect diagram.

[0066] Fig.10 is u d and Curve effect diagram.

[0067] Fig.11 is u d The trigger effect diagram. DETAILED DESCRIPTION

[0068] The present invention provides a permanent magnet synchronous motor preset time control method based on event triggering, comprising the following steps:

[0069] A. Establishing a permanent magnet synchronous motor model

[0070] The dynamics of the permanent magnet synchronous motor system is described by the following equation:

[0071]

[0072] In the dq coordinate rotating reference system of the permanent magnet synchronous motor, u d represents the d-axis component of the stator voltage in the rotating coordinate system, u q represents the q-axis component of the stator voltage in the rotating coordinate system; R s represents the armature resistance; i d represents the d-axis component of the stator current in the rotating coordinate system, i q represents the q-axis component of the stator current in the rotating coordinate system; L d represents the d-axis component of the stator inductance in the rotating coordinate system, L q represents the q-axis component of the stator inductance in the rotating coordinate system; ω represents the rotor angular velocity. Φ f represents the inertial flux link, θ represents the rotor angle, and p is the number of pole pairs.

[0073] In order to simplify the permanent magnet synchronous motor system model, let

[0074] x1=θ,x2=ω,x3=i q ,x4=i d

[0075]

[0076] Among them, x1 represents the rotor position, x2 represents the angular velocity, x3 represents the q-axis current, and x4 represents the d-axis current.

[0077] The state space expression of permanent magnet synchronous motor is:

[0078]

[0079] in f3(x)=b3x2+b1x3+b2x2x4, f4(x)=c1x4+c2x2x3, (x=[x1,x2,x3,x4] T ). y is the output, d l (t) represents an unknown external disturbance, which exists satisfy u q ,u d The input voltage of the system, y represents the control system output, x represents the state vector of the system, and x = [x1, x2, x3, x4] T .f i(x) represents the unknown nonlinear dynamics of the system and satisfies f i (x(0))=0, where i=2, 3 and 4.

[0080] B. Introducing fuzzy logic system

[0081] Nonlinear dynamics i (x) is the unknown system state variable x i is unmeasurable. The coupling between the two brings great trouble to the design of the controller. In order to overcome the influence of unknown nonlinear dynamics on controller design, we designed the FLSs nonlinear function approximator based on the estimated value of the system state as follows:

[0082]

[0083] is the ideal weight, φ i (·) is the fuzzy basis vector with x as input, ε i is the approximation error, which is caused by an unknown positive constant For the boundary, require

[0084] Permanent Magnet Synchronous Motor System Approximated by Fuzzy Logic System

[0085]

[0086] C. Introducing the state observer

[0087] The model of the permanent magnet synchronous motor system after the state observer is introduced is as follows

[0088]

[0089] in Represents the estimated state variable is the estimated value of the output signal, for The estimated value of .

[0090] The state observer error definition is described as:

[0091]

[0092] The equation for the observed error of the permanent magnet synchronous motor system is obtained

[0093]

[0094] in: ε=(0,ε1,ε2,ε2) T d=(d1,d2,d3,d4) T

[0095] in:

[0096] D. Preset time filter

[0097] The filter is referenced in the controller design process, and the corresponding coordinate transformation is as follows:

[0098]

[0099] where y d It represents the reference signal that the system output y is tracking. This is a smooth function. z1 is the tracking error. i is the dynamic surface error, α i-1 The intermediate control signal of the filter can be obtained by the preset time filter as follows:

[0100]

[0101] where γ = ρ / 2 1+η / 2 , ρ=[(4n+1)N] η / 2 , T d and η are key control design parameters that determine the convergence speed and design accuracy of the system. d >0,η=η1 / η2,η1>0,η2>0 are even and odd numbers respectively, and satisfy η1<η2, and comprehensively consider the preset time stability of the system, and the design parameters also need to meet s i-1 =w i-1 -α i-1 is the filtering error, α i-1 is the intermediate control signal; i is the filter design parameter, satisfying Design parameters for the filter.

[0102] E. Constructing Lyapunov functions

[0103]

[0104] in,

[0105] F. Design of virtual control signal and parameter adaptation law

[0106] Construct the virtual control signal as

[0107]

[0108] The constructed parameter adaptive law is

[0109]

[0110] G. Reference event trigger mechanism and design controller

[0111] Select the dynamic event trigger controller:

[0112]

[0113] in Design constants, There exist parameters |r1(t)|≤1,|r2(t)|≤1, for We have controller

[0114]

[0115] The present invention is further described below in conjunction with the accompanying drawings. Figure 1 As shown. The unknown nonlinear dynamics are approximated by fuzzy logic system, the unmeasurable state is estimated by state observer, and the preset time filter is designed to avoid the explosion of computational complexity. Based on the adaptive backstepping recursive technology, an event trigger mechanism consisting of a controller to actuator channel is constructed. The goal of this invention is to make the output signal x1 track the reference signal y d , proving the preset time stability of the closed-loop system, ensuring that all signals remain stable within the predetermined time interval.

[0116] Figure 2-11 is the simulation result, where Figure 2 is the reference signal y d And the output signal x1 tracking effect; Figure 3-4 For state x i and The curve, Figure 5-6 Enter u for the controller d and u q , Figure 7 is the permanent magnet synchronous motor system state tracking error z i , Figure 8 and Fig.10 Represent the controller u q and u d The trigger diagram, Fig. 9 and Fig.11 Indicates u q and u d The effect diagram of the event trigger interval. The above simulation result diagram shows the effectiveness and feasibility of the adaptive preset time event trigger control method of the permanent magnet synchronous motor system.

[0117] The present invention is not limited to this embodiment, and any equivalent concepts or changes within the technical scope disclosed by the present invention are included in the protection scope of the present invention.

Claims

1. A method for controlling a permanent magnet synchronous motor preset time based on event triggering, characterized in that: The steps include: Step 1: construct a dynamic model of the permanent magnet motor and write it into a state space expression. The specific process is as follows; The constructed permanent magnet motor dynamic model is described by the following equation: In the dq coordinate rotating reference system of the permanent magnet synchronous motor, u d represents the d-axis component of the stator voltage in the rotating coordinate system, u q represents the q-axis component of the stator voltage in the rotating coordinate system; R s represents the armature resistance; i d represents the d-axis component of the stator current in the rotating coordinate system, i q represents the q-axis component of the stator current in the rotating coordinate system; L d represents the d-axis component of the stator inductance in the rotating coordinate system, L q represents the q-axis component of the stator inductance in the rotating coordinate system; ω represents the rotor angular velocity; Φ f represents the inertial flux link, θ represents the rotor angle, and p is the number of pole pairs; In order to simplify the permanent magnet synchronous motor system model, let Among them, x1 represents the rotor position, x2 represents the angular velocity, x3 represents the q-axis current, and x4 represents the d-axis current; The state space expression of permanent magnet synchronous motor is: in f3(x)=b3x2+b1x3+b2x2x4, f4(x)=c1x4+c2x2x3, x=[x1,x2,x3,x4] T ; y is output, d l (t) represents an unknown external disturbance, which exists satisfy u q ,u d The input voltage of the system, y represents the control system output, x represents the state vector of the system, and x = [x1, x2, x3, x4] T ;f i (x) represents the unknown nonlinear dynamics of the system and satisfies f i (x(0))=0, where i=2, 3 and 4; Step 2: Introduce a state observer and use the estimated state variables Rewrite the spatial expression of the permanent magnet motor; Step 3: Preset the time filter and use coordinate transformation to convert the error to obtain the dynamic surface error z i The expression is as follows: where y d It represents the reference signal that the system output y is tracking. This is a smooth function. z1 is the tracking error. i is the dynamic surface error, α i-1 is the filter intermediate control signal, which is obtained through the preset time filter as follows: where γ = ρ / 2 1+η / 2 , ρ=[(4n+1)N] η / 2 , T d and η are key control design parameters; T d >0,η=η1 / η2,η1>0,η2>0 are even and odd numbers respectively, and satisfy η1<η2. Considering the preset time stability of the system, the design parameters also need to satisfy s i-1 =w i-1 -α i-1 is the filtering error, α i-1 is the intermediate control signal; i is the filter design parameter, satisfying Design parameters for the filter; Step 4: construct the Lyapunov function, design the virtual controller and parameter adaptation law; transform the dynamic surface error z i And the estimated state variable x is input into the parameter adaptive law and the virtual controller to obtain the intermediate control signal α i-1 ; The intermediate control signal α i-1 Enter the preset time filter in step 3 and loop; At the same time, the intermediate control signal α i-1 Input dynamic events trigger the controller to obtain the control signal θ l (t); The constructed Lyapunov function is: in, The virtual controller is: are design constants. Indicates is the input fuzzy basis vector, Indicates is the input fuzzy basis vector, Indicates is the input fuzzy basis vector; represents the estimated value of the state vector x2, represents the estimated value of the state vector x3; The parameter adaptation law is The dynamic event triggering controller is: Step 5, calculating the output of the controller according to the event triggering mechanism; The event triggering mechanism is: t k+1 =inf{t>t k ||γ l (t)|>m(t)|u l (t)|+n(t)} (24) in is the design constant, γ l (t) = θ l (t)-u l (t); There exist parameters |r1(t)|≤1,|r2(t)|≤1, for The controller is represented as:

2. The method for controlling the preset time of a permanent magnet synchronous motor based on event triggering according to claim 1, characterized in that: For nonlinear dynamics f i (x), the FLSs nonlinear function approximator is designed as follows: is the ideal weight, φ i (x) is the fuzzy basis vector with x as input, ε i is the approximation error, which is caused by an unknown positive constant For the boundary, require Permanent Magnet Synchronous Motor System Approximated by Fuzzy Logic System 3. The method for controlling the preset time of a permanent magnet synchronous motor based on event triggering according to claim 2 is characterized in that: In step 2, the state observer is introduced to write the spatial expression of the permanent magnet motor as follows: The model of the permanent magnet synchronous motor system after the state observer is introduced is as follows in Represents the estimated state variable is the estimated value of the output signal, for The estimated value of .

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