CN109560736A - Method for controlling permanent magnet synchronous motor based on second-order terminal sliding formwork - Google Patents

Method for controlling permanent magnet synchronous motor based on second-order terminal sliding formwork Download PDF

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CN109560736A
CN109560736A CN201811547753.9A CN201811547753A CN109560736A CN 109560736 A CN109560736 A CN 109560736A CN 201811547753 A CN201811547753 A CN 201811547753A CN 109560736 A CN109560736 A CN 109560736A
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sliding mode
value
permanent magnet
axis current
synchronous motor
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CN109560736B (en
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樊英
毛晨阳
张秋实
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Southeast University
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Southeast University
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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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/05—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/22—Current control, e.g. using a current control loop
    • 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
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)
  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses a kind of method for controlling permanent magnet synchronous motor based on second-order terminal sliding formwork, including step 1, dq shaft current i under rotor coordinatedAnd iqIt obtains；Step 2, q shaft current given value iq' obtain；Step 3, load torque observationIt obtains；Step 4, q shaft current given value after compensationIt obtains；Step 5, the input voltage u under α β coordinate systemαAnd uβAcquisition；Step 6, using dSPACE of SVPWM technology, the u that step 5 is obtainedαAnd uβIt is converted into the on-off signal for acting on control three-phase inverter power device, it is final to drive permanent magnet synchronous motor operating.For the present invention by the way that current loop controller is used track with zero error device, speed ring realizes the high-precision control to permanent magnet synchronous motor using second-order terminal sliding mode controller；To solve the permanent magnet synchronous motor of small rotary inertia when load sudden change or given rotating speed are mutated, the larger problem of velocity variations amplitude.

Description

Permanent magnet synchronous motor control method based on second-order terminal sliding mode
Technical Field
The invention relates to the technical field of permanent magnet synchronous motors, in particular to a permanent magnet synchronous motor control method based on a second-order terminal sliding mode.
Background
The permanent magnet synchronous motor has the characteristics of high efficiency, small volume, simple structure and the like, and is widely applied to the fields of aerospace, household appliances, electric automobiles and the like in recent years. However, as a multivariable, strongly coupled, nonlinear system, the performance of the conventional linear control such as PI control is susceptible to system uncertainty and external disturbance, and secondly, the pole of the motor changes with the change of the rotation speed when PI control is adopted, so that the conventional PI control cannot achieve a high-performance control characteristic in the range of full-speed section. For a general permanent magnet synchronous motor with small rotational inertia, when a load suddenly changes, the traditional PI controller cannot well inhibit load disturbance, so that the rotating speed of the motor is greatly changed, and therefore, in some occasions with higher precision requirements, higher requirements are provided for a control system.
The sliding mode variable structure control has the advantages of strong robustness to uncertain disturbance, fast dynamic response and the like, can still obtain good tracking performance when external disturbance and parameters change, and has fast dynamic response speed. In the common sliding mode control, a linear sliding hyperplane is usually selected, so that the tracking error gradually converges to zero after the system reaches a sliding mode, and the speed of gradual convergence can be arbitrarily adjusted by selecting parameters of the sliding mode surface, however, the state tracking error cannot converge to zero within a limited time. The terminal sliding mode introduces a nonlinear function in the design of a sliding hyperplane, so that the tracking error on the sliding mode surface can be converged to zero in a limited time.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a control method of a permanent magnet synchronous motor based on a second-order terminal sliding mode aiming at the defects of the prior art, the control method of the permanent magnet synchronous motor based on the second-order terminal sliding mode realizes high-precision control of the permanent magnet synchronous motor by adopting a current loop controller and a third-order terminal sliding mode controller as a speed loop; therefore, the problem that the speed change range is large when the load or the given rotating speed of the permanent magnet synchronous motor with small moment of inertia suddenly changes is solved.
In order to solve the technical problems, the invention adopts the technical scheme that:
a permanent magnet synchronous motor control method based on a second-order terminal sliding mode comprises the following steps.
Step 1, dq axis current i under a rotor coordinate systemdAnd iqObtaining: measuring and calculating the actual rotating speed omega of the permanent magnet synchronous motor through an encoder in each periodrAnd the three-phase current i of the permanent magnet synchronous motor is acquired through the sampling circuita、ibAnd ic(ii) a Will make three-phase current ia、ibAnd icCarrying out Clark conversion and Park conversion to obtain dq axis current i under a rotor coordinate systemdAnd iq。
Step 2, setting value i of q-axis currentq' obtaining: setting the given rotation speed of the permanent magnet synchronous motorAnd the actual rotating speed omega acquired in the step 1rMaking a difference, and outputting to obtain a q-axis current given value i through a second-order terminal sliding mode speed controllerq′。
Step 3, load torque observed valueObtaining: the actual rotating speed omega acquired in the step 1 is usedrAnd q-axis current i obtained by conversionqInputting the load torque into a nonlinear extended state observer, and outputting the load torque observed value by the extended state observer
Step 4, compensating the set value of the q-axis currentObtaining: observing the load torque obtained in the step 3Feedforward compensation is carried out to a second-order terminal sliding mode speed controller, and then the second-order terminal sliding mode speed controller sets the given value i of the q-axis current obtained in the step 2q' Compensation is carried out, and a compensated q-axis current set value is output
Step 5, input voltage u under αβ coordinate systemαAnd uβObtaining: by usingVector control of (2) is toThe compensated q-axis current given value obtained in step 4And dq axis current i acquired in step 1d、iqAll input into a dead-beat controller which outputs the input voltage u of the permanent magnet synchronous motor under a rotor coordinate systemd、uqObtaining the input voltage u under αβ coordinate system through inverse Park conversionαAnd uβ。
Step 6, adopting a space voltage vector pulse width modulation technology to convert u obtained in the step 5 into uαAnd uβAnd the signal is converted into a switching signal for controlling a three-phase inverter power device, and finally the permanent magnet synchronous motor is driven to operate.
In step 2, the given value i of q-axis currentqThe' acquisition method includes the following steps.
Step 21, establishing a discrete sliding mode surface of a second-order terminal sliding mode speed controller: the discrete sliding mode surface of the established second-order terminal sliding mode speed controller is as follows:
wherein x is1(k) Discrete value of rotation speed error at time k, TsTo sample time, s0(k) Is a discrete value of the zero-order sliding mode surface k moment, s0(k +1) is a discrete value of a zero-order sliding mode surface k +1 moment; s1(k) Is a discrete value of k time of a first-order slip form surface, s1(k +1) is a discrete value of a first-order sliding mode surface k +1 moment; s2(k) Is a discrete value of the second order sliding mode surface k moment, r1、p1、r2、p2The surface parameters of the sliding mode are given constants;
step 22, obtaining a third order difference equation of the rotation speed error: the third order difference equation of the obtained rotating speed error is as follows:
wherein x is3(k +1) is the second derivative x of the speed error3Discrete value at time k +1, x3(k) As second derivative x of the speed error3Discrete value at time k, x2(k) As the first derivative x of the speed error2Discrete values at time k.
In addition, the first and second substrates are,in the formula, J is the moment of inertia, P represents the number of pole pairs of the motor,is a permanent magnetic linkage, B is a friction coefficient, TLIs the load torque; fdAs a system disturbance.
Step 23, according to the third-order difference equation of the rotating speed error obtained in the step 22 and the discrete sliding mode surface of the second-order terminal sliding mode speed controller established in the step 21, obtaining an output value i 'of the second-order terminal sliding mode speed controller'q(k) Comprises the following steps:
in formula (12), iq' (K) is the discrete value of the given value of the q-axis current at the moment of K, K is the sliding mode switching gain, α1、α2、β1、β2For the output parameter of the sliding mode, r1、p1、r2、p2For the parameters of the sliding mode surface, in order to avoid infinite setting of q-axis current, r is required to be satisfied1>2,p1>2；r2>1,p2>1。
In step 3, the nonlinear extended state observer design equation is as follows:
wherein,is the observed value of the rotor speed, e is the error between the observed value of the rotor speed and the actual value, P is the number of pole pairs of the motor,is a permanent magnet flux linkage, J is moment of inertia, iqIs the q-axis current, and is,as observed value of torque, gamma1、γ2Is a positive coefficient, γ1Determines the speed of convergence, gamma, of the extended state observer2Determined by the maximum rate of change of the load disturbance, y — fal (e, α, epsilon) is a nonlinear function defined as follows:
where sat is the saturation function, α is the normal number taken to be 0.5, and ε represents the linear length of the fal function.
In step 4, the obtained compensated q-axis current given valueIs represented as follows:
wherein,in order to provide a load torque feed-forward gain,as observed values of torqueThe discrete value at time k after filtering by the low-pass filter.
In step 5, the deadbeat controller includes a current prediction module and a voltage calculation module.
The current prediction module is used for predicting the dq axis current i of the permanent magnet synchronous motor according to the current control periodd(k) And iq(k) And the last period stator voltage ud(k-1) and uq(k-1) calculating a predicted value of the dq-axis current of the PMSM in the next control period
The voltage calculation module uses the predicted value of the stator dq axis current for the next control periodAnd a given value of the compensated stator dq-axis currentCalculated in step 4Calculating the stator voltage u of the periodd(k)、uq(k)。
The invention has the following beneficial effects:
the method takes a rotating speed error as an input, a second-order terminal sliding mode speed controller takes the deviation between a given rotating speed and a feedback rotating speed as an input quantity, and a q-axis current given value is output through a second-order terminal sliding mode control quantity; the problem that the speed change amplitude is too large when the load torque suddenly changes is solved through sliding mode control output containing second-order terminal sliding mode surface information, the system can quickly track the given speed in a dynamic state, and the running performance of the small-moment-inertia permanent magnet synchronous motor is improved. The feedforward compensation of the system disturbance observed by the extended state observer can further reduce the value of the switching gain of the terminal sliding mode controller, weaken buffeting, improve the disturbance resistance of the system and realize high-precision vector control on the permanent magnet motor.
Drawings
Fig. 1 is a block diagram of a speed and current double closed loop control of a medium permanent magnet synchronous motor according to the present invention.
Fig. 2 is a block diagram of current predictive control of the deadbeat controller of the present invention.
FIG. 3 is a comparison graph of simulation of the rotating speed performance of a permanent magnet synchronous motor.
Among them are: 10. a permanent magnet synchronous motor; 20. a three-phase inverter.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific preferred embodiments.
As shown in fig. 1, a method for controlling a permanent magnet synchronous motor based on a second-order terminal sliding mode includes the following steps.
Step 1, dq axis current i under a rotor coordinate systemdAnd iqObtaining: at each period, measuring and calculating by encoder (also called decoder, installed on rotor shaft of permanent magnet synchronous motor, outputting discrete position signal in real time)Obtaining the actual rotating speed omega of the permanent magnet synchronous motorrThe three-phase current i of the permanent magnet synchronous motor is acquired by a sampling circuit (such as a current sensor and the like)a、ibAnd ic(ii) a Will make three-phase current ia、ibAnd icCarrying out Clark transformation and Park transformation to obtain dq axis current i under a rotor coordinate system (also called αβ coordinate system)dAnd iq。
Step 2, setting value i of q-axis currentq' obtaining: setting the given rotation speed of the permanent magnet synchronous motorAnd the actual rotating speed omega acquired in the step 1rMaking a difference, and outputting to obtain a q-axis current given value i through a second-order terminal sliding mode speed controllerq′。
Given value of q-axis current iqThe' obtaining method comprises the following steps:
step 21, establishing a discrete sliding mode surface of a second-order terminal sliding mode speed controller: the discrete sliding mode surface of the established second-order terminal sliding mode speed controller is as follows:
wherein x is1(k) Discrete value of rotation speed error at time k, TsIs a sampling time, e.g. the interval from k to k +1 times, s0(k) Is a discrete value of the zero-order sliding mode surface k moment, s0(k +1) is a discrete value of a zero-order sliding mode surface k +1 moment; s1(k) Is a discrete value of k time of a first-order slip form surface, s1(k +1) is a discrete value of a first-order sliding mode surface k +1 moment; s2(k) Is a discrete value of the second order sliding mode surface k moment, r1、p1、r2、p2The parameters of the sliding mode surface are given constants.
And step 22, obtaining a third-order difference equation of the rotating speed error.
Assuming a given rotational speedSelecting the system state variables without change
In the formula (2), the reaction mixture is,for a given speed, ωrIs the actual speed of the motor, x1As error in rotational speed, x2As first derivative of the speed error, x3The second derivative of the speed error.
The state variables from which the discrete domain is derived by euler forward discretization are as follows:
in the formula (3), x1(k) Discrete value of rotation speed error at k time, x1(k +1) is the error x of the rotation speed1Discrete value at time k +1, x2(k) As first derivative x of the speed error2Discrete value at time k, x2(k +1) is the first derivative x of the speed error2Discrete value at time k +1, x3(k) As second derivative x of the speed error3Discrete values at time k.
The motor motion equation and the electromagnetic torque equation are as follows:
in the formula (4), TeIs an electromagnetic torque; t isLIs the load torque; j is moment of inertia; p is the number of pole pairs of the motor;is a permanent magnetic linkage; i.e. iqStator quadrature axis current, also called stator q-axis current; b represents a friction coefficient.
Substituting an electromagnetic torque equation into a motor motion equation, and obtaining a discrete model of a speed ring through Euler forward dispersion as follows:
ωr(k+1)＝ωr(k)+b*iq(k)+Fd(5)
in addition, the first and second substrates are,in the formula, J is the moment of inertia, P represents the number of pole pairs of the motor,is a permanent magnetic linkage, B is a friction coefficient, TLIs the load torque; fdAs a system disturbance.
The current loop state space equation for the continuous domain is as follows:
in the formula idIs d-axis current, iqIs a q-axis current, udIs d-axis voltage, uqIs q-axis voltage, L is dq-axis inductance, R is motor stator phase resistance, TsIs the sampling time.
By utilizing Euler forward dispersion and considering sampling delay, a discrete domain state space equation of a motor current loop can be obtained as follows:
in the above formula, id(k +1) is the current at the moment of d-axis k +1, iq(k +1) is the current at the time of q-axis k +1, id(k) Current at time k of d-axis iq(k) Current at time k of q axis, ud(k-1) is the voltage at the time of d-axis k-1, uq(k-1) is the voltage at the time of q-axis k-1.
The control target is designed to reach the given value i in the k +2 periodrefI.e. i (k +2) ═ irefThen the voltage for k-period is given as follows:
FIG. 2 is a control block diagram of a deadbeat current loop controller. According to the deadbeat current loop controller designed according to the above formula, there is a two-beat delay between the input and the output.
The transfer function of the current loop is substituted into the discrete model of the rotating speed loop to obtain a new rotating speed loop model as follows:
ωr(k+3)＝ωr(k+2)+b*iq(k)+Fd(9)
the discrete state equation of the rotational speed error according to the selected system state variable is as follows:
the third order difference equation of the rotating speed error can be obtained by the rotating speed error discrete state space equation:
and (3) obtaining a discrete sliding mode surface equation of the second-order terminal sliding mode speed controller in the step 21 by euler forward dispersion.
Step 23, according to the third order difference equation of the rotation speed error obtained in step 22 and established in step 21Obtaining a discrete sliding mode surface of a second-order terminal sliding mode speed controller to obtain an output value i 'of the second-order terminal sliding mode speed controller'q(k) Comprises the following steps:
in formula (12), iq' (K) is the discrete value of the given value of the q-axis current at the moment of K, K is the sliding mode switching gain, α1、α2、β1、β2For the output parameter of the sliding mode, r1、p1、r2、p2For the parameters of the sliding mode surface, in order to avoid infinite setting of q-axis current, r is required to be satisfied1>2,p1>2；r2>1,p2>1。
Step 3, load torque observed valueObtaining: the actual rotating speed omega acquired in the step 1 is usedrAnd q-axis current i obtained by conversionqInputting the load torque into a nonlinear extended state observer, and outputting the load torque observed value by the extended state observer
The nonlinear extended state observer design equation is as follows:
wherein,is the observed value of the rotor speed, e is the error between the observed value of the rotor speed and the actual value, P is the number of pole pairs of the motor,is a permanent magnet flux linkage, J is moment of inertia, iqIs the q-axis current, and is,as observed value of torque, gamma1、γ2Is a positive coefficient, γ1Determines the speed of convergence, gamma, of the extended state observer2Determined by the maximum rate of change of the load disturbance, y — fal (e, α, epsilon) is a nonlinear function defined as follows:
where sat is the saturation function, α is the normal number taken to be 0.5, and ε represents the linear length of the fal function.
Step 4, compensating the set value of the q-axis currentObtaining: observing the load torque obtained in the step 3Is divided byThe feed-forward compensation is carried out until the given value of the q-axis current in the second-order terminal sliding mode speed controller is reached, and then the second-order terminal sliding mode speed controller sets the given value i of the q-axis current obtained in the step 2q' Compensation is carried out, and a compensated q-axis current set value is output
As can be seen from FIG. 1, the load torque observation is passed through a load torque feedforward gain KLIs compensated into a current iq"in the form of a web.
In step 4, the obtained compensated q-axis current given valueIs represented as follows:
wherein,in order to provide a load torque feed-forward gain,as observed values of torqueThe discrete value at time k after filtering by the low-pass filter.
Step 5, input voltage u under αβ coordinate systemαAnd uβObtaining: by usingVector control of (2) is toThe compensated q-axis current given value obtained in step 4And dq axis current i acquired in step 1d、iqAll input into a dead-beat controller which outputs the input voltage u of the permanent magnet synchronous motor under a rotor coordinate systemd、uqObtaining the input voltage u under αβ coordinate system through inverse Park conversionαAnd uβ。
In step 5, the deadbeat controller includes a current prediction module and a voltage calculation module. The current prediction module is used for predicting the dq axis current i of the permanent magnet synchronous motor according to the current control periodd(k) And iq(k) And the last period stator voltage ud(k-1) and uq(k-1) calculating a predicted value of the dq-axis current of the PMSM in the next control period
The voltage calculation module uses the predicted value of the stator dq axis current for the next control periodAnd a given value of the compensated stator dq-axis currentCalculated in step 4Calculating the stator voltage u of the periodd(k)、uq(k)。
Step 6, adopting a space voltage vector pulse width modulation (SVPWM) technology to convert u obtained in the step 5 into uαAnd uβAnd the signal is converted into a switching signal for controlling a three-phase inverter power device, and finally the permanent magnet synchronous motor is driven to operate.
In order to verify the effectiveness of the three-order discrete terminal sliding mode provided by the invention, a simulation platform based on Simulink is established.
Fig. 3 shows the rotating speed waveform of the small-moment-of-inertia permanent magnet synchronous motor under a three-order discrete terminal sliding mode controller, and it can be seen that the rotating speed variation amplitude of the permanent magnet synchronous motor under the invention is smaller than that of the conventional PI controller when the load and the given rotating speed suddenly change.
Although the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the details of the embodiments, and various equivalent modifications can be made within the technical spirit of the present invention, and the scope of the present invention is also within the scope of the present invention.

Claims (5)

1. A permanent magnet synchronous motor control method based on a second-order terminal sliding mode is characterized by comprising the following steps: the method comprises the following steps:
step 1, dq axis current i under a rotor coordinate systemdAnd iqObtaining: measuring and calculating the actual rotating speed omega of the permanent magnet synchronous motor through an encoder in each periodrAnd the three-phase current i of the permanent magnet synchronous motor is acquired through the sampling circuita、ibAnd ic(ii) a Will make three-phase current ia、ibAnd icPerforming Clark transformation and Park transformation to obtain a rotor coordinate systemLower dq axis current idAnd iq；
Step 2, setting value i of q-axis currentq' obtaining: setting the given rotation speed of the permanent magnet synchronous motorAnd the actual rotating speed omega acquired in the step 1rMaking a difference, and outputting to obtain a q-axis current given value i through a second-order terminal sliding mode speed controllerq′；
Step 3, load torque observed valueObtaining: the actual rotating speed omega acquired in the step 1 is usedrAnd q-axis current i obtained by conversionqInputting the load torque into a nonlinear extended state observer, and outputting the load torque observed value by the extended state observer
Step 4, compensating the set value of the q-axis currentObtaining: observing the load torque obtained in the step 3Feedforward compensation is carried out to a second-order terminal sliding mode speed controller, and then the second-order terminal sliding mode speed controller sets the given value i of the q-axis current obtained in the step 2q' Compensation is carried out, and a compensated q-axis current set value is output
Step 5, input voltage u under αβ coordinate systemαAnd uβObtaining: by usingVector control of (2) is toThe compensated q-axis current given value obtained in step 4And dq axis current i acquired in step 1d、iqAll input into a dead-beat controller which outputs the input voltage u of the permanent magnet synchronous motor under a rotor coordinate systemd、uqObtaining the input voltage u under αβ coordinate system through inverse Park conversionαAnd uβ；
Step 6, adopting a space voltage vector pulse width modulation technology to convert u obtained in the step 5 into uαAnd uβAnd the signal is converted into a switching signal for controlling a three-phase inverter power device, and finally the permanent magnet synchronous motor is driven to operate.
2. The control method of the permanent magnet synchronous motor based on the second-order terminal sliding mode according to claim 1, characterized in that: in step 2, the given value i of q-axis currentqThe' obtaining method comprises the following steps:
step 21, establishing a discrete sliding mode surface of a second-order terminal sliding mode speed controller: the discrete sliding mode surface of the established second-order terminal sliding mode speed controller is as follows:
wherein x is1(k) Discrete value of rotation speed error at time k, TsTo sample time, s0(k) Is a discrete value of the zero-order sliding mode surface k moment, s0(k +1) is a discrete value of a zero-order sliding mode surface k +1 moment; s1(k) Is a discrete value of k time of a first-order slip form surface, s1(k +1) is a discrete value of a first-order sliding mode surface k +1 moment; s2(k) Is a discrete value of the second order sliding mode surface k moment, r1、p1、r2、p2The surface parameters of the sliding mode are given constants;
step 22, obtaining a third order difference equation of the rotation speed error: the third order difference equation of the obtained rotating speed error is as follows:
wherein x is3(k +1) is the second derivative x of the speed error3Discrete value at time k +1, x3(k) As second derivative x of the speed error3Discrete value at time k, x2(k) As the first derivative x of the speed error2A discrete value at time k;
in addition, the first and second substrates are,in the formula, J is the moment of inertia, P represents the number of pole pairs of the motor,is a permanent magnetic linkage, B is a friction coefficient, TLIs the load torque; fdConsidering as a system disturbance;
step 23, according to the third-order difference equation of the rotating speed error obtained in the step 22 and the discrete sliding mode surface of the second-order terminal sliding mode speed controller established in the step 21, obtaining an output value i 'of the second-order terminal sliding mode speed controller'q(k) Comprises the following steps:
in formula (12), iq' (K) is the discrete value of the given value of the q-axis current at the moment of K, K is the sliding mode switching gain, α1、α2、β1、β2For the output parameter of the sliding mode, r1、p1、r2、p2For the parameters of the sliding mode surface, in order to avoid infinite setting of q-axis current, r is required to be satisfied1>2,p1>2；r2>1,p2>1。
3. The control method of the permanent magnet synchronous motor based on the second-order terminal sliding mode according to claim 2 is characterized in that: in step 3, the nonlinear extended state observer design equation is as follows:
wherein,is the observed value of the rotor speed, e is the error between the observed value of the rotor speed and the actual value, P is the number of pole pairs of the motor,is a permanent magnet flux linkage, J is moment of inertia, iqIs the q-axis current, and is,as observed value of torque, gamma1、γ2Is a positive coefficient, γ1Determines the speed of convergence, gamma, of the extended state observer2Determined by the maximum rate of change of the load disturbance, y — fal (e, α, epsilon) is a nonlinear function defined as follows:
where sat is the saturation function, α is the normal number taken to be 0.5, and ε represents the linear length of the fal function.
4. The second order terminal sliding mode based permanent magnet according to claim 3The control method of the magnetic synchronous motor is characterized in that: in step 4, the obtained compensated q-axis current given valueIs represented as follows:
wherein,in order to provide a load torque feed-forward gain,as observed values of torqueThe discrete value at time k after filtering by the low-pass filter.
5. The control method of the permanent magnet synchronous motor based on the second-order terminal sliding mode according to claim 1, characterized in that: in step 5, the dead beat controller comprises a current prediction module and a voltage calculation module;
the current prediction module is used for predicting the dq axis current i of the permanent magnet synchronous motor according to the current control periodd(k) And iq(k) And the last period stator voltage ud(k-1) and uq(k-1) calculating a predicted value of the dq-axis current of the PMSM in the next control periodThe voltage calculation module uses the predicted value of the stator dq axis current for the next control periodAnd a given value of the compensated stator dq-axis currentCalculated in step 4Calculating the stator voltage u of the periodd(k)、uq(k)。
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CN110289795A (en) * 2019-05-29 2019-09-27 南京金崎新能源动力研究院有限公司 A kind of Over Electric Motor with PMSM control system and control method
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CN113992067A (en) * 2021-08-30 2022-01-28 江苏高倍智能装备有限公司 Torque balance control method and system for annular knitting machine and storage device
CN114104013A (en) * 2021-11-12 2022-03-01 中国矿业大学 Speed control method for inhibiting wheel sliding of mining unmanned electric locomotive
CN114123892A (en) * 2021-11-12 2022-03-01 江南大学 Observer-based linear traction system terminal sliding mode control method and system
CN117341489A (en) * 2023-09-05 2024-01-05 西南交通大学 Train stepless coupling prediction adhesion control method for permanent magnet traction system
CN118157541A (en) * 2024-01-30 2024-06-07 北方工业大学 Control method of permanent magnet synchronous linear motor

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CN109873586A (en) * 2019-04-12 2019-06-11 湖南大学 A kind of electromechanics parameter identification method and system based on High-Order Sliding Mode observer
CN110011584A (en) * 2019-04-24 2019-07-12 广东工业大学 A kind of method for compensating vibration of single-rotor compressor, system and associated component
CN110289795A (en) * 2019-05-29 2019-09-27 南京金崎新能源动力研究院有限公司 A kind of Over Electric Motor with PMSM control system and control method
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CN110492817A (en) * 2019-08-05 2019-11-22 北方工业大学 A kind of direct prediction of speed control method and equipment of permanent magnet synchronous motor
CN110995086A (en) * 2019-12-05 2020-04-10 珠海格力电器股份有限公司 Permanent magnet synchronous motor, control method and device thereof and storage medium
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CN111245324B (en) * 2019-12-27 2024-01-23 深圳市合信自动化技术有限公司 Method for adjusting poles of torque observer
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CN112087172B (en) * 2020-07-20 2021-12-28 北京理工大学 Improved dead-beat prediction current control method for permanent magnet synchronous motor
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CN118157541A (en) * 2024-01-30 2024-06-07 北方工业大学 Control method of permanent magnet synchronous linear motor

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