CN107070336A

CN107070336A - The two patterns paste fractional order System with Sliding Mode Controller and method of permanent magnet linear synchronous motor

Info

Publication number: CN107070336A
Application number: CN201710102504.8A
Authority: CN
Inventors: 孙宜标; 王亚朋; 刘春芳
Original assignee: Shenyang University of Technology
Current assignee: Dongneng Shenyang Energy Engineering Technology Co ltd
Priority date: 2017-02-24
Filing date: 2017-02-24
Publication date: 2017-08-18
Anticipated expiration: 2037-02-24
Also published as: CN107070336B

Abstract

The two patterns paste fractional order System with Sliding Mode Controller and method of permanent magnet linear synchronous motor, the control technology obtains the margin of error according to PM linear servo system given speed signal and feedback speed signal subtraction, fractional order sliding-mode surface is designed with this margin of error, item is switched based on fractional order Theoretical Design sliding formwork control, and gain and discontinuous function product in switching item are replaced using interval two patterns fuzzy controllers, verify that system is stable according to Lyapunov functions；Interval two patterns fuzzy controllers and fractional order sliding-mode surface are introduced in design, and using based on fractional calculus theoretical switching, can effectively reduce buffeting；The uncertain problem of fuzzy systems fuzzy rule presence is solved simultaneously, improves the robustness of system, final the inventive method realizes the robustness of raising system, and weakens the chattering phenomenon of system.

Description

Two-type fuzzy fractional order sliding mode control system and method of permanent magnet linear synchronous motor

Technical Field

The invention belongs to the technical field of numerical control, and particularly relates to a two-type fuzzy fractional order sliding mode system and a two-type fuzzy fractional order sliding mode method for a permanent magnet linear synchronous motor.

Technical Field

The numerical control machine tool is used as an important basis of the traditional machine industry manufacturing and heavy machining industry, and along with the development of the society, higher and higher requirements are put forward on the numerical control machining technology with high speed and high precision. The traditional feeding system of the numerical control machine tool is mainly in a form of a rotating motor and a ball screw, and positive and negative gaps, friction and elastic deformation among intermediate ring sections in the form increase the nonlinear error of the system, so that the requirement of high-speed and high-precision technical production is limited to be difficult to achieve.

The linear motor transmission cancels an intermediate mechanical transmission mechanism, overcomes the defects caused by an intermediate transmission link of the traditional driving mode, obviously improves the dynamic sensitivity, the processing precision and the reliability of the machine tool, and has very obvious advantages in a high-precision and quick-response micro-feed servo system. However, due to the direct driving characteristic, uncertain factors such as load disturbance and motor parameter change directly act on the linear motor rotor, and new higher requirements are provided for the design of the controller.

In order to realize a high-speed high-precision direct drive feeding and positioning system, researchers propose various control strategies, for example, a controller is designed by adopting an adaptive control theory, so that the influence of parameter change on the system can be effectively overcome, but the effect is not good under the conditions of rapid parameter change and high external interference frequency. The controller is designed by adopting a sliding mode variable structure control theory, has the advantages of strong robustness and simple realization, and can cause a buffeting phenomenon due to the discontinuity of the control action. The fractional calculus theory and the sliding mode control are combined, and a fractional sliding mode approach law is designed, so that the system state can smoothly and slowly converge to the original point, and the difficulty in selecting the parameters of the controller is increased. The fuzzy control theory is adopted to design the controller, the method does not need an object mathematical model, can fully utilize the information of a control expert and has the advantage of considerable robustness, and is often superior to the effect of conventional control particularly under the condition that the system has uncertain factors, but the fuzzy control still faces the problems that the parameters of the fuzzy controller can be determined only by repeated trial and error, and systematic analysis and comprehensive methods such as stability analysis and the like are lacked. The controller is designed by adopting a fuzzy sliding mode control theory, the method has small degree of dependence on a model of a system, can fully utilize information of a control expert and has the advantage of quite robustness, and the buffeting phenomenon of general sliding mode control is reduced or avoided.

Disclosure of Invention

Object of the Invention

Aiming at the defects in the prior art, the invention provides a two-type fuzzy fractional order sliding mode control system and a two-type fuzzy fractional order sliding mode control method for a permanent magnet linear synchronous motor, which combine sliding mode control with a fractional order calculus theory and an interval two-type fuzzy system, can effectively weaken the phenomenon of sliding mode control buffeting, have invariance to the parameter change and external disturbance of the system, improve the robustness of the system and aim to solve the problems in the past.

The technical scheme is as follows:

the control system designed by the invention comprises a speed controller and a hardware part of the whole system. Wherein the speed controller uses an interval two-type fuzzy fractional order sliding mode control design.

The interval type fuzzy fractional order sliding mode controller comprises the following parts:

1. and establishing a fractional order sliding mode surface. Define the system tracking error as: e-v^*-v, wherein v^*And v are respectively a given value and an actual value of the system speed, and a fractional order PI as a formula (1) is established^αD^αSlip form surface

Wherein k is_pAnd k_iIs a non-zero positive number;represents a fractional calculus operator, and when α (0 < α < 1) represents a fractional differentiation, thenRepresenting a fractional order integral.

2. The sliding mode control law is designed as

u＝u_eq+u_sw(2)

Wherein u is_eqFor an equivalent control term, consisting ofIt is determined that the expression can be found as:

wherein M is the mass of the rotor of the linear motor, k_fIs the electromagnetic thrust coefficient, B_vIs viscous friction factor, e ═ v^*-v is the system velocity tracking error, where v^*And v are the set and actual values of the system speed, respectively.

U in formula (2)_swFor switching control items, the expression is calculated as follows:

wherein, K_sIs a negative constant value, and s is the slip form surface.

Equivalent control term u_eqAnd a handover control item u_swIn formula (2), the following are present:

since the control performance of the system is influenced by the sliding mode control switching item, if K in the switching item_sThe absolute value of the value is too large, and the system has large buffeting; conversely, the robustness of the system is reduced. Because the servo system of the permanent magnet linear synchronous motor is easy to be disturbed by uncertain factors and the disturbance is not easy to be measured, the invention adopts the interval two-type fuzzy controller to replace the K in the formula (4)_sTerm sgn(s), the input of the interval two-type fuzzy controller is the sliding mode surface s defined by the formula (1), the output is Deltau, then the formula (4) is

The control method is embedded into a DSP control circuit to realize the speed control of the permanent magnet linear synchronous motor servo system.

3. The hardware implementation of the two-type fuzzy fractional order sliding mode control system comprises a main circuit, a control circuit and a control object; the control circuit comprises a DSP, a position and speed detection circuit, a current detection circuit, an optical coupling isolation circuit, a drive circuit and a fault detection and protection circuit; the main circuit comprises a voltage regulating circuit, a rectifying and filtering unit and an IPM inverter unit; the control object is a three-phase permanent magnet linear synchronous motor, and a grating ruler is arranged on the machine body. The SCI port of the DSP is connected with an upper computer, the SPI port of the DSP is connected with a display circuit, and the GPIO port of the DSP is connected with an I/O interface circuit; the fault detection and protection circuit is connected with the control power supply. The DSP employs a TMS320F28335 processor.

4. The method is finally realized by a control program embedded in a DSP processor, and comprises the following specific steps:

step 1, initializing a system;

step 2, initializing a DSP system;

step 3, initializing a register and variables;

step 4, initializing an interrupt vector;

step 5, opening interruption;

does step 6 end the run? If yes, go to step 9;

step 7, whether the underflow interrupt of the general timer is generated or not is judged, and otherwise, the step 6 is carried out;

step 8 executes T1 interrupt processing sub-control program; carrying out step 6;

step 9, storing data;

step 10, turning off the interrupt;

step 11 ends.

The T1 interrupt processing sub-control program of the step 8 comprises the following steps:

step 1, protecting a field;

step 2, reading the encoder value to obtain an electrical angle;

step 3, current sampling;

step 3, CLARK transformation;

step 5, PARK conversion;

step 6, judging whether speed adjustment is needed; otherwise, entering a step 8;

step 7, calling a speed adjusting processing sub-control program;

step 8 d q axis current adjustment;

step 9, inverse PARK transformation;

step 10, SVPWM output;

step 11, restoring the site;

step 12 interrupts the return.

The speed regulation interrupt processing sub-control program of the step 7 comprises the following steps:

step 1, starting a speed regulation interruption sub-control program;

step 2, reading an encoder value;

step 3, calculating an angle;

step 4, calculating the speed;

step 5, calculating a speed feedback error;

step 6, setting initial working condition parameters of the two-type fuzzy fractional order sliding mode variable structure;

step 7, judging whether the sliding mode is on a preset sliding mode surface; if yes, go to step 9;

step 8 calculating u_sw；

Step 9 calculation of u_eq；

Step 10, calculating and outputting a current command, namely, an interval two-type fuzzy fractional order sliding mode control law u-u_eq+u_sw；

Step 11, interrupting and returning;

the invention has the advantages that: aiming at a Permanent Magnet Linear Synchronous Motor (PMLSM) servo system, the invention provides a two-type fuzzy fractional order sliding mode control system and a method of the permanent magnet linear synchronous motor; an interval two-type fuzzy controller and a fractional order sliding mode surface are introduced in the design, and a switching term based on a fractional order calculus theory is adopted, so that buffeting can be effectively reduced; meanwhile, the method solves the problem of uncertainty of fuzzy rules of a fuzzy system, improves the robustness of the system, and finally improves the robustness of the system and weakens the buffeting phenomenon of the system.

Drawings

FIG. 1 is a block diagram of a two-type fuzzy fractional order sliding mode control permanent magnet synchronous linear servo system of the present invention.

FIG. 2 is a block two-type fuzzy set with uncertain center values.

FIG. 3 is a block diagram of a block two-type fuzzy logic system.

FIG. 4 is a hardware schematic diagram of a control system implementing the present invention.

FIG. 5 is a main flow chart of the implementation of the two-type fuzzy fractional order sliding mode control software.

Fig. 6 is a flowchart of a current loop implementation procedure (i.e., a flowchart of a T1 interrupt processing sub-control procedure).

FIG. 7 is a flow chart of a speed adjustment processing sub-control routine.

Fig. 8(a) is a schematic diagram of a main circuit of the motor drive system.

FIG. 8(b) A, B is a schematic diagram of a phase current sampling circuit.

Fig. 8(c) is a schematic diagram of a grating scale signal sampling circuit.

FIG. 9 is a membership function of the bin two type fuzzy controller input s.

FIG. 10 is a membership function of the output Δ u of the two-type fuzzy controller in interval.

FIG. 11 is a graph of a speed step response versus test for a one-type fuzzy sliding mode and a two-type fuzzy fractional order sliding mode control system.

FIG. 12 is a cross-axis current i of the output of the two-type fuzzy fractional order sliding mode controller_qTest curves.

FIG. 13 is a velocity step response curve before and after a change in a system parameter using a two-type fuzzy fractional order sliding mode controller.

Detailed Description

The invention is further described below with reference to the accompanying drawings:

FIG. 1 is a diagram of the two-type fuzzy fractional order sliding mode control system of permanent magnet linear synchronous motorA block diagram, wherein v^*The given value of the system speed is d is the external disturbance, and the system tracking error is e-v^*-v。

The main steps for realizing the invention are as follows:

the method comprises the following steps: establishing mathematical model of permanent magnet linear synchronous motor

The d-q axis model of the permanent magnet linear synchronous motor is as follows

In the formula

In the formula, ω_rPi v/tau, wherein v is the linear velocity of the rotor; u. of_d、u_q、i_d、i_q、L_d、L_q、ψ_d、ψ_qD-q axis voltage, current, inductance, flux linkage, respectively; r_sIs a rotor resistor; psi_fThe flux linkage component of the permanent magnet on the rotor winding straight shaft; τ is the pole pitch.

The electromagnetic thrust expression of the permanent magnet linear synchronous motor is

Because L in the surface-mounted permanent magnet linear synchronous motor_d＝L_qThen (9) can be represented as

In the formula: p is a radical of_nIs the number of pole pairs, k_fIs the electromagnetic thrust coefficient.

The mechanical motion equation of the permanent magnet synchronous linear motor is

In the formula: l is the mover displacement; m is the total mass of the rotor and the carried load; b is_vIs the viscous friction factor; d (t) is external interference, d (t) ═ F_fric+F_rip+F_l，F_fricIs friction force, expression thereofv is the linear velocity of the rotor;thrust fluctuations, F, for end effects_ripplem40 is the amplitude of the thrust ripple produced by the end effect, θ₀The initial phase electrical angle is set to 0. l is the displacement of the rotor, and tau is the polar distance; f_lIs the load resistance.

Let state quantity x be [ x ]_lx₂]^T＝[l v]^T，u＝i_qFor inputting the control quantity, the state equation of the permanent magnet synchronous linear motor obtained by the formula (11) is

Step two: fractional order PI^αD^αDesign of slip form surface

Defining: the fractional calculus operator is expressed ast₀T is the upper and lower limits of the operator; (RL-type) Riemann-Liouville fractional calculus of the continuously integrable function f (t) is defined as

In the formula: m is an integer, and m-1<α<m，t>t₀(ii) a τ denotes the function f (t) at [ t ]₀，t]Any value within the range; gamma function (. cndot.) is defined asWherein z is the value of the right half plane of the complex plane, namely Re (z) > 0. t represents a function (. cndot.) at [0, ∞]Any value of (c). .

In order to solve the problem that the fractional order differential integral value of the function can not be directly and accurately calculated, the invention adopts an integer order Oustaloup filter to approximate a fractional order differential operator D^α. The transfer function of the filter is as follows

Wherein G(s) is a complex function, k ∈ [ -N, N]N is the order of the filter, (ω_b,ω_h) For a given filtering frequency interval α is the order of the fractional calculus.

Designing a fractional order PI as shown in the following formula^αD^αSlip form surface

Wherein k is_pAnd k_iNon-zero normal number;represents a fractional calculus operator, and when α (0 < α < 1) represents a fractional differentiation, thenRepresenting a fractional order integral; e is the system velocity tracking error.

Step three: the sliding mode control law is designed as

u＝u_eq+u_sw(16)

Wherein u is_swA switching item for sliding mode control; u. of_eqFor equivalent control part of sliding-mode control, from the derivative of the sliding-mode surface sDetermine if

Wherein,is the derivative of the systematic tracking error.

ByRespectively given speeds v for the movers^*And the derivative of the mover output speed v, combining equation (12) and equation (18), can be obtained

Wherein M is the rotor mass; k is a radical of_fThe electromagnetic thrust coefficient of the permanent magnet synchronous linear motor is obtained; b is_vIs the viscous friction factor.

Defining handover control itemss is a slip form face of formula (15), K_sIs a negative constant value.

Then the formula (19) becomes

Step four: since the control performance of the system is influenced by the sliding mode control switching item, if K in the switching item_sThe absolute value of the value is too large, and the system has large buffeting; conversely, the robustness of the system is reduced. Because the servo system of the permanent magnet linear synchronous motor is easy to be disturbed by uncertain factors and the disturbance is not easy to be measured, the invention adopts an interval two-type fuzzy controller to replace the K in the formula (20)_sTerm sgn(s), the input of the interval two-type fuzzy controller is the sliding mode surface s in the formula (15), and the output is Δ u.

FIG. 2 is a block two type fuzzy set with an uncertain center value, the block two type fuzzy Gaussian membership function is composed of an adjustable uncertain center value and a standard deviation value of a type fuzzy Gaussian membership function, and x is the input of the block two type fuzzy system, and the block two type fuzzy function is provided with an adjustable uncertain center value [ m₁,m₂]The interval type II Gaussian membership function with adjustable standard deviation sigma is as follows

As can be seen from FIG. 2, the zonesThe binary type fuzzy set is a domain describing a fuzzy set of uncertainty of the membership function, and is bounded by a conventional fuzzy membership function, an upper bound of the domain is represented by UMF, a lower bound of the domain is represented by LMF, and the domain is called an uncertainty domain (FOU), as shown in gray part of fig. 2. UMF and LMF of interval type two fuzzy membership function respectivelyIs shown as μ in FIG. 2₂、μ₁。

The interval type two fuzzy logic system is similar to the first type fuzzy logic system, and includes five parts of a fuzzifier, a rule base, an inference engine, a downgrader and a defuzzifier, as shown in fig. 3, but the front and back parts of the fuzzy logic system are replaced by interval type two fuzzy sets. The invention adopts a Mamdani type interval type two fuzzy system, and the interval type two fuzzy system used by the invention is composed of fuzzy rules in an IF-THEN form:

wherein s is a sliding mode surface in the formula (15) and is input of an interval two-type fuzzy system; y is the output of the interval type two fuzzy system,is a set of rule-front-parts,is a rule back-part set; i is 1, 2, …, W is a fuzzy rule number, and W is a positive constant. The front and back element sets of the fuzzy rule are both interval type fuzzy sets. Based on a multiplier-inference engine and a single-valued fuzzy device, obtaining a reduced order set through a set-of-sets (COS) model reduction as follows

Wherein ^ represents a logical sum, Y_cosIs fuzzy set by back-partTwo end points y of the central interval_lAnd y_rA set of decided intervals;representing a back-part fuzzy setThe set of central intervals.

The clear output after the ambiguity resolution by the gravity center method is

Wherein, y_lAnd y_rIs composed of

Wherein,

by substituting equations (28) and (29) for equation (27), the output of the two-type interval ambiguity is obtained as

Let y be Δ u, wherein the present invention adopts 7 fuzzy rules, and the input and output corresponding fuzzy linguistic variables are: PB (positive big), PM (middle big), PS (positive small), ZO (zero), NS (negative small), NM (negative middle), NB (negative big), fuzzy rules are as follows

R¹:IF s isPB,THEN Δu isNB；

R²:IF s isPM,THEN Δu isNM；

R³:IF s isPS,THEN Δu isNS；

R⁴:IF s isZO,THEN Δu isZO；

R⁵:IF s isNS,THEN Δu isPS；

R⁶:IF s isNM,THEN Δu isPM；

R⁷:IF s isNB,THEN Δu isPB；

Obtaining fuzzy controller output by using multiplier-type inference engine, single-valued fuzzy machine, set-Center (COS) degradation type and gravity-Center ambiguity resolution

Wherein,

the formula (20) is changed to

Wherein M is a moverAn amount; k is a radical of_fThe electromagnetic thrust coefficient of the permanent magnet synchronous linear motor is obtained; b is_vIs the viscous friction factor; k is a radical of_pAnd k_iNon-zero normal number;represents a fractional calculus operator, and when α (0 < α < 1) represents a fractional differentiation, thenRepresenting a fractional order integral; e-v^*V system velocity tracking error, where v^*Is the given value of the system speed, v is the output speed of the rotor, and delta u is the output of the two-type fuzzy system.

Step five: and writing a DSP program part for realizing the two-type fuzzy fractional order sliding mode control law.

The control algorithm of the invention is realized by an embedded DSP program. The flow chart of the main control program is shown in fig. 5, and the specific steps are as follows:

the first step is as follows: starting;

the second step is that: initializing a DSP system;

the third step: initializing program data;

the fourth step: allowing TN1, TN2 interrupts;

the fifth step: initiating a T1 underflow interrupt;

and a sixth step: opening a master interrupt;

the seventh step: is the run finished? Yes, the ninth step is executed. Otherwise, executing the eighth step.

Eighth step: is there an interrupt request? Yes, call T1 to interrupt the handler. Otherwise, executing the seventh step.

The ninth step: storing the data;

the tenth step: turning off the interrupt;

the eleventh step: and (6) ending.

As shown in fig. 6, the TN1 interrupt processing subroutine flowchart, i.e., the current loop T1 interrupt processing subroutine flowchart specifically includes the following steps:

the first step is as follows: the TN1 interrupt sub-control routine begins;

the second step is that: protecting the site;

the third step: reading the encoder signal;

the fourth step: current sampling, CLARK transformation and PARK transformation;

the fifth step: judging whether speed adjustment is needed, if not, entering the step (7);

and a sixth step: the speed adjustment interrupts the process control routine;

the seventh step: d. adjusting q-axis current;

eighth step: inverse PARK transform;

the ninth step: calculating CMPPx and PWM output;

the tenth step: restoring the site;

the eleventh step: and returning the interrupt.

The calculation flow chart of the sixth speed adjustment interrupt processing subroutine, i.e. the two-type fuzzy fractional order sliding mode control law in the TN1 interrupt program is shown in fig. 7, and is executed according to the following steps:

the first step is as follows: starting interruption;

the second step is that: reading the encoder signal;

the third step: calculating an electrical angle and calculating speed;

the fourth step: calculating a speed error;

the fifth step: setting initial working condition parameters of a two-type fuzzy fractional order sliding mode variable structure;

and a sixth step: judging whether the sliding mode is on a preset sliding mode surface; if yes, go to step 9;

the seventh step: calculating u_sw；

Eighth step: calculating u_eq；

The ninth step: calculating and outputting a current command, namely a two-type fuzzy fractional order sliding mode control law u ═ u_eq+u_sw；

The tenth step: and returning the interrupt.

Step six: hardware implementation of the two-type fuzzy fractional order sliding mode control system of the invention

FIG. 8 is a schematic diagram of a hardware control system implementing the present invention. The system comprises a main circuit, a control circuit and a control object; the control circuit comprises a DSP, a position and speed detection circuit, a current detection circuit, an optical coupling isolation circuit, a drive circuit and a fault detection and protection circuit; the DSP adopts TMS320F28335 chip of TI company. The QEP port of the DSP is connected with a position and speed detection circuit, the ADC port of the DSP is connected with a current detection circuit, the PWM port and the PDPINT port of the DSP are connected with an optical coupling isolation circuit, the optical coupling isolation circuit is connected with a driving circuit and a fault detection and protection circuit, and the driving circuit is connected with an IPM inversion unit; the main circuit comprises a voltage regulating circuit, a rectifying and filtering unit and an IPM inverter unit; the control object is a permanent magnet linear synchronous motor, and a grating ruler is arranged on the machine body; the voltage regulating circuit is connected with the rectifying and filtering unit, the rectifying and filtering unit is connected with the IPM inversion unit, and the IPM inversion unit is connected with the three-phase permanent magnet linear synchronous motor.

The SCI port of the DSP is connected with an upper computer, the SPI port of the DSP is connected with a display circuit, and the GPIO port of the DSP is connected with an I/O interface circuit; the fault detection and protection circuit is connected with the control power supply.

A main circuit of the control system for realizing the invention is shown in fig. 8(a), and a voltage regulating circuit adopts a reverse voltage regulating module EUV-25A-II, so that 0-220V isolation voltage regulation can be realized. The rectification filtering unit adopts bridge type uncontrollable rectification and large-capacitance filtering and is matched with a proper resistance-capacitance absorption circuit, so that constant direct-current voltage required by IPM operation can be obtained. The IPM adopts a Fuji 6MBP50RA060 intelligent power module, the withstand voltage is 600V, the maximum current is 50A, and the maximum working frequency is 20 kHz. The IPM is powered by four independent 15V driving power supplies. The main power input terminals (P, N), the output terminals (U, V, W) and the main terminals are fixed by screws, so that current transmission can be realized. P, N is the input terminal of the main power supply after rectification, conversion, smoothing and filtering of the frequency converter, P is the positive terminal, N is the negative terminal, the three-phase alternating current output by the inverter is connected to the motor through the output terminal U, V, W.

The core of the control circuit is a TMS320F28335 processor, and a matched development board comprises a target read-only memory, an analog interface, an eCAN interface, a serial boot ROM, a user indicator light, a reset circuit, an asynchronous serial port which can be configured as RS232/RS422/RS485, an SPI synchronous serial port and an off-chip 256K 16-bit RAM.

Current sampling in a practical control system adopts LEM Hall current sensors LT 58-S7. A, B phase current is detected by two Hall current sensors to obtain a current signal, the current signal is converted into a voltage signal of 0-3.3V through a current sampling circuit, and finally the voltage signal is converted into a binary number with 12-bit precision through an A/D conversion module of TMS320LF28335 and stored in a numerical value register. A. The B-phase current sampling circuit is shown in fig. 8 (B). The adjustable resistor VR2 adjusts the amplitude of the signal, the adjustable resistor VR1 adjusts the offset of the signal, the signal can be adjusted to 0-3.3V by adjusting the two resistors, and then the signal is sent to the AD0 and AD1 pins of the DSP. The voltage regulator tube is used for preventing the signal sent into the DSP from exceeding 3.3V, so that the DSP is damaged by high voltage. The operational amplifier adopts OP27, and the power is connected with positive and negative 15V voltage, and the capacitor is indirectly decoupled between the voltage and the ground. The input end of the circuit is connected with the capacitor for filtering so as to remove the interference of high-frequency signals and improve the sampling precision.

The A-phase pulse signal and the B-phase pulse signal output by the grating ruler are isolated by a quick optical coupler 6N137, the signal level is converted from 5V to 3.3V through a voltage division circuit, and finally the signals are connected to two paths of orthogonal coding pulse interfaces QEP1 and QEP2 of a DSP. The circuit principle is shown in fig. 8 (c). The linear motor driving circuit mainly comprises an intelligent power module, the IRAMS10UP60B is selected, the linear motor driving circuit is suitable for a motor with larger power, and the power range of the motor which can be driven by the linear motor driving circuit is 400-750W; a PWM control signal generated by a DSP chip on a control board is input into a power module to control the turn-off of 3 bridge arms and generate a proper driving voltage, and HIN1 and LIN1 in a motion diagram of a driving linear motor are respectively control signals of an upper bridge arm and a lower bridge arm of a first phase and are effective at low level. The operating voltage VDD of IRAMS10UP60B is 15V, VSS is ground, and two decoupling capacitors are connected in parallel to both ends for good decoupling. The power chip has over-temperature and over-current protection, and can play a self-protection role when the circuit is abnormal.

An example of the invention

The parameter of the permanent magnet linear synchronous motor is M-8 kg, k_f＝50.7N/A，B_v12 Ns/m. Frictional forceThrust fluctuations F produced by end effects_ripV and l are the speed and displacement of the mover, respectively, 40cos (392 l).

Two-type fuzzy fractional order sliding mode parameters: k is a radical of_p＝354，k_i＝0.001，α＝0.98，(ω_b,ω_h) Has a value of (10)^-3,10³) N is 2, the membership function of the input s of the interval type two fuzzy controller is shown in fig. 9, and the membership function of the output Δ u is shown in fig. 10.

Based on the above parameters, when v is given^*The motor is started in no-load mode at 1m/s, and F is added when t is 0.5s_lThe speed step response curves for the one-type fuzzy sliding mode and the two-type fuzzy fractional order sliding mode control systems are shown in fig. 11 as a dashed line and a solid line, respectively, at 200N load disturbance. The experimental result shows that the response time of the system controlled by the two-type fuzzy fractional order sliding mode is shorter, the maximum value of the speed reduction after disturbance is 0.061m/s, and the recovery time is 0.06 s; the maximum speed drop value of the system controlled by the one-mode fuzzy sliding mode is 0.077m/s after disturbance, and the recovery time is0.12s, indicating that the method of the invention has strong robustness. FIG. 12 shows the system i when a two-type fuzzy fractional order sliding mode controller is used_qThe output curve, it can be seen that the system is almost buffeting free. Fig. 13 is a speed step response curve of two-type fuzzy fractional order sliding mode control for changing the rotor mass M to 2 times after the permanent magnet linear synchronous motor is started, the system response time before and after the parameter change is almost unchanged, the maximum speed reduction value after the parameter change is disturbed by the sudden load is 0.061M/s, the maximum speed reduction value after the parameter change is disturbed by the sudden load is 0.041M/s, and it can be known that the influence of the parameter change on the system performance is small. The two-type fuzzy fractional order sliding mode control can weaken buffeting and improve the robustness of the system.

Claims

1. A two-type fuzzy fractional order sliding mode control system and method of a permanent magnet linear synchronous motor are characterized in that: the control technology subtracts a given speed signal and a feedback speed signal according to a permanent magnet linear synchronous motor servo system to obtain an error amount, designs a fractional order sliding mode surface according to the error amount, designs a sliding mode control switching item based on a fractional order theory, replaces the product of gain and a discontinuous function in the switching item by an interval two-type fuzzy controller, and verifies that the system is stable according to a Lyapunov function; the whole system comprises a main circuit, a control circuit and a control object; the control circuit comprises a DSP, a position and speed detection circuit, a current detection circuit, an optical coupling isolation circuit, a drive circuit and a fault detection and protection circuit; the DSP adopts TMS320F28335 chips of TI company; the QEP port of the DSP is connected with a position and speed detection circuit, the ADC port of the DSP is connected with a current detection circuit, the PWM port and the PDPINT port of the DSP are connected with an optical coupling isolation circuit, the optical coupling isolation circuit is connected with a driving circuit and a fault detection and protection circuit, and the driving circuit is connected with an IPM inversion unit; the main circuit comprises a voltage regulating circuit, a rectifying and filtering unit and an IPM inverter unit; the control object is a permanent magnet linear synchronous motor, and a grating ruler is arranged on the machine body; the voltage regulating circuit is connected with the rectifying and filtering unit, the rectifying and filtering unit is connected with the IPM inversion unit, and the IPM inversion unit is connected with the three-phase permanent magnet linear synchronous motor.

2. The two-type fuzzy fractional order sliding mode control system and method of the permanent magnet linear synchronous motor according to claim 1, characterized in that: selecting fractional order PI^αD^αA slip form surface;

the tracking error of the system is e ═ v^*-v, wherein v^*Establishing fractional order PI for given value of system speed^αD^αThe slip form surface is as follows:

<mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mi>e</mi> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>D</mi> <mi>t</mi> <mi>&alpha;</mi> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>

wherein k is_pAnd k_iIs a non-zero normal number and is,representing a fractional order differential operator, representing α (0 < α < 1) order derivatives;

the control law is designed as follows:

u＝u_eq+u_sw(2)

wherein u is_eqFor sliding-mode control of equivalent control terms, u_swSwitching items are controlled by a sliding mode; u. of_eqByIs determined as shown in the following formula

<mrow> <msub> <mi>u</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mi>M</mi> <msub> <mi>k</mi> <mi>f</mi> </msub> </mfrac> <mo>&lsqb;</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mn>2</mn> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>B</mi> <mi>v</mi> </msub> <mi>M</mi> </mfrac> <mi>v</mi> <mo>+</mo> <msup> <mi>v</mi> <mo>*</mo> </msup> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>

In the formula: m is the mover and the carried load mass, k_fIs the electromagnetic thrust coefficient, B_vIs the viscous friction coefficient.

3. The two-type fuzzy fractional order sliding mode control system and method of the permanent magnet linear synchronous motor according to claim 2, characterized in that: designing a sliding mode control switching item based on a fractional order theory, and replacing the product of gain and discontinuous function in the switching item by adopting an interval two-type fuzzy controller;

defining handover control itemsK_sFor negative constant value, the present invention adopts interval two-type fuzzy controller to replace K_sTerm sgn(s).

4. The two-type fuzzy fractional order sliding mode control system and method of the permanent magnet linear synchronous motor according to claim 3, characterized in that: the interval type two fuzzy controller is single-input single-output, and the membership functions of the input and the output are interval type two fuzzy Gaussian membership functions; and obtaining fuzzy controller output by adopting a multiplier-type inference engine, a single-value fuzzifier, a set center degradation type and gravity center ambiguity resolution.

5. The two-type fuzzy fractional order sliding mode control system and method of the permanent magnet linear synchronous motor according to claim 2, characterized in that:

<mrow> <msub> <mi>u</mi> <mrow> <mi>s</mi> <mi>w</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mi>M</mi> <msub> <mi>k</mi> <mi>f</mi> </msub> </mfrac> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>K</mi> <mi>s</mi> </msub> <mi>s</mi> <mi>g</mi> <mi>n</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow>

wherein, K_sIs a negative constant value;

<mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>M</mi> <msub> <mi>k</mi> <mi>f</mi> </msub> </mfrac> <mo>&lsqb;</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mn>2</mn> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>B</mi> <mi>v</mi> </msub> <mi>M</mi> </mfrac> <mi>v</mi> <mo>+</mo> <msup> <mi>v</mi> <mo>*</mo> </msup> <mo>+</mo> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>K</mi> <mi>s</mi> </msub> <mi>s</mi> <mi>g</mi> <mi>n</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>;</mo> </mrow>

since the control performance of the system is influenced by the sliding mode control switching item, if K in the switching item_sThe absolute value of the value is too large, and the system has large buffeting; conversely, the robustness of the system is reduced; because the servo system of the permanent magnet linear synchronous motor is easy to be disturbed by uncertain factors and the disturbance is not easy to be measured, the invention adopts the interval two-type fuzzy controller to replace the K in the formula (4)_sTerm sgn(s), interval two type modulusThe fuzzy controller inputs the sliding mode surface s defined by the formula (1), the output is delta u, and then the formula (4) is

<mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>M</mi> <msub> <mi>k</mi> <mi>f</mi> </msub> </mfrac> <mo>&lsqb;</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mn>2</mn> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>B</mi> <mi>v</mi> </msub> <mi>M</mi> </mfrac> <mi>v</mi> <mo>+</mo> <msup> <mi>v</mi> <mo>*</mo> </msup> <mo>+</mo> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>u</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>

6. The two-type fuzzy fractional order sliding mode control system and method of the permanent magnet linear synchronous motor according to claim 1, characterized in that:

the method comprises the following steps:

the method comprises the following steps: establishing a mathematical model of the permanent magnet linear synchronous motor:

<mrow> <msub> <mi>u</mi> <mi>d</mi> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mi>d</mi> </msub> <mo>+</mo> <msub> <mover> <mi>&psi;</mi> <mo>&CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>-</mo> <msub> <mi>&omega;</mi> <mi>r</mi> </msub> <msub> <mi>&psi;</mi> <mi>q</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>u</mi> <mi>q</mi> </msub> <mo>=</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msub> <mi>i</mi> <mi>q</mi> </msub> <mo>+</mo> <msub> <mover> <mi>&psi;</mi> <mo>&CenterDot;</mo> </mover> <mi>q</mi> </msub> <mo>+</mo> <msub> <mi>&omega;</mi> <mi>r</mi> </msub> <msub> <mi>&psi;</mi> <mi>d</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>

In the formula

In the formula, ω_rPi v/tau, wherein v is the linear velocity of the rotor; u. of_d、u_q、i_d、i_q、L_d、L_q、ψ_d、ψ_qD-q axis voltage, current, inductance, flux linkage, respectively; r_sIs a rotor resistor; psi_fThe flux linkage component of the permanent magnet on the rotor winding straight shaft; tau is a polar distance;

Because L in the surface-mounted permanent magnet linear synchronous motor_d＝L_qThen (9) is represented as

In the formula: p is a radical of_nIs the number of pole pairs, k_fIs the electromagnetic thrust coefficient;

In the formula: l is the mover displacement; m is the total mass of the rotor and the carried load; b is_vIs the viscous friction factor; d (t) is external interference, d (t) ═ F_fric+F_rip+F_l，F_fricIs friction force, expression thereofv is the linear velocity of the rotor;thrust fluctuations, F, for end effects_ripplem40 is the amplitude of the thrust ripple produced by the end effect, θ₀Is the initial phase electrical angle; l is the displacement of the rotor, and tau is the polar distance; f_lIs the load resistance;

let state quantity x be [ x ]_lx₂]^T＝[l v]^TL and v are respectively the displacement and linear velocity of the rotor; u-i_qFor inputting the control quantity, the state equation of the permanent magnet synchronous linear motor obtained by the formula (11) is

<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>x</mi> <mo>&CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mi>M</mi> </mfrac> <mrow> <mo>(</mo> <msub> <mi>B</mi> <mi>v</mi> </msub> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mi>f</mi> </msub> <mi>u</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <mi>d</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>

Wherein,andare respectively a state variable x₁And x₁A derivative of (a);

step two: fractional order PI^αD^αDesign of slip form surface

Defining: the fractional calculus operator is expressed ast₀T is the upper and lower limits of the operator, α is the order of the fractional calculus, and the (RL type) Riemann-Liouville fractional calculus of the continuous integrable function f (t) is defined as

In the formula: m is an integer, and m-1<α<m，t>t₀(ii) a τ denotes the function f (t) at [ t ]₀，t]Any value within the range; gamma function (·) is determinedIs defined asWherein z is the value of the right half plane of the complex plane, namely Re (z) is more than 0; t represents a function (. cndot.) at [0, ∞]Any value of (a);

in order to solve the problem that the fractional order differential integral value of the function cannot be directly and accurately calculated, the invention adopts an integer order Oustaloup filter to approximate the fractional order differential operatorThe transfer function of this filter is as follows:

<mrow> <mi>G</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>K</mi> <msubsup> <mo>&Pi;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mo>-</mo> <mi>N</mi> </mrow> <mi>N</mi> </msubsup> <mfrac> <mrow> <mi>s</mi> <mo>+</mo> <msubsup> <mi>&omega;</mi> <mi>k</mi> <mo>&prime;</mo> </msubsup> </mrow> <mrow> <mi>s</mi> <mo>+</mo> <msub> <mi>&omega;</mi> <mi>k</mi> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>

wherein G(s) is a complex function, k ∈ [ -N, N]N is the order of the filter, (ω_b,ω_h) For a given filtering frequency interval, α is the order of the fractional calculus;

<mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mi>e</mi> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>D</mi> <mi>t</mi> <mi>&alpha;</mi> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>

Wherein k is_pAnd k_iNon-zero normal number;represents a fractional calculus operator, and when α (0 < α < 1) represents a fractional differentiation, thenRepresenting a fractional order integral; e is the system speed tracking error;

step three: the sliding mode control law is designed as

u＝u_eq+u_sw(16)

<mrow> <mover> <mi>s</mi> <mo>&CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>D</mi> <mi>t</mi> <mi>&alpha;</mi> </msubsup> <mrow> <mo>(</mo> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mover> <mi>s</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mn>2</mn> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mo>)</mo> </mrow> <mo>+</mo> <mover> <mi>e</mi> <mo>&CenterDot;</mo> </mover> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>

Wherein,is the derivative of the systematic tracking error;

by Respectively given speeds v for the movers^*And the derivative of the mover output speed v; combining formula (12) and formula (18) to obtain:

<mrow> <msub> <mi>u</mi> <mrow> <mi>e</mi> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mi>M</mi> <msub> <mi>k</mi> <mi>f</mi> </msub> </mfrac> <mo>&lsqb;</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mn>2</mn> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>B</mi> <mi>v</mi> </msub> <mi>M</mi> </mfrac> <mi>v</mi> <mo>+</mo> <msup> <mi>v</mi> <mo>*</mo> </msup> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> </mrow>

wherein M is the rotor mass; k is a radical of_fThe electromagnetic thrust coefficient of the permanent magnet synchronous linear motor is obtained; b is_vIs the viscous friction factor;

defining handover control itemsK_sIs a negative constant value;

then the formula (19) becomes

<mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>M</mi> <msub> <mi>k</mi> <mi>f</mi> </msub> </mfrac> <mo>&lsqb;</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mn>2</mn> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>B</mi> <mi>v</mi> </msub> <mi>M</mi> </mfrac> <mi>v</mi> <mo>+</mo> <msup> <mi>v</mi> <mo>*</mo> </msup> <mo>+</mo> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>K</mi> <mi>s</mi> </msub> <mi>s</mi> <mi>g</mi> <mi>n</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>

Step four: since the control performance of the system is influenced by the sliding mode control switching item, if K in the switching item_sThe absolute value of the value is too large, and the system has large buffeting; conversely, the robustness of the system is reduced; because the servo system of the permanent magnet linear synchronous motor is easy to be disturbed by uncertain factors and the disturbance is not easy to be measured, the invention adopts an interval two-type fuzzy controller to replace the K in the formula (20)_ssgn(s) term, the input of the interval two-type fuzzy controller is the sliding mode surface s in the formula (15), and the output is delta u;

the method uses an interval type two fuzzy set with an uncertain center value, and an interval type two fuzzy Gaussian membership function is subjected to membership by a type one fuzzy GaussianFunction of adjustable uncertainty center value and standard deviation value, with adjustable uncertainty center value [ m ]₁,m₂]The interval type II Gaussian membership function with adjustable standard deviation sigma is as follows

<mrow> <msub> <mi>&mu;</mi> <mover> <mi>A</mi> <mo>~</mo> </mover> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>exp</mi> <mo>&lsqb;</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>x</mi> <mo>-</mo> <mi>m</mi> </mrow> <mi>&sigma;</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&rsqb;</mo> <mo>,</mo> <mi>m</mi> <mo>&Element;</mo> <mo>&lsqb;</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow>

Wherein x is the input quantity of the interval two-type fuzzy system;

the interval type two fuzzy set is a domain, the domain describes a fuzzy set of uncertainty of a membership function, and takes a traditional fuzzy membership function as a constraint boundary, the upper boundary of the domain is represented by UMF, the lower boundary of the domain is represented by LMF, and the domain is called as an uncertainty domain; UMF and LMF of interval type two fuzzy membership function respectively Is shown as μ in FIG. 2₂、μ₁；

The interval type two fuzzy logic system is similar to the first type fuzzy logic system and comprises five parts, namely a fuzzifier, a rule base, an inference engine, a degrader and a defuzzifier, wherein the front part and the rear part of the fuzzy logic system are replaced by an interval type two fuzzy set; the invention adopts a Mamdani type interval type two fuzzy system, and the interval type two fuzzy system used by the method consists of fuzzy rules in an IF-THEN form:

wherein s is the sliding mode surface in the formula (15) and is the input of the interval type two fuzzy system, y is the output of the interval type two fuzzy system,is a set of rule-front-parts,is a rule back-part set; i is 1, 2, …, W is a fuzzy rule number, W is a positive constant; the fuzzy rule front and back part sets are interval type fuzzy sets; based on a multiplier-inference engine and a single-valued fuzzy device, obtaining a reduced order set through a set-of-sets (COS) model reduction as follows

<mrow> <msub> <mi>Y</mi> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <msup> <mi>Y</mi> <mn>1</mn> </msup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>Y</mi> <mi>W</mi> </msup> <mo>,</mo> <msup> <mi>A</mi> <mn>1</mn> </msup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>A</mi> <mi>W</mi> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mo>&lsqb;</mo> <msub> <mi>y</mi> <mi>l</mi> </msub> <mo>,</mo> <msub> <mi>y</mi> <mi>r</mi> </msub> <mo>&rsqb;</mo> <mo>=</mo> <msub> <mo>&Integral;</mo> <msup> <mi>y</mi> <mn>1</mn> </msup> </msub> <mn>...</mn> <msub> <mo>&Integral;</mo> <msup> <mi>y</mi> <mi>W</mi> </msup> </msub> <mn>...</mn> <msub> <mo>&Integral;</mo> <msup> <mi>f</mi> <mn>1</mn> </msup> </msub> <mn>...</mn> <msub> <mo>&Integral;</mo> <msup> <mi>y</mi> <mi>W</mi> </msup> </msub> <mrow> <mo>(</mo> <mfrac> <mn>1</mn> <mrow> <msubsup> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>W</mi> </msubsup> <msup> <mi>f</mi> <mi>i</mi> </msup> <msup> <mi>y</mi> <mi>i</mi> </msup> <mo>/</mo> <msubsup> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>W</mi> </msubsup> <msup> <mi>f</mi> <mi>i</mi> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> </mrow>

Wherein ^ represents a logical sum, Y_cosIs fuzzy set by back-partTwo end points y of the central interval_lAnd y_rA set of decided intervals;representing a back-part fuzzy setA set of central intervals of (a);

the clear output after the ambiguity resolution by the gravity center method is

Wherein, y_lAnd y_rIs composed of

<mrow> <msub> <mi>y</mi> <mi>l</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>W</mi> </msubsup> <msubsup> <mi>f</mi> <mi>l</mi> <mi>i</mi> </msubsup> <msup> <mi>y</mi> <mi>i</mi> </msup> </mrow> <mrow> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>W</mi> </msubsup> <msubsup> <mi>f</mi> <mi>l</mi> <mi>i</mi> </msubsup> </mrow> </mfrac> <mo>=</mo> <msubsup> <mi>&theta;</mi> <mi>l</mi> <mi>T</mi> </msubsup> <msub> <mi>&xi;</mi> <mi>l</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow>

<mrow> <msub> <mi>y</mi> <mi>r</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>W</mi> </msubsup> <msubsup> <mi>f</mi> <mi>r</mi> <mi>i</mi> </msubsup> <msup> <mi>y</mi> <mi>i</mi> </msup> </mrow> <mrow> <msubsup> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>W</mi> </msubsup> <msubsup> <mi>f</mi> <mi>r</mi> <mi>i</mi> </msubsup> </mrow> </mfrac> <mo>=</mo> <msubsup> <mi>&theta;</mi> <mi>r</mi> <mi>T</mi> </msubsup> <msub> <mi>&xi;</mi> <mi>r</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> </mrow>

Wherein,

substituting equations (28) and (29) for equation (27) to obtain the output of the interval type two-type fuzzy device as

<mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>&theta;</mi> <mi>l</mi> <mi>T</mi> </msubsup> <msub> <mi>&xi;</mi> <mi>l</mi> </msub> <mo>+</mo> <msubsup> <mi>&theta;</mi> <mi>r</mi> <mi>T</mi> </msubsup> <msub> <mi>&xi;</mi> <mi>r</mi> </msub> </mrow> <mn>2</mn> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>30</mn> <mo>)</mo> </mrow> </mrow>

Let y be Δ u, wherein the present invention adopts 7 fuzzy rules, and the input and output corresponding fuzzy linguistic variables are: PB (just large),

PM (middle), PS (small positive), ZO (zero), NS (small negative), NM (middle negative), NB (big negative), fuzzy rules are as follows

R¹:IF s isPB,THENΔu isNB；

R²:IF s isPM,THENΔu isNM；

R³:IF s isPS,THENΔu isNS；

R⁴:IF s isZO,THENΔu isZO；

R⁵:IF s isNS,THENΔu isPS；

R⁶:IF s isNM,THENΔu isPM；

R⁷:IF s isNB,THENΔu isPB；

<mrow> <mi>&Delta;</mi> <mi>u</mi> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>&theta;</mi> <mi>l</mi> <mi>T</mi> </msubsup> <msub> <mi>&xi;</mi> <mi>l</mi> </msub> <mo>+</mo> <msubsup> <mi>&theta;</mi> <mi>r</mi> <mi>T</mi> </msubsup> <msub> <mi>&xi;</mi> <mi>r</mi> </msub> </mrow> <mn>2</mn> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow>

Wherein,

the formula (20) is changed to

<mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mi>M</mi> <msub> <mi>k</mi> <mi>f</mi> </msub> </mfrac> <mo>&lsqb;</mo> <msub> <mi>k</mi> <mi>p</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mi>i</mi> </msub> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mn>2</mn> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>e</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <msub> <mi>B</mi> <mi>v</mi> </msub> <mi>M</mi> </mfrac> <mi>v</mi> <mo>+</mo> <msup> <mi>v</mi> <mo>*</mo> </msup> <mo>+</mo> <msubsup> <mi>D</mi> <mi>t</mi> <mrow> <mo>-</mo> <mi>&alpha;</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>&Delta;</mi> <mi>u</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mrow>

Wherein M is the rotor mass; k is a radical of_fThe electromagnetic thrust coefficient of the permanent magnet synchronous linear motor is obtained; b is_vIs the viscous friction factor; k is a radical of_pAnd k_iNon-zero normal number;represents a fractional calculus operator, and when α (0 < α < 1) represents a fractional differentiation, thenRepresenting a fractional order integral; e-v^*V system velocity tracking error, where v^*The set value of the system speed is, v is the output speed of the rotor, and delta u is the output of the two-type fuzzy system;

step five: and compiling a DSP program part for realizing the interval two-type fuzzy fractional order sliding mode control law.

7. The two-type fuzzy fractional order sliding mode control system and method of the permanent magnet linear synchronous motor according to claim 1, characterized in that: the DSP adopts TMS320F28335 to process, and the control method comprises the following steps in DSP program implementation:

step 1, initializing a system;

step 2, initializing a DSP system;

step 3, initializing a register and variables;

step 4, initializing an interrupt vector;

step 5, opening interruption;

does step 6 end the run? If yes, go to step 9;

step 9, storing data;

step 10, turning off the interrupt;

step 11 ends.

8. The two-type fuzzy fractional order sliding mode control system and method of the permanent magnet linear synchronous motor according to claim 7, wherein: the T1 interrupt processing sub-control program in step 8 has the following steps:

step 1, protecting a field;

step 2, reading the encoder value to obtain an electrical angle;

step 3, current sampling;

step 3, CLARK transformation;

step 5, PARK conversion;

step 7, calling a speed adjusting processing sub-control program;

step 8 d q axis current adjustment;

step 9, inverse PARK transformation;

step 10, SVPWM output;

step 11, restoring the site;

step 12 interrupts the return.

9. The two-type fuzzy fractional order sliding mode control system and method of the permanent magnet linear synchronous motor according to claim 8, wherein: the speed regulation interrupt processing sub-control program of the step 7 comprises the following steps:

step 1, starting a speed regulation interruption sub-control program;

step 2, reading an encoder value;

step 3, calculating an angle;

step 4, calculating the speed;

step 5, calculating a speed feedback error;

step 8 calculating u_sw；

Step 9 calculation of u_eq；

Step 10, calculating and outputting a current command, namely a two-type fuzzy fractional order sliding mode control law u-u_eq+u_sw；

Step 11 interrupts the return.