CN112701975A - Self-adaptive backlash oscillation suppression method for double-inertia servo system - Google Patents

Self-adaptive backlash oscillation suppression method for double-inertia servo system Download PDF

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CN112701975A
CN112701975A CN202011553665.7A CN202011553665A CN112701975A CN 112701975 A CN112701975 A CN 112701975A CN 202011553665 A CN202011553665 A CN 202011553665A CN 112701975 A CN112701975 A CN 112701975A
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backlash
individual
sliding mode
inertia
double
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CN112701975B (en
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尹忠刚
李通
白聪
罗培恩
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Xian University of Technology
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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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • H02P25/024—Synchronous motors controlled by supply frequency
    • H02P25/026—Synchronous motors controlled by supply frequency thereby detecting the rotor position
    • 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
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/34—Modelling or simulation for control purposes
    • 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
    • H02P2205/00—Indexing scheme relating to controlling arrangements characterised by the control loops
    • H02P2205/01—Current loop, i.e. comparison of the motor current with a current reference
    • 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
    • H02P2205/00—Indexing scheme relating to controlling arrangements characterised by the control loops
    • H02P2205/07—Speed loop, i.e. comparison of the motor speed with a speed reference
    • 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

Abstract

The invention discloses a self-adaptive backlash oscillation suppression method for a double-inertia servo system, which specifically comprises the following steps: step 1, establishing a mathematical model of a permanent magnet synchronous motor to obtain an electromagnetic torque expression; step 2, establishing a dynamic mathematical model of the double-inertia servo transmission system by taking the rotating speed and the position as state variables; step 3, designing the sliding mode control rate of the sliding mode controller by adopting a sliding mode control method for the rotating speed ring based on the mathematical model of the double-inertia system dynamics obtained in the step 2 and the electromagnetic torque expression in the step 1; and 4, establishing a micro-asymmetric dead zone model, and identifying parameters of the micro-asymmetric dead zone model by adopting a differential evolution algorithm, wherein the identified parameters are unknown non-micro backlash shaft torque disturbance term parameters of the sliding mode control rate in the step 3. The invention solves the problem of oscillation caused by backlash in the conventional double-inertia servo system.

Description

Self-adaptive backlash oscillation suppression method for double-inertia servo system
Technical Field
The invention belongs to the technical field of high-precision alternating current servo control systems, and relates to a self-adaptive backlash oscillation suppression method for a double-inertia servo system.
Background
With the continuous development of servo driving technology, high performance servo systems have been widely applied in various fields, and related research and development have also received much attention. The servo system is firstly used for military and national defense, such as radar tracking and positioning, automatic aiming, missile launching and the like, is widely applied to industry later, and is suitable for numerical control machines, paper machines, mechanical arms, milling machines and the like. Direct drive systems with high stiffness drive components are used primarily for high performance industrial applications.
The servo drive control technology plays a significant role in intelligent manufacturing and industrial digitization. However, in actual conditions, some non-linear phenomena, such as non-linear friction, backlash and external interference, are common to mechanical systems. Among these non-linearities, the presence of backlash in the transmission significantly reduces the performance of the servo system. In order to ensure the normal operation of the gear transmission system, a certain gap is reserved on the premise of gear meshing, the larger the size of the gear is, the larger the corresponding gap is, and the transmission system is generally in multi-stage transmission, and the existence of the gap can make the mechanical resonance more severe and even make the control system divergent. When a part is processed by a full-digital numerical control machine tool, the processed surface is rough due to oscillation of gear transmission, and the estimated economic loss is caused; and in an industrial robot, when the mechanical arm is positioned, the tail end of the mechanical arm generates a buffeting phenomenon, so that stable stop and accurate stop cannot be realized, the adjusting time of the system is prolonged, the working efficiency is reduced, and some mechanical arms can even disperse the system to cause casualties. The sliding mode variable structure control is characterized in that the structure of the system is not fixed, and dynamic adjustment is performed according to the current state of the system, so that the system moves according to a preset sliding mode. In addition, the existence of the non-linearity of the backlash makes it difficult for the controller to accurately model unknown items of the system, and the defect directly influences the control performance of the dual-inertia servo system.
Disclosure of Invention
The invention aims to provide a self-adaptive backlash oscillation suppression method for a double-inertia servo system, which solves the problem of oscillation caused by backlash in the conventional double-inertia servo system.
The technical scheme adopted by the invention is that the self-adaptive backlash oscillation suppression method of the double-inertia servo system specifically comprises the following steps:
step 1, establishing a mathematical model of a permanent magnet synchronous motor under a d-q coordinate system to obtain an electromagnetic torque expression;
step 2, establishing a dynamic mathematical model of the double-inertia servo transmission system by taking the rotating speed and the position as state variables;
step 3, designing the sliding mode control rate of the sliding mode controller by adopting a sliding mode control method for the rotating speed ring based on the mathematical model of the double-inertia system dynamics obtained in the step 2 and the electromagnetic torque expression in the step 1;
step 4, establishing a micro-asymmetric dead zone model, and adopting a differential evolution algorithm to carry out parameter k on the micro-asymmetric dead zone modelr、kl、αr、αlAnd lambda is identified, and the identified parameters are unknown non-microminiature backlash shaft torque disturbance term parameters of the sliding mode control rate in the step 3.
The present invention is also characterized in that,
the specific process of the step 1 is as follows:
electromagnetic torque T under d-q coordinate systemeThe expression is shown in the following formula (1):
Te＝1.5np(ψdiq-ψqid)＝1.5np[ψfiq+(Ld-Lq)idiq] (1)；
wherein idIs the d-axis stator current component; i.e. iqIs the q-axis stator current component; l isdIs the d-axis stator inductance component; l isqA stator inductance component that is the q-axis; psifIs a rotor permanent magnet flux linkage; n ispThe number of pole pairs of the permanent magnet synchronous motor is; psidIs a d-axis flux linkage; psiqIs a q-axis flux linkage.
In the step 2, a dynamic mathematical model of the double-inertia servo transmission system is shown in the following formula (2):
Figure BDA0002857710230000031
wherein, JmIs the driving side inertia; b ismDrive side friction damping; j. the design is a squarelIs the driven side inertia; b islIs driven side friction damping; ksThe elastic coefficient of the transmission shaft; b issFriction damping is adopted; omegamA drive side rotational speed; omegalThe rotation speed of the driven side; thetamIs a driving side position; thetalIs at the driven side position;
Figure BDA0002857710230000032
is the drive side position differential;
Figure BDA0002857710230000033
is the driven side position differential; t iss[θ]Is the shaft torque; t islIs the load torque.
The sliding mode control rate in step 3 is shown in the following formula (3):
Figure BDA0002857710230000034
wherein the content of the first and second substances,
Figure BDA0002857710230000035
s is a slip form surface; c is a constant greater than 0; epsilon is the sliding mode gain; k is a constant greater than 0;
Figure BDA0002857710230000036
giving a differential for the rotation speed;
Figure BDA0002857710230000037
setting for q-axis current;
Figure BDA0002857710230000038
feedback for the driving side rotating speed; sign () is a function of the sign,
Figure BDA0002857710230000039
is the differential of the shaft torque.
The specific process of the step 4 is as follows:
step 4.1, establishing an asymmetric differentiable dead zone model shown in the following formula (4):
Figure BDA00028577102300000310
wherein θ is θm-θl(ii) a λ is a softness coefficient greater than 0; k is a radical ofrIs the slope of the dead zone of the positive half shaft; k is a radical oflIs the negative half-axis dead-zone slope; alpha is alpharIs a positive half shaft dead zone angle; alpha is alphalIs a negative half-shaft dead zone angle;
step 4.2, adopting a differential evolution algorithm to carry out the asymmetric microminiature area model parameter kr、kl、αr、αlAnd identifying the lambda parameter, specifically:
firstly, establishing a population and initializing the population, assuming NP is the size of the population scale, selecting n-dimensional vector parameters x as the number of variables to be identifiedij，i＝1,2,…,NP；j＝1,2,…,n，Xi＝[xi1,xi2,…,xin]To obtain xi,jThe expression of (a) is as follows:
xi,j＝xi,jmin+rand(0,1)*(xi,jmax-xi,jmin) (5)；
wherein x isi,jmaxAnd xi,jminRespectively an upper limit value and a lower limit value of the individual vector; xiRepresents the ith "chromosome" or individual of the 0 th generation in the population; x is the number ofi,jThe ith "chromosome" representing the 0 th generation in the population or the jth "gene" of the individual; rand (0,1) represents random numbers uniformly distributed in the (0,1) interval;
4.3, generating a difference vector, and carrying out mutation operation to obtain a variant individual
Figure BDA0002857710230000041
As shown in the following equation (6):
Figure BDA0002857710230000042
wherein r1, r2, r3 are E {1,2, …, NP }, and r1, r2, r3 and i cannot be the same; f is a variation factor, and F belongs to [0,1 ]]；
Figure BDA0002857710230000043
A j-th "genetic" variant individual representing the i-th "chromosome" of the k + 1-th generation of the variant individual;
Figure BDA0002857710230000044
a j-th "gene" individual representing the r1 th "chromosome" in the k-th generation of individuals;
Figure BDA0002857710230000045
a j-th "gene" individual representing the r2 th "chromosome" in the k-th generation of individuals;
Figure BDA0002857710230000046
a j-th "gene" individual representing the r3 th "chromosome" in the k-th generation of individuals;
step 4.4, performing cross operation to obtain a test vector
Figure BDA0002857710230000047
The specific expression of the crossover operation is as follows:
Figure BDA0002857710230000048
wherein eta is an arbitrary number greater than 0 and less than 1; cRIs a cross factor, CRThe value range is [0,1 ]]；qjE {1,2 …, n }, as a random integer；
Figure BDA0002857710230000051
A j-th "gene" test individual representing the i-th "chromosome" of the k + 1-th generation of the test individual;
in step 4.5, a selection operation is performed to generate k +1 generation individuals
Figure BDA0002857710230000052
As shown in the following equation (8):
Figure BDA0002857710230000053
where f is the objective function as follows:
Figure BDA0002857710230000054
wherein e is1(t) is the position error at time t; t isposi_r-indexIs a position rise time index; t isspeed_r-indexIs a rotating speed rising time index; delta NindexIs a rotating speed error index; t isre-indexThe rotating speed recovery time index after loading; t isposi_rSystem position rise time; t isspeed_rThe system rotation speed rise time; delta N is the system rotation speed error; t isreThe system rotating speed recovery time after loading;
substituting the selected individual, namely the identified unknown parameter into the asymmetric microminiature area model to obtain the system corresponding position error e1(T), rotation error Δ N, position rise time Tposi_rSystem speed rise time Tspeed_rThe responses are brought into an objective function f, the objective function f is minimized after a plurality of iterations, the individual at the moment is the optimal individual, and the identified parameter kr、kl、αr、αlAnd lambda is the unknown non-microminiature backlash shaft torque disturbance term parameter of the sliding mode control rate in the step 3.
The self-adaptive backlash oscillation suppression method for the double-inertia servo system has the beneficial effects that the self-adaptive backlash oscillation suppression method for the double-inertia servo system solves the problems of mechanical oscillation and impact oscillation caused by backlash; even when the backlash changes, the backlash model can be accurately identified, and shaft torque disturbance generated by the backlash is compensated in the controller in time, so that backlash oscillation is eliminated, and the stability, robustness and positioning accuracy of the system are improved.
Drawings
FIG. 1 is a block flow diagram of an adaptive backlash oscillation suppression method for a dual-inertia servo system according to the present invention;
FIG. 2 is a block flow diagram of an adaptive backlash oscillation suppression method for a dual-inertia servo system according to the present invention;
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a self-adaptive backlash oscillation suppression method for a double-inertia servo system, and as shown in figure 1, a double-inertia servo control system with backlash comprises three-loop control of a position loop, a speed loop and a current loop. Phase current ia、ib、icObtaining a stator current component i under a two-phase static coordinate system through Clarke transformation after being measured by a current sensorα、iβThen obtaining a stator current component i under a two-phase rotating coordinate system through Park conversiond、iq. Position pulse given by theta*Given by the upper computer, θ*Position theta obtained from the driven encoder sidelThe difference is input to a position regulator, the output of which is used as the speed setting
Figure BDA0002857710230000062
Drive side rotor speed ωmMeasured by incremental encoders, omegamWith speed given
Figure BDA0002857710230000063
The difference is input into a sliding mode controller, and the output of the sliding mode controller is used as a quadrature axis current instruction value iq *Direct axis current command value id *＝0，id、iqAre respectively connected with id *And iq *After making difference, output u of current regulatord、uqThen outputting u through Park inverse transformationα、uβFinally, six paths of PWM signals are output through the space vector pulse width modulation module to be supplied to an inverter to work, and the inverter enables the DC bus voltage UdcThe PWM wave is applied to the permanent magnet synchronous motor to realize the positioning of the driven side.
The method specifically comprises the following steps:
step 1, establishing a mathematical model of a permanent magnet synchronous motor under a d-q coordinate system to obtain an electromagnetic torque expression; the specific process of the step 1 is as follows:
in a d-q coordinate system, a mathematical model of the permanent magnet synchronous motor is as follows:
Figure BDA0002857710230000061
wherein u isd、uqD-axis component of the stator voltage and q-axis component of the stator voltage respectively; psid、ψqRespectively a d-axis component of the stator flux linkage and a q-axis component of the stator flux linkage; i.e. idIs a d-axis stator current component, iqIs the q-axis stator current component; rsIs a stator resistor; thetamIs the drive side position.
The flux linkage equation is:
Figure BDA0002857710230000071
the input power P of the permanent magnet synchronous motor is as follows:
Figure BDA0002857710230000072
the electromagnetic torque obtained by bringing the formula (1) and the formula (2) into the formula (3) does work as follows:
Figure BDA0002857710230000073
and (4) bringing the formula (2) into the formula (4), wherein the electromagnetic torque expression is as follows:
Te＝1.5np[ψfiq+(Ld-Lq)idiq] (5)；
wherein idIs the d-axis stator current component; i.e. iqIs the q-axis stator current component; l isdIs the d-axis stator inductance component; l isqA stator inductance component of q; ΨfIs a rotor permanent magnet flux linkage; n ispThe number of pole pairs of the permanent magnet synchronous motor is.
Step 2, establishing a dynamic mathematical model of the double-inertia servo transmission system by taking the rotating speed and the position as state variables;
the mathematical model of the dynamics of the double-inertia servo transmission system in the step 2 is shown in the following formula (6):
Figure BDA0002857710230000074
wherein, JmIs the driving side inertia; b ismDrive side friction damping; j. the design is a squarelIs the driven side inertia; b islIs driven side friction damping; ksThe elastic coefficient of the transmission shaft; b issFriction damping is adopted; omegamA drive side rotational speed; omegalThe rotation speed of the driven side; thetamIs a driving side position; thetalIs at the driven side position;
Figure BDA0002857710230000081
is the drive side position differential;
Figure BDA0002857710230000082
is the driven side position differential; t iss[θ]Is the shaft torque; t islIs the load torque.
Step 3, designing the sliding mode control rate of the sliding mode controller by adopting a sliding mode control method for the rotating speed ring based on the mathematical model of the double-inertia system dynamics obtained in the step 2 and the electromagnetic torque expression in the step 1;
establishing a slip form surface s is:
Figure BDA0002857710230000083
wherein the content of the first and second substances,
Figure BDA0002857710230000084
Figure BDA0002857710230000085
setting the rotating speed of the driving side; c is a constant greater than 0.
The sliding mode controller adopts an exponential approximation rule as follows:
Figure BDA0002857710230000086
wherein epsilon is the sliding mode gain; k is a constant greater than 0; sign () is a sign function.
Neglecting the friction coefficient, the sliding mode controller output expression obtained by taking equation (7) into equation (8) to derive the combined equation (6) is as follows:
Figure BDA0002857710230000087
wherein the content of the first and second substances,
Figure BDA0002857710230000088
s is a slip form surface; c is a constant greater than 0; epsilon is the sliding mode gain; k is a constant greater than 0;
Figure BDA0002857710230000089
giving a differential for the rotation speed;
Figure BDA00028577102300000810
setting for q-axis current;
Figure BDA00028577102300000811
feedback for the driving side rotating speed; sign () is a function of the sign,
Figure BDA00028577102300000812
is the differential of the shaft torque.
And 4, establishing an equivalent microminiature asymmetric dead zone model for the unknown non-microminiature backlash shaft torque disturbance term of the sliding mode control rate in the step 3, and accurately compensating unknown disturbance generated by backlash in a controller. Since the dead zone parameters of the system are unknown parts, model parameters need to be optimized. According to the obtained equivalent micro-asymmetric dead zone model, a differential evolution algorithm is adopted to carry out on the parameter k of the equivalent micro-asymmetric dead zone modelr、kl、αr、αlAnd lambda is identified, and the equivalent asymmetric microminiature area model parameters are repeatedly optimized through a differential evolution algorithm according to the real-time response of the servo system, so that the objective function value is smaller and smaller until the static and dynamic performance of the system meets the set index. After finite algebra is optimized, the system finally reaches the index requirement, and k at the momentr、kl、αr、αlλ is the most suitable equivalent asymmetric differentiable zone model parameter, and the process is shown in fig. 2.
In step 4.1, aiming at the unknown ultramicro backlash shaft torque disturbance term of the sliding mode control rate in step 3, the invention provides an asymmetric microminiature area model, and because the parameter of the asymmetric microminiature area model is unknown, the invention adopts a differential evolution algorithm to carry out differential evolution on the parameter k of the proposed asymmetric microminiature area modelr、kl、αr、αlAnd lambda is identified, and the asymmetric differentiable dead zone model has the following formula:
Figure BDA0002857710230000092
wherein θ is θm-θl(ii) a Lambda is the softness coefficient more than 0; k is a radical ofrIs the slope of the dead zone of the positive half shaft; k is a radical oflIs the negative half-axis dead-zone slope; alpha is alpharIs a positive half shaft dead zone angle; alpha is alphalIs a negative half-axis dead-zone angle.
In step 4.2, the differential evolution algorithm is adopted to carry out asymmetric micro-deathRegion model parameter kr、kl、αr、αlFirstly establishing a population and initializing the population, supposing NP is the size of the population scale, selecting n-dimensional vector parameter x as the number of variables to be identifiedij(i＝1,2,…,NP；j＝1,2,…,n)，Xi＝[xi1,xi2,…,xin]Then x can be calculatedi,jThe expression of (a) is as follows:
xi,j＝xi,jmin+rand(0,1)*(xi,jmax-xi,jmin) (11)；
wherein x isi,jmaxAnd xi,jminRespectively an upper limit value and a lower limit value of the individual vector; xiThe ith "chromosome" (or individual) representing the 0 th generation in the population; x is the number ofi,jThe jth "gene" representing the ith "chromosome" (or individual) of the 0 th generation in the population; rand (0,1) represents random numbers uniformly distributed in the (0,1) interval.
In step 4.3, generating difference vector, performing mutation operation to obtain variant individual
Figure BDA0002857710230000093
As follows:
Figure BDA0002857710230000091
wherein r1, r2, r3 belongs to {1,2, …, NP }, and can not be the same as i; f is a variation factor, and F belongs to [0,1 ]]；
Figure BDA0002857710230000104
A j-th "genetic" variant individual representing the i-th "chromosome" of the k + 1-th generation of the variant individual;
Figure BDA0002857710230000105
a j-th "gene" individual representing the r1 th "chromosome" in the k-th generation of individuals;
Figure BDA0002857710230000106
in representation of an individualThe j th "gene" individual of the r2 th "chromosome" of the k generation;
Figure BDA0002857710230000107
represents the j 'gene' individual of r3 th chromosome of the k generation of individuals.
In step 4.4, cross operation is performed to obtain test vectors
Figure BDA0002857710230000108
The specific expression of the crossover operation is as follows:
Figure BDA0002857710230000101
wherein eta isjIs any number greater than 0 and less than 1; cRIs a cross factor and has a value range of [0,1 ]]；qjE {1,2 …, n };
Figure BDA0002857710230000109
the j-th "gene" test individual representing the i-th "chromosome" of the k + 1-th generation in the test individual.
In step 4.5, a selection operation is performed to generate k +1 generation individuals
Figure BDA00028577102300001010
As follows:
Figure BDA0002857710230000102
where f is the objective function as follows:
Figure BDA0002857710230000103
wherein e is1(t) is the position error at time t; t isposi_r-indexIs a position rise time index; t isspeed_r-indexIs a rotating speed rising time index; delta NindexIs error in rotation speedA difference index; t isre-indexThe rotating speed recovery time index after loading; t isposi_rSystem position rise time; t isspeed_rThe system rotation speed rise time; delta N is the system rotation speed error; t isreThe system rotating speed recovery time after loading.
Substituting the selected individual, namely the identified unknown parameter into the asymmetric microminiature area model to obtain the system corresponding position error e1(T), rotation error Δ N, position rise time Tposi_rSystem speed rise time Tspeed_rWhen the responses are brought into the objective function f, the objective function f is minimized after multiple iterations, the closer the model at the moment is to the system model, the more the individual is the most individual, namely kr、kl、αr、αlLambda optimum parameter.

Claims (5)

1. A self-adaptive backlash oscillation suppression method of a dual-inertia servo system is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1, establishing a mathematical model of a permanent magnet synchronous motor under a d-q coordinate system to obtain an electromagnetic torque expression;
step 2, establishing a dynamic mathematical model of the double-inertia servo transmission system by taking the rotating speed and the position as state variables;
step 3, designing the sliding mode control rate of the sliding mode controller by adopting a sliding mode control method for the rotating speed ring based on the mathematical model of the double-inertia system dynamics obtained in the step 2 and the electromagnetic torque expression in the step 1;
step 4, establishing a micro-asymmetric dead zone model, and adopting a differential evolution algorithm to carry out parameter k on the micro-asymmetric dead zone modelr、kl、αr、αlAnd lambda is identified, and the identified parameters are unknown non-microminiature backlash shaft torque disturbance term parameters of the sliding mode control rate in the step 3.
2. The adaptive backlash oscillation suppression method for a dual inertia servo system according to claim 1, wherein: the specific process of the step 1 is as follows:
in d-q coordinatesSystem of electromagnetic torque TeThe expression is shown in the following formula (1):
Te＝1.5np(ψdiq-ψqid)＝1.5np[ψfiq+(Ld-Lq)idiq] (1)；
wherein idIs the d-axis stator current component; i.e. iqIs the q-axis stator current component; l isdIs the d-axis stator inductance component; l isqA stator inductance component that is the q-axis; psifIs a rotor permanent magnet flux linkage; n ispThe number of pole pairs of the permanent magnet synchronous motor is; psidIs a d-axis flux linkage; psiqIs a q-axis flux linkage.
3. The adaptive backlash oscillation suppression method for a dual inertia servo system according to claim 2, wherein: the mathematical model of the dynamics of the double-inertia servo transmission system in the step 2 is shown in the following formula (2):
Figure FDA0002857710220000021
wherein, JmIs the driving side inertia; b ismDrive side friction damping; j. the design is a squarelIs the driven side inertia; b islIs driven side friction damping; ksThe elastic coefficient of the transmission shaft; b issFriction damping is adopted; omegamA drive side rotational speed; omegalThe rotation speed of the driven side; thetamIs a driving side position; thetalIs at the driven side position;
Figure FDA0002857710220000029
is the drive side position differential;
Figure FDA00028577102200000210
is the driven side position differential; t iss[θ]Is the shaft torque; t islIs the load torque.
4. The adaptive backlash oscillation suppression method for a dual inertia servo system according to claim 3, wherein: the sliding mode control rate in the step 3 is shown in the following formula (3):
Figure FDA0002857710220000022
wherein the content of the first and second substances,
Figure FDA0002857710220000023
s is a slip form surface; c is a constant greater than 0; epsilon is the sliding mode gain; k is a constant greater than 0;
Figure FDA0002857710220000024
giving a differential for the rotation speed;
Figure FDA0002857710220000025
setting for q-axis current;
Figure FDA0002857710220000026
feedback for the driving side rotating speed; sign () is a function of the sign,
Figure FDA0002857710220000027
is the differential of the shaft torque.
5. The adaptive backlash oscillation suppression method for a dual inertia servo system according to claim 4, wherein: the specific process of the step 4 is as follows:
step 4.1, establishing an asymmetric differentiable dead zone model shown in the following formula (4):
Figure FDA0002857710220000028
wherein θ is θm-θl(ii) a λ is a softness coefficient greater than 0; k is a radical ofrIs the slope of the dead zone of the positive half shaft；klIs the negative half-axis dead-zone slope; alpha is alpharIs a positive half shaft dead zone angle; alpha is alphalIs a negative half-shaft dead zone angle;
step 4.2, adopting a differential evolution algorithm to carry out the asymmetric microminiature area model parameter kr、kl、αr、αlAnd identifying the lambda parameter, specifically:
firstly, establishing a population and initializing the population, assuming NP is the size of the population scale, selecting n-dimensional vector parameters x as the number of variables to be identifiedij，i＝1,2,…,NP；j＝1,2,…,n，Xi＝[xi1,xi2,…,xin]To obtain xi,jThe expression of (a) is as follows:
xi,j＝xi,jmin+rand(0,1)*(xi,jmax-xi,jmin) (5)；
wherein x isi,jmaxAnd xi,jminRespectively an upper limit value and a lower limit value of the individual vector; xiRepresents the ith "chromosome" or individual of the 0 th generation in the population; x is the number ofi,jThe ith "chromosome" representing the 0 th generation in the population or the jth "gene" of the individual; rand (0,1) represents random numbers uniformly distributed in the (0,1) interval;
4.3, generating a difference vector, and carrying out mutation operation to obtain a variant individual
Figure FDA0002857710220000031
As shown in the following equation (6):
Figure FDA0002857710220000032
wherein r1, r2, r3 are E {1,2, …, NP }, and r1, r2, r3 and i cannot be the same; f is a variation factor, and F belongs to [0,1 ]]；
Figure FDA0002857710220000033
A j-th "genetic" variant individual representing the i-th "chromosome" of the k + 1-th generation of the variant individual;
Figure FDA0002857710220000034
a j-th "gene" individual representing the r1 th "chromosome" in the k-th generation of individuals;
Figure FDA0002857710220000035
a j-th "gene" individual representing the r2 th "chromosome" in the k-th generation of individuals;
Figure FDA0002857710220000036
a j-th "gene" individual representing the r3 th "chromosome" in the k-th generation of individuals;
step 4.4, performing cross operation to obtain a test vector
Figure FDA0002857710220000037
The specific expression of the crossover operation is as follows:
Figure FDA0002857710220000038
wherein eta isjIs any number greater than 0 and less than 1; cRIs a cross factor, CRThe value range is [0,1 ]]；qjE {1,2 …, n };
Figure FDA0002857710220000039
a j-th "gene" test individual representing the i-th "chromosome" of the k + 1-th generation of the test individual;
in step 4.5, a selection operation is performed to generate k +1 generation individuals
Figure FDA0002857710220000041
As shown in the following equation (8):
Figure FDA0002857710220000042
where f is the objective function as follows:
Figure FDA0002857710220000043
wherein e is1(t) is the position error at time t; t isposi_r-indexIs a position rise time index; t isspeed_r-indexIs a rotating speed rising time index; delta NindexIs a rotating speed error index; t isre-indexThe rotating speed recovery time index after loading; t isposi_rSystem position rise time; t isspeed_rThe system rotation speed rise time; delta N is the system rotation speed error; t isreThe system rotating speed recovery time after loading;
substituting the selected individual, namely the identified unknown parameter into the asymmetric microminiature area model to obtain the system corresponding position error e1(T), rotation error Δ N, position rise time Tposi_rSystem speed rise time Tspeed_rThe responses are brought into an objective function f, the objective function f is minimized after a plurality of iterations, the individual at the moment is the optimal individual, and the identified parameter kr、kl、αr、αlAnd lambda is the unknown non-microminiature backlash shaft torque disturbance term parameter of the sliding mode control rate in the step 3.
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