CN112701975B - 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 PDFInfo
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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 a sliding mode control rate of a sliding mode controller by the rotating speed ring by adopting a sliding mode control method 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
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 a gear transmission system, a certain clearance is reserved on the premise of gear meshing, the larger the size of a gear is, the larger the corresponding backlash is, and the transmission system is generally in multi-stage transmission, and the existence of the backlash can cause mechanical resonance to be more severe, and even cause the divergence of a control system. For example, when a full digital numerical control machine tool is used for processing parts, the processed surface is rough due to oscillation of gear transmission, and the economic loss which cannot be estimated 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 invention adopts the technical scheme that a self-adaptive backlash oscillation suppression method of a double-inertia servo system specifically comprises the following steps of:
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 is a radical of an alcoholqA 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):
wherein, JmIs the driving side inertia; b ismDrive side friction damping; j is a unit oflTo be driven fromDynamic side inertia; b islIs driven side friction damping; ksThe elastic coefficient of the transmission shaft; bsFriction damping is adopted; omegamA drive side rotational speed; omegalThe rotation speed of the driven side; thetamIs a driving side position; theta.theta.lIs at the driven side position;is the drive side position differential;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):
wherein,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;giving a differential for the rotation speed;setting for q-axis current;feedback for the driving side rotating speed; sign () is a function of the sign,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):
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 (alpha) ("alpha")lIs 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 individualAs shown in the following equation (6):
wherein r1, r2, r3 are epsilon {1,2, …, NP }, and r1, r2, r3 and i cannot be the same; f is a variation factor, and F belongs to [0,1 ]];A j-th "genetic" variant individual representing the i-th "chromosome" of the k + 1-th generation of the variant individual;a j-th "gene" individual representing the r1 th "chromosome" in the k-th generation of individuals;a j-th "gene" individual representing the r2 th "chromosome" in the k-th generation of individuals;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 vectorThe specific expression of the crossover operation is as follows:
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 };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 individualsAs shown in the following equation (8):
where f is the objective function as follows:
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 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 speed error Δ N, position rise time Tposi_rAnd the rising time T of the system rotation speedspeed_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.
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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 settingDrive side rotor speed ωmMeasured by incremental encoders, omegamWith speed givenThe 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:
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:
the input power P of the permanent magnet synchronous motor is as follows:
the electromagnetic torque obtained by bringing the formula (1) and the formula (2) into the formula (3) does work as follows:
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; ΨfA rotor permanent magnet flux linkage; n ispIs the pole pair number of the permanent magnet synchronous motor.
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):
wherein, JmIs the driving side inertia; b ismDriving 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 drive side position; thetalIs at the driven side position;is the drive side position differential;is the driven side position differential; t iss[θ]Is the shaft torque; t is a unit oflIs 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:
The sliding mode controller adopts an exponential approximation rule as follows:
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:
wherein,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;giving a differential for the rotation speed;setting for q-axis current;feedback for the driving side rotating speed; sign () is a function of the sign,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 system dead zone parameters 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, as the most suitable equivalent asymmetric differentiable zone model parameter, the process is as shown in fig. 2.
In step 4.1, aiming at the unknown non-microminiature backlash shaft torque disturbance item 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 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:
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 (alpha) ("alpha")lIs a negative half-axis dead-zone angle.
In step 4.2, a differential evolution algorithm is adopted to carry out on asymmetric differentiable dead zone model parameters 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,xi,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 individualAs follows:
wherein r1, r2, r3 belongs to {1,2, …, NP }, and the r1, r2, r3 do not belong to the same as i; f is a variation factor, and F belongs to [0,1 ]];A j-th "genetic" variant individual representing the i-th "chromosome" of the k + 1-th generation of the variant individual;a j 'gene' individual representing the r1 th "chromosome" in the k generation of individuals;a j-th "gene" individual representing the r2 th "chromosome" in the k-th generation of individuals;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 vectorsThe specific expression of the crossover operation is as follows:
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 };the j-th "gene" test individual representing the i-th "chromosome" of the k + 1-th generation in the test individual.
where f is the objective function as follows:
wherein e is1(t) is the position error at time t; t is a unit ofposi_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 is a unit ofposi_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 equal response is brought into an objective function f, and the objective function is obtained after multiple iterationsThe number f is minimized, and the closer the model is to the system model, the more the individual is the most individual, i.e. kr、kl、αr、αlAnd lambda is an 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:
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 ispTo a permanent magnetPole pair number of the magnetic synchronous motor; 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):
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;is the drive side position differential;is the driven side position differential; t iss[θ]Is the shaft torque; t islFor load torque, θ ═ θm-θl。
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):
wherein,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;giving a differential for the rotation speed;setting for q-axis current;driving side rotational speed differential; sign () is a function of the sign,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):
wherein θ ═ 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;
step 4.3, generating difference vector, performing mutation operation to obtain variant individualAs shown in the following equation (6):
wherein r1, r2, r3 are epsilon {1,2, …, NP }, and r1, r2, r3 and i cannot be the same; f is a variation factor, and F belongs to [0,1 ]];A j-th "genetic" variant individual representing the i-th "chromosome" of the k + 1-th generation of the variant individual;a j-th "gene" individual representing the r1 th "chromosome" in the k-th generation of individuals;a j-th "gene" individual representing the r2 th "chromosome" in the k-th generation of individuals;express anThe j th "gene" individual of r3 th "chromosome" in the kth generation of the body;
step 4.4, performing cross operation to obtain a test vectorThe specific expression of the crossover operation is as follows:
wherein etajIs any number greater than 0 and less than 1; cRIs a cross factor, CRThe value range is [0,1 ]];qjE {1,2 …, n };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 individualsAs shown in the following equation (8):
where f is the objective function as follows:
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_rIs the system positionA rise time; t isspeed_rThe system rotation speed rise time; delta N is the system rotation speed error; t is a unit ofreThe 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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