阅读说明：本技术 基于惯量辨识的多电机伺服系统自抗扰滑模速度控制方法 (More motor servo system active disturbance rejection sliding mode speed control methods based on inertia identification ) 是由 吴益飞 刘洋 郭健 陈庆伟 李胜 关妍 张宇 吴鑫煜 吴红婷 季周历 高珺宁 于 2019-08-01 设计创作，主要内容包括：本发明公开了一种基于惯量辨识的多电机伺服系统自抗扰滑模速度控制方法,方法包括：构建多电机伺服系统的动力学方程；利用模型参考自适应法对多电机伺服系统输入的负载惯量进行辨识；根据一阶跟踪微分器、二阶扩张状态观测器以及多电机伺服系统速度环中的扰动构建一阶自抗扰模型,并获取非线性状态误差反馈控制律；基于双曲正切柔化切换函数改进趋近律,构造带积分的滑模控制对非线性状态误差反馈控制律进行补偿优化,获得最终的控制律,进而实现多电机伺服系统自抗扰滑模速度控制。本发明相对于分区PID控制和积分滑模控制,在变惯量情况下,复合控制策略对惯量变化情况具有更好的适应性,能取得更好的控制效果,控制系统的鲁棒性强。(More motor servo system active disturbance rejection sliding mode speed control methods based on inertia identification that the invention discloses a kind of, method includes: the kinetics equation for constructing more motor servo systems；It is recognized using the load inertia that model reference adaptive method inputs more motor servo systems；Single order active disturbance rejection model is constructed according to the disturbance in first-order tracking differentiator, Second Order Eso and more motor servo system speed rings, and obtains nonlinear state error Feedback Control Laws；Based on tanh softening switching function improved reaching law, the sliding formwork control of structural belt integral compensates optimization to nonlinear state error Feedback Control Laws, obtains final control law, and then realize more motor servo system active disturbance rejection sliding mode speed controls.The present invention is relative to subregion PID control and integral sliding mode control, and in Variable inertia, Compound Control Strategy has better adaptability to inertia situation of change, can obtain better control effect, the strong robustness of control system.)

1. a kind of more motor servo system active disturbance rejection sliding mode speed control methods based on inertia identification, which is characterized in that including Following steps:

The kinetics equation of step 1, the more motor servo systems of building；

Step 2 is recognized using the load inertia that model reference adaptive method inputs more motor servo systems；

Step 3, be directed to the more motor servo systems of Variable inertia, according to first-order tracking differentiator, Second Order Eso and Disturbance in more motor servo system speed rings constructs single order active disturbance rejection model, and obtains the non-thread character of single order active disturbance rejection model State error Feedback Control Laws；

Step 4 is based on tanh softening switching function improved reaching law, and the sliding formwork control of structural belt integral is to single order active disturbance rejection The nonlinear state error Feedback Control Laws of model compensate optimization, obtain final control law, and then realize that more motors are watched Dress system active disturbance rejection sliding mode speed control.

2. more motor servo system active disturbance rejection sliding mode speed control methods according to claim 1 based on inertia identification, It is characterized in that, the kinetics equation of the more motor servo systems of building described in step 1:

In formula, J_i=J_mi+J_ci/K_R ², b_i=b_mi+b_ci/K_R ², C_ei=n_piΨ_fi, θ_iFor the mechanical angular displacement of motor, ω_iFor motor Angular speed, θ_LFor the angular displacement of load, ω_LFor the angular speed of load, J_miFor the rotary inertia of motor, J_ciFor pinion gear etc. Imitate rotary inertia, K_RFor the reduction ratio of planetary reduction gear, C_TiFor motor torque coefficient, i_qiFor vector controlled component q shaft current, b_miIndicate the equivalent viscous coefficient of friction of each motor, b_ciIndicate equivalent viscosity friction coefficient, K_LTo engage coefficient of elasticity, K_GFor the reduction ratio of gear and bull gear, Δ_2iFor non-linear factor and some other modeling indeterminate, J_LFor gear ring namely bear The equivalent moment of inertia of load, b_LFor the equivalent viscous coefficient of friction of gear ring,For the angular speed of load, Δ₁To load gear side Indeterminate, R_siFor stator winding phase resistance, L_qiFor the stator inductance of q axis, n_piFor number of pole-pairs, Ψ_fiFor motor permanent magnet magnetic Chain, U_qiFor motor q axis equivalent voltage.

3. more motor servo system active disturbance rejection sliding mode speed control methods according to claim 1 based on inertia identification, It is characterized in that, being distinguished described in step 2 using the load inertia that model reference adaptive method inputs more motor servo systems Know, specifically:

Step 2-1, load inertia is converted to motor shaft:

In formula, n is real electrical machinery number, J_i、J_LThe respectively inertia of motor and load, K_LTo engage coefficient of elasticity, K_GFor gear With the reduction ratio of bull gear, by conversion to the load inertia J on motor shaft_i' identification obtain J_LVariation；

Step 2-2, according to the kinetics equation of more motor servo systems, ignore friction and nonlinear disturbance, obtain inertia and angle Rate pattern are as follows:

In formula, T_eFor electromagnetic torque, T_LFor load torque；

Step 2-3, by formula (3) discretization, sampling time T is set_s, it obtains:

In formula, ω_m(k) it is actual speed, replaces k to obtain with k-1:

One T_sInterior load torque remains unchanged, i.e. T_L(k-1)=T_L(k-2), above formula (4) (5) are arranged and two formulas are subtracted each other into acquisition Final discrete equation are as follows:

Step 2-4, model reference adaptive method includes reference model and adjustable model, for shown in above-mentioned formula (6) from Equation is dissipated, is enabledΔT_e(k-1)=T_e(k-1)-T_e(k-2), then it is such as public that reference model such as formula (7), adjustable model are obtained Formula (8):

ω_m(k)=2 ω_m(k-1)-ω_m(k-2)+γΔT_e(k-1) (7)

In formula,To estimate revolving speed, the error with actual speed is

Equation is recognized according to the iteration that error e (k) and Popov hyperstability theory obtain model reference adaptive method:

In formula, β is gain factor,To recognize target, change the identification effect that the algorithm is adjusted to have obtained in gain factor；

According toAnd among the aboveThe identification to load inertia can be completed.

4. more motor servo system active disturbance rejection sliding mode speed control methods according to claim 1 based on inertia identification, It is characterized in that, the more motor servo systems of Variable inertia are directed to described in step 3, according to first-order tracking differentiator, second order expansion state Disturbance in observer and multi- drive synchronization servo-system speed ring constructs single order active disturbance rejection model, and obtains single order active disturbance rejection The nonlinear state error Feedback Control Laws of model, specifically:

Step 3-1, according in first-order tracking differentiator, Second Order Eso and more motor servo system speed rings Disturbance building single order active disturbance rejection model are as follows:

In formula, y is the actual value of motor speed, z₁For export revolving speed pursuit gain,For the acceleration for exporting revolving speed, z₂For speed The estimated value of the comprehensive disturbance of ring is spent,For the acceleration of comprehensive disturbance estimated value, b₁For compensation factor, β₁,β₂For gain factor, u For control amount, γ₁,γ₂For noise coefficient, α₁,α₂For velocity error index, ω_virFor the speed of virtual spindle motor,For The equivalent moment of inertia estimated value of virtual main shaft, b_virIndicate damped coefficient；

Wherein, the formula of the first-order tracking differentiator are as follows:

In formula,

In formula, v is speed preset value,For transition signal, z₁For the pursuit gain for exporting revolving speed, z₁- v is speed error value, adjustable Parameter r is directly proportional to tracking velocity, and fal is nonlinear function, and α is velocity error index, and γ is noise coefficient, and sgn is symbol Function；

The Second Order Eso formula are as follows:

Disturbance in more motor servo system speed rings are as follows:

In formula, J_virFor the equivalent moment of inertia of virtual main shaft, T_LvirTo convert the load torque for arriving motor shaft end；

Step 3-2, formula (10) are based on, enabledIt obtains:

For formula (15), enable:

The nonlinear state error Feedback Control Laws of single order active disturbance rejection model are obtained according to formula (15), formula (16) are as follows:

5. more motor servo system active disturbance rejections sliding mode speed control side according to claim 1 or 4 based on inertia identification Method, which is characterized in that tanh softening switching function improved reaching law, the sliding formwork control of structural belt integral are based on described in step 4 System compensates optimization to the nonlinear state error Feedback Control Laws of single order active disturbance rejection model, obtains final control law, into And realize more motor servo system active disturbance rejection sliding mode speed controls, specifically:

Step 4-1, according to description close to the most common exponent approximation Reaching Law of motion process and tanh softening switching function, Obtain improved exponentially approaching rule are as follows:

In formula, S is sliding-mode surface, and ε is gain coefficient, and tanh (S) is tanh softening switching function, | x |^λFor state variable Power item ,-kS are exponential approach item；

It is wherein, described to describe close to the most common exponent approximation Reaching Law of motion process are as follows:

In formula, sgn is sign function；

Step 4-2, the sliding formwork control of structural belt integral:

Construct sliding-mode surface:

S=e₁=v₁-z₁ (20)

It takesTake differential that can obtain sliding-mode surface:

According to the Reaching Law of formula (21) and step 4-1Obtain sliding formwork control are as follows:

u₀=-ε tanh (e₁)|e₁|^λ-ke₁ (22)

Step 4-3, optimization is compensated using nonlinear state error Feedback Control Laws of the formula (22) to single order active disturbance rejection model, Obtain final control law are as follows:

Technical field

The invention belongs to more motor servo system fields, especially a kind of more motor servo systems based on inertia identification are certainly Anti-interference sliding mode speed control method.

Background technique

In order to quickly trace into the air mobile target to emerge one after another, the servo-system driving power of weapon is greatly increased. It, need to be using the joint driving load of multiple motors for the problem of single motor driving power deficiency.It is loaded and is solved using multi-motor driving Certainly driving power can be improved in scheme, increases system redundancy and improves operational reliability.

In practical applications, the presence of the interference of the difference, system of the parameter of electric machine, mechanical bearing and gear clearance factor is led The mission nonlinear of cause can make the net synchronization capability of system be deteriorated, this will affect the reliability and accuracy of system.It is mostly electric realizing On the basis of machine synchronous operation, variation for the violent of load inertia and in short-term, servo-system needs more intelligent control reason By keeping control system more stable and steady.

In order to eliminate influence of the load inertia to the dynamic property of servo-system, stable state accuracy, system robustness, both at home and abroad Scholar has been some researchs, document " Adaptive synchronization of networked multi-agent Systems considering transient responses and disturbances " is calculated using adaptive tracing Method, tracks the state of load inertia, but on-line identification and the overlong time for correcting load inertia；Paper " Sliding- mode control-based adaptive PID control with compensation controller for Motion synchronization of dual servo system " devises a kind of self-adaptive PID based on sliding formwork control Control method derives the adjustment law of PID controller gain parameter based on gradient descent method according to the presence of sliding-mode surface, but It is the presence due to buffeting, so that sliding formwork control quality decline.These methods all have some limitations, and individually with control Product matter is not high, and servo-system needs more intelligent control theory, keeps control system more stable and steady.For nonlinear system The control problem of system, Sliding mode variable structure control are one of good solutions.But due to the presence and mathematical modulo of buffeting The reason of type is approximate model leads to sliding formwork control quality decline.

Summary of the invention

It is certainly anti-that the purpose of the present invention is to provide a kind of more motor servo systems with better conforming to property and control effect Disturb sliding mode speed control method.

The technical solution for realizing the aim of the invention is as follows: a kind of more motor servo system active disturbance rejections based on inertia identification Sliding mode speed control method, comprising the following steps:

The kinetics equation of step 1, the more motor servo systems of building；

Step 2 is recognized using the load inertia that model reference adaptive method inputs more motor servo systems；

Step 3 is directed to the more motor servo systems of Variable inertia, according to first-order tracking differentiator, Second Order Eso And the disturbance in more motor servo system speed rings constructs single order active disturbance rejection model, and obtains the non-thread of single order active disturbance rejection model Property state error Feedback Control Laws；

Step 4, be based on tanh softening switching function improved reaching law, structural belt integral sliding formwork control to single order from The nonlinear state error Feedback Control Laws of anti-interference model compensate optimization, obtain final control law, and then realize mostly electric Machine servo system active disturbance rejection sliding mode speed control.

Compared with prior art, the present invention its remarkable advantage are as follows: 1) independent of the accurate mathematical model of controll plant, Different load inertias can accurately be picked out；2) it can effectively weaken chattering phenomenon caused by sliding formwork control and reduce stable state Error；3) in Variable inertia, system response time can be made not slack-off, and keeps preferable tracking accuracy；It 4) will be certainly anti- It the technologies such as disturbs, is adaptive and combining the high performance Control platform of acquisition with sliding mode technology, it can also under uncertain perturbation action To guarantee to control precision, relative to subregion PID control and integral sliding mode control, in Variable inertia, Compound Control Strategy pair Inertia situation of change has better adaptability, can obtain better control effect, the strong robustness of control system.

Present invention is further described in detail with reference to the accompanying drawing.

Detailed description of the invention

Fig. 1 is more motor servo system structural block diagrams.

Fig. 2 is more motor servo system sliding mode speed control block diagrams.

Fig. 3 is that the present invention is based on more motor servo system speed control block diagrams of Compound Control Strategy.

Specific embodiment

The present invention is based on more motor servo system active disturbance rejection sliding mode speed control methods of inertia identification, including following step It is rapid:

The kinetics equation of step 1, the more motor servo systems of building；

Step 2 is recognized using the load inertia that model reference adaptive method inputs more motor servo systems；

Step 3 is directed to the more motor servo systems of Variable inertia, according to first-order tracking differentiator, Second Order Eso And the disturbance in more motor servo system speed rings constructs single order active disturbance rejection model, and obtains the non-thread of single order active disturbance rejection model Property state error Feedback Control Laws；

Step 4, be based on tanh softening switching function improved reaching law, structural belt integral sliding formwork control to single order from The nonlinear state error Feedback Control Laws of anti-interference model compensate optimization, obtain final control law, and then realize mostly electric Machine servo system active disturbance rejection sliding mode speed control.

Further, in conjunction with Fig. 1, step 1 constructs the kinetics equation of more motor servo systems:

In formula, J_i=J_mi+J_ci/K_R ², b_i=b_mi+b_ci/K_R ², C_ei=n_piΨ_fi, θ_iFor the mechanical angular displacement of motor, ω_iFor The angular speed of motor, θ_LFor the angular displacement of load, ω_LFor the angular speed of load, J_miFor the rotary inertia of motor, J_ciFor pinion gear Equivalent moment of inertia, K_RFor the reduction ratio of planetary reduction gear, C_TiFor motor torque coefficient, i_qiFor vector controlled component q axis electricity Stream, b_miIndicate the equivalent viscous coefficient of friction of each motor, b_ciIndicate equivalent viscosity friction coefficient, K_LFor engagement elasticity system Number, K_GFor the reduction ratio of gear and bull gear, Δ_2iFor non-linear factor and some other modeling indeterminate, J_LFor gear ring The equivalent moment of inertia loaded, b_LFor the equivalent viscous coefficient of friction of gear ring,For the angular speed of load, Δ₁To load tooth Take turns the indeterminate of side, R_siFor stator winding phase resistance, L_qiFor the stator inductance of q axis, n_piFor number of pole-pairs, Ψ_fiFor motor permanent magnetism Body magnetic linkage, U_qiFor motor q axis equivalent voltage.

Further, the load inertia more motor servo systems inputted using model reference adaptive method in step 2 into Row identification, specifically:

Step 2-1, load inertia is converted to motor shaft:

In formula, n is real electrical machinery number, J_i、J_LThe respectively inertia of motor and load, K_LTo engage coefficient of elasticity, K_GFor The reduction ratio of gear and bull gear, by conversion to the load inertia J on motor shaft_i' identification obtain J_LVariation；

Step 2-2, according to the kinetics equation of more motor servo systems, ignore friction and nonlinear disturbance, obtain inertia With angular speed model are as follows:

In formula, T_eFor electromagnetic torque, T_LFor load torque；

Step 2-3, by formula (3) discretization, sampling time T is set_s, it obtains:

In formula, ω_m(k) it is actual speed, replaces k to obtain with k-1:

One T_sInterior load torque remains unchanged, i.e. T_L(k-1)=T_L(k-2), above formula (4) (5) are arranged and subtract each other two formulas Obtain final discrete equation are as follows:

Step 2-4, model reference adaptive method includes reference model and adjustable model, for shown in above-mentioned formula (6) Discrete equation, enableThen obtain reference model such as formula (7), adjustable model Such as formula (8):

ω_m(k)=2 ω_m(k-1)-ω_m(k-2)+γΔT_e(k-1) (7)

In formula,To estimate revolving speed, the error with actual speed is

Equation is recognized according to the iteration that error e (k) and Popov hyperstability theory obtain model reference adaptive method:

In formula, β is gain factor,To recognize target, change gain factor is adjusted the algorithm and is distinguished with what is obtained Know effect；

According toAnd among the aboveThe identification to load inertia can be completed.

Further, in step 3 be directed to the more motor servo systems of Variable inertia as shown in Fig. 2, according to first-order tracking differentiator, Disturbance in Second Order Eso and multi- drive synchronization servo-system speed ring constructs single order active disturbance rejection model, and obtains The nonlinear state error Feedback Control Laws of single order active disturbance rejection model are taken, specifically:

Step 3-1, according to first-order tracking differentiator, Second Order Eso and more motor servo system speed rings In disturbance construct single order active disturbance rejection model are as follows:

In formula, y is the actual value of motor speed, z₁For export revolving speed pursuit gain,For the acceleration for exporting revolving speed, z₂ The estimated value of disturbance is integrated for speed ring,For the acceleration of comprehensive disturbance estimated value, b₁For compensation factor, β₁,β₂For gain because Son, u are control amount, γ₁,γ₂For noise coefficient, α₁,α₂For velocity error index, ω_virFor the speed of virtual spindle motor,For the equivalent moment of inertia estimated value of virtual main shaft, b_virIndicate damped coefficient；

Wherein, the formula of first-order tracking differentiator are as follows:

In formula,

In formula, v is speed preset value,For transition signal, z₁For the pursuit gain for exporting revolving speed, z₁- v is speed error value, Adjustable parameter r is directly proportional to tracking velocity, and fal is nonlinear function, and α is velocity error index, and γ is noise coefficient, and sgn is Sign function；

Second Order Eso formula are as follows:

Disturbance in more motor servo system speed rings are as follows:

In formula, J_virFor the equivalent moment of inertia of virtual main shaft, T_LvirTo convert the load torque for arriving motor shaft end；

Step 3-2, formula (10) are based on, enabledIt obtains:

For formula (15), enable:

The nonlinear state error Feedback Control Laws of single order active disturbance rejection model are obtained according to formula (15), formula (16) are as follows:

Further, tanh softening switching function improved reaching law, the sliding formwork control of structural belt integral are based in step 4 System compensates optimization to the nonlinear state error Feedback Control Laws of single order active disturbance rejection model, obtains final control law, into And realize more motor servo system active disturbance rejection sliding mode speed controls as shown in figure 3, specifically:

Step 4-1, switched according to description close to the most common exponent approximation Reaching Law of motion process and tanh softening Function obtains improved exponentially approaching rule are as follows:

In formula, S is sliding-mode surface, and ε is gain coefficient, and tanh (S) is tanh softening switching function, | x |^λFor state change The power item of amount ,-kS are exponential approach item；

Wherein, it describes close to the most common exponent approximation Reaching Law of motion process are as follows:

In formula, sgn is sign function；

Step 4-2, the sliding formwork control of structural belt integral:

Construct sliding-mode surface:

S=e₁=v₁-z₁ (20)

It takesTake differential that can obtain sliding-mode surface:

According to the Reaching Law of formula (21) and step 4-1Obtain sliding formwork control are as follows:

u₀=-ε tanh (e₁)|e₁|^λ-ke₁ (22)

Step 4-3, it is compensated using nonlinear state error Feedback Control Laws of the formula (22) to single order active disturbance rejection model Optimization, obtains final control law are as follows:

The present invention is based on more motor servo system active disturbance rejection sliding mode speed control methods of inertia identification, relative to subregion PID control and integral sliding mode control, in Variable inertia, Compound Control Strategy, which has inertia situation of change, preferably to be adapted to Property, better control effect, the strong robustness of control system can be obtained.