CN106208824A - Multi-motor synchronous control method based on active disturbance rejection iterative learning - Google Patents

Abstract

A multi-motor synchronous control method based on active disturbance rejection iterative learning comprises establishing a mathematical model of a multi-motor system, and initializing system states and control parameters; designing a multi-motor speed tracking controller based on an iterative learning method; an iterative extended state observer is designed by combining an active disturbance rejection control strategy, and unknown items in the system are effectively estimated and compensated through repeated iteration; an improved adjacent coupling strategy is provided for designing multi-motor synchronous control. The invention can effectively solve the problem of speed consistency of the multi-motor system, improve the rapid convergence performance and tracking precision of the system and enhance the robustness of the multi-motor system.

Description

A kind of multi-motor synchronous control method based on active disturbance rejection iterative learning

Technical field

The invention belongs to multi_motor control field, relate to a kind of deviation average coupled mode based on active disturbance rejection iterative learning many Electric system control method, especially for Synchronization Control and the tracing control of the multi-machine system containing indeterminate.

Background technology

In daily industrial production activities, single motor drives load the most customary, but, in some occasion, Single motor drives load to need to pay the highest Financial cost.Such as the load of large inertia, it would be desirable to individually designed It is driven by one high-power motor, and do so not only needs to pay high cost, does not also meet industry instantly and sets The trend that standby streamlined produces.In the industrial occasions that some are special, it is irreplaceable that multi-drive synchronization drives control still to play Effect, such as multi-pass straight drawing machine, shaftless printing press, in the middle of thin film winder.In the middle of these occasions, many department of electrical engineering System is devised to make a return journey and follows the tracks of the signal specified and keep identical speed to run.Net synchronization capability is that multi-machine system is evaluated One important indicator, it is highly susceptible to the impact such as Parameters variation and external disturbance of some indeterminates, synchronous error mistake In the case of great, not only can affect production efficiency, serious to result even in production line out of service.Therefore, one good with Track controller and isochronous controller design the realization tool for multi-machine system performance and are of great significance.

Between in the past few decades, different control methods has been had to be used in the middle of the tracing control of many motors.Such as Sliding mode theory, robust algorithm, adaptive algorithm, active disturbance rejection algorithm etc..Each of which has respective advantage, such as disturbance rejection Performance is good, and stability proves easily, effectively estimates estimating system nonlinear terms, etc., but they also have it to have problems, example Such as the buffeting problem of sliding formwork, the precision of robust control is the highest, and active disturbance rejection stability proves more difficulty, adaptive range of application Limited etc..The applicable object of iterative learning control is industrial machine mechanical arm or streamlined production line so has repeating motion character Industrial system, its target is to realize the at utmost tracking to reference signal in finite time interval.Iterative learning control Make and revise current controlled quentity controlled variable by last tracking error, thus improve the tracking accuracy of system operation next time.Iteration Study controls to be not required to the mathematical models of constructing system, and this point is similar with Active Disturbance Rejection Control, in order to improve repeatedly The error convergence speed of generation study, scholars combine the control algolithm of various advanced person, it is proposed that adaptive iteration learns, and BP is neural Network iterative learning, finite time iterative learning etc. complex control algorithm, effectively improve the control performance of iterative learning.But It is that adaptive iterative learning control requires that the unknown portions of system must is fulfilled for linear parameterization condition, so makes iteration Practise the scope of application controlled to be substantially reduced.Active disturbance rejection is by Nonlinear Tracking Differentiator, extended state observer, nonlinear Feedback Control rule three Part composition, wherein, the effect of Nonlinear Tracking Differentiator is the transient process of schedule system desired signal, it is to avoid overshoot occurs in system Amount；Extended state observer can either the state variable of estimating system, it is also possible to effectively estimate the location indeterminate of system； Nonlinear Feedback Control rule has good effect for suppression system disturbance.Therefore, combine both for solving certainly The restrictive condition adapting to iterative learning will be fairly obvious.The system being based only on active disturbance rejection is run on a timeline, and System based on iterative learning is to carry out in iteration axle, so both be combined in still rarely has relevant research both at home and abroad.

In order to improve the performance of Synchronization Control further, various synchronous control structures are suggested and have been applied to many In the middle of motor in synchrony controls, wherein, parallel control is to enter commercial Application, under this configuration, all of motor quilt the earliest Given same reference signal, but there is no coupled relation between motor, so synchronization accuracy is poor；Then, researcher is had to carry Go out a kind of primary and secondary structure to design multi-machine system, be effectively increased the tracking accuracy of motor but from motor disturbance rejection Can be deteriorated；At present, along with deepening continuously of research, increasing synchronization structure has been had to be suggested raising multi-machine system Performance, include adjacent coupled structure among these, annular coupled structure, electronic virtual longitudinal axis structure etc..But, based on these Controller designed by method is the most complicated, and design one is improved adjacent coupled type synchronization structure and realized multi-machine system control System is necessary.

Summary of the invention

Net synchronization capability and tracking performance in order to solve the multi-machine system with indeterminate are poor, global convergence ability Slower deficiency, makes the tracking that each motor can be stable go up given signal and keep consistent speed to run, the present invention Providing the multi-motor synchronous control method of a kind of active disturbance rejection iterative learning, the method designs many motors based on iterative learning method Tracing control is restrained, and combines the performance of active disturbance rejection stragetic innovation tracing control rule；Synchronization Control rule is based on error mean coupling knot Structure designs, and makes system have quick global convergence ability.

As follows in order to solve the technical scheme of above-mentioned technical problem proposition:

A kind of multi-motor synchronous control method based on active disturbance rejection iterative learning, comprises the following steps:

Step 1, sets up multi-machine system mathematical model, initializes system mode and controls parameter, and process is as follows:

1.1, multi-machine system model is as follows:

${\stackrel{\·}{\mathrm{\ω}}}_i\left(t\right)=\frac{1.5{\mathrm{\Ωn}}_p{\mathrm{\ψ}}_f}{J}{i}_q-\frac{\mathrm{\Ω}}{J}{\mathrm{\ω}}_i\left(t\right)-\frac{1}{J}{T}_L---\left(1\right)$

Wherein, n_pNumber of pole-pairs for motor；ψ_fFor rotor magnetic linkage；J is the rotary inertia of load；Ω is viscous friction Coefficient；ω_i(t) for being the speed of i-th rotor, i=1 ..., n；T_LLoad torque for motor；i_qFor motor stator q Size of current on axle；

1.2, make u_i(t, k)=i_q；D_i(t, k)=Δ A_iu_i(t,k)+ΔB_ix_i(t,k)+(C_i+ΔC_i)T_L；x_i(t, k)=ω_i(t)；Formula (1) is converted into following form:

${\stackrel{\·}{x}}_i(t,k)=A_i{u}_i(t,k)+B_i{x}_i(t,k)+D_i---\left(2\right)$

ΔA_i, Δ B_i, Δ C_iIt it is all the variable quantity of parameter；x_i(t k) is the measured state of system；T is the time；K is iteration Number of times；

1.3, definition speed Tracking error is:

e_i(t, k)=x_d(t,k)-x_i(t,k) (3)

Wherein, x_dFor i-th motor command rate signal, the speed synchronous error defining adjacent motor is:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_1(t,k)=e_1(t,k)-e_2(t,k)\\ .\\ .\\ .\\ {\mathrm{\ϵ}}_i(t,k)=e_i(t,k)-e_{i+1}(t,k)\\ .\\ .\\ .\\ {\mathrm{\ϵ}}_n(t,k)=e_n(t,k)-e_1(t,k)\end{array}\right.---\left(4\right)$

Wherein, n is normal amount；

Definition Adjacent coupling error is:

$\left\{\begin{array}{c}{e_1}^{*}(t,k)=v_a{\mathrm{\ϵ}}_1(t,k)-v_b{\mathrm{\ϵ}}_n(t,k)\\ .\\ .\\ .\\ {e_i}^{*}(t,k)=v_a{\mathrm{\ϵ}}_i(t,k)-v_b{\mathrm{\ϵ}}_{i-1}(t,k)\\ .\\ .\\ .\\ {e_n}^{*}(t,k)=v_a{\mathrm{\ϵ}}_n\left(t\right)-v_b{\mathrm{\ϵ}}_{n-1}(t,k)\end{array}\right.---\left(5\right)$

Wherein, v_aAnd v_bIt is all normal amount, and meets v_a ⁿ≠v_b ⁿ；

OrderThen formula (5) is reduced to

A* ε=E (6)

A matrix is performed equivalent transformation, it is thus achieved that following upper triangular matrix:

When meeting condition v_a ⁿ≠v_b ⁿTime, A is a non-singular matrix, then obtains formula (6) and only has unique solution, once E= 0_n×1, then ε=0_n×1, desin speed isochronous controller is to guarantee E → 0_n×1；

Step 2, speed Tracking and speed synchronous controller design, process is as follows:

2.1, formula (2) contains non-zero initial error, and design Nonlinear Tracking Differentiator is for transition process arranging:

$\left\{\begin{array}{c}{\mathrm{\η}}_0(t,k)=v_1(t,k)-x_d(t,k)\\ {\stackrel{\·}{v}}_1(t,k)=-r.fal({\mathrm{\η}}_0,a,\mathrm{\δ})\end{array}\right.---\left(8\right)$

Wherein, v₁(t k) is x_d(t, tracking signal k)；η₀(t k) is x_dTracking error；A, δ, r are normal amount； Fal (.) is nonlinear function, is represented as:

$fal(\mathrm{\η},a,\mathrm{\δ})=\left\{\begin{array}{cc}|\mathrm{\η}{|}^a\mathrm{sgn}\left(\mathrm{\η}\right)& \left|\mathrm{\η}\right|>\mathrm{\δ}\\ \frac{\mathrm{\η}}{{\mathrm{\δ}}^{1-a}}& \left|\mathrm{\η}\right|\≤\mathrm{\δ}\end{array}\right.---\left(9\right)$

Wherein, η, δ are normal amount；After finite time Nonlinear Tracking Differentiator adjusts, tracking error is expressed as again:

e_i(t, k)=x_i(t,k)-v₁(t,k) (10)

2.2, iteration extended state observer is designed as:

$\left\{\begin{array}{c}{\mathrm{\δ}}_i(t,k)=z_i(t,k)-x_i(t,k)\\ z_{ri}(t,k)={\stackrel{\·}{z}}_i(t,k)=fal\left({\mathrm{\δ}}_i\right(t,k\left)\right)\\ z_{ri}(t,k)=z_{ri}(t,k-1)+{\mathrm{\Λ\δ}}_i(t,k)\end{array}\right.---\left(11\right)$

Wherein, z_i(t, k) and z_r(t k) is respectively x_iObservation with disturbance total with system；For z_i(t, a k) Rank differential signal；δ_i(t k) is x_iObservation error；Λ is normal amount；

2.3, design nonlinear Feedback Control rule is:

$\left\{\begin{array}{c}{\mathrm{\η}}_1(t,k)=v_1(t,k)-z_i(t,k)\\ u_{0i}(t,k)={\mathrm{\β}}_{3}fal({\mathrm{\η}}_1,a,\mathrm{\δ})\\ u_{ti}(t,k)=u_{0i}(t,k)-z_{ri}(t,k)/b_0\end{array}\right.---\left(12\right)$

Wherein, u_0i(t is k) not consider that the control in the case of disturbance inputs；u_ti(t is k) to consider the speed in the case of disturbance Degree tracing control input signal；b₀And β₃It it is normal amount；

2.4, design sliding-mode surface is:

$S_i(t,k)=e_i^{*}(t,k)+\mathrm{\γ}.{\∫}_0^t{e}_i^{*}\left(\mathrm{\τ}\right)d\mathrm{\τ}---\left(13\right)$

Wherein, γ is normal number, and speed synchronous controller based on extended state observer is designed to:

$\begin{array}{c}{u^{\′}}_{si}(t,k)=\frac{1}{A}\[-z_{ri}(t,k)+B_i{x}_i(t,k)+\frac{v_a}{v_a+v_b}{\stackrel{\·}{x}}_{i+1}+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i+1}(t,k)\\ +\frac{\mathrm{\γ}}{v_a+v_b}{e}_{i+1}^{*}(t,k)-l_{i}sign\left(S_i\right)\]\end{array}---\left(14\right)$

Wherein, l_iIt is to control gain, meets l_i≥|D_i| >=0, sliding formwork control law guarantees that state variable is stable at sliding-mode surface On；

2.5, design adaptive speed isochronous controller based on extended state observer design as follows:

${u^{\′}}_{si}(t,k)=\frac{1}{A}\[-z_{2i}+B_i{x}_i+\frac{v_a}{v_a+v_b}{\stackrel{\·}{x}}_{i+1}+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i-1}+\frac{\mathrm{\γ}}{v_a+v_b}{e}_{i+1}^{*}-{\hat{l}}_{i}sign\left(S_i\right)\]---\left(15\right)$

Wherein, sign (.) is sign function；It isEstimation signal, its adaptive law is:

Wherein, l_m＞ 0, σ ＞ 0,For infinitesimal constant；

Formula (15) is brought in the middle of formula (2), has:

$\begin{array}{c}{\stackrel{\·}{x}}_i(t,k)=-z_{ri}(t,k)+\frac{v_a}{v_a+w}{\stackrel{\·}{x}}_{i+1}(t,k)+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i-1}(t,k)\\ +\frac{\mathrm{\γ}}{v_a+v_b}{e}_i^{*}-{\hat{l}}_{i}sign\left(S_i\right)+D_i(t,k)\end{array}---\left(17\right)$

2.6, select following Lyapunov function:

$V_i=\frac{1}{2}{S}_i^2+\frac{1}{2\mathrm{\ρ}}{\tilde{l}}_i^2---\left(18\right)$

WhereinTo V derivation, ifDecision-making system is stable.

The method that the present invention combines iteration expansion state device based on active disturbance rejection, devises the synchronization control of a kind of multi-machine system Method processed, is solving multi-machine system stationary problem simultaneously, is being effectively improved the Fast Convergent performance of system, it is achieved multi-machine system Ground accurately controls.

The technology of the present invention is contemplated that: for the multi-machine system with Nonlinear uncertainty, the present invention is based on non-thread Property active disturbance rejection iterative learning method design many motor speeds tracking control unit, concrete first by finite time Nonlinear Tracking Differentiator phase of adjustment Hoping reference signal, transition process arranging, then the unknown in the effective estimating system of design iteration extended state observer is uncertain Property item, both can guarantee that motor tracking error restrained in the time domain, also can guarantee that it was restrained in iteration territory.Meanwhile, propose to change Enter type adjacent coupled control strategy design multi-motor synchronous control device.The invention provides one and can be effectively improved many motors together The method of step systematic function, it is ensured that multi-machine system is capable of preferably controlling effect.

The invention have the benefit that tracing control and the Synchronization Control realizing many motors, be effectively improved many motors with Track precision and net synchronization capability, improve the Fast Convergent performance of system.

Accompanying drawing explanation

Fig. 1 is the control flow chart of the present invention；

Fig. 2 is the tracking velocity signal of four motors, and wherein, Fig. 2 (a) is the tracking velocity signal of motor 1；Fig. 2 (b) is electricity The tracking velocity signal of machine 2；Fig. 2 (c) is the tracking velocity signal of motor 3；Fig. 2 (d) is the tracking velocity signal of motor 4；

The speed Tracking error of the motor 1 when Fig. 3 is iteration 2 times；

The speed Tracking error of the motor 1 when Fig. 4 is iteration 20 times；

Fig. 5 is the synchronous error signal of four motors；

Fig. 6 is the extended state observer tracking signal for quantity of state；

Fig. 7 is the extended state observer tracking signal for the unknown；

Detailed description of the invention

The present invention will be further described below in conjunction with the accompanying drawings.

With reference to Fig. 1-Fig. 7, a kind of multi-motor synchronous control method based on active disturbance rejection iterative learning, comprise the following steps:

Step 1, sets up multi-machine system mathematical model, initializes system mode and controls parameter, and process is as follows:

1.1, multi-machine system model is as follows:

${\stackrel{\·}{\mathrm{\ω}}}_i\left(t\right)=\frac{1.5{\mathrm{\Ωn}}_p{\mathrm{\ψ}}_f}{J}{i}_q-\frac{\mathrm{\Ω}}{J}{\mathrm{\ω}}_i\left(t\right)-\frac{1}{J}{T}_L---\left(1\right)$

Wherein, n_pNumber of pole-pairs for motor；ψ_fFor rotor magnetic linkage；J is the rotary inertia of load；Ω is viscous friction Coefficient；ω_i(t) for being the speed of i-th rotor, i=1 ..., n,；T_LLoad torque for motor；i_qFor motor stator q Size of current on axle；

1.2, make u_i(t, k)=i_q；D_i(t, k)=Δ A_iu_i(t,k)+ΔB_ix_i(t,k)+(C_i+ΔC_i)T_L；x_i(t, k)=ω_i(t)；Formula (1) is converted into following form:

${\stackrel{\·}{x}}_i(t,k)=A_i{u}_i(t,k)+B_i{x}_i(t,k)+D_i---\left(2\right)$

ΔA_i, Δ B_i, Δ C_iIt it is all the variable quantity of parameter；x_i(t k) is the measured state of system；T is the time；K is iteration Number of times；

1.3, definition speed Tracking error is:

e_i(t, k)=x_d(t,k)-x_i(t,k) (3)

Wherein, x_dFor i-th motor command rate signal, it is all consistent for all of motor, defines adjacent electricity The speed synchronous error of machine is:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_1(t,k)=e_1(t,k)-e_2(t,k)\\ .\\ .\\ .\\ {\mathrm{\ϵ}}_i(t,k)=e_i(t,k)-e_{i+1}(t,k)\\ .\\ .\\ .\\ {\mathrm{\ϵ}}_n(t,k)=e_n(t,k)-e_1(t,k)\end{array}\right.---\left(4\right)$

Wherein, n is normal amount；

Definition Adjacent coupling error is:

$\left\{\begin{array}{c}{e_1}^{*}(t,k)=v_a{\mathrm{\ϵ}}_1(t,k)-v_b{\mathrm{\ϵ}}_n(t,k)\\ .\\ .\\ .\\ {e_i}^{*}(t,k)=v_a{\mathrm{\ϵ}}_i(t,k)-v_b{\mathrm{\ϵ}}_{i-1}(t,k)\\ .\\ .\\ .\\ {e_n}^{*}(t,k)=v_a{\mathrm{\ϵ}}_n\left(t\right)-v_b{\mathrm{\ϵ}}_{n-1}(t,k)\end{array}\right.---\left(5\right)$

Wherein, v_aAnd v_bIt is all normal amount, and meets v_a ⁿ≠v_b ⁿ；

OrderThen formula (5) is reduced to

A* ε=E (6)

A matrix is performed equivalent transformation, it is thus achieved that following upper triangular matrix:

When meeting condition v_a ⁿ≠v_b ⁿTime, A is a non-singular matrix, then obtains formula (6) and only has unique solution, once E= 0_n×1, then ε=0_n×1, control purpose and be converted to desin speed isochronous controller to guarantee E → 0_n×1；

Step 2, speed Tracking and speed synchronous controller design, process is as follows:

2.1, formula (2) contains non-zero initial error, and in order to realize system perfect tracking, design Nonlinear Tracking Differentiator is used for arranging Transient process:

$\left\{\begin{array}{c}{\mathrm{\η}}_0(t,k)=v_1(t,k)-x_d(t,k)\\ {\stackrel{\·}{v}}_1(t,k)=-r.fal({\mathrm{\η}}_0,a,\mathrm{\δ})\end{array}\right.---\left(8\right)$

Wherein, v₁(t k) is x_d(t, tracking signal k)；η₀(t k) is x_dTracking error；A, δ, r are normal amount； Fal (.) is nonlinear function, is represented as:

$fal(\mathrm{\η},a,\mathrm{\δ})=\left\{\begin{array}{cc}|\mathrm{\η}{|}^a\mathrm{sgn}\left(\mathrm{\η}\right)& \left|\mathrm{\η}\right|>\mathrm{\δ}\\ \frac{\mathrm{\η}}{{\mathrm{\δ}}^{1-a}}& \left|\mathrm{\η}\right|\≤\mathrm{\δ}\end{array}\right.---\left(9\right)$

Wherein, η, δ are normal amount；After finite time Nonlinear Tracking Differentiator adjusts, tracking error is expressed as again:

e_i(t, k)=x_i(t,k)-v₁(t,k) (10)

2.2, iteration extended state observer is designed as:

$\left\{\begin{array}{c}{\mathrm{\δ}}_i(t,k)=z_i(t,k)-x_i(t,k)\\ z_{ri}(t,k)={\stackrel{\·}{z}}_i(t,k)=fal\left({\mathrm{\δ}}_i\right(t,k\left)\right)\\ z_{ri}(t,k)=z_{ri}(t,k-1)+{\mathrm{\Λ\δ}}_i(t,k)\end{array}\right.---\left(11\right)$

Wherein, z_i(t, k) and z_r(t k) is respectively x_iObservation with disturbance total with system；For z_i(t, a k) Rank differential signal；δ_i(t k) is x_iObservation error；Λ is normal amount；

2.3, design nonlinear Feedback Control rule is:

$\left\{\begin{array}{c}{\mathrm{\η}}_1(t,k)=v_1(t,k)-z_i(t,k)\\ u_{0i}(t,k)={\mathrm{\β}}_{3}fal({\mathrm{\η}}_1,a,\mathrm{\δ})\\ u_{ti}(t,k)=u_{0i}(t,k)-z_{ri}(t,k)/b_0\end{array}\right.---\left(12\right)$

Wherein, u_0i(t is k) not consider that the control in the case of disturbance inputs；u_ti(t is k) to consider the speed in the case of disturbance Degree tracing control input signal；b₀And β₃It it is normal amount；

2.4, design sliding-mode surface is:

$S_i(t,k)=e_i^{*}(t,k)+\mathrm{\γ}.{\∫}_0^t{e}_i^{*}\left(\mathrm{\τ}\right)d\mathrm{\τ}---\left(13\right)$

Wherein, γ is normal number, and speed synchronous controller based on extended state observer is designed to:

$\begin{array}{c}{u^{\′}}_{si}(t,k)=\frac{1}{A}\[-z_{ri}(t,k)+B_i{x}_i(t,k)+\frac{v_a}{v_a+v_b}{\stackrel{\·}{x}}_{i+1}+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i+1}(t,k)\\ +\frac{\mathrm{\γ}}{v_a+v_b}{e}_{i+1}^{*}(t,k)-l_{i}sign\left(S_i\right)\]\end{array}---\left(14\right)$

Wherein, l_iIt is to control gain, meets l_i≥|D_i| >=0, sliding formwork control law guarantees that state variable is stable at sliding-mode surface On；

2.5, design adaptive speed isochronous controller based on extended state observer design as follows:

${u^{\′}}_{si}(t,k)=\frac{1}{A}\[-z_{2i}+B_i{x}_i+\frac{v_a}{v_a+v_b}{\stackrel{\·}{x}}_{i+1}+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i-1}+\frac{\mathrm{\γ}}{v_a+v_b}{e}_{i+1}^{*}-{\hat{l}}_{i}sign\left(S_i\right)\]$

$\left(15\right)$

Wherein, sign (.) is sign function；It isEstimation signal, its adaptive law is:

Wherein, l_m＞ 0, σ ＞ 0,For infinitesimal constant；

Formula (15) is brought in the middle of formula (2), has:

$\begin{array}{c}{\stackrel{\·}{x}}_i(t,k)=-z_{ri}(t,k)+\frac{v_a}{v_a+w}{\stackrel{\·}{x}}_{i+1}(t,k)+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i-1}(t,k)\\ +\frac{\mathrm{\γ}}{v_a+v_b}{e}_i^{*}-{\hat{l}}_{i}sign\left(S_i\right)+D_i(t,k)\end{array}---\left(17\right)$

2.6, select following Lyapunov function:

$V_i=\frac{1}{2}{S}_i^2+\frac{1}{2\mathrm{\ρ}}{\tilde{l}}_i^2---\left(18\right)$

WhereinTo V derivation, ifDecision-making system is stable.

For effectiveness and the superiority of checking institute extracting method, the present invention carries out following emulation experiment, arranges in emulation experiment Initial condition and partial parameters, it may be assumed that n in system equation_p1=4, n_p2=4, n_p3=4, n_p4=4, J₁=0.0081, J₂= 0.0083, J₃=0.0074, J₄=0.0066, ψ_f1=0.067, ψ_f2=0.071, ψ_f3=0.075, ψ_f4=0.068, Ω₁= 0.0005, Ω₂=0.00047, Ω₃=0.00055, Ω₄=0.00063, wherein, subscript represents the 1st, 2,3,4 motor；Speed Degree controller parameter is α=0.4, η₀=0.1, η₁=0.2, a=0.6, δ=0.61, b₀=51, r=500, β₂=5000, β₃= 600, r=1800；Isochronous controller parameter is v_a=2, v_b=1, Λ=30, l=500, ξ=0.5, γ=0.6, The parameter of adaptive law is l_m=0.15, σ=0.01；System each state initial value, iteration extended state observer state are initial Value and control signal u_siInitial value is all set to 0.The desired speed signal of motor is x_d=1000 revs/min, initial load torque Being set as 1N, when 0.2 second, load torque sported 10N.

Fig. 2-Fig. 7 is four motor speed output signals and tracking error analogous diagram, as seen from Figure 2, four motors Output speed signal all achieves preferable tracking effect for desired signal；As seen from Figure 4 the stable state under iteration 2 times with Track error has been up to 0.1 rev/min, and in Fig. 3, the steady track error maximum under iteration 20 times only has 0.03 rev/min；By Fig. 5 can be seen that the synchronous error of many motors finally achieves and preferably restrains effect；Be can be seen that iteration expands by Fig. 6 and Fig. 7 Open state observer for quantity of state and the estimated preferable effect of the unknown；From the point of view of the result of emulation experiment, based on certainly The synchronous control system for multiple motors of anti-interference iterative learning can effectively solve the speed sync problem of multi-machine system, and improves system Fast Convergent performance, it is achieved the concordance of multi_motor control and tracing property.

The simulation comparison experiment that the present invention that described above is is given is in order to show the superiority of designed method, it is clear that this Invention is not limited only to examples detailed above, without departing from essence spirit of the present invention and without departing from model involved by flesh and blood of the present invention On the premise of enclosing, it can be made all deformation to be carried out.Control program designed by the present invention is to the how electricity containing indeterminate Machine system has good control effect, can be effectively improved tracking performance and the net synchronization capability of system, make multi-machine system realize Stable operation.

Claims (1)

1. a multi-motor synchronous control method based on active disturbance rejection iterative learning, it is characterised in that: described control method includes Following steps:

Step 1, sets up multi-machine system mathematical model, initializes system mode and controls parameter, and process is as follows:

1.1, multi-machine system model is as follows:

${\stackrel{\·}{\mathrm{\ω}}}_i\left(t\right)=\frac{1.5{\mathrm{\Ωn}}_p{\mathrm{\ψ}}_f}{J}{i}_q-\frac{\mathrm{\Ω}}{J}{\mathrm{\ω}}_i\left(t\right)-\frac{1}{J}{T}_L---\left(1\right)$

Wherein, n_pNumber of pole-pairs for motor；ψ_fFor rotor magnetic linkage；J is the rotary inertia of load；Ω is viscous friction coefficient； ω_i(t) for being the speed of i-th rotor, i=1 ..., n,；T_LLoad torque for motor；i_qFor on motor stator q axle Size of current；

1.2, make u_i(t, k)=i_q；D_i(t, k)=Δ A_iu_i(t,k)+ΔB_ix_i(t,k)+(C_i+ΔC_i)T_L；x_i(t, k)=ω_i(t)；Formula (1) is converted into following form:

${\stackrel{\·}{x}}_i(t,k)=A_i{u}_i(t,k)+B_i{x}_i(t,k)+D_i---\left(2\right)$

ΔA_i, Δ B_i, Δ C_iIt it is all the variable quantity of parameter；x_i(t k) is the measured state of system；T is the time；K is iterations；

1.3, definition speed Tracking error is:

e_i(t, k)=x_d(t,k)-x_i(t,k) (3)

Wherein, x_dFor i-th motor command rate signal, the speed synchronous error defining adjacent motor is:

$\left\{\begin{array}{c}{\mathrm{\ϵ}}_1(t,k)=e_1(t,k)-e_2(t,k)\\ \begin{array}{c}.\\ .\\ .\end{array}\\ {\mathrm{\ϵ}}_i(t,k)=e_i(t,k)-e_{i+1}(t,k)\\ \begin{array}{c}.\\ .\\ .\end{array}\\ {\mathrm{\ϵ}}_n(t,k)=e_n(t,k)-e_1(t,k)\end{array}\right.---\left(4\right)$

Wherein, n is normal amount；

Definition Adjacent coupling error is:

$\left\{\begin{array}{c}{e_1}^{*}(t,k)=v_a{\mathrm{\ϵ}}_1(t,k)-v_b{\mathrm{\ϵ}}_n(t,k)\\ \begin{array}{c}.\\ .\\ .\end{array}\\ {e_i}^{*}(t,k)=v_a{\mathrm{\ϵ}}_i(t,k)-v_b{\mathrm{\ϵ}}_{i-1}(t,k)\\ \begin{array}{c}.\\ .\\ .\end{array}\\ {e_n}^{*}(t,k)=v_a{\mathrm{\ϵ}}_n\left(t\right)-v_b{\mathrm{\ϵ}}_{n-1}(t,k)\end{array}\right.---\left(5\right)$

Wherein, v_aAnd v_bIt is all normal amount, and meets v_a ⁿ≠v_b ⁿ；

OrderThen formula (5) is reduced to

A* ε=E (6)

A matrix is performed equivalent transformation, it is thus achieved that following upper triangular matrix:

When meeting condition v_a ⁿ≠v_b ⁿTime, A is a non-singular matrix, then obtains formula (6) and only has unique solution, once E=0_n×1, that ε=0_n×1, desin speed isochronous controller is to guarantee E → 0_n×1；

Step 2, speed Tracking and speed synchronous controller design, process is as follows:

2.1, formula (2) contains non-zero initial error, and design Nonlinear Tracking Differentiator is for transition process arranging:

$\left\{\begin{array}{c}{\mathrm{\η}}_0(t,k)=v_1(t,k)-x_d(t,k)\\ {\stackrel{\·}{v}}_1\left(t,k\right)=-r.fal\left({\mathrm{\η}}_0,a,\mathrm{\δ}\right)\end{array}\right.---\left(8\right)$

Wherein, v₁(t k) is x_d(t, tracking signal k)；η₀(t k) is x_dTracking error；A, δ, r are normal amount；

Fal (.) is nonlinear function, is represented as:

$fal(\mathrm{\η},a,\mathrm{\δ})=\left\{\begin{array}{cc}|\mathrm{\η}{|}^a\mathrm{sgn}\left(\mathrm{\η}\right)& \left|\mathrm{\η}\right|>\mathrm{\δ}\\ \frac{\mathrm{\η}}{{\mathrm{\δ}}^{1-a}}& \left|\mathrm{\η}\right|\≤\mathrm{\δ}\end{array}\right.---\left(9\right)$

Wherein, η, δ are normal amount；After finite time Nonlinear Tracking Differentiator adjusts, tracking error is expressed as again:

e_i(t, k)=x_i(t,k)-v₁(t,k) (10)

2.2, iteration extended state observer is designed as:

$\left\{\begin{array}{c}{\mathrm{\δ}}_i(t,k)=z_i(t,k)-x_i(t,k)\\ z_{ri}(t,k)={\stackrel{\·}{z}}_i(t,k)=-{\mathrm{\β}}_2.fal\left({\mathrm{\δ}}_i\right(t,k\left)\right)\\ z_{ri}(t,k)=z_{ri}(t,k-1)+{\mathrm{\Λ\δ}}_i(t,k)\end{array}\right.---\left(11\right)$

Wherein, z_i(t, k) and z_r(t k) is respectively x_iObservation with disturbance total with system；For z_i(t, single order k) is micro- Sub-signal；δ_i(t k) is x_iObservation error；Λ is normal amount；

2.3, design nonlinear Feedback Control rule is:

$\left\{\begin{array}{c}{\mathrm{\η}}_1(t,k)=v_1(t,k)-z_i(t,k)\\ u_{0i}(t,k)={\mathrm{\β}}_{3}fal({\mathrm{\η}}_1,a,\mathrm{\δ})\\ u_{ti}(t,k)=u_{0i}(t,k)-z_{ri}(t,k)/b_0\end{array}\right.---\left(12\right)$

Wherein, u_0i(t is k) not consider that the control in the case of disturbance inputs；u_ti(t, k) be consider speed in the case of disturbance with Track controls input signal；b₀And β₃It it is normal amount；

2.4, design sliding-mode surface is:

$S_i(t,k)=e_i^{*}(t,k)+\mathrm{\γ}.{\∫}_0^t{e}_i^{*}\left(\mathrm{\τ}\right)d\mathrm{\τ}---\left(13\right)$

Wherein, γ is normal number, and speed synchronous controller based on extended state observer is designed to:

$\begin{array}{c}{u^{\′}}_{si}\left(t,k\right)=\frac{1}{A}\[-z_{ri}\left(t,k\right)+B_i{x}_i\left(t,k\right)+\frac{v_a}{v_a+v_b}{\stackrel{\·}{x}}_{i+1}+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i-1}\left(t,k\right)\\ +\frac{\mathrm{\γ}}{v_a+v_b}{e}_{i+1}^{*}\left(t,k\right)-l_{i}sign\left(S_i\right)\]\end{array}---\left(14\right)$

Wherein, l_iIt is to control gain, meets l_i≥|D_i| >=0, sliding formwork control law guarantees that state variable is stable on sliding-mode surface；

2.5, design adaptive speed isochronous controller based on extended state observer design as follows:

${u^{\′}}_{si}\left(t,k\right)=\frac{1}{A}\[-z_{2i}+B_i{x}_i+\frac{v_a}{v_a+v_b}{\stackrel{\·}{x}}_{i+1}+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i-1}+\frac{\mathrm{\γ}}{v_a+v_b}{e}_{i+1}^{*}-{\hat{l}}_{i}sign\left(S_i\right)\]---\left(15\right)$

Wherein, sign (.) is sign function；It isEstimation signal, its adaptive law is:

Wherein, l_m＞ 0, σ ＞ 0,For infinitesimal constant；

Formula (15) is brought in the middle of formula (2), has:

$\begin{array}{c}{\stackrel{\·}{x}}_i\left(t,k\right)=-z_{ri}\left(t,k\right)+\frac{v_a}{v_a+w}{\stackrel{\·}{x}}_{i+1}\left(t,k\right)+\frac{v_b}{v_a+v_b}{\stackrel{\·}{x}}_{i-1}\left(t,k\right)\\ +\frac{\mathrm{\γ}}{v_a+v_b}{e}_i^{*}-{\hat{l}}_{i}sign\left(S_i\right)+D_i\left(t,k\right)\end{array}---\left(17\right)$

2.6, select following Lyapunov function:

$V_i=\frac{1}{2}{S}_i^2+\frac{1}{2\mathrm{\ρ}}{\tilde{l}}_i^2---\left(18\right)$

WhereinTo V derivation, ifDecision-making system is stable.