CN105846741A - Double-permanent magnet synchronous motor chaos synchronization control method based on extended state observer - Google Patents

Abstract

A double-permanent magnet synchronous motor chaos synchronization control method based on an extended state observer comprises the steps of building a chaos model of a permanent magnet synchronous motor system, defining a synchronization error system, designing a nonlinear extended state observer, and designing an adaptive sliding mode controller. Through coordinate transformation, the chaos model of the permanent magnet synchronous motor system is built, and the synchronization error system is defined. The nonlinear extended state observer is designed to estimate and compensate uncertain items and external disturbance in the system. The adaptive sliding mode controller is designed to ensure that the state error between master and slave systems is stabilized quickly and converges to zero. Finally, synchronous control of the system is realized. The influence of chaos phenomenon and external disturbance in the system is compensated, the chattering problem of the traditional sliding mode control method is improved, the robustness of the system is enhanced, and chaos synchronization control of a double-permanent magnet synchronous motor system is realized.

Description

Double permagnetic synchronous motor Control of Chaotic Synchronization method based on extended state observer

Technical field

The present invention relates to a kind of double permagnetic synchronous motor adaptive chaos synchronization controlling parties based on extended state observer Method, it is adaptable to the chaos controlling to motor.

Background technology

Permagnetic synchronous motor (permanent magnet synchronous motor, PMSM) is that one is the most changeable Amount, close coupling nonlinear system, be widely used in the various high-performance systems such as robot, aviation aircraft and servo turntable control In system.But, there are some researches show, there is serious chaotic characteristic in PMSM, which results in the irregular operation of motor, have impact on electricity The stability of machine, but also the loss of motor can be increased the weight of, the serious service life reducing motor.Double permagnetic synchronous motors are one Typical Chaotic Synchronous device, drive system drives servo system to realize Coupled Chaotic Systems based on a coupled signal Synchronize, even if driving just the same with the state equation of servo system, under small initial condition, the operation shape of two systems State also can be completely different.Therefore, the chaos phenomenon in how compensation system, it is achieved the Control of Chaotic Synchronization of double permagnetic synchronous motors It it is a problem demanding prompt solution.

Extended state observer (Extended State Observer, ESO) is a kind of novel nonlinear state observation Device, by the inside and outside disturbance in system is expanded into new single order state, recycles specific nonlinearity erron feedback, then selects Select suitable observer parameter, just can obtain the observer of all states of system, the most also include the uncertain of system model Property and the observation of unknown disturbance.Therefore, it is possible not only to make the quantity of state of control object to reappear, and it is estimated that controls The uncertain factor of object model and the instantaneous value of interference this " expansion state ".This electricity being very suitable for there is chaos phenomenon Machine system.

Sliding mode variable structure control method has complete adaptivity and robustness, once enters sliding formwork state, system mode Transfer the most no longer affected by change and the external disturbance of systematic parameter, but general sliding formwork controls, and arrives in system mode When reaching sliding-mode surface, convergence equilibrium point can be backed across in equilibrium point both sides, thus produce buffeting problem.Therefore, much improve Sliding-mode method is suggested.Wherein, adaptive sliding mode method based on adaptive law can weaken fixed gain arrange carried the most at that time Problem buffeted by the controller come, and improves stability and the robustness of system, system can be made to have preferably again simultaneously and follow the tracks of effect Really.

Summary of the invention

In order to realize the Synchronization Control of permagnetic synchronous motor, overcome the components of system as directed state of prior art and disturbance not simultaneously Can survey, tradition sliding-mode control easily produces the deficiency of buffeting problem, and the present invention proposes a kind of based on extended state observer Double permagnetic synchronous motor Control of Chaotic Synchronization methods, compensate chaos phenomenon impact, solve tradition sliding formwork exist buffeting ask Topic.Utilize coordinate transform to set up the Brunovsky canonical form of double permanent-magnet synchronous chaos system, use extended state observer (Extended State Observer, ESO) estimates and the indeterminate in compensation system and external disturbance.Meanwhile, use certainly Adapt to sliding-mode control and draw controlled quentity controlled variable, it is achieved that the Chaotic Synchronous of double permagnetic synchronous motors.

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

A kind of double permagnetic synchronous motor Control of Chaotic Synchronization methods based on extended state observer, comprise the following steps:

Step 1, sets up the chaotic model of permagnetic synchronous motor system as shown in formula (1), and initialize system mode and Associated control parameters；

Wherein,For state variable, represent d-axis and quadrature axis stator current and rotor angle frequency respectively；WithRepresent d-axis and the stator voltage of quadrature axis；For external torque；σ and γ is constant parameter, whereinTime, external torqueThen formula (1) is rewritten as

OrderThen formula (2) is rewritten as

Wherein, x₁,x₂,x₃For state variable, σ and γ is systematic parameter, and formula (3) is active system, and servo system is as follows:

Step 2, defines synchronization error system, and augmentation system state；

2.1, define e₁=y₁-x₁, e₂=y₂-x₂, e₃=y₃-x₃, obtain following error system:

Due to

Formula (5) is rewritten as

Formula (7) is decomposed into following two subsystems

With

Work as e₁, e₂When converging to zero point, haveSetting up, design controller u makes the e in subsystem₁, e₂Converge to zero Point；

If

Then system (8) is converted to Brunovsky canonical form as follows

Wherein, a (e)=σ [γ e₁+e₁e₃-e₃y₁-e₁y₃-e₂-σ(e₂-e₁)], b=σ；

2.2, there is indeterminate a (e) and unknown parameter b in system, and design extended state observer estimates unknown state And indeterminate；Make a₀=a (e)+Δ bu, Δ b=b-b₀, wherein b₀For the estimated value of b, by definition expansion state g₃=a₀, Then system (11) is rewritten as following equivalents

Step 3, design nonlinear extension state observer and adaptive sliding mode controller；

3.1, make z_i, i=1,2,3 is respectively state variable g in system (12)_iObservation, definition observation error is e_oi =z_i-g_i, then nonlinear extension state observer expression formula is

Wherein, β₁,β₂,β₃＞ 0 is observer gain；Fal () is the continuous power letter near initial point with linearity range Number, expression formula is

Wherein, i=1,2,3, δ ＞ 0 represent the siding-to-siding block length of linearity range, 0 ＜ α_i＜ 1；

3.2, sliding-mode surface design is as follows:

S=g₂+λ₁g₁ (15)

The first derivative of s is

Wherein, λ₁＞ 0 is for controlling parameter.

By formula (16), traditional sliding mode controller design based on extended state observer (13) is

Wherein, k^*＞ 0 and meet k^*≥d₃+λ₁d₂, d₂For observation error e_o2The upper bound, d₃For observation error e_o3The upper bound；

3.3, the thought of incorporating parametric adaptive law, design adaptive sliding mode controller is as follows:

Wherein, k=k (t) is controller parameter, and its adaptive law is:

Wherein, k_m＞ 0, μ ＞ 0 is the least normal number, is used for guaranteeing k ＞ 0.

The present invention combines extended state observer and adaptive sliding-mode observer method, devises based on extended state observer Double permagnetic synchronous motor system self-adaption sliding mode controllers.Estimated by extended state observer and the most true in compensation system Determine item and external disturbance, and design adaptive sliding mode controller, it is ensured that the synchronization of master-slave system.

The technology of the present invention is contemplated that: owing to there is chaos phenomenon in double permagnetic synchronous motor systems, adds outside dry The impact disturbed, the state being easily caused master-slave system runs asynchronous situation instability even occur.For existing with chaos Double permagnetic synchronous motor systems of elephant, in conjunction with extended state observer and adaptive sliding-mode observer method, devise a kind of based on Double permagnetic synchronous motor Control of Chaotic Synchronization methods of extended state observer, eliminate chaos phenomenon as much as possible and outside is dry Disturb the impact on system synchronization.By setting up new expansion state, design extended state observer is estimated and the system of compensation is the most true Determine item and external disturbance, design adaptive sliding mode controller simultaneously, it is achieved the Synchronization Control of master-slave system.

In emulation experiment, respectively to traditional sliding-mode control (SMC+ESO) based on extended state observer and base Adaptive sliding-mode observer method (ASMC+ESO) in extended state observer contrasts, to highlight the superior of the inventive method Property.

Accompanying drawing explanation

Fig. 1 (a) is system mode x of SMC+ESO method₁,y₁Response curve；

Fig. 1 (b) is system mode x of SMC+ESO method₂,y₂Response curve；

Fig. 1 (c) is system mode x of SMC+ESO method₃,y₃Response curve；

Fig. 1 (d) is system mode x of ASMC+ESO method₁,y₁Response curve；

Fig. 1 (e) is system mode x of ASMC+ESO method₂,y₂Response curve；

Fig. 1 (f) is system mode x of ASMC+ESO method₃,y₃Response curve；

Fig. 2 (a) is extended state observer observation error e of SMC+ESO method_o1Curve；

Fig. 2 (b) is extended state observer observation error e of SMC+ESO method_o2Curve；

Fig. 2 (c) is extended state observer observation error e of SMC+ESO method_o3Curve；

Fig. 2 (d) is extended state observer observation error e of ASMC+ESO method_o1Curve；

Fig. 2 (e) is extended state observer observation error e of ASMC+ESO method_o2Curve；

Fig. 2 (f) is extended state observer observation error e of ASMC+ESO method_o3Curve；

Fig. 3 (a) is synchronous error e of SMC+ESO method₁Curve；

Fig. 3 (b) is synchronous error e of SMC+ESO method₂Curve；

Fig. 3 (c) is synchronous error e of SMC+ESO method₃Curve；

Fig. 3 (d) is synchronous error e of ASMC+ESO method₁Curve；

Fig. 3 (e) is synchronous error e of ASMC+ESO method₂Curve；

Fig. 3 (f) is synchronous error e of ASMC+ESO method₃Curve；

Fig. 4 (a) is the curve of the controller signals u of SMC+ESO method；

Fig. 4 (b) is the curve of the controller signals u of ASMC+ESO method；

Fig. 5 is the curve of the auto-adaptive parameter k in ASMC+ESO method；

Fig. 6 is the flow chart of double permagnetic synchronous motor Control of Chaotic Synchronization method based on extended state observer.

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. 6, a kind of double permagnetic synchronous motor Control of Chaotic Synchronization methods based on extended state observer, bag Include following steps:

Step 1, sets up the chaotic model of permagnetic synchronous motor system as shown in formula (1), and initialize system mode and Associated control parameters；

Wherein,For state variable, represent d-axis and quadrature axis stator current and rotor angle frequency respectively；WithRepresent d-axis and the stator voltage of quadrature axis；For external torque；σ and γ is constant parameter, whereinTime, external torqueThen formula (1) is rewritten as

OrderThen formula (2) is rewritten as

Wherein, x₁,x₂,x₃For state variable, σ and γ is systematic parameter, and formula (3) is active system, driven system

Unite as follows:

Step 2, defines synchronization error system, and augmentation system state；

2.1, define e₁=y₁-x₁, e₂=y₂-x₂, e₃=y₃-x₃, obtain following error system:

Due to

Formula (5) is rewritten as

Formula (7) is decomposed into following two subsystems

With

Work as e₁, e₂When converging to zero point, haveSet up；Design controller u makes the e in subsystem₁, e₂Converge to zero Point；

If

Then system (8) is converted to Brunovsky canonical form as follows

Wherein, a (e)=σ [γ e₁+e₁e₃-e₃y₁-e₁y₃-e₂-σ(e₂-e₁)], b=σ；

2.2, there is indeterminate a (e) and unknown parameter b in system, and design extended state observer estimates unknown state And indeterminate；Make a₀=a (e)+Δ bu, Δ b=b-b₀, wherein b₀For the estimated value of b, by definition expansion state g₃=a₀, Then system (11) is rewritten as following equivalents

Step 3, design nonlinear extension state observer and adaptive sliding mode controller；

3.1, make z_i, i=1,2,3 is respectively state variable g in system (12)_iObservation, definition observation error is e_oi =z_i-g_i, then nonlinear extension state observer expression formula is

Wherein, β₁,β₂,β₃＞ 0 is observer gain；Fal () is the continuous power letter near initial point with linearity range Number, expression formula is

Wherein, i=1,2,3, δ ＞ 0 represent the siding-to-siding block length of linearity range, 0 ＜ α_i＜ 1；

3.2, sliding-mode surface design is as follows:

S=g₂+λ₁g₁ (15)

The first derivative of s is

Wherein, λ₁＞ 0 is for controlling parameter；

By formula (16), traditional sliding mode controller (SMC+ESO) based on extended state observer (13) is designed as

Wherein, k^*＞ 0 and meet k^*≥d₃+λ₁d₂, d₂For observation error e_o2The upper bound, d₃For observation error e_o3The upper bound；

3.3, the thought of incorporating parametric adaptive law, design adaptive sliding mode controller is as follows:

Wherein, k=k (t) is controller parameter, and its adaptive law is:

Wherein, k_m＞ 0, μ ＞ 0 is the least normal number, is used for guaranteeing k ＞ 0.

For effectiveness and the superiority of checking institute extracting method, the present invention carries out emulation experiment by compared with control method.Imitative It is identical that initial condition in true experiment arranges holding with partial parameters, it may be assumed that sampling time T_s=0.01s, initial condition is (x₁ (0),x₂(0),x₃(0))=(-5,1 ,-3)；(y₁(0),y₂(0),y₃(0))=(-1,0.01,20)；Sliding formwork is seen with expansion state The parameter that arranges surveying device is λ₁=10, b₀=5, β₁=60, β₂=200, β₃=0.01, α₁=0.5, α₂=0.25, α₃=0.125, δ=0.01, σ=5.46.It addition, control parameter k in SMC+ESO^*=12, and control parameter k in ASMC+ESO_m=0.15, ε=0.01, μ=0.0001.Final control effect as Figure 1-Figure 5,

By Fig. 1-Fig. 3 it can be seen that two kinds of sliding-mode control based on extended state observer all can well be accomplished Chaotic Synchronous, extended state observer error and error system can converge to rapidly zero, control effect the most essentially identical.But from Fig. 4 is it is found that the vibration amplitude of controller signals of ASMC+ESO method is substantially less than SMC+ESO method, the most favourable Stability contorting in system.Fig. 5 gives the curve of auto-adaptive parameter k (t) in ASMC+ESO method, can from curve Going out, parameter k (t) in the method is finally converged in about 8.4, is slightly less than in SMC+ESO method the most given control gain k^*=12, the contrast of these group data conforms exactly to analysis as above.

Above describe the present invention and compare a comparison example of additive method, from the point of view of comparing result, the side of the present invention Method can effectively estimation compensation system exist chaos phenomenon and external disturbance, eliminate sliding formwork control exist buffeting problem, strengthen The robustness of system and anti-interference, it is ensured that the Chaotic Synchronous of master-slave system.Obviously the present invention is more than being limited to examples detailed above, On the basis of the present invention, other different systems can also be accurately controlled.

Claims (1)

1. double permagnetic synchronous motor Control of Chaotic Synchronization methods based on extended state observer, it is characterised in that: include Following steps:

Step 1, the chaotic model of foundation permagnetic synchronous motor system as shown in formula (1), and initialize system mode and be correlated with Control parameter；

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_d}{dt}=-{\tilde{i}}_d+{\widetilde{\mathrm{\ω}}}_m{\tilde{i}}_q+{\tilde{u}}_d\\ \frac{d{\tilde{i}}_q}{dt}=-{\tilde{i}}_q-{\widetilde{\mathrm{\ω}}}_m{\tilde{i}}_d+\mathrm{\γ}{\widetilde{\mathrm{\ω}}}_m+{\tilde{u}}_q\\ \frac{d{\widetilde{\mathrm{\ω}}}_m}{dt}=\mathrm{\σ}({\tilde{i}}_q-{\widetilde{\mathrm{\ω}}}_m)-{\tilde{T}}_L\end{array}\right.---\left(1\right)$

Wherein,For state variable, represent d-axis and quadrature axis stator current and rotor angle frequency respectively；WithRepresent d-axis and the stator voltage of quadrature axis；For external torque；σ and γ is constant parameter, whereinTime, External torqueThen formula (1) is rewritten as

$\left\{\begin{array}{c}\frac{d{\tilde{i}}_d}{dt}=-{\tilde{i}}_d+{\widetilde{\mathrm{\ω}}}_m{\tilde{i}}_q+{\tilde{u}}_d\\ \frac{d{\tilde{i}}_q}{dt}=-{\tilde{i}}_q-{\widetilde{\mathrm{\ω}}}_m{\tilde{i}}_d+\mathrm{\γ}{\widetilde{\mathrm{\ω}}}_m\\ \frac{d{\widetilde{\mathrm{\ω}}}_m}{dt}=\mathrm{\σ}({\tilde{i}}_q-{\widetilde{\mathrm{\ω}}}_m)\end{array}\right.---\left(2\right)$

Order $x_1={\widetilde{\mathrm{\ω}}}_m,x_2={\tilde{i}}_q,x_3={\tilde{i}}_d,$ Then formula (2) is rewritten as

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=\mathrm{\σ}(x_2-x_1)\\ {\stackrel{\·}{x}}_2={\mathrm{\γx}}_1-x_1{x}_3-x_2\\ {\stackrel{\·}{x}}_3=x_1{x}_2-x_3\end{array}\right.---\left(3\right)$

Wherein, x₁,x₂,x₃For state variable, σ and γ is systematic parameter, and formula (3) is active system, and servo system is as follows:

$\left\{\begin{array}{c}{\stackrel{\·}{y}}_1=\mathrm{\σ}(y_2-y_1)\\ {\stackrel{\·}{y}}_2={\mathrm{\γy}}_1-y_1{y}_3-y_2+u\\ {\stackrel{\·}{y}}_3=y_1{y}_2-y_3\end{array}\right.---\left(4\right)$

Step 2, defines synchronization error system, and augmentation system state；

2.1, define e₁=y₁-x₁, e₂=y₂-x₂, e₃=y₃-x₃, obtain following error system:

$\left\{\begin{array}{c}{\stackrel{\·}{e}}_1=\mathrm{\σ}(e_2-e_1)\\ {\stackrel{\·}{e}}_2={\mathrm{\γe}}_1-y_1{y}_3+x_1{x}_3-e_2+u\\ {\stackrel{\·}{e}}_3=y_1{y}_2-x_1{x}_2-e_3\end{array}\right.---\left(5\right)$

Due to

$\left\{\begin{array}{c}{y}_1{y}_3-x_1{x}_3=-e_1{e}_3+e_1{y}_3+e_3{y}_1\\ y_1{y}_2-x_1{x}_2=-e_1{e}_2+e_1{y}_2+e_2{y}_1\end{array}\right.---\left(6\right)$

Formula (5) is rewritten as

$\left\{\begin{array}{c}{\stackrel{\·}{e}}_1=\mathrm{\σ}(e_2-e_1)\\ {\stackrel{\·}{e}}_2={\mathrm{\γe}}_1+e_1{e}_3-e_1{y}_3-e_3{y}_1-e_2+u\\ {\stackrel{\·}{e}}_3=-e_1{e}_2+e_1{y}_2+e_2{y}_1-e_3\end{array}\right.---\left(7\right)$

Formula (7) is decomposed into following two subsystems

$\left\{\begin{array}{c}{\stackrel{\·}{e}}_1=\mathrm{\σ}(e_2-e_1)\\ {\stackrel{\·}{e}}_2={\mathrm{\γe}}_1+e_1{e}_3-e_1{y}_3-e_3{y}_1-e_2+u\end{array}\right.---\left(8\right)$

With

${\stackrel{\·}{e}}_3=-e_1{e}_2+e_1{y}_2+e_2{y}_1-e_3---\left(9\right)$

Work as e₁, e₂When converging to zero point, haveSetting up, design controller u makes the e in subsystem₁, e₂Converge to zero point；

If

$\left\{\begin{array}{c}{g}_1=e_1\\ g_2=\mathrm{\σ}(e_2-e_1)\end{array}\right.---\left(10\right)$

Then system (8) is converted to Brunovsky canonical form as follows

$\left\{\begin{array}{c}{\stackrel{\·}{g}}_1=g_2\\ {\stackrel{\·}{g}}_2=a\left(e\right)+bu\end{array}\right.---\left(11\right)$

Wherein, a (e)=σ [γ e₁+e₁e₃-e₃y₁-e₁y₃-e₂-σ(e₂-e₁)], b=σ；

2.2, there is indeterminate a (e) and unknown parameter b in system, and design extended state observer estimates unknown state and not Determine item；Make a₀=a (e)+Δ bu, Δ b=b-b₀, wherein b₀For the estimated value of b, by definition expansion state g₃=a₀, then it is System (11) is rewritten as following equivalents

$\left\{\begin{array}{c}{\stackrel{\·}{g}}_1=g_2\\ {\stackrel{\·}{g}}_2=g_3+b_{0}u\\ {\stackrel{\·}{g}}_3={\stackrel{\·}{a}}_0\end{array}\right.---\left(12\right)$

Step 3, design nonlinear extension state observer and adaptive sliding mode controller；

3.1, make z_i, i=1,2,3 is respectively state variable g in system (12)_iObservation, definition observation error is e_oi=z_i- g_i, then nonlinear extension state observer expression formula is

$\left\{\begin{array}{c}{\stackrel{\·}{z}}_1=z_2-{\mathrm{\β}}_1{e}_{01}\\ {\stackrel{\·}{z}}_2=z_3-{\mathrm{\β}}_{2}fal(e_{01},{\mathrm{\α}}_1,\mathrm{\δ})+b_{0}u\\ {\stackrel{\·}{z}}_3=-{\mathrm{\β}}_{3}fal(e_{01},{\mathrm{\α}}_2,\mathrm{\δ})\end{array}\right.---\left(13\right)$

Wherein, β₁,β₂,β₃＞ 0 is observer gain；Fal () is the continuous power function near initial point with linearity range, table Reaching formula is

$\begin{array}{c}fal(e_{01},{\mathrm{\α}}_i,\mathrm{\δ})\\ =\left\{\begin{array}{cc}\frac{e_{01}}{{\mathrm{\δ}}^{1-{\mathrm{\α}}_i}}& \left|e_{01}\right|\≤\mathrm{\δ}\\ |e_{01}{|}^{{\mathrm{\α}}_i}sign\left(e_{01}\right)& \left|e_{01}\right|>\mathrm{\δ}\end{array}\right.\end{array}---\left(14\right)$

Wherein, i=1,2,3, δ ＞ 0 represent the siding-to-siding block length of linearity range, 0 ＜ α_i＜ 1；

3.2, sliding-mode surface design is as follows:

S=g₂+λ₁g₁ (15)

The first derivative of s is

$\begin{array}{c}\stackrel{\·}{s}={\stackrel{\·}{g}}_2+{\mathrm{\λ}}_1{\stackrel{\·}{g}}_1\\ =g_3+b_{0}u+{\mathrm{\λ}}_1{g}_2\end{array}---\left(16\right)$

Wherein, λ₁＞ 0 is for controlling parameter；

By formula (16), traditional sliding mode controller design based on extended state observer (13) is

$u^{*}=\frac{1}{b_0}(-z_3-{\mathrm{\λ}}_1{z}_2-k^{*}sign(s\left)\right)---\left(17\right)$

Wherein, k^*＞ 0 and meet k^*≥d₃+λ₁d₂, d₂For observation error e_o2The upper bound, d₃For observation error e_o3The upper bound；

3.3, the thought of incorporating parametric adaptive law, design adaptive sliding mode controller is as follows:

$u=\frac{1}{b_0}(-z_3-{\mathrm{\λ}}_1{z}_2-ksign(s\left)\right)---\left(18\right)$

Wherein, k=k (t) is controller parameter, and its adaptive law is:

$\stackrel{\·}{k}=\left\{\begin{array}{cc}{k}_m\left|s\right|sign\left(\right|s|-\mathrm{\ϵ})& k>\mathrm{\μ}\\ \mathrm{\μ}& k\≤\mathrm{\μ}\end{array}\right.---\left(19\right)$

Wherein, k_m＞ 0, μ ＞ 0 is the least normal number, is used for guaranteeing k ＞ 0.