CN106788044A - A kind of permagnetic synchronous motor self adaptation non-singular terminal sliding-mode control based on interference observer - Google Patents

Abstract

The present invention relates to a kind of permagnetic synchronous motor self adaptation non-singular terminal sliding-mode control based on interference observer, in the speed ring of permanent magnet synchronous motor vector control system, introduce self adaptation non-singular terminal sliding mode controller, it is characterized in that, propose a kind of adaptive rate exponentially approaching rule, the Reaching Law introduces the single order norm of state variable, according to state variable apart from equalization point far and near self-adaptative adjustment exponential approach speed and constant speed velocity of approach, so as to realize weakening system chatter while shortening the convergence time.Meanwhile, for its exterior interference and load disturbance problem, devise interference observer, and its observation fed back into the design of sliding mode controller.The present invention can rapidly track rotating speed when system is interfered and loads appearance fluctuation, reduce system overshoot and stable state static difference, greatly strengthen the robustness of system.

Description

A kind of permagnetic synchronous motor self adaptation non-singular terminal sliding formwork based on interference observer Control method

Technical field

The invention belongs to permagnetic synchronous motor control field, it is related to a kind of sliding-mode control based on interference observer.

Background technology

Permagnetic synchronous motor (Permanent Magnet Synchronous Motor, PMSM) has small volume, structure Simply, many advantages, such as efficiency high so that it is used widely in fields such as Digit Control Machine Tool, medicine equipment, Aero-Space, but Because permagnetic synchronous motor is a multivariable, non-linear, close coupling complex object, when system is subject to inner parameter or the external world When the factors such as disturbance influence, conventional PI controls can not meet the requirement of high performance control, and Self Adaptive Control, Based Intelligent Control It is difficult to be applied in Practical Project Deng due to algorithm complexity.

Sliding mode variable structure control is a kind of nonlinear Control, and it switches rule using control, by different control actions Between switching, produce a kind of unrelated with original system, according to the motion of the state trajectory for making a reservation for " sliding mode ", make system mode Desired point is reached, so as to realize system control.Because desired trajectory and control object inner parameter and external disturbance are unrelated, therefore Sliding mode variable structure control is less demanding to model accuracy, has strong robustness to Parameter Perturbation, external disturbance.In recent years increasingly Be applied to Sliding mode variable structure control in AC servo by many scholars.

Although the research to sliding moding structure achieves certain achievement at present, there is still a need for entering one on control performance Step is improved.Non-singular terminal sliding formwork control is a kind of new sliding-mode control for occurring in recent years, and it is by purposefully changing Become switching function, the singularity problem of existing TSM control presence is directly solved from sliding mode design in terms of, realize and be The global nonsingular control of system；It inherits the finite time convergence control characteristic of terminal sliding mode again simultaneously, with traditional linear sliding mode Control is compared, and control system Finite-time convergence can be made to desired trajectory, and with stable state accuracy higher, is particularly well-suited to At a high speed, high-precision control.But buffeting problem is still present, it is difficult to reach preferable control effect.

The content of the invention

It is an object of the invention to solve in the prior art, control system for permanent-magnet synchronous motor response is slow, system chatter, The problems such as interference rejection ability difference, propose a kind of self adaptation non-singular terminal sliding-mode control based on interference observer.

In order to solve the above-mentioned technical problem, the invention provides solution below.

A kind of adaptive terminal sliding-mode control based on interference observer, using self adaptation non-singular terminal sliding formwork control Device processed is combined with interference observer.Self adaptation non-singular terminal sliding mode controller, it is characterised in that propose a kind of adaptive strain Fast exponentially approaching rule, the Reaching Law introduces the single order norm of state variable, according to state variable apart from the far and near adaptive of equalization point Adjustment index velocity of approach and constant speed velocity of approach are answered, so as to realize weakening system chatter while shortening the convergence time.

Reaching Law design is as follows：

Wherein:It is the single order norm of system state variables, k ＞ 0, ε ＞ 0, c ＞ 0, n ＞ 0.

Control system for permanent-magnet synchronous motor uses vector controlled, i.e. i in the present invention_d=0, under d-q coordinate systems, permanent magnetism is same Walking motor speed Mathematical Modeling is：

Wherein：ω is rotor velocity, i_qIt is q shaft currents, P is torque winding number of pole-pairs, ψ_fIt is permanent magnet pole and stator The magnetic linkage of winding interlinkage, J is rotary inertia, and F is the coefficient of friction of rotor and load, T_LIt is load torque.

With reference to permagnetic synchronous motor Mathematical Modeling, definition status variable chooses sliding-mode surface：

Design control law is：

Consider parameters in electrical machines uncertain factor：

Wherein：G (t)=T_L-Ji_qΔa+JωΔb+JΔd

The interference observer of construction system：

In formula：ForEstimate,It is the estimate of y=ω；Input variable u =1.5P ψ_fi_q；C=[1 0]；L=[l₁ l₂]^TIt is feedback matrix.

In disturbance-observer value feedforward compensation to the sliding mode controller that observer is obtained, new control law can be obtained：

Wherein：To add the new q shaft currents set-point obtained after interference observer value of feedback,It is the observation of g (t) Value.

Technical scheme beneficial effect proposed by the present invention is that the proposition of adaptive rate exponentially approaching rule is effectively improved The global fast convergence of state variable in TSM control, rapidly tracing motor rotation speed and can realize shortening convergence System chatter is weakened while time.The addition of interference observer, there is provided before load disturbance and parameter uncertainty Feedback compensation, enhances the robustness of system.

Brief description of the drawings

Fig. 1 permagnetic synchronous motor vector controlled block diagrams.

Fig. 2 is based on the self adaptation non-singular terminal sliding-mode control design flow diagram of interference observer.

Shock load adaptive N TSMC and common sliding formwork rate curve comparison diagram during Fig. 3 1000r/min.

Adaptive N TSMC and common sliding formwork rate curve comparison diagram when Fig. 4 rotating speeds are mutated.

Interference observer observed result figure during Fig. 5 g (t)=- 5.

Interference observer observed result figure during Fig. 6 g (t)=0.05sin (t).

Specific embodiment

To make the purpose of the present invention, technical scheme and advantage are more explicit, below will be by permagnetic synchronous motor control Example processed is described in further detail to embodiments of the present invention.

A kind of adaptive terminal sliding-mode control based on interference observer disclosed by the invention, it is adaptable to permanent-magnet synchronous The vector controlled of motor, is mainly made up of two parts of self adaptation non-singular terminal controller and interference observer.Specific implementation Mode has following steps：

1) adaptive rate exponentially approaching rule is designed

Consider following second order Uncertain nonlinear dynamical system：

Wherein：X=[x₁ x₂]^TIt is system state variables；b(x)≠0；Z (t) is that system does not know and external disturbance；U is Control input.When carrying out sliding mode controller design using conventional exponentially approaching rule for system (1), its Reaching Law is：

The Reaching Law includes two parts：It is exponential approach, its solution is s=s (0) e^-kt；For Constant speed convergence.Coefficient k in formula (2), ε does not have self-adjusting function, and for diverse location state variable, its convergence can not Reach optimum performance.The present invention proposes a kind of adaptive rate exponentially approaching rule：

Wherein：It is the single order norm of system state variables, k ＞ 0, ε ＞ 0, c ＞ 0, n ＞ 0.

The single order norm of the adaptive rate exponentially approaching rule state variable, with system mode apart from equalization point distance and Self-adaptative adjustment exponential approach speed and constant speed velocity of approach.The transient solution of exponential approach is in formula (3)When | |_x||₁Very big, exponential damping speed is substantially shorter much larger than the exponential damping speed of formula (2) The nearly time, now, constant speed convergence convergence speedMuch smaller than the ε in formula (2).When | |_x||₁Very little, it is possible to increase adjust Save coefficient c to shorten its sliding formwork arrival time, while reducing system chatter.When the state variable x for choosing is in system stabilization process In it is unlimited when being intended to zero, adaptive rate exponentially approaching rule just deteriorates to general index number Reaching Law.

Self adaptation non-singular terminal sliding mode controller is designed using the Reaching Law, adaptive N TSMC is designated as (Nonsingular Terminal Sliding Model Control)。

2) stability analysis of Reaching Law

In order to prove the stability of designed Reaching Law, Lyapunov functions are chosen

To above formula derivation

ByUnderstand, the adaptive N TSMC according to designed by adaptive rate exponentially approaching rule is stable, system shape State can be in Finite-time convergence to sliding-mode surface.

3) permagnetic synchronous motor rotating speed Mathematical Modeling is set up

The control system for permanent-magnet synchronous motor mentioned in the present invention uses vector controlled, i.e. i_d=0, under d-q coordinate systems, Permagnetic synchronous motor rotating speed Mathematical Modeling is：

Wherein：ω is rotor velocity, i_qIt is q shaft currents, P is torque winding number of pole-pairs, ψ_fIt is permanent magnet pole and stator The magnetic linkage of winding interlinkage, J is rotary inertia, and F is the coefficient of friction of rotor and load, T_LIt is load torque.

4) self adaptation non-singular terminal controller is designed

Rotational speed governor is used for accurate tracking speed preset ω^*.Definable state variable：

Can be obtained by formula (4) and (5)：

For control system for permanent-magnet synchronous motor, sliding-mode surface is chosen：

Design i_qMeet following control law：

Wherein：G (t) is total uncertain interference that load torque and parameter perturbation are produced.

5) interference observer is designed

From formula (8), Uncertainty g (t) is contained in the control law using the design of adaptive rate exponentially approaching rule, And g (t) is unknown quantity, it is impossible to measure, therefore come real-time monitored load change and parameter perturbation present invention introduces interference observer.

According to formula (4), it is considered to parameters in electrical machines uncertain factor：

Wherein：G (t)=T_L-Ji_qΔa+JωΔb+JΔd

Following system can be write out according to formula (9)

Wherein：X=[ω g (t)]^T；C=[1 0]；Output variable y=ω；It is defeated Enter variable u=1.5P ψ_fi_q。

From modern control theory, (A, C) can see for Observable pair, i.e. original system, existence observer.

Construct said system state observer be：

Wherein：It is x=[ω g (t)]^TEstimate,It is the estimate of y=ω；L=[l₁ l₂ ]^TIt is feedback matrix.

Observer error equation is：

As long as therefore the characteristic value of matrix (A-LC) has a negative real part, state error e just can gradually level off to zero, by machine The method of electricity configuration, can be by the POLE PLACEMENT USING of error equation (12) in Left half-plane, to ensure that systematic error levels off to zero.6) Obtain final adaptive N TSMC

The disturbance-observer value that interference observer is obtainedFormula (8) is updated to, control law newly can be finally obtained：

Wherein：To add the new q shaft currents set-point obtained after interference observer value of feedback.

Load torque and parameter perturbation are fed back in given current value as known quantity by formula (13), when load occurs When change or parameter are disturbed, controller can timely respond to its interference variations.

As shown in figure 3, to be based on interference observer adaptive N TSMC methods and common sliding-mode control described in this patent Emulation obtains rate curve contrast, it can be seen that when permagnetic synchronous motor rotating speed is set as 1000r/min, adaptive N TSMC Response speed to be faster than common SMC, and system and does not buffet substantially.In shock load, adaptive N TSMC shows more It is good robustness.As shown in figure 4, in velocity jump emulation experiment, the adaptive N TSMC jitter amplitudes described in this patent It is smaller, show more good speed characteristics.

As shown in Figure 5 and Figure 6, when giving external disturbance value g (t) for -5 and 0.05sin (t) respectively, observer can be with standard Really interference value is observed, and can rapidly track interference variations, enhance the antijamming capability of system.

To sum up, the sliding-mode control of a kind of permagnetic synchronous motor of the invention.In permagnetic synchronous motor vector controlled system The speed ring of system, introduces self adaptation non-singular terminal sliding mode controller, proposes a kind of adaptive rate exponentially approaching rule, the convergence Rule introduce state variable single order norm, according to state variable apart from equalization point far and near self-adaptative adjustment exponential approach speed with Constant speed velocity of approach, so as to realize weakening system chatter while shortening the convergence time.Meanwhile, for its exterior interference and Load disturbance problem, devises interference observer, and its observation fed back into the design of sliding mode controller.The present invention is being System be interfered and load appearance fluctuation when, can rapidly track rotating speed, reduction system overshoot and stable state static difference are greatly enhanced The robustness of system.

In the description of this specification, reference term " one embodiment ", " some embodiments ", " illustrative examples ", The description of " example ", " specific example " or " some examples " etc. means to combine specific features, the knot that the embodiment or example are described Structure, material or feature are contained at least one embodiment of the invention or example.In this manual, to above-mentioned term Schematic representation is not necessarily referring to identical embodiment or example.And, the specific features of description, structure, material or spy Point can in an appropriate manner be combined in one or more any embodiments or example.

Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that：Not Can these embodiments be carried out with various changes, modification, replacement and modification in the case of departing from principle of the invention and objective, this The scope of invention is limited by claim and its equivalent.

Claims (5)

1. a kind of permagnetic synchronous motor self adaptation non-singular terminal sliding-mode control based on interference observer, its feature exists In, adaptive rate exponentially approaching rule is designed, the Reaching Law introduces the single order norm of state variable, flat according to state variable distance The far and near self-adaptative adjustment exponential approach speed and constant speed velocity of approach of weighing apparatus point；Permagnetic synchronous motor rotating speed Mathematical Modeling is set up, In the speed ring of permanent magnet synchronous motor vector control system, self adaptation non-singular terminal sliding mode controller is introduced；Design interference is seen Survey device, and its observation is fed back into the design of sliding mode controller.

2. a kind of permagnetic synchronous motor self adaptation non-singular terminal sliding formwork based on interference observer according to claim 1 Control method, it is characterised in that the adaptive rate exponentially approaching rule, designs as follows：

$\stackrel{\·}{s}=-\mathrm{\ϵ}\frac{1}{1+c\left|\right|x|{|}_1}\mathrm{sgn}\left(s\right)-(k+c|\left|x\right|{|}_1)s$

Wherein：It is the single order norm of system state variables, k ＞ 0, ε ＞ 0, c ＞ 0, n ＞ 0；The adaptive rate refers to The single order norm of number Reaching Law state variables, with system mode apart from equalization point distance and self-adaptative adjustment exponential approach speed And constant speed velocity of approach；The transient solution of exponential approach is

3. a kind of permagnetic synchronous motor self adaptation non-singular terminal sliding formwork based on interference observer according to claim 2 Control method, it is characterised in that need to carry out the stability analysis of Reaching Law after designing adaptive rate exponentially approaching rule.

4. a kind of permagnetic synchronous motor self adaptation non-singular terminal sliding formwork based on interference observer according to claim 1 Control method, it is characterised in that the speed ring in permanent magnet synchronous motor vector control system, introduces self adaptation nonsingular end Hold sliding mode controller process be：

Step 1, control system for permanent-magnet synchronous motor uses vector controlled, makes i_d=0, under d-q coordinate systems, permagnetic synchronous motor Rotating speed Mathematical Modeling is：

$\frac{d\mathrm{\ω}}{dt}=\frac{1.5{\mathrm{P\ψ}}_f}{J}{i}_q-\frac{F}{J}\mathrm{\ω}-\frac{1}{J}{T}_L---\left(4\right)$

Wherein：ω is rotor velocity, i_qIt is q shaft currents, P is torque winding number of pole-pairs, ψ_fIt is permanent magnet pole and stator winding The magnetic linkage of interlinkage, J is rotary inertia, and F is the coefficient of friction of rotor and load, T_LIt is load torque；

Step 2, designs self adaptation non-singular terminal controller：

Rotational speed governor is used for accurate tracking speed preset ω^*, definition status variable：

$\left\{\begin{array}{c}{x}_1={\mathrm{\ω}}^{*}-\mathrm{\ω}\\ x_2={\stackrel{\·}{x}}_1=-\stackrel{\·}{\mathrm{\ω}}\end{array}\right.---\left(5\right)$

Can be obtained by formula (4) and (5)：

${\stackrel{\·}{x}}_2=\frac{1.5{\mathrm{P\ψ}}_f}{J}{\stackrel{\·}{i}}_q-\frac{F}{J}{x}_2-\frac{1}{J}{\stackrel{\·}{T}}_L---\left(6\right)$

For control system for permanent-magnet synchronous motor, sliding-mode surface is chosen：

$s=x_1+\frac{1}{\mathrm{\β}}{x}_2^{p/q}---\left(7\right)$

Design i_qMeet following control law：

$i_q=\frac{J}{1.5{\mathrm{P\ψ}}_f}\{{\∫}_0^t\[-\frac{F}{J}{x}_2+\mathrm{\β}\frac{q}{p}{x}_2^{2-\frac{p}{q}}+\mathrm{\ϵ}\frac{1}{1+c\left|\right|x|{|}_1}\mathrm{sgn}\left(s\right)+(k+c|\left|x\right|{|}_1)s\]dt+\frac{g\left(t\right)}{J}\}---\left(8\right)$

Wherein：i_qIt is the set-point of q shaft currents, P is torque winding number of pole-pairs, ψ_fFor permanent magnet pole interlinks with stator winding Magnetic linkage, J is rotary inertia, and F is the coefficient of friction of rotor and load, and p and q (p ＞ q) is positive odd number, 1 ＜ p/q ＜ 2, β ＞ 0, k ＞ 0It is load torque and the uncertain factor of parameter.

5. a kind of permagnetic synchronous motor self adaptation non-singular terminal sliding formwork based on interference observer according to claim 4 Control method, it is characterised in that the interference observer of construction is：

$\left\{\begin{array}{c}{\hat{x}}^{\′}=A\hat{x}+Bu+L(y-\hat{y})\\ \hat{y}=C\hat{x}\end{array}\right.---\left(11\right)$

Wherein：It is x=[ω g (t)]^TEstimate,It is the estimate of y=ω；L=[l₁ l₂]^TFor Feedback matrix；The disturbance-observer value that interference observer is obtainedIt is updated to formula (8)：

$i_q=\frac{J}{1.5{\mathrm{P\ψ}}_f}\{{\∫}_0^t\[-\frac{F}{J}{x}_2+\mathrm{\β}\frac{q}{p}{x}_2^{2-\frac{p}{q}}+\mathrm{\ϵ}\frac{1}{1+c\left|\right|x|{|}_1}\mathrm{sgn}\left(s\right)+(k+c|\left|x\right|{|}_1)s\]dt+\frac{g\left(t\right)}{J}\}---\left(8\right)$

Control law newly can finally be obtained：

$i_q^{*}=\frac{J}{1.5{\mathrm{P\ψ}}_f}\{{\∫}_0^t\[-\frac{F}{J}{x}_2+\mathrm{\β}\frac{q}{p}{x}_2^{2-\frac{p}{q}}+\mathrm{\ϵ}\frac{1}{1+c\left|\right|x|{|}_1}\mathrm{sgn}\left(s\right)+(k+c|\left|x\right|{|}_1)s\]dt+\frac{\hat{g}\left(t\right)}{J}\}---\left(13\right)$

Wherein：To add the new q shaft currents set-point obtained after interference observer value of feedback.