CN106788044B - A kind of adaptive non-singular terminal sliding-mode control of permanent magnet synchronous motor based on interference observer - Google Patents
A kind of adaptive non-singular terminal sliding-mode control of permanent magnet synchronous motor based on interference observer Download PDFInfo
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- CN106788044B CN106788044B CN201710082647.7A CN201710082647A CN106788044B CN 106788044 B CN106788044 B CN 106788044B CN 201710082647 A CN201710082647 A CN 201710082647A CN 106788044 B CN106788044 B CN 106788044B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
- H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
Abstract
The present invention relates to a kind of adaptive non-singular terminal sliding-mode controls of permanent magnet synchronous motor based on interference observer, in the speed ring of permanent magnet synchronous motor vector control system, introduce adaptive non-singular terminal sliding mode controller, it is characterized in that, it is proposed a kind of adaptive rate exponentially approaching rule, the single order norm of Reaching Law introducing state variable, the adaptive adjustment index velocity of approach of distance and constant speed velocity of approach according to state variable apart from equalization point, weaken system chatter while to realize the shortening approach time.Meanwhile for exterior interference and load disturbance problem, interference observer is devised, and by its observation feedback into the design of sliding mode controller.The present invention can rapidly track revolving speed when system is interfered and loads and fluctuates, and reduce system overshoot and stable state static difference, greatly strengthen the robustness of system.
Description
Technical field
The invention belongs to permanent magnet synchronous motor control fields, are related to a kind of sliding-mode control based on interference observer.
Background technique
Permanent magnet synchronous motor (Permanent Magnet Synchronous Motor, PMSM) has small in size, structure
Simply, many advantages, such as high-efficient, so that it is used widely in fields such as numerically-controlled machine tool, medical instrument, aerospaces, but
Since permanent magnet synchronous motor is a multivariable, non-linear, close coupling complex object, when system is by inner parameter or the external world
When the factors such as disturbance influence, conventional PI control is not able to satisfy the requirement of high performance control, and self adaptive control, intelligent control
It is difficult to apply in practical projects Deng due to algorithm complexity.
Sliding mode variable structure control is a kind of nonlinear Control, it is using control switching rule, by different control actions
Between switching, generate a kind of unrelated with original system, according to the movement for the state trajectory for making a reservation for " sliding mode ", make system mode
Reach desired point, to realize system control.Since desired trajectory and control object inner parameter and external disturbance are unrelated,
Sliding mode variable structure control is of less demanding to model accuracy, has strong robustness to Parameter Perturbation, external disturbance.In recent years increasingly
Sliding mode variable structure control is applied in AC servo by more scholars.
Although achieving certain achievement to the research of sliding moding structure at present, still need on control performance into one
Step improves.Non-singular terminal sliding formwork control is a kind of novel sliding-mode control occurred in recent years, it is by purposefully changing
Become switching function, directly solve singularity problem existing for existing TSM control in terms of sliding mode design, realizes and be
The nonsingular control of the overall situation 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 enabled to desired trajectory, and stable state accuracy with higher, especially suitable for
At a high speed, high-precision control.But still have buffeting problem, it is difficult to reach ideal control effect.
Summary of the invention
It is an object of the invention to solve in the prior art, control system for permanent-magnet synchronous motor response slowly, system chatter,
The problems such as interference rejection ability is poor proposes a kind of adaptive non-singular terminal sliding-mode control based on interference observer.
In order to solve the above-mentioned technical problems, the present invention provides following solution.
A kind of adaptive terminal sliding-mode control based on interference observer, using adaptive non-singular terminal sliding formwork control
Device processed is combined with interference observer.Adaptive non-singular terminal sliding mode controller, which is characterized in that propose a kind of adaptive strain
Fast exponentially approaching rule, the Reaching Law introduce the single order norm of state variable, and the distance according to state variable apart from equalization point is adaptive
Adjustment index velocity of approach and constant speed velocity of approach are answered, weakens system chatter while to realize the shortening approach time.
Reaching Law design is as follows:
Wherein:For 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 inventiond=0, under d-q coordinate system, permanent magnetism is same
Walk motor speed mathematical model are as follows:
Wherein: ω is rotor velocity, iqFor q shaft current, P is torque winding number of pole-pairs, ψfFor permanent magnet pole and stator
The magnetic linkage of winding interlinkage, J are rotary inertia, and F is the coefficient of friction of rotor and load, TLFor load torque.
In conjunction with permanent magnet synchronous motor mathematical model, definition status variable chooses sliding-mode surface:
Design control law are as follows:
Consider parameters in electrical machines uncertain factor:
Wherein: g (t)=TL-JiqΔa+JωΔb+JΔd
The interference observer of construction system:
In formula:ForEstimated value,For the estimated value of y=ω；Input variable u
=1.5P ψfiq；C=[1 0]；L=[l1 l2]TFor feedback matrix.
The disturbance-observer value feedforward compensation that observer is obtained is into sliding mode controller, available new control law:
Wherein:For the new q shaft current given value obtained after interference observer value of feedback is added,For the observation of g (t)
Value.
Technical solution beneficial effect proposed by the present invention is that the proposition of adaptive rate exponentially approaching rule effectively improves
The global fast convergence of state variable in TSM control rapidly tracing motor rotation speed and can shorten approach realizing
System chatter is weakened while time.The addition of interference observer is provided to before load disturbance and parameter uncertainty
Feedback compensation, enhances the robustness of system.
Detailed description of the invention
Fig. 1 permanent magnet synchronous motor vector controlled block diagram.
Adaptive non-singular terminal sliding-mode control design flow diagram of the Fig. 2 based on interference observer.
Shock load adaptive N TSMC and common sliding formwork rate curve comparison diagram when Fig. 3 1000r/min.
Adaptive N TSMC and common sliding formwork rate curve comparison diagram when Fig. 4 revolving speed is mutated.
Interference observer observed result figure when Fig. 5 g (t)=- 5.
Interference observer observed result figure when Fig. 6 g (t)=0.05sin (t).
Specific embodiment
To make the purpose of the present invention, technical solution and advantage are more explicit, will pass through permanent magnet synchronous motor control below
Example processed is described in further detail embodiments of the present invention.
A kind of adaptive terminal sliding-mode control based on interference observer disclosed by the invention is suitable for permanent-magnet synchronous
The vector controlled of motor is mainly made of two parts of adaptive 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]TFor system state variables；b(x)≠0；Z (t) does not know for system and external disturbance；U is
Control input.When carrying out sliding mode controller design using conventional exponentially approaching rule for system (1), Reaching Law are as follows:
The Reaching Law includes two parts:For exponential approach item, solution is s=s (0) e-kt；For
Constant speed approaches item.Coefficient k in formula (2), ε do not have self-adjusting function, and for different location state variable, convergence cannot
Reach optimum performance.The present invention proposes a kind of adaptive rate exponentially approaching rule:
Wherein:For 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, distance with system mode apart from equalization point and
Adaptive adjustment index velocity of approach and constant speed velocity of approach.The transient solution of exponential approach item is in formula (3)When | |x||1Very big, exponential damping speed is much larger than the exponential damping speed of formula (2), is substantially shorter
The nearly time, at this point, constant speed approach item approaches rateMuch smaller than the ε in formula (2).When | |x||1Very little, it is possible to increase adjust
Coefficient c is saved to shorten its sliding formwork arrival time, while reducing system chatter.When the state variable x of selection is in system stabilization process
In when being infinitely intended to zero, adaptive rate exponentially approaching rule is just degenerated for general index number Reaching Law.
Adaptive non-singular terminal sliding mode controller is designed using the Reaching Law, is denoted as adaptive N TSMC
(Nonsingular Terminal Sliding Model Control)。
2) stability analysis of Reaching Law
In order to prove the stability of designed Reaching Law, Lyapunov function is chosen
To above formula derivation
ByIt is found that the adaptive N TSMC according to designed by adaptive rate exponentially approaching rule is stable, system
State can be in Finite-time convergence to sliding-mode surface.
3) permanent magnet synchronous motor revolving speed mathematical model is established
Control system for permanent-magnet synchronous motor mentioned in the present invention uses vector controlled, i.e. id=0, under d-q coordinate system,
Permanent magnet synchronous motor revolving speed mathematical model are as follows:
Wherein: ω is rotor velocity, iqFor q shaft current, P is torque winding number of pole-pairs, ψfFor permanent magnet pole and stator
The magnetic linkage of winding interlinkage, J are rotary inertia, and F is the coefficient of friction of rotor and load, TLFor load torque.
4) adaptive non-singular terminal controller is designed
Rotational speed governor gives ω for accurate tracking velocity*.It can define state variable:
It can be obtained by formula (4) and (5):
For control system for permanent-magnet synchronous motor, sliding-mode surface is chosen:
Design iqMeet rule control as follows:
Wherein: g (t) is load torque and total uncertain interference that parameter perturbation generates.
5) interference observer is designed
By formula (8) it is found that containing Uncertainty g (t) in the control law designed using adaptive rate exponentially approaching rule,
And g (t) is unknown quantity, is unable to measure, therefore present invention introduces interference observers to observe load variation and parameter perturbation in real time.
According to formula (4), parameters in electrical machines uncertain factor is considered:
Wherein: g (t)=TL-JiqΔa+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 ψfiq。
By modern control theory it is found that (A, C) is Observable pair, i.e. original system can be seen, existence observer.
Construct the state observer of above system are as follows:
Wherein:For x=[ω g (t)]TEstimated value,For the estimated value of y=ω；L=[l1
l2]TFor feedback matrix.
Observer error equation are as follows:
As long as therefore the characteristic value of matrix (A-LC) has negative real part, state error e just can level off to zero gradually, pass through machine
The method of electricity configuration, can be by the POLE PLACEMENT USING of error equation (12) in Left half-plane, to guarantee that systematic error levels off to zero.6)
Obtain final adaptive N TSMC
The disturbance-observer value that interference observer is obtainedFormula (8) are updated to, control law newly can be finally obtained:
Wherein:For the new q shaft current given value obtained after interference observer value of feedback is added.
It is fed back using load torque and parameter perturbation as known quantity into given current value by formula (13), when load occurs
When variation or parameter disturb, controller can timely respond to its interference variations.
As shown in figure 3, to be based on interference observer adaptive N TSMC method and common sliding-mode control described in this patent
Emulation obtains rate curve comparison, it can be seen that when setting permanent magnet synchronous motor revolving speed as 1000r/min, adaptive N TSMC
Response speed to be faster than common SMC, and system substantially and does not buffet.In shock load, adaptive N TSMC is shown more
For good robustness.As shown in figure 4, in velocity jump emulation experiment, adaptive N TSMC jitter amplitude described in this patent
It is smaller, show be more good speed characteristics.
As shown in Figure 5 and Figure 6, when given external disturbance value g (t) is -5 and 0.05sin (t) respectively, observer can be quasi-
It really observes interference value, and interference variations can be tracked rapidly, enhance the anti-interference ability of system.
To sum up, the sliding-mode control of a kind of permanent magnet synchronous motor of the invention.In permanent magnet synchronous motor vector controlled system
The speed ring of system introduces adaptive non-singular terminal sliding mode controller, proposes a kind of adaptive rate exponentially approaching rule, the approach
Rule introduces the single order norm of state variable, the adaptive adjustment index velocity of approach of distance according to state variable apart from equalization point with
Constant speed velocity of approach weakens system chatter while to realize the shortening approach time.Meanwhile for exterior interference and
Load disturbance problem devises interference observer, and by its observation feedback into the design of sliding mode controller.The present invention is being
System is interfered and load when fluctuating, and can rapidly be tracked revolving speed, reduction system overshoot and stable state static difference, be 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 specific features described in conjunction with this embodiment or example, knot
Structure, material or feature are included at least one embodiment or example of the invention.In the present specification, to above-mentioned term
Schematic representation may not refer to the same embodiment or example.Moreover, specific features, structure, material or the spy of description
Point can be combined in any suitable manner in any one or more of the embodiments or examples.
Although an embodiment of the present invention has been shown and described, it will be understood by those skilled in the art that: not
A variety of change, modification, replacement and modification can be carried out to these embodiments in the case where being detached from the principle of the present invention and objective, this
The range of invention is defined by the claims and their equivalents.
Claims (4)
1. a kind of adaptive non-singular terminal sliding-mode control of permanent magnet synchronous motor based on interference observer, feature exist
In design adaptive rate exponentially approaching rule, the Reaching Law introduces the single order norm of state variable, flat according to state variable distance
The adaptive adjustment index velocity of approach of distance and constant speed velocity of approach of weighing apparatus point；Permanent magnet synchronous motor revolving speed mathematical model is established,
In the speed ring of permanent magnet synchronous motor vector control system, adaptive non-singular terminal sliding mode controller is introduced；Design interference is seen
Device is surveyed, and by its observation feedback into the design of sliding mode controller；
The adaptive rate exponentially approaching rule designs as follows:
Wherein:For the single order norm of system state variables, k > 0, ε > 0, c > 0, n > 0；The adaptive rate
The single order norm of exponentially approaching rule state variable, the far and near and adaptive adjustment index with system mode apart from equalization point approach speed
Degree and constant speed velocity of approach；The transient solution of exponential approach item is
2. the adaptive non-singular terminal sliding formwork of a kind of permanent magnet synchronous motor based on interference observer according to claim 1
Control method, which is characterized in that design the stability analysis for needing to carry out Reaching Law after adaptive rate exponentially approaching rule.
3. the adaptive non-singular terminal sliding formwork of a kind of permanent magnet synchronous motor based on interference observer according to claim 1
Control method, which is characterized in that the speed ring in permanent magnet synchronous motor vector control system introduces adaptive nonsingular end
Hold the process of sliding mode controller are as follows:
Step 1, control system for permanent-magnet synchronous motor uses vector controlled, enables id=0, under d-q coordinate system, permanent magnet synchronous motor
Revolving speed mathematical model are as follows:
Wherein: ω is rotor velocity, iqFor q shaft current, P is torque winding number of pole-pairs, ψfFor permanent magnet pole and stator winding
The magnetic linkage of interlinkage, J are rotary inertia, and F is the coefficient of friction of rotor and load, TLFor load torque；
Step 2, adaptive non-singular terminal controller is designed:
Rotational speed governor gives ω for accurate tracking velocity*, definition status variable:
It can be obtained by formula (4) and (5):
For control system for permanent-magnet synchronous motor, sliding-mode surface is chosen:
Design iqMeet rule control as follows:
Wherein: i 'qFor the given value of q shaft current, P is torque winding number of pole-pairs, ψfIt interlinks for permanent magnet pole with stator winding
Magnetic linkage, J are rotary inertia, and F is the coefficient of friction of rotor and load, and p and q are positive odd number, 1 < p/q < 2, β > 0, k > 0, ε >
0, c > 0, g (t) are the uncertain factor of load torque and parameter.
4. the adaptive non-singular terminal sliding formwork of a kind of permanent magnet synchronous motor based on interference observer according to claim 3
Control method, which is characterized in that the interference observer of construction are as follows:
Wherein:C=[1 0],For x=[ω g (t)]TEstimation
Value,For the estimated value of y=ω；L=[l1 l2]TFor feedback matrix；The disturbance-observer value that interference observer is obtained
It is updated to formula (8):
Control law newly can finally be obtained:
Wherein:For the new q shaft current given value obtained after interference observer value of feedback is added.
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| CN105591524B (en) * | 2016-02-24 | 2018-04-24 | 江苏大学 | A kind of permanent magnetism speed differential clutch and its adaptive non-singular terminal sliding formwork method for controlling number of revolution |
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