CN107656437B - Magnetic suspension rotor system based on disturbance observer mismatches the control method of disturbance - Google Patents
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Abstract
NEW TYPE OF COMPOSITE control method disclosed in this invention based on disturbance observer, the mismatch that can be used for inhibiting in voltage-controlled type magnetic bearing system disturb.It establishes the dynamic model for mismatching and disturbing lower voltage-controlled type magnetic bearing system based on physical law, equivalent magnetic suspension rotor dynamic system is reconstructed by introducing new state variable, disturbance will be mismatched in equivalent system is divided into compatible portion and non-matching part, compatible portion carries out AF panel by robust controller, and non-matching part carries out Interference Cancellation by design point perturbation observer.Mismatch proposed by the present invention disturbs control method, suspends control with important references meaning to the high-precision of magnetic bearing system.
Description
Technical field
The invention belongs to Aerospace Control technical field of research, in particular to a kind of magnetic suspension rotor based on disturbance observer
System mismatches the control method of disturbance.
Background technique
Compared to conventional mechanical bearings, magnetic suspension system has lot of advantages, as revolving speed is higher, abrasion less, without lubrication,
Longer life expectancy.Exactly because these advantages, it is many that magnetic suspension system is applied successfully to flywheel, control-moment gyro and pump etc.
Field.There are two types of control models for magnetic axis suspension control system: current control mode and voltage mode control.Generally speaking, voltage
Control model is better than current control mode.On the one hand, the input of voltage mode control is coil windings voltage, is to compare current control
The more accurate system input variable of mode；On the other hand, the power amplifier under current control mode is more than voltage mode control
It is complicated and expensive.Voltage mode control compared to current control mode there are many advantage, but voltage-controlled type magnetic suspension system
The dynamic property of system is also increasingly complex: external disturbance by from the different path effect of control input in magnetic suspension system, just shape
It is disturbed at the mismatch for being unsatisfactory for matching condition.The mismatch in voltage-controlled type magnetic suspension system how is inhibited to disturb
The problem challenging as one.
Modern robust control method has been widely used for voltage-controlled type magnetic suspension system, in the stability of the system of raising
Some significant effects are achieved in terms of dynamic property.The linearisation in voltage mode control of uniaxial magnetic-levitation system, benefit
When improving the linearity and closed loop robustness, magnetic suspension system high speed rotor cover with different feedback methods to external disturbance
Stability and controllability, and using a kind of robust integrated control method come the problems such as collocation structure resonance in research
Column.However research mentioned above mainly inhibits external disturbance and uncertainty by way of feedback regulation, cannot directly,
Inhibit the uncertainty of strong external disturbance and target compensation in time.
It combines the composite control method of robust control and disturbance observer quietly to rise as a result, and is successfully applied to disturb
Meet in the various engineering systems of matching condition, such as electric system, power converter system, hard disk driver system, robot
System etc..In this composite control method, disturbance observer can observe unknown disturbance, and make compensation to these disturbances,
And not to sacrifice the performance of basic controller as cost.With the magnetic suspension rotor system matching disturbance based on disturbance observer
The research of suppressing method deepens continuously, and researcher wants to inhibit in external disturbance by this composite control method
Mismatch disturbance.
It is asked as follows as it can be seen that the control method for mismatching Disturbance Rejection in voltage-controlled type magnetic suspension rotor system at present exists
Topic: 1) inhibiting external disturbance and object uncertain in the way of feedback regulation, only weakens and mismatches disturbance to output
It influences, cannot inhibit external disturbance and target compensation uncertain directly, in time；2) compensation performance for mismatching disturbance exists
It is to be obtained with the cost for sacrificing the performance indicator of basic controller to a certain extent.
Summary of the invention
For the control method for overcoming the shortcomings of existing voltage-controlled type magnetic suspension rotor system, provide a kind of based on disturbance
The NEW TYPE OF COMPOSITE control method of observer can use disturbance using the Compound Control Strategy based on improved disturbance observer
Observer observes unknown disturbance, and makes compensation to these disturbances, and does not realize using the performance for sacrificing basic controller as cost
The inhibition of external disturbance in voltage-controlled type magnetic suspension rotor system.
NEW TYPE OF COMPOSITE control method disclosed in this invention based on disturbance observer, can be used for inhibiting voltage-controlled type magnetic
Mismatch disturbance in bearing arrangement.It, which establishes to mismatch based on physical law, disturbs the dynamic of lower voltage-controlled type magnetic bearing system
States model reconstructs equivalent magnetic suspension rotor dynamic system by introducing new state variable, disturbs mismatch in equivalent system
Dynamic to be divided into compatible portion and non-matching part, compatible portion carries out AF panel by robust controller, and non-matching part passes through
Design point perturbation observer carries out Interference Cancellation.The following steps are included:
1) dynamic model for mismatching and disturbing lower voltage-controlled type magnetic suspension rotor system is established, voltage-controlled type magnetic is obtained
The state equation of bearing control system；
2) equivalent system that magnetic suspension rotor system is reconstructed by introducing new state variable will mismatch disturbance and be divided into
Match and mismatch two parts；
3) the state space disturbance observer for designing broad sense is observed the mismatch disturbance part in equivalent system；
4) the disturbance estimated value of the disturbance observer observation obtained according to step 3), introduced in basic robust controller etc.
Effect compensation, realizes the inhibition to external disturbance, and obtain improved multiplex control system；
5) stability analysis is carried out to improved multiplex control system, calculates basic robust controller and disturbance observer
Control gain.
Further, the state equation for the voltage-controlled type magnetic bearing control system that step 1) is established are as follows:
In formula, d (s；T) total disturbance is indicated, s is rotor displacement, and t is time, u=[us]T, x=[x1,x2,x3]T, x1=
S,x3=isIt is state variable,It is the speed of rotor, isIt is control electric current, state matrix are as follows:
In formula, m is the quality of rigid rotator, and R is coil resistance, and L is coil inductance,WithIt indicates in operating point (is
=iN, s=sN) control electric current and position stiffness.
Further, d (s is always disturbed；T) include Parameters variation and external disturbance, indicate are as follows:
d(s；T)=Δ Ki(s；t)is(t)+ΔKs(s；t)s(t)+fd(t)
In formula, fdIt is external disturbance, Δ Ki(s；And Δ K t)s(s；It t) is Parameters variation amount.
Further, the new state variable η (t) of the step 2) substitutes the state variable i in original systems(t), new shape
State variable is defined as:
η (t)=is(t)-id(t)(8)
Equivalent voltage-controlled type magnetic bearing control system can indicate are as follows:
In formula, disturbance d (s is mismatched；T) it is divided into two parts:WithAssuming that disturbance observation
Device can progressively track disturbance, i.e. when t → ∞,
Further, the step 3) includes the following steps:
Introduce an auxiliary vector ω (s；T), total disturbance d (s is redefined；T) are as follows:
d(s；T)=V ω (s；t) (10)
In formula, W and V are coefficient matrixes；
Composite system is made of state variable (7) and disturbance variable (11), is indicated are as follows:
According to the design method of state observer, disturbance observer can design subsystem below:
In formula, σ (t) is the equivalent output of subsystem, can be by observing feedback quantityTo improve observation
Device precision；According to the structure of disturbance observer, disturbance variable can be derivedExpression formula is as follows:
By auxiliary variableIt substitutes into (14), disappears on the right side of (14)Disturbance observer can be with
It indicates are as follows:
In formula, W and V are coefficient matrix, ω (s；It t) is auxiliary vector, auxiliary variable
It is disturbance variable.
Further, if W=0, the disturbance observer model of V=I, unknown disturbance prediction device can simplify are as follows:
Further, the step 4) includes:
Matching is disturbed, composite controller may be designed as:
In formula, KkFor the feedback oscillator determined by the performance of closed-loop system, feedback control can make the state in system
Variable is stablized to zero, i.e., as t → 0, s (t) → 0,is(t)→0。
For the robustness for guaranteeing closed-loop system, a feedback robust controller is introduced in equivalent system, is indicated are as follows:
ud(t)=Kx*(t) (18)
In formula,K is the feedback oscillator for meeting H ∞；
After improvement, the input of magnetic bearing control system becomes:
us=ud+Rid(19)；
Disturbance observer equation (16) and state feedback robust controller equation (18) are substituted into equation (9), improved
Multiplex control system equation afterwards are as follows:
In formula, B3=[0 0 1/Ki]T, ed(s；It t) is disturbance observation error,
It enablesIt can indicate are as follows:
In formula,
Further, stability analysis is carried out to improved composite system, corresponding controller gain and sight is calculated
Device gain is surveyed, is specifically included:
In composite system (25), due toWithIt is all H2Convergence in norm, so disturbanceIt is also H2
Convergence in norm, to reduce disturbanceInfluence, using the robust control scheme with H ∞ performance indicator, H ∞ controller
The stabilization of system can not only be kept, it is also possible that output reference value meets the following conditions:
In formula, λ is the normal number for indicating interference rejection capability, and new system stochastic stability is shown below and meets H ∞
The necessary condition of performance, i.e. proof linear matrix inequality (LMI)；
In composite system (25), any λ > 0, there are matrix Q1> 0, Q2> 0 and R1, R2Meet:
In formula, Ξ1=sym (AQ1+B1R1), Ξ2=sym (- R2B2).Sym () indicates a matrix operation, for symmetrical square
Battle array M has sym (M)=M+MT；
To obtain working as controller gainObserver gainWhen, composite system (25) robust
Property Asymptotic Stability, and meet
The advantages of the present invention over the prior art are that:
(1) disturbance and uncertainty are handled by state variable, rather than output variable；
(2) do not change the structure of basic controller, and will suspension robust controller property retention substantially in optimum state；
(3) non-matching part carries out Interference Cancellation by design point perturbation observer.
Detailed description of the invention
Fig. 1 is magnetic bearing control system block diagram；
Fig. 2 is the relational graph of stiffness parameters and different operating point, and figure (a) indicates KiVariable, figure (b) indicate KsVariable；
Fig. 3 is the structure chart of the composite control method based on disturbance observer；
Fig. 4 is the structure chart of state space disturbance observer.
Specific embodiment
Technical solution of the present invention is described in detail with reference to the accompanying drawing.
Step 1: establishing the dynamic model for mismatching and disturbing lower voltage-controlled type magnetic suspension rotor system
As shown in Figure 1 it is the detailed maps of magnetic suspension rotor system, controls voltage usIt is converted by power amplifier
Coil current is, make rotor stability be suspended in center to generate expected electromagnetic force.
According to Newton's law, the kinetic model of axial magnetic suspension rotor-support-foundation system is:
In formula, m is the quality of rigid rotator, FsIt is electromagnetic force, fdIt is external disturbance, s is rotor displacement.
According to Maxwell's law it is found that electromagnetic force and the deviation of control electric current and nominal air gap are in non-linear relation.It is non-
Linear electromagnetic power are as follows:
In formula, k=0.25 μ0aN2It is and pole-face region a, electromagnetic coil number N, the magnetic permeability μ of air0Relevant electromagnet
Constant.i0And s0It is bias current and nominal air gap, isIt is control electric current.According to the control strategy proposed in invention, power amplification
The control electric current of device is generated by control voltage.To some operating point (is=iN, s=sN) Taylor series expansion is carried out,
Nonlinear magnetic forces approximate linearization can be obtained:
In formula,WithIt indicates in operating point (is=iN, s=sN) electric current and position stiffness.It is obvious thatWithNo
Always constant, they can change with the variation of operating point.In rated operation point (is=0, s=0), expression formula can simplify
Are as follows:
By operating point (is=iN, s=sN) at expression formula and rated operation point (is=0, s=0) at expression formula connection
It is vertical, the relational graph of available stiffness parameters as shown in Figure 2 and different operating point.It can be seen that and rated operation point in Fig. 2
Between error it is bigger, the variation of stiffness parameters is bigger.Therefore, the nonlinear characteristic and nominal operation of current stiffness and position stiffness
The constant coefficient and disturbance parameter of point are related, obtain:
ΔKi(s；And Δ K t)s(s；It t) is Parameters variation amount, s is rotor displacement, and t is the time.(3) and (4) are substituted into
(1), magnetic bearing control system dynamic model can indicate are as follows:
In formula, G1=Ks/m,G2=Ki/m,G3=1/m, d (s；T) total disturbance, including Parameters variation and external disturbance are indicated,
It is defined as:
d(s；T)=Δ Ki(s；t)is(t)+ΔKs(s；t)s(t)+fd(t)
According to Kirchhoff's second law, the dynamical equation of voltage-to-current are as follows:
In formula, R is coil resistance, and L is coil inductance.Therefore the state equation of voltage-controlled type magnetic bearing control system
Are as follows:
In formula, u=[us]T, x=[x1,x2,x3]T。x1=s,x3=isIt is all state variable, state matrix are as follows:
From B1And B2As can be seen that input signal, in Article 3 control channel, disturbance component is in the second control channel
On.It disturbs and inputs through different channelings in system, just form mismatch disturbance.
It is worth noting that, the present invention is Parameters variation and external disturbance to be integrated the total disturbance for the system of being thought of as,
Repartition as a whole as matching and non-matching part, without individually discuss Parameters variation and external disturbance with the presence or absence of
Match and non-matching part.
Step 2: establishing the equivalent system of voltage-controlled type magnetic suspension rotor system
In order to offset the disturbance of the mismatch in external disturbance, need to change initial system, so that mismatching disturbance can
Meet matching condition.
Fig. 3 show the compound control structure figure based on disturbance observer, in new state variable substitution original system
State variable is(t), new state variable may be defined as:
η (t)=is(t)-id(t) (8)
Therefore, equivalent system can indicate are as follows:
The equivalent system expression formula shown in (9) can be seen that mismatch disturbance d (s；T) two parts can be divided into:WithAssuming that disturbance observer can progressively track disturbance, i.e. when t → ∞,
So only being disturbed in the equivalent system shown in (9)It always exists.In addition, from expression formula
It can be seen that disturbanceWith new input ud(t) on same channel, that is to say, that disturbanceMeet matching condition.
Therefore, it mismatches disturbance and is converted into the amount that can satisfy matching disturbance, new system is also just equivalent to original system shown in (7).
Step 3: the design of generalized state perturbation observer
This generalized state perturbation observer can observe unknown disturbance, be not limited to a certain particular model.Fig. 4
It, can be by observing feedback quantity for the structure chart of state space disturbance observerTo improve the precision of state observer.
Introduce an auxiliary vector ω (s；T), total disturbance d (s is redefined；T) are as follows:
d(s；T)=V ω (s；t) (10)
In formula, W and V are coefficient matrixes.
Want to derive disturbance quantity d (s；T) expression formula will first find out disturbance variable ω (s；t).Composite system is become by state
It measures (7) and disturbance variable (11) is constituted, can indicate are as follows:
As can be seen that equation (12) are similar with the structure of reduced dimension observer.According to the design method of state observer, disturbance
Observer can design subsystem below:
σ (t) is the equivalent output of subsystem.
According to the structure of observer, disturbance variable can be derivedExpression formula are as follows:
It is the estimated value of disturbance variable, by auxiliary variableIt substitutes into (14), disappear (14) right side
SideDisturbance observer can indicate are as follows:
If W=0, V=I, the disturbance observer model of unknown disturbance can be indicated are as follows:
Step 4: improved Composite Controller Design
Matching is disturbed, composite controller may be designed as:
In formula, KkFor feedback oscillator, determined by the performance of closed-loop system.Feedback control can slowly in elimination system shape
State variable, i.e., as t → 0, s (t) → 0,is(t)→0.But in voltage-controlled type magnetic bearing control system,
Due to mismatching the presence of disturbance, traditional composite controller is no longer applicable in.
In order to offset the mismatch disturbance generated due to state variable, needs to change initial system, disturbed so that mismatching
It is dynamic to can satisfy matching condition.
In order to guarantee the robustness of this closed-loop system, need to design a feedback robust control in the system shown in (9)
Device processed can indicate are as follows:
ud(t)=Kx*(t) (18)
In formula,K is the feedback oscillator for meeting H ∞.Feedback control strategy can be kept
When the performance, i.e. t → ∞ of system, s (t) → 0,is(t)→id(t).Although coil current is stablized by certain deviation
Value, but what mismatches disturbance uniquely influences rotor without, can satisfy the suspension requirement of magnetic bearings control.
In equivalent system, the initial input voltage u of magnetic bearing control systemsAre as follows:
us=ud+Rid (19)
Disturbance observer equation (16) and state feedback robust controller equation (18) are substituted into equation (9), are newly
The equation of system are as follows:
In formula, B3=[0 0 1/Ki]T, ed(s；T) it is disturbance observation error, may be defined as:
Therefore, the dynamical equation of disturbance observation error can indicate are as follows:
(16) are substituted into (22), the dynamical equation of disturbance observation error can indicate again are as follows:
By dynamical equation (23) simultaneous of the equation (9) of new system and observation error, multiplex control system equation after improvement
Are as follows:
It enablesIt can indicate are as follows:
In formula,
The output reference value of composite system are as follows:
In formula, D=[D1,D2] it be designer is the weighting matrix for meeting system performance and selecting.
Step 5: the analysis of improved composite controller stability
In composite system (25), due toWithIt is all H2Convergence in norm, so disturbanceIt is also H2
Convergence in norm.Therefore, it is disturbed to reduceInfluence, we using have H ∞ performance indicator robust control side
Case.H ∞ controller can not only keep the stabilization of system, it is also possible that output reference value meets the following conditions:
In formula, λ is the normal number for indicating interference rejection capability, and new system stochastic stability is shown below and meets H ∞
The necessary condition of performance, i.e. proof linear matrix inequality (LMI).
Theorem: in composite system (25), any λ > 0, there are matrix Q1> 0, Q2> 0 and R1, R2Meet:
In formula, Ξ1=sym (AQ1+B1R1), Ξ2=sym (- R2B2).Sym () indicates a matrix operation, for symmetrical square
Battle array M has sym (M)=M+MT.Controller gainObserver gainWhen, composite system (25) robustness
Asymptotic Stability.In addition, he also meets
It proves: proving that (28) meet H ∞ performance in Bounded Real Lemma, on the basis of LMI.
(25) are substituted into (28), are enabled:
In formula, Θ1=sym [P1(A+B1K)], Θ2=sym (- P2EB2).Enable Q1=P1 -1, R1=KQ1, R2=P2E, (29)
Premultiplication diagonal matrix { Q respectively1, I, I, I, I }, then the right side multiplies diagonal matrix { Q1, I, I, I, I }, the conclusion of available (27).
The foregoing is only a preferred embodiment of the present invention, is not intended to restrict the invention, for the skill of this field
For art personnel, the invention may be variously modified and varied.All within the spirits and principles of the present invention, made any to repair
Change, equivalent replacement, improvement etc., should all be included in the protection scope of the present invention.
Claims (8)
1. the control method that the magnetic suspension rotor system based on disturbance observer mismatches disturbance, which is characterized in that including following
Step:
1) dynamic model for mismatching and disturbing lower voltage-controlled type magnetic suspension rotor system is established, voltage-controlled type magnetic bearing is obtained
The state equation of control system；
2) equivalent system that magnetic suspension rotor system is reconstructed by introducing new state variable, will mismatch disturbance be divided into matching and
Mismatch two parts；
3) the state space disturbance observer for designing broad sense is observed the mismatch disturbance part in equivalent system；
4) design basis robust controller, according to the disturbance estimated value for the disturbance observer observation that step 3) obtains, in basic Shandong
Equivalent compensation is introduced in stick controller, realizes the inhibition to external disturbance, and obtain improved multiplex control system；
5) stability analysis is carried out to improved multiplex control system, calculates the control of basic robust controller and disturbance observer
Gain processed.
2. control method according to claim 1, which is characterized in that the voltage-controlled type magnetic axis that the step 1) is established
Hold the state equation of control system are as follows:
In formula, d (s；T) total disturbance is indicated, s is rotor displacement, and t is time, u=[us]T, x=[x1,x2,x3]T, x1=s,x3=isIt is state variable,It is the speed of rotor, isIt is control electric current, state matrix are as follows:
In formula, m is the quality of rigid rotator, and R is coil resistance, and L is coil inductance,WithIt indicates in operating point (is=iN,
S=sN) control electric current and position stiffness.
3. control method according to claim 2, which is characterized in that total disturbance d (s；It t) include Parameters variation and outer
Portion's interference, indicates are as follows:
d(s；T)=△ Ki(s；t)is(t)+△Ks(s；t)s(t)+fd(t)
In formula, fdIt is external disturbance, △ Ki(s；And △ K t)s(s；It t) is Parameters variation amount.
4. control method according to claim 3, which is characterized in that the step 2) is substituted with new state variable η (t)
State variable i in original systems(t), new state variable-definition are as follows:
η (t)=is(t)-id(t) (8)
Equivalent voltage-controlled type magnetic bearing control system can indicate are as follows:
In formula, disturbance d (s is mismatched；T) it is divided into two parts:WithAssuming that disturbance observer can
Progressively to track disturbance, i.e. when t → ∞,
5. control method according to claim 4, which is characterized in that the step 3) includes the following steps:
Introduce an auxiliary vector ω (s；T), total disturbance d (s is redefined；T) are as follows:
d(s；T)=V ω (s；t) (10)
In formula, W and V are coefficient matrixes；
Composite system is made of state variable (7) and disturbance variable (11), is indicated are as follows:
According to the design method of state observer, disturbance observer can design subsystem below:
In formula, σ (t) is the equivalent output of subsystem, can be by observing feedback quantityTo improve observer precision；According to
The structure of disturbance observer can derive disturbance variableExpression formula is as follows:
By auxiliary variableIt substitutes into (14), disappears on the right side of (14)Disturbance observer can indicate
Are as follows:
In formula, W and V are coefficient matrix, ω (s；It t) is auxiliary vector, auxiliary variable It is to disturb
Dynamic variable.
6. control method according to claim 5, which is characterized in that set W=0, V=I, the disturbance of unknown disturbance prediction device
Observer model can simplify are as follows:
7. control method according to claim 5 or 6, which is characterized in that the step 4) includes:
Matching is disturbed, composite controller may be designed as:
In formula, KkFor the feedback oscillator determined by the performance of closed-loop system, feedback control can make the state variable in system steady
Determine to zero, i.e., as t → 0, s (t) → 0,is(t)→0；
For the robustness for guaranteeing closed-loop system, a feedback robust controller is introduced in equivalent system, is indicated are as follows:
ud(t)=Kx*(t) (18)
In formula,K is the feedback oscillator for meeting H ∞；
After improvement, the input of magnetic bearing control system becomes:
us=ud+Rid(19)；
Disturbance observer equation (16) and state feedback robust controller equation (18) are substituted into equation (9), it is multiple after being improved
Close control system equation are as follows:
In formula, B3=[0 0 1/Ki]T, ed(s；It t) is disturbance observation error,
It enables(24) it can indicate are as follows:
In formula,
8. control method according to claim 7, which is characterized in that the step 5) carries out improved composite system steady
Qualitative analysis is calculated corresponding controller gain and observer gain, specifically includes: in composite system (25), due toWithIt is all H2Convergence in norm, so disturbanceIt is also H2Convergence in norm, to reduce disturbance's
It influences, using the robust control scheme with H ∞ performance indicator, H ∞ controller can not only keep the stabilization of system, moreover it is possible to make
Reference value must be exported and meet the following conditions:
In formula, λ is the normal number for indicating interference rejection capability, and new system stochastic stability is shown below and meets H ∞ performance
Necessary condition, i.e., proof linear matrix inequality (LMI)；
In composite system (25), any λ > 0, there are matrix Q1> 0, Q2> 0 and R1, R2Meet:
In formula, Ξ1=sym (AQ1+B1R1), Ξ2=sym (- R2B2)；Sym () indicates a matrix operation, has for symmetrical matrix M
Sym (M)=M+MT；
It obtains working as controller gainObserver gainWhen, composite system (25) robustness Asymptotic Stability,
And meet
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| CN108828951B (en) * | 2018-07-20 | 2019-12-24 | 南京航空航天大学 | Magnetic suspension bearing multi-model robust undisturbed switching control method |
| CN109491245B (en) * | 2018-10-30 | 2021-09-10 | 江苏大学 | Disturbance compensation control method of CSTR system |
| CN109828451B (en) * | 2019-01-11 | 2021-11-23 | 江苏大学 | Construction method of four-degree-of-freedom magnetic bearing controller of flywheel battery for electric automobile |
| CN109861498B (en) * | 2019-02-18 | 2020-06-16 | 浙江工业大学 | Unknown input observer-based buck DC converter sliding mode control method |
| CN112256048B (en) * | 2020-10-13 | 2022-02-11 | 北京航空航天大学 | CMG frame system speed adjusting method with optimized mixed sensitivity |
| CN113341714B (en) * | 2021-06-02 | 2022-05-27 | 南京工业大学 | Method for counteracting same frequency interference of magnetic suspension bearing rotor control system |
| CN116989063B (en) * | 2023-08-30 | 2024-03-19 | 石家庄铁道大学 | Active magnetic suspension bearing control method and system based on equivalent input interference |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103425051A (en) * | 2013-08-21 | 2013-12-04 | 北京航空航天大学 | Unbalance identification and vibration suppression control system for magnetic suspension rotating machinery |
| CN103558857A (en) * | 2013-11-14 | 2014-02-05 | 东南大学 | Distributed composite anti-interference attitude control method of BTT flying machine |
| CN104166345A (en) * | 2014-08-01 | 2014-11-26 | 中国人民解放军装备学院 | Decoupling and disturbance-attenuation method for rotor system of magnetic suspension control moment gyroscope |
| CN104950919A (en) * | 2015-06-17 | 2015-09-30 | 北京航空航天大学 | Method for designing stability parameters of self-adapting filter of self-balancing system of magnetic suspension rotor |
| CN105783898A (en) * | 2016-04-28 | 2016-07-20 | 北京航空航天大学 | Magnetic suspension rotor harmonic vibration suppression method based on frequency-domain self-adaption LMS (least mean square) algorithm |
| CN106849790A (en) * | 2017-01-05 | 2017-06-13 | 江苏大学 | A kind of new sliding-mode control for mismatching the disturbed fault-tolerant permanent-magnetism linear motor system of cylinder |
-
2017
- 2017-08-14 CN CN201710692093.2A patent/CN107656437B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103425051A (en) * | 2013-08-21 | 2013-12-04 | 北京航空航天大学 | Unbalance identification and vibration suppression control system for magnetic suspension rotating machinery |
| CN103558857A (en) * | 2013-11-14 | 2014-02-05 | 东南大学 | Distributed composite anti-interference attitude control method of BTT flying machine |
| CN104166345A (en) * | 2014-08-01 | 2014-11-26 | 中国人民解放军装备学院 | Decoupling and disturbance-attenuation method for rotor system of magnetic suspension control moment gyroscope |
| CN104950919A (en) * | 2015-06-17 | 2015-09-30 | 北京航空航天大学 | Method for designing stability parameters of self-adapting filter of self-balancing system of magnetic suspension rotor |
| CN105783898A (en) * | 2016-04-28 | 2016-07-20 | 北京航空航天大学 | Magnetic suspension rotor harmonic vibration suppression method based on frequency-domain self-adaption LMS (least mean square) algorithm |
| CN106849790A (en) * | 2017-01-05 | 2017-06-13 | 江苏大学 | A kind of new sliding-mode control for mismatching the disturbed fault-tolerant permanent-magnetism linear motor system of cylinder |
Non-Patent Citations (5)
| Title |
|---|
| 一类不匹配不确定动态***的鲁棒执行器故障检测与重构;赵瑾等;《化工学报》;20080715(第07期);第307-311页 |
| 临近空间拦截弹的非奇异终端滑模控制;郭超等;《Journal of Astronautics》;20150131;第58-66页 |
| 基于干扰观测器的磁悬浮姿控飞轮电机控制;周新秀等;《北京航空航天大学学报》;20121130;第1459-1468页 |
| 基于干扰观测器的磁悬浮转子扰动抑制方法;丁力等;《轴承》;20090831;第6-9页 |
| 基于广义扩张状态观测器的干扰不匹配离散***状态反馈控制;张文安等;《控制与决策》;20160630;第1128-1132页 |
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