CN107807525A - The adaptive total state about beam control method of direct current motor system with dead band - Google Patents

The adaptive total state about beam control method of direct current motor system with dead band Download PDF

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CN107807525A
CN107807525A CN201711012615.6A CN201711012615A CN107807525A CN 107807525 A CN107807525 A CN 107807525A CN 201711012615 A CN201711012615 A CN 201711012615A CN 107807525 A CN107807525 A CN 107807525A
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mrow
msub
mfrac
msubsup
lambda
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王占山
刘磊
高浩源
柳义鹏
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Northeastern University China
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Northeastern University China
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The present invention provides a kind of adaptive total state about beam control method of the direct current motor system with dead band, is related to DC MOTOR CONTROL technical field.The mathematical modeling that this method passes through dc motor of the foundation with pattern without friction, and then establish non-linear input model, that is dead-zone model, based on radial basis function neural network design point Feedback Adaptive Controller, in the direct current motor system of operation, angular position measurement is carried out with the optical encoder of quadrature decoder chip, accesses the feedback of status adaptive controller.Adoption status Feedback Adaptive Controller of the present invention, it can be inputted based on dead band, improve the overall performance of direct current generator unit and the control accuracy of system, eliminate influence of the asymmetric dead band to direct current generator, it can be good at being lifted the running status of direct current unit, ensure the stability of power output.

Description

The adaptive total state about beam control method of direct current motor system with dead band
Technical field
The present invention relates to DC MOTOR CONTROL technical field, more particularly to a kind of direct current motor system with dead band is adaptive Answer total state about beam control method.
Background technology
In recent years, Power Electronic Technique, magnetic material technology, rotor dynamics, computer technology, Digital Signal Processing The development of device, intelligent controller and control theory, promote direct current generator into the emphasis direction studied now, meanwhile, direct current Machine is because with efficiency high, control is simple, the features such as low-maintenance, is widely used in industrial circle.As modern scientist is managed The development of opinion, the application being accurately controlled in engineering system become increasingly prevalent.However, for many engineering systems, Due to dead band, frictional force and the presence for installing gap, accurate control is greatly restricted.The fifties in last century, DC servo System starts to be widely used in industrial circle.However, the shortcomings due to direct current generator in itself, as commutator and brush are easy Abrasion, limited from rotating speed, processing and manufacturing complexity etc., its performance is often limited to dead band, and this is one important non-linear defeated Enter phenomenon, greatly limit the further development of DC servomechanism.
DC MOTOR CONTROL is the core of system normal operation, and its control technology is one of key technology of direct current generator, In close relations with the other parts of direct current generator, it is accurately controlled, perfect function will directly affect the safety of whole system With efficiency.In direct current motor system, the presence in dead band causes between actual output voltage and given voltage there is deviation, The distortion of load phase current is caused, therefore the torque of voltage also produces fluctuation, or even have influence on the stability of motor.
The content of the invention
The technical problem to be solved in the present invention is to be directed to above-mentioned the deficiencies in the prior art, there is provided a kind of direct current with dead band The adaptive total state about beam control method of machine system, adoption status Feedback Adaptive Controller, dead band can be based on and inputted, carried The high overall performance of direct current generator unit and the control accuracy of system, ensure the stability of power output.
In order to solve the above technical problems, the technical solution used in the present invention is：
A kind of adaptive total state about beam control method of direct current motor system with dead band, comprises the following steps：
Step 1：The mathematical modeling of the dc motor with pattern without friction is established, as shown in formula (1)；
Wherein, α1(t) be motor Angle Position；J is known inertia, f and TfIt is viscous friction respectively and non-linear rubs Wipe；D (t) is unknown disturbances, is met | | d (t) | |≤dM, dMIt is d (t) upper bounds；T is motor torque, the control with asymmetric dead band System input is relevant；Y ∈ R are output；
Step 2：Consider non-linear input phenomenon be present in the mathematical modeling of dc motor, that is, dead band be present, establish non- Linear input model, i.e. dead-zone model, as shown in formula (2)：
Wherein, u (t) is the control input in asymmetric dead band； mrAnd m (t)l(t) respectively represent Dead Zone curve left slope and Right slope, brAnd b (t)l(t) breakpoint of unbalanced input, m are representedr(t)、ml(t)、brAnd b (t)l(t) all it is arithmetic number；
Step 3：Design point Feedback Adaptive Controller, as shown in formula (20) so that direct current motor system realize with Track error levels off to zero, meanwhile, all signals in the controller closed loop are all bounded；
Wherein, u=u (t), m=m (t)；k2It is design parameter, e1、e2For tracking error, e1=α1-yd, e2=α2-η1； yd(t) it is the reference locus of system output, yd(t) first derivative to the time and second dervative are bounded, Y1And Y2Constant, the scope of reference locus be for y dWithIt is known constant；Represent Neutral net weight W*Estimation；S (z) is Base Function；η1For virtual controlling,k1It is positive constant；λ1It is a positive constant, And λ3=(1- |y d|)2It is to represent in e1State space in constrainPositive constant；λ4It is design parameter； Q=q (e1), it is a sign function, q ()：R → { 0,1 } is described as
Step 4：In the direct current motor system of operation, Angle Position survey is carried out with the optical encoder of quadrature decoder chip Amount, the feedback of status adaptive controller shown in access type (20).
The specific design method of the step 3 feedback of status adaptive controller is as follows：
Step 3.1：Selection includes the function V of barrier function1As candidate's liapunov function, as shown in formula (4)；
V1As liapunov function in sectionWithBetween be piecewise smooth, and It is continuous differentiable function；
Step 3.2：According to candidate's liapunov function V1Liapunov function is obtained after conversionAfter conversion Liapunov functionDesign control input u*；Liapunov functionAs shown in formula (10), control input u*Such as Shown in formula (13)；
Wherein, k2It is a constant,And make unknown functionB= b(t)；
Step 3.3：Estimate unknown function M using radial basis function neural network, as shown in formula (16), and then obtain Actual feedback of status adaptive controller u；
M=W*TS(z(t))+ε(z(t)) (16)
Wherein,ε (z (t)) is approximate error, meets ε≤ε*, ε*＞ 0 is normal Number；
Choose shown in adaptive law such as formula (25)：
Wherein, Γ=Γ-1＞ 0 is a constant matrices.
It is using beneficial effect caused by above-mentioned technical proposal：Direct current motor system provided by the invention with dead band Adaptive total state about beam control method, using feedback of status self-adaptation control method, successfully overcome currently available technology Situation about can not be inputted based on dead band, for many engineering systems, such as servomotor and mechanical connection, limited performance in Dead band and the shortcomings that can not go actually to solve；The overall performance of direct current generator unit and the control accuracy of system are improved, substantially Eliminate influence of the asymmetric dead band to direct current generator.Dedicated for direct current generator the feedback of status based on dead area compensation from The use of adaptive control method, solve well in direct current motor system operation, interference of the asymmetric dead band to whole system And influence, it can be good at the running status of lifting direct current unit, ensure the stability of power output.
Brief description of the drawings
Fig. 1 is that the adaptive total state of the direct current motor system provided in an embodiment of the present invention with dead band constrains control flow Figure；
Fig. 2 is the Nonlinear Characteristic Curve schematic diagram of nonlinear dead-zone provided in an embodiment of the present invention；
Fig. 3 is state α provided in an embodiment of the present invention1With reference signal yd(t) geometric locus schematic diagram；
Fig. 4 is the curve synoptic diagram of control input provided in an embodiment of the present invention；
Fig. 5 is adaptive law provided in an embodiment of the present inventionGeometric locus schematic diagram.
Embodiment
With reference to the accompanying drawings and examples, the embodiment of the present invention is described in further detail.Implement below Example is used to illustrate the present invention, but is not limited to the scope of the present invention.
The adaptive total state about beam control method of a kind of direct current motor system with dead band, as shown in figure 1, the present embodiment Method it is as described below.
Step 1：The mathematical modeling of the dc motor with pattern without friction is established, as shown in formula (1), i.e.,
Wherein, α1(t) be motor Angle Position；J is known inertia, f and TfIt is viscous friction respectively and non-linear rubs Wipe；D (t) is unknown disturbances, | | d (t) | |≤dM, dMIt is d (t) upper bounds；T is motor torque, defeated with the control in asymmetric dead band Enter relevant；Y ∈ R are output.
Step 2：Consider non-linear input (dead band) phenomenon in the mathematical modeling of dc motor be present, establish non-linear defeated Enter model, i.e. dead-zone model；And reference signal is provided, propose control targe.
Step 2.1：Asymmetric dead band D (u (t)) model is defined, as shown in formula (2), i.e.,
Wherein, u (t) is the control input in asymmetric dead band；, mrAnd m (t)l(t) divide Not Biao Shi Dead Zone curve left slope and right slope；br(t) and bl(t) breakpoint of unbalanced input, m are representedr(t)、ml(t)、brAnd b (t)l(t) all it is arithmetic number.Asymmetric dead band it is non-thread Property is as shown in Fig. 2 the left slope m of parameterrWith right slope mlIt is known.Ordermin(mrbr, mlbl)=b。
Step 2.2：For DC motor model (1) and dead-zone model (2), setting reference locus yd(t) its satisfaction, is made： Reference locus yd(t) first derivative to the time and second dervative are bounded, i.e.,Y1And Y2It is constant. In addition, the scope of reference locus is y dWithIt is known constant.
Control targe：Design a kind of total state about beam control method of adaptive radial base neural net so that direct current Machine system realizes that tracking error levels off to zero, i.e.,Meanwhile all signals in the closed loop are all Bounded.
Step 3：Design point Feedback Adaptive Controller so that direct current motor system realizes that tracking error levels off to zero, Meanwhile all signals in the controller closed loop are all bounded, specific design method is as follows.
Step 3.1：Selection includes the function V of barrier function1As candidate's liapunov function, as shown in formula (4), I.e.
Wherein, e1=α1-ydFor tracking error, ydIt is reference signal；λ1It is a positive constant,And λ3 =(1- |y d|)2It is to represent in e1State space in constrainPositive constant；q(e1) it is a symbol letter Number, q ()：R → { 0,1 } is described asV1As liapunov function, in section WithBetween be piecewise smooth.
Again because in section e1∈(-λ3, 0] in, draw
Equally, in section e1∈(-λ3, 0] on, it can be deduced that
Therefore, V can be obtained1It is continuous differentiable function.In order to which symbol is convenient, by q (e1) it is abbreviated as q.
V1First derivative be
Choosing virtual controlling is
k1It is positive constant, then can obtains
Section 1 in above formula is anon-normal, and Section 2 will be disappeared in the next step.
Step 3.2：Using liapunov functionDesign control input u*；Liapunov functionSuch as formula (10) It is shown, i.e.,
Then,Derivative be
It can be drawn by formula (8)
Ideally, design shown in control input such as formula (13), i.e.,
Wherein, k2It is a design constant, F is shown below,
To put it more simply, make functionFormula (13) is substituted into formula (11), can be obtained
It is possible to obtain error signal e1And e2Asymptotic convergence is to zero.
Step 3.3：With radial basis function neural network come the unknown function M in approximating step 3.2, adaptive state is obtained Feedback controller.
Due to parameter TfIt is not available with f, so M is unknown, it is, being unavailable in practice.For Solves the uncertainty of parameter, the present embodiment estimates M using radial basis function neural network, as shown in formula (16).
M=W*TS(z(t))+ε(z(t)) (16)
Wherein,ε (z (t)) is approximate error, meets ε≤ε*, ε*＞ 0 is normal Number；It is preferable constant-weight vector, l is neural network node number, for the ease of analysis, this reality Example is applied by ideal weight vector W*It is defined as asking for minimizing | ε (z (t)) |,Value when W, i.e.,
Wherein, S (z (t))=[S1(z (t)) ..., Sl(z(t))]TIt is neutral net base vector, chooses Si(z (t)) is normal Gaussian function, as shown in formula (18).
Wherein, μi=[μi1..., μis]TAnd τiIt is center and the width of Gaussian function respectively, s is neutral net input dimension Number.
Further, unknown function M can be expressed as to the approximate form of neutral net, i.e.,
Wherein,It is neutral net ideal weight vector W*Estimation.
So as to design point Feedback Adaptive Controller u, as shown in formula (20).
Due to approaching unknown function M using neutral net, so being needed in stability analysis in liapunov function Middle quadratic term of the increase with neural network weight parameter estimating error, i.e.,
Wherein,It is neutral net weight evaluated error；Γ=Γ-1＞ 0 is a constant matrices.V2One Order derivative is expressed as
Controller (20) is brought into formula (22), obtains formula (23),
Using Young inequality, obtain
Adaptive law is designed, as shown in formula (25), i.e.,
Then formula (23) can be write as the form of formula (26).
Step 4：In the direct current motor system of operation, Angle Position survey is carried out with the optical encoder of quadrature decoder chip Amount, access state Feedback Adaptive Controller.
First, angular position measurement is carried out with the optical encoder of quadrature decoder chip.Angular speed is by by breaking up position Measurement is put to be calculated.Direct current motor system in the present embodiment is shown below.
Then, the unknown dynamic of approximation system is carried out by using radial base neural net.In the present embodiment, inertia J= 0.0143[Kg·m2], f and TfIt is immesurable viscous friction respectively (as the increase of movement velocity, frictional force are linear Increase, frictional force now is viscous friction) and immesurable non-linear friction.D is that the outside changed over time is done Disturb, d=0.05sint.Motor torque T is relevant with the control input u (t) by asymmetric dead band, i.e. T=D (u (t)).It is non- Symmetrical dead band D (u's (t)) is described as follows
It controls purpose to be to ensure that y follows the desired trajectory y specifieddA small neighbourhood and closed-loop system to zero is all Signal is bounded.In the present embodiment, reference signal yd=0.05sin 2t-0.7.
For approaching the radial basis function neural network W of unknown functionTS (z) includes 25 nodes, neutral net center μi (i=1 ..., 25) is evenly distributed on region [- 4,4] × [- 4,4] × [- 4,4], width τi=1.5.Choose design parameter For Γ=2.5I, k1=0.5, k2=0.5, λ1=0.25, λ2=2, neutral net weight initial value isSystem shape The primary condition of state is α1(0)=- 0.5,
In an operating direct current motor system (i.e. formula (27)) with dead band, access state feedback adaptive control After device (i.e. formula (20)) processed, the effect of gained is as shown in Fig. 3~Fig. 5.Wherein Fig. 3 gives state α1(solid line) and reference Signal yd(t) track of (dotted line).Apparent two curves are almost what is coincided together, i.e. orbit error e1Almost converge to Zero, that is to say, that obtained a good tracking effect.Fig. 4 depicts the curve of control input, while shows that control is defeated The boundedness entered.Fig. 5 illustrates adaptive lawTrack, it can be seen thatIt is bounded.Therefore, with the present invention Method, has obtained a good tracing property, and all signals of closed-loop system are all bounded, while direct current motor system Tracking error can converge to a small compact set.
Finally it should be noted that：The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although The present invention is described in detail with reference to the foregoing embodiments, it will be understood by those within the art that：It still may be used To be modified to the technical scheme described in previous embodiment, either which part or all technical characteristic are carried out etc. With replacement；And these modifications or replacement, the essence of appropriate technical solution is departed from what the claims in the present invention were limited Scope.

Claims (2)

  1. A kind of 1. adaptive total state about beam control method of direct current motor system with dead band, it is characterised in that：Including following Step：
    Step 1：The mathematical modeling of the dc motor with pattern without friction is established, as shown in formula (1)；
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>J</mi> <msub> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>f</mi> <msub> <mover> <mi>&amp;alpha;</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>T</mi> <mi>f</mi> </msub> <mo>+</mo> <mi>d</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>T</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, α1(t) be motor Angle Position；J is known inertia, f and TfIt is viscous friction and non-linear friction respectively；d (t) it is unknown disturbances, meets | | d (t) | |≤dM, dMIt is d (t) upper bounds；T is motor torque, the control input with asymmetric dead band It is relevant；Y ∈ R are output；
    Step 2：Consider non-linear input phenomenon be present in the mathematical modeling of dc motor, that is, dead band be present, establish non-linear Input model, i.e. dead-zone model, as shown in formula (2)：
    <mrow> <mi>T</mi> <mo>=</mo> <mi>D</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mi>m</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>b</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>)</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;GreaterEqual;</mo> <msub> <mi>b</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>b</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&lt;</mo> <msub> <mi>b</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mi>u</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>b</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>)</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>u</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <mo>-</mo> <msub> <mi>b</mi> <mi>l</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, u (t) is the control input in asymmetric dead band； mrAnd m (t)l(t) respectively represent Dead Zone curve left slope and Right slope, brAnd b (t)l(t) breakpoint of unbalanced input, m are representedr(t)、ml(t)、brAnd b (t)l(t) all it is arithmetic number；
    Step 3：Design point Feedback Adaptive Controller, as shown in formula (20) so that direct current motor system realizes that tracking misses Difference levels off to zero, meanwhile, all signals in the controller closed loop are all bounded；
    <mrow> <mi>u</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mi>J</mi> <mi>m</mi> </mfrac> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>+</mo> <mfrac> <mi>J</mi> <mi>m</mi> </mfrac> <msub> <mover> <mi>&amp;eta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>1</mn> </msub> <mo>+</mo> <mfrac> <mi>J</mi> <mi>m</mi> </mfrac> <msup> <mover> <mi>W</mi> <mo>^</mo> </mover> <mi>T</mi> </msup> <mi>S</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>-</mo> <mfrac> <mi>J</mi> <mi>m</mi> </mfrac> <mrow> <mo>(</mo> <mfrac> <mi>q</mi> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>2</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>q</mi> </mrow> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>3</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;lambda;</mi> <mn>4</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, u=u (t), m=m (t)；k2It is design parameter, e1、e2For tracking error, e1=α1-yd, e2=α2-η1；yd(t) it is The reference locus of system output, yd(t) first derivative to the time and second dervative are bounded, Y1With Y2Constant, the scope of reference locus be for y dWithIt is known constant；Represent neutral net weight W*Estimation；S (z) is Base Function；η1For virtual controlling,k1It is positive constant；λ1It is a positive constant, WithIt is to represent in e1State space in constrainPositive constant；λ4It is design parameter；q =q (e1), it is a sign function, q ()：R → { 0,1 } is described as
    Step 4：In the direct current motor system of operation, angular position measurement is carried out with the optical encoder of quadrature decoder chip, is connect Enter the feedback of status adaptive controller shown in formula (20).
  2. 2. the adaptive total state about beam control method of the direct current motor system according to claim 1 with dead band, it is special Sign is：The specific design method of the step 3 feedback of status adaptive controller is as follows：
    Step 3.1：Selection includes the function V of barrier function1As candidate's liapunov function, as shown in formula (4)；
    <mrow> <msub> <mi>V</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mi>q</mi> <mrow> <mo>(</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mi>l</mi> <mi>n</mi> <mfrac> <msub> <mi>&amp;lambda;</mi> <mn>2</mn> </msub> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>2</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <mfrac> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>q</mi> <mo>(</mo> <msub> <mi>e</mi> <mn>1</mn> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mi>l</mi> <mi>n</mi> <mfrac> <msub> <mi>&amp;lambda;</mi> <mn>3</mn> </msub> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>3</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    V1As liapunov function in sectionWithBetween be piecewise smooth, and be connect Continuous differentiable function；
    Step 3.2：According to candidate's liapunov function V1Liapunov function is obtained after conversionUsing Lee after conversion Ya Punuofu functionsAn ancient weapon made of bamboo meter control input u*；Liapunov functionAs shown in formula (10), control input u*Such as formula (13) shown in；
    <mrow> <msubsup> <mi>V</mi> <mn>2</mn> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>V</mi> <mn>1</mn> </msub> <mo>+</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mfrac> <msub> <mi>&amp;lambda;</mi> <mn>4</mn> </msub> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>4</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msup> <mi>u</mi> <mo>*</mo> </msup> <mo>=</mo> <mo>-</mo> <mfrac> <mi>J</mi> <mi>m</mi> </mfrac> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>e</mi> <mn>2</mn> </msub> <mo>-</mo> <mfrac> <mi>J</mi> <mi>m</mi> </mfrac> <mrow> <mo>(</mo> <mfrac> <mi>q</mi> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>2</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>1</mn> <mo>-</mo> <mi>q</mi> </mrow> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>3</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>1</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <mo>)</mo> </mrow> <msub> <mi>&amp;lambda;</mi> <mn>1</mn> </msub> <msub> <mi>e</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;lambda;</mi> <mn>4</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <mi>F</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, k2It is a constant,And make unknown function
    Step 3.3：Estimate unknown function M using radial basis function neural network, as shown in formula (16), and then obtain reality Feedback of status adaptive controller u；
    M=W*TS(z(t))+ε(z(t)) (16)
    Wherein,ε (z (t)) is approximate error, meets ε≤ε*, ε*＞ 0 is constant；
    Choose shown in adaptive law such as formula (25)：
    <mrow> <mover> <mover> <mi>W</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <msub> <mi>&amp;lambda;</mi> <mn>4</mn> </msub> <mo>-</mo> <msubsup> <mi>e</mi> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mfrac> <msub> <mi>&amp;Gamma;Se</mi> <mn>2</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, Γ=Γ-1＞ 0 is a constant matrices.
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