CN103197562A - Rotary-table servo system neural network control method - Google Patents

Abstract

A rotary-table servo system neural network control method comprises (1) building a mechanical dynamic model of a permanent magnet synchronous motor rotary-table servo system, and initializing the system state, sampling time and relative control parameters; (2) according to the differential mean value theorem, enabling a non-linear input dead zone in the system to linearly approximate to a simple time-varying system, avoiding complex calculation of dead-zone inverse compensation, and finally inferring a rotary-table servo system model provided with an unknown dead zone; (3) at each sampling moment, calculating and controlling a system tracking error, a fast terminal sliding mode surface and a first-order derivative of the system; (4) based on the rotary-table servo system model provided with the unknown dead zone, selecting a neural network approaching unknown trend, designing an adaptive robust finite-time neural network controller according to the system tracking error, the fast terminal sliding mode surface and the first-order derivative of the system, and updating a neural network weight matrix; and (5) entering the next sampling moment, and repetitively executing the steps from (3) to (5).

Description

Table servo system neural network control method

Technical field

The present invention relates to the control method of a kind of table servo system, particularly have the table servo system self-adaption robust finite time neural network control method in unknown non-linear input dead band.

Background technology

The dead band nonlinear element extensively is present in Hydrauservo System, servo electrical machinery system and other Industrial Engineering fields.The existence in dead band tends to cause the efficient of control system to reduce or even inefficacy.Therefore, for improving control performance, essential at compensation and the control method in dead band.Traditional dead-zone compensation method generally is inversion model or the approximate inverse model of setting up the dead band, and by estimating the bound parameter designing adaptive controller in dead band, with the influence in compensation dead band.Yet in nonlinear system such as table servo system, the inversion model in dead band often is difficult for accurately obtaining.

Sliding formwork control is also named and is become structure control, is the special nonlinear Control of a class in essence, and non-linear behavior is the uncontinuity of control.As a kind of nonlinear control method commonly used, sliding-mode control has that algorithm is simple, response speed soon, advantage such as noise and parameter perturbation strong robustness to external world.Therefore, sliding-mode control is widely used in fields such as robot, motor, aircraft.Traditional linear sliding-mode control can guarantee the asymptotic convergence of controlled system tracking error, that is: tracking error can converge to equilibrium point in the infinitely-great time in theory.In order to improve the speed of convergence of system keeps track error, generally increase nonlinear terms on the basis of linear sliding formwork, the rapid track and control by design kinematic nonlinearity sliding-mode surface realization system is called the terminal sliding mode control method.This method can guarantee to reach in system state at the appointed time the tracking fully to expectation state.Yet owing to introduced the fractional exponent item in the design of sliding-mode surface, may there be the problem of singular value in the terminal sliding mode method and when initial state slower problem of speed of convergence during away from equilibrium point.

Summary of the invention

The present invention will overcome the dead band inversion model that exists in the existing table servo system control method and be difficult to problems such as accurate acquisition, control rate is slow, control accuracy is not high, a kind of complicated calculations of avoiding the dead band inversion model is provided, improve control rate and control accuracy table servo system self-adaption robust finite time neural network control method (Adaptive Robust Finite-Time Neural Control, ARFTNC).Guarantee to exist under the situation in the uncertain and unknown dead band of system model, realize the finite time rapid track and control of table servo system.

Have the table servo system self-adaption robust finite time neural network control method in unknown dead band, comprise following key step:

Step 1. is set up the mechanical dynamic model of permagnetic synchronous motor table servo system, initialization system state, sampling time and relevant control parameter;

Step 2. is a simple time-varying system according to Order Derivatives in Differential Mid-Value Theorem with the non-linear input dead band linear-apporximation in the system, avoids the complicated calculations of the contrary compensation in dead band, finally derives the table servo system model that has unknown dead band;

Step 3. is in each sampling instant, the tracking error of calculating control system, fast terminal sliding-mode surface and first order derivative thereof;

Step 4. is based on the table servo system model that has unknown dead band, it is dynamically unknown to select neural network to approach, design ADAPTIVE ROBUST finite time nerve network controller according to system keeps track error, fast terminal sliding-mode surface and first order derivative thereof, upgrade the neural network weight matrix;

Step 5. enters next sampling instant, repeated execution of steps (3)-(5).

Further, the mechanical dynamic model of the described permagnetic synchronous motor table servo of step 1 system can be described as:

$m\stackrel{\·\·}{x}+f^{*}(\stackrel{\‾}{x},t)+d^{*}(\stackrel{\‾}{x},t)=k_0^{*}u\left(t\right)$ (1)

y=x(t)

Wherein,

U (t) ∈ R, y (t) ∈ R represents system state respectively, control input voltage and motor output.X represents the position, and m represents load quality, The expression ride gain,

Be friction force, Be to comprise the bounded Disturbance Model of measuring noise, electromagnetic interference (EMI) and other unknown terms.

Order $f(\stackrel{\‾}{x},t)=f^{*}(\stackrel{\‾}{x},t)/m,$ $d(\stackrel{\‾}{x},t)=d^{*}(\stackrel{\‾}{x},t)/m,$ $k_0=k_0^{*}/m,$ Then system of equations (1) can be rewritten as

$\stackrel{\·\·}{x}=-h(\stackrel{\‾}{x},t)+k_{0}u\left(t\right)$ (2)

y=x(t)

Wherein, $h(\stackrel{\‾}{x},t)=f(\stackrel{\‾}{x},t)+d(\stackrel{\‾}{x},t).$

U (t) is the output signal in following non-linear dead band

$u\left(t\right)=G\left(v\left(t\right)\right)=\left\{\begin{array}{ccc}{g}_r\left(v\right)& \mathrm{if}& v\left(t\right)\&GreaterEqual;b_{\mathrm{<figure-callout\; id="0"\; label="r"\; filenames="HDA00003036012800022.png,HDA00003036012800031.png"\; state="\{\{state\}\}">r</figure-callout>}}\\ 0& \mathrm{if}& b_l<v\left(t\right)<b_r\\ g_l\left(v\right)& \mathrm{if}& v\left(t\right)\&le;b_l\end{array}\right.---\left(3\right)$

Wherein, v (t) is dead band input (working control signal), g _l(v) and g _r(v) be unknown nonlinear smoothing function, b _lAnd b _rBe unknown skip distance parameter.

Further, described step 2 is made up of following steps:

1) according to Order Derivatives in Differential Mid-Value Theorem, there is ξ _l∈ (∞, b _l) and ξ _r∈ (b _r,+∞) makes

$g_l\left(v\right)=g_l^{\&prime;}\left({\mathrm{\&xi;}}_l\right)(v-b_l),$ $\&ForAll;v\&Element;(-\&infin;,b_r]---\left(4\right)$

Wherein, ξ _l∈ (∞, b _l],

$g_r\left(v\right)=g_r^{\&prime;}\left({\mathrm{\&xi;}}_r\right)(v-b_r),$ $\&ForAll;v\&Element;[b_l,+\&infin;)---\left(5\right)$

Wherein, ξ _r∈ [b _r,+∞).

2) by equation (2)-(5), the table servo system model that can have unknown dead band is:

(6)

y=x(t)

Wherein, | ρ (t) |≤ρ _N, ρ _N0 satisfy ρ _N=(g _R1+ g _L1) max{b _r,-b _l,

$\mathrm{\&rho;}\left(t\right)=\left\{\begin{array}{ccc}-g_r^{\&prime;}\left({\mathrm{\&xi;}}_r\right)b_r& \mathrm{if}& v\left(t\right)\&GreaterEqual;b_r\\ -[g_l^{\&prime;}\left({\mathrm{\&xi;}}_l\right)+g_r^{\&prime;}\left({\mathrm{\&xi;}}_r\right)]v\left(t\right)& \mathrm{if}& b_l<v\left(t\right)<b_r\\ -g_l^{\&prime;}\left({\mathrm{\&xi;}}_l\right)b_l& \mathrm{if}& v\left(t\right)\&le;b_l\end{array}\right.---\left(7\right)$

Wherein, ξ _l∈ (∞, b _l], ξ _r∈ [b _r,+∞),

And

Further, described step 3 can be made up of following steps:

1) based on table servo system model (6), the tracking error of definition control system is

e=y _d-y (9)

Wherein, y _dThe desired trajectory that can lead for second order.

2) its expression formula of fast terminal sliding-mode surface is as follows:

$s=\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}_{1}e+{\mathrm{\&lambda;}}_2{\left|e\right|}^{\mathrm{\&gamma;}}\mathrm{sgn}\left(e\right)---\left(10\right)$

Wherein, e ∈ R is tracking error, | e| represents the absolute value of e, the e sign function of sgn (e) expression; λ ₁, λ ₂0 be constant.

3) to equation (10) both sides differentiate, can derive in conjunction with (6):

(11)

Wherein, the expression formula of nonlinear function κ is

$\mathrm{\&kappa;}={\stackrel{\&CenterDot;\&CenterDot;}{y}}_d+{\mathrm{\&lambda;}}_1\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}_2\mathrm{\&gamma;}{\left|e\right|}^{\mathrm{\&gamma;}-1}\stackrel{\&CenterDot;}{e}+h(\stackrel{\&OverBar;}{x},t)-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00003036012800022.png,HDA00003036012800031.png"\; state="\{\{state\}\}">k</figure-callout>}}_0\mathrm{\&rho;}\left(t\right)---\left(12\right)$

Further, described step 4 can be made up of following steps:

1) at permagnetic synchronous motor table servo system (6), based on formula (10) and (11) design ADAPTIVE ROBUST finite time nerve network controller, structure is as follows:

v(t)=v ₀+v ₁+v ₂ (13)

$v_0={\hat{W}}^T\mathrm{\&phi;}\left(X\right)---\left(14\right)$

v ₁=k ₁s+k ₂|s| ^rsgn(s) (15)

v ₂=(δ ₁+δ ₂)sgn(s) (16)

Wherein, v ₀The expression neural network estimator is used for the dynamically unknown of approximation system;

The desirable weights W of expression neural network ^*Estimated value, φ (X) is the basis function of neural network, X is the neural network input vector; v ₁Be feedback controller, be used for guaranteeing that tracking error can rapidly converge to sliding-mode surface in finite time; v ₂Be the robust item, the robustness the when system of assurance exists approximate error and weights evaluated error; k ₁0, k ₂0 for control parameter; δ ₁For greater than neural network approximate error upper limit ε _NConstant, that is: δ ₁ε _Nδ ₂Be a positive constant, satisfy

Be the neural network weight evaluated error.

2) the weights adjusting rule of design neural network is:

$\stackrel{\stackrel{\&CenterDot;}{^}}{W}=\mathrm{\&Gamma;\&phi;}\left(X\right)s---\left(17\right)$

Wherein, Γ is the symmetric matrix of positive definite, and φ (X) is chosen as the Sigmoid function, and expression-form is as follows:

$\mathrm{\&phi;}\left(X\right)=\frac{a}{{b+e}^{(-X/c)}}+d---\left(18\right)$

Wherein, a〉0, b 0, c 0, d＜0 is respectively constant parameter.

3) with in controller formula (13)-Shi (16) substitution formula (11), can obtain following closed-loop system dynamic equation:

Wherein, ε≤ε _NBe the neural network approximate error;

Be the neural network weight evaluated error.

4) design Lyapunov function respectively

With

Can prove that then all signals in the closed-loop control system (6) all are uniformly bounded.Simultaneously, the system keeps track error e can converge to equilibrium point e=0 in finite time.

Technical conceive of the present invention is: at the permagnetic synchronous motor table servo system that has unknown non-linear input dead band, design a kind of ADAPTIVE ROBUST finite time neural network control method based on fast terminal sliding formwork principle.According to Order Derivatives in Differential Mid-Value Theorem, non-linear dead band can be simple time-varying system by linear-apporximation, thereby has avoided the complicated calculations of the contrary compensation in dead band.The design of controller can effectively be avoided the singular value problem in the general terminal sliding mode controller based on improved fast terminal sliding formwork principle.The neural network of employing Sigmoid basis function is approached the unknown nonlinear terms in the table servo system, and increases the approximate error of robust item compensation neural network in controller architecture.The invention provides a kind of table servo system self-adaption control method of avoiding complicated calculations, raising control rate and the control accuracy of dead band inversion model.Guarantee to exist under the situation in the uncertain and unknown dead band of system model, realize the finite time rapid track and control of table servo system.

Advantage of the present invention is: the efficiency of algorithm height, can avoid the complicated calculations of dead band inversion model, and improve control rate and control accuracy.

Description of drawings

Fig. 1 is non-linear dead band model;

Fig. 2 is permagnetic synchronous motor table servo system;

Fig. 3 is permagnetic synchronous motor servo-drive system position control block diagram;

Fig. 4 is the basic procedure of ARFTNC algorithm;

Fig. 5 is the tracking error contrast of ARFTNC algorithm;

Fig. 6 is the control signal contrast of ARFTNC algorithm.

Embodiment

With reference to accompanying drawing 1-4, have the design of the table servo system self-adaption robust finite time neural network control method in unknown dead band, may further comprise the steps:

1. set up the mechanical dynamic model of permagnetic synchronous motor table servo system:

$m\stackrel{\&CenterDot;\&CenterDot;}{x}+f^{*}(\stackrel{\&OverBar;}{x},t)+d^{*}(\stackrel{\&OverBar;}{x},t)={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00003036012800022.png,HDA00003036012800031.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^{*}u\left(t\right)$ (1)

y=x(t)

Wherein,

Y (t) ∈ R represents system state respectively, control input voltage and motor output.X represents the position, and m represents load quality,

The expression ride gain, Be friction force,

Be to comprise the bounded Disturbance Model of measuring noise, electromagnetic interference (EMI) and other unknown terms.

Order $f(\stackrel{\&OverBar;}{x},t)=f^{*}(\stackrel{\&OverBar;}{x},t)/m,$ $d(\stackrel{\&OverBar;}{x},t)=d^{*}(\stackrel{\&OverBar;}{x},t)/m,$ ${\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00003036012800022.png,HDA00003036012800031.png"\; state="\{\{state\}\}">k</figure-callout>}}_0={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00003036012800022.png,HDA00003036012800031.png"\; state="\{\{state\}\}">k</figure-callout>}}_0^{*}/m,$ Then system of equations (1) can be rewritten as

$\stackrel{\&CenterDot;\&CenterDot;}{x}=-h(\stackrel{\&OverBar;}{x},t)+k_{0}u\left(t\right)$ (2)

y=x(t)

Wherein, $h(\stackrel{\&OverBar;}{x},t)=f(\stackrel{\&OverBar;}{x},t)+d(\stackrel{\&OverBar;}{x},t).$

As shown in Figure 1, u (t) is the output signal in following non-linear dead band

$u\left(t\right)=G\left(v\left(t\right)\right)=\left\{\begin{array}{ccc}{g}_r\left(v\right)& \mathrm{if}& v\left(t\right)\&GreaterEqual;{\mathrm{<figure-callout\; id="0"\; label="b\; r"\; filenames="HDA00003036012800022.png,HDA00003036012800031.png"\; state="\{\{state\}\}">b</figure-callout>}}_r\\ 0& \mathrm{if}& b_l<v\left(t\right)<b_r\\ g_l\left(v\right)& \mathrm{if}& v\left(t\right)\&le;b_l\end{array}\right.---\left(3\right)$

Wherein, v (t) is dead band input (working control signal), g _l(v) and g _r(v) be unknown nonlinear smoothing function, b _lAnd b _rBe unknown skip distance parameter.

2. according to Order Derivatives in Differential Mid-Value Theorem, be a simple time-varying system with the non-linear input dead band linear-apporximation in the system, avoid the complicated calculations of the contrary compensation in dead band, finally derive the table servo system model that has unknown dead band.

1) according to Order Derivatives in Differential Mid-Value Theorem, there is ξ _l∈ (∞, b _l) and ξ _r∈ (b _r,+∞) makes

$g_l\left(v\right)=g_l^{\&prime;}\left({\mathrm{\&xi;}}_l\right)(v-b_l),$ $\&ForAll;v\&Element;(-\&infin;,b_r]---\left(4\right)$

Wherein, ξ _l∈ (∞, b _l],

$g_r\left(v\right)=g_r^{\&prime;}\left({\mathrm{\&xi;}}_r\right)(v-b_r),$ $\&ForAll;v\&Element;[b_l,+\&infin;)---\left(5\right)$

Wherein, ξ _r∈ [b _r,+∞).

2) by equation (2)-(5), the table servo system model that can have unknown dead band is:

(6)

y=x(t)

Wherein, | ρ (t) |≤ρ _N, ρ _N0 satisfy ρ _N=(g _R1+ g _L1) max{b _r,-b _l,

$\mathrm{\&rho;}\left(t\right)=\left\{\begin{array}{ccc}-g_r^{\&prime;}\left({\mathrm{\&xi;}}_r\right)b_r& \mathrm{if}& v\left(t\right)\&GreaterEqual;b_r\\ -[g_l^{\&prime;}\left({\mathrm{\&xi;}}_l\right)+g_r^{\&prime;}\left({\mathrm{\&xi;}}_r\right)]v\left(t\right)& \mathrm{if}& b_l<v\left(t\right)<b_r\\ -g_l^{\&prime;}\left({\mathrm{\&xi;}}_l\right)b_l& \mathrm{if}& v\left(t\right)\&le;b_l\end{array}\right.---\left(7\right)$

Wherein, ξ _l∈ (∞, b _l], ξ _r∈ [b _r,+∞),

And

3. in each sampling instant, the tracking error of calculating control system, fast terminal sliding-mode surface and first order derivative thereof.

1) based on table servo system model (6), the tracking error of definition control system is

e=y _d-y (9)

Wherein, y _dThe desired trajectory that can lead for second order.

2) its expression formula of fast terminal sliding-mode surface is as follows:

$s=\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}_{1}e+{\mathrm{\&lambda;}}_2{\left|e\right|}^{\mathrm{\&gamma;}}\mathrm{sgn}\left(e\right)---\left(10\right)$

Wherein, e ∈ R is tracking error, | e| represents the absolute value of e, the e sign function of sgn (e) expression; λ ₁, λ ₂0 be constant.

3) to equation (10) both sides differentiate, can derive in conjunction with (6):

(11)

Wherein, the expression formula of nonlinear function κ is

$\mathrm{\&kappa;}={\stackrel{\&CenterDot;\&CenterDot;}{y}}_d+{\mathrm{\&lambda;}}_1\stackrel{\&CenterDot;}{e}+{\mathrm{\&lambda;}}_2\mathrm{\&gamma;}{\left|e\right|}^{\mathrm{\&gamma;}-1}\stackrel{\&CenterDot;}{e}+h(\stackrel{\&OverBar;}{x},t)-{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA00003036012800022.png,HDA00003036012800031.png"\; state="\{\{state\}\}">k</figure-callout>}}_0\mathrm{\&rho;}\left(t\right)---\left(12\right)$

4. based on the table servo system model (6) that has unknown dead band, it is dynamically unknown to select neural network to approach, design ADAPTIVE ROBUST finite time nerve network controller according to system keeps track error, fast terminal sliding-mode surface and first order derivative thereof, upgrade the neural network weight matrix.

1) at permagnetic synchronous motor table servo system (6), based on formula (10) and (11) design ADAPTIVE ROBUST finite time nerve network controller, structure is as follows:

v(t)=v ₀+v ₁+v ₂ (13)

${\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="HDA00003036012800022.png,HDA00003036012800031.png"\; state="\{\{state\}\}">v</figure-callout>}}_0={\hat{W}}^T\mathrm{\&phi;}\left(X\right)---\left(14\right)$

v ₁=k ₁s+k ₂|s| ^rsgn(s) (15)

v ₂=(δ ₁+δ ₂)sgn(s) (16)

Wherein, v ₀The expression neural network estimator is used for the dynamically unknown of approximation system;

The desirable weights W of expression neural network ^*Estimated value, φ (X) is the basis function of neural network, X is the neural network input vector; v ₁Be feedback controller, be used for guaranteeing that tracking error can rapidly converge to sliding-mode surface in finite time; v ₂Be the robust item, the robustness the when system of assurance exists approximate error and weights evaluated error; k ₁0, k ₂0 for control parameter; δ ₁For greater than neural network approximate error upper limit ε _NConstant, that is: δ ₁ε _Nδ ₂Be a positive constant, satisfy

Be the neural network weight evaluated error.

2) the weights adjusting rule of design neural network is:

$\stackrel{\stackrel{\&CenterDot;}{^}}{W}=\mathrm{\&Gamma;\&phi;}\left(X\right)s---\left(17\right)$

Wherein, Γ is the symmetric matrix of positive definite, and φ (X) is chosen as the Sigmoid function, and expression-form is as follows:

$\mathrm{\&phi;}\left(X\right)=\frac{a}{b{+e}^{(-X/c)}}+d---\left(18\right)$

Wherein, a〉0, b 0, c 0, d＜0 is respectively constant parameter.

3) with in controller formula (13)-Shi (16) substitution formula (11), can obtain following closed-loop system dynamic equation:

Wherein, ε≤ε _NBe the neural network approximate error;

Be the neural network weight evaluated error.

4) design Lyapunov function respectively

With

Can prove that then all signals in the closed-loop control system (6) all are uniformly bounded.Simultaneously, the system keeps track error e can converge to equilibrium point e=0 in finite time.

5. enter next sampling instant, repeated execution of steps (3)-(5).

The turret systems of experiment usefulness adopts Mitsubishi's permagnetic synchronous motor, and the motor model (HC-UFS13, HC-KFS23); Motor shaft carries incremental optical-electricity encoder as feedback element; Motor driver adopts Mitsubishi's AC servo to drive, and model (MR-J2S-10A, MR-J2S-20A); Motor control card adopts and closes the TMS320F2812 development board that the crowd reaches company, and development environment is CCS3.0; Host computer is ordinary PC (two PCI slot).The original state of experimental system is set to: the sampling period of system is T=0.01s; The sinusoidal tracking signal of expectation is y _d=0.6sin (2 π t/5).

In order to verify the superiority of this algorithm, the present invention is respectively with regard to ADAPTIVE ROBUST finite time ANN (Artificial Neural Network) Control (Adaptive Robust Finite-Time Neural Control, ARFTNC), neural network terminal sliding mode control (Neural-Network based Terminal Sliding Mode Control, NNTSMC), linear sliding formwork control (Neural-Network based Linear Sliding Mode Control, NNLSMC) and the PID control method contrast.The controller of four kinds of methods and parameter thereof are given as follows respectively:

1) ARFTNC: the fast terminal sliding-mode surface is formula (10), and controller is formula (13)-(16), and neural network weight more new law is formula (17).The parameter of neural network is set to: Γ=0.05, a=2, b=10, c=1, d=-10; The parameter of sliding-mode surface is set to: λ ₁=15, λ ₂=0.1, γ=9/11; Controller parameter is chosen as: k ₁=0.6, k ₂=0.1, r=9/11, δ ₁=δ ₂=0.001.

2) NNTSMC: the terminal sliding mode face is

Neural network weight more new law is formula (17), and the expression formula of controller is:

$v={\hat{W}}^T\mathrm{\&phi;}\left(X\right)+k_3{\left|s\right|}^r\mathrm{sgn}\left(s\right)+({\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_2)\mathrm{sgn}\left(s\right)---\left(20\right)$

Wherein, k ₃=0.6, r=9/11, δ ₁=δ ₂=0.001.The parameter of neural network is identical with the fast terminal sliding-mode control, and the parameter of sliding-mode surface is set to: λ ₀=10, γ=9/11.

3) NNLSMC: linear sliding-mode surface is

Neural network weight more new law is formula (17), and its controller expression formula is:

$v={\hat{W}}^T\mathrm{\&phi;}\left(X\right)+k_{4}s+({\mathrm{\&delta;}}_1+{\mathrm{\&delta;}}_2)\mathrm{sgn}\left(s\right)---\left(21\right)$

Wherein, k ₄=0.4, δ ₁=δ ₂=0.001.The parameter of sliding-mode surface is set to:

4) PID control: the expression formula of controller is

$v=k_{P}e+k_D\stackrel{\&CenterDot;}{e}+k_I{\&Integral;}_0^{t}e\left(t\right)\mathrm{dt}---\left(22\right)$

Wherein, k _P=12, k _D=0.6, k _I=0.4.

The superiority of the ARFTNC algorithm that the present invention proposes is embodied in:

1) contrast NNTSMC method, ARFTNC method controller neutral line item k ₁S can guarantee that the ARFTNC method has speed of convergence faster than NNTSMC method;

2) contrast NNLSMC method, nonlinear terms k in the ARFTNC method controller ₂| s| ^rSgn (s) can guarantee that the ARFTNC method has littler tracking error than NNLSMC method;

Contrast as can be seen from the experimental result of Fig. 5 and Fig. 6:

1) for the table servo system that has unknown dead band, traditional PID control method is difficult to reach follows the tracks of the control effect preferably;

2) in the contrast of other three kinds of control methods, because system initial state is away from expectation state, therefore, the NNTSMC method is bigger in control tracking error in early stage, and convergence time is longer;

3) during near expectation state, tracking error is relatively large in system state for the NNLSMC method;

4) the ARFTNC method of the present invention design then combines the advantage of NNTSMC method and NNLSMC method effectively, not only early stage the tracking error converges faster, and the later stage tracking error is less.

What more than set forth is the good optimization effect that a embodiment that the present invention provides shows, obviously the present invention just is not limited to above-described embodiment, can do all distortion to it under the prerequisite of the related scope of flesh and blood of the present invention and is implemented not departing from essence spirit of the present invention and do not exceed.

And, although the illustrated tracking and controlling method of above-described embodiment carries out at TMS320F2812 series exploitation plate and corresponding making software, purpose is that interest of clarity is clear, also can realize in other occasions by adopting related hardwares such as TMS32 series exploitation plate in addition.

Claims (1)

1. table servo system neural network control method may further comprise the steps:

Step 1. is set up the mechanical dynamic model of permagnetic synchronous motor table servo system:

(1)

y=x(t)

Wherein,

U (t) ∈ R, y (t) ∈ R represents system state respectively, control input voltage and motor output.X represents the position, and m represents load quality,

The expression ride gain,

Be friction force,

Be to comprise the bounded Disturbance Model of measuring noise, electromagnetic interference (EMI) and other unknown terms.

Order

Then system of equations (1) can be rewritten as

(2)

y=x(t)

Wherein,

As shown in Figure 1, u (t) is the output signal in following non-linear dead band

Wherein, v (t) is dead band input (working control signal), g _l(v) and g _r(v) be unknown nonlinear smoothing function, b _lAnd b _rBe unknown skip distance parameter.

Step 2. is a simple time-varying system according to Order Derivatives in Differential Mid-Value Theorem with the non-linear input dead band linear-apporximation in the system, avoids the complicated calculations of the contrary compensation in dead band, finally derives the table servo system model that has unknown dead band.

1) according to Order Derivatives in Differential Mid-Value Theorem, there is ξ _l∈ (∞, b _l) and ξ _r∈ (b _r,+∞) makes

Wherein, ξ _l∈ (∞, b _l],

Wherein, ξ _r∈ [b _r,+∞).

2) by equation (2)-(5), the table servo system model that can have unknown dead band is:

(6)

y=x(t)

Wherein, | ρ (t) |≤ρ _N, ρ _N0 satisfy ρ _N=(g _R1+ g _L1) max{b _r,-b _l,

Wherein, ξ _l∈ (∞, b _l], ξ _r∈ [b _r,+∞),

And

Step 3. is in each sampling instant, the tracking error of calculating control system, fast terminal sliding-mode surface and first order derivative thereof.

1) based on table servo system model (6), the tracking error of definition control system is

e=y _d-y (9)

Wherein, y _dThe desired trajectory that can lead for second order.

2) its expression formula of fast terminal sliding-mode surface is as follows:

Wherein, e ∈ R is tracking error, | e| represents the absolute value of e, the e sign function of sgn (e) expression; λ ₁, λ ₂0 be constant.

3) to equation (10) both sides differentiate, can derive in conjunction with (6):

(11)

Wherein, the expression formula of nonlinear function κ is

Step 4. is based on the table servo system model (6) that has unknown dead band, it is dynamically unknown to select neural network to approach, design ADAPTIVE ROBUST finite time nerve network controller according to system keeps track error, fast terminal sliding-mode surface and first order derivative thereof, upgrade the neural network weight matrix.

1) at permagnetic synchronous motor table servo system (6), based on formula (10) and (11) design ADAPTIVE ROBUST finite time nerve network controller, structure is as follows:

v(t)=v ₀+v ₁+v ₂ (13)

v ₁=k ₁s+k ₂|s| ^rsgn(s) (15)

v ₂=(δ ₁+δ ₂)sgn(s) (16)

Wherein, v ₀The expression neural network estimator is used for the dynamically unknown of approximation system;

The desirable weights W of expression neural network ^*Estimated value, φ (X) is the basis function of neural network, X is the neural network input vector; v ₁Be feedback controller, be used for guaranteeing that tracking error can rapidly converge to sliding-mode surface in finite time; v ₂Be the robust item, the robustness the when system of assurance exists approximate error and weights evaluated error; k ₁0, k ₂0 for control parameter; δ ₁For greater than neural network approximate error upper limit ε _NConstant, that is: δ ₁ε _Nδ ₂Be a positive constant, satisfy

Be the neural network weight evaluated error.

2) the weights adjusting rule of design neural network is:

Wherein, Γ is the symmetric matrix of positive definite, and φ (X) is chosen as the Sigmoid function, and expression-form is as follows:

Wherein, a〉0, b 0, c 0, d＜0 is respectively constant parameter.

3) with in controller formula (13)-Shi (16) substitution formula (11), can obtain following closed-loop system dynamic equation:

Wherein, ε≤ε _NBe the neural network approximate error;

Be the neural network weight evaluated error.

4) design Lyapunov function respectively

With

Can prove that then all signals in the closed-loop control system (6) all are uniformly bounded.Simultaneously, the system keeps track error e can converge to equilibrium point e=0 in finite time.

Step 5. enters next sampling instant, repeated execution of steps (3)-(5).

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