CN105159091A - Ultrasonic motor adaptability recursive neural network control system - Google Patents

Abstract

The invention relates to an ultrasonic motor adaptability recursive neural network control system, comprising a base and an ultrasonic motor arranged thereon, wherein an output shaft on one side of the ultrasonic motor is connected with a photoelectric encoder, an output shaft on the other side of the ultrasonic motor is connected with a flywheel inertia load, an output shaft of the flywheel inertia load is connected with a torque sensor through a coupling, and the signal output ends of the photoelectric encoder and the torque sensor are respectively connected to a control system. The control system is composed of an adaptability recursive neural network controller and a motor, a recursive neural network is used for estimating an unknown dynamic function, and the adaptability learning law of recursive neural network parameters is obtained by the Lyapunov stability theorem. The ultrasonic motor adaptability recursive neural network control system is high in control accuracy, simple and compact in structure and good in using effect.

Description

A kind of supersonic motor adaptability recursion nerve network control system

Technical field

The present invention relates to electric machine controller field, particularly a kind of supersonic motor adaptability recursion nerve network control system.

Background technology

Existing supersonic motor recursion nerve network control system, when motor rotor position starts to depart from reference command, the increase with error is adjusted incoming frequency to recursion neural network automatically thus impact controls electric current.When controlled system has Parameters variation and external load disturbance, the recursion nerve network controller of this error-driven can reduce both impacts on controlled system trace performance above-mentioned.Therefore the Position And Velocity of motor controls to obtain good dynamic perfromance.

Summary of the invention

The object of the present invention is to provide a kind of supersonic motor adaptability recursion nerve network control system, to overcome the defect existed in prior art.

For achieving the above object, technical scheme of the present invention is: a kind of supersonic motor adaptability recursion nerve network control system, comprise: a pedestal and the supersonic motor be arranged on this pedestal, described supersonic motor side output shaft is connected with a photoelectric encoder, and described supersonic motor opposite side output shaft is connected with a flywheel inertia load one end; The output shaft of described flywheel inertia load is connected with a torque sensor through a spring coupling; The signal output part of described photoelectric encoder and the signal output part of described torque sensor are all connected to a control system; Described supersonic motor, described photoelectric encoder and described torque sensor are corresponding to be respectively fixed on described pedestal through supersonic motor fixed support, photoelectric encoder fixed support and torque sensor fixed support.

In an embodiment of the present invention, described control system comprises a supersonic motor Drive and Control Circuit; Described supersonic motor Drive and Control Circuit comprises a control chip circuit and a driving chip circuit; The signal output part of described photoelectric encoder is connected with the input end of described control chip circuit; The output terminal of described control chip circuit is connected with the input end of described driving chip circuit, to drive described driving chip circuit; The driving frequency conditioning signal output terminal of described driving chip circuit and driving half-bridge circuit conditioning signal output terminal respectively correspondence are connected with described supersonic motor input end; Described driving chip circuit produces driving frequency conditioning signal and drives half-bridge circuit conditioning signal, controls exporting the frequency of described supersonic motor A, B two phase PWM, phase place and break-make to.

In an embodiment of the present invention, control chip circuit in described control system estimates the unknown kinematic function of described control system by recursion neural network estimator, and pass through the anglec of rotation of supersonic motor rotor described in recursion ANN (Artificial Neural Network) Control, and obtained the adaptability learning rule of described recursion neural network estimator by Liapunov function, to guarantee the stability of recursion neural network.

In an embodiment of the present invention, the adaptability learning rule of described recursion neural network estimator is as follows:

$\stackrel{\·}{\hat{W}}={\mathrm{\η}}_1(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})E\left(t\right),$

$\stackrel{\·}{\hat{d}}={\mathrm{\η}}_2\hat{W}{T}_{\mathrm{\δ}}E\left(t\right),$

$\stackrel{\·}{\hat{v}}={\mathrm{\η}}_3\hat{W}{T}_{v}E\left(t\right),$

$\stackrel{\·}{\hat{r}}={\mathrm{\η}}_4\hat{W}{T}_{r}E\left(t\right);$

Robustness controller is:

Adaptability general collection indeterminate estimated value is:

The differential of Liapunov function is:

$\begin{array}{c}{\stackrel{\·}{V}}_L=E\left(t\right)\[(B_p{A}_p-K_e)E\left(t\right)+{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})+{\hat{W}}^T(T_d^T\tilde{d}+T_v^T\tilde{v}+T_r^{T}r+h-u_r)\]\\ -{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})E\left(t\right)-{\tilde{d}}^T\hat{W}{T}_d^{T}E\left(t\right)-{\tilde{v}}^T\hat{W}{T}_v^{T}E\left(t\right)-{\tilde{r}}^T\hat{W}{T}_v^{T}E\left(t\right)\frac{1}{{\mathrm{\η}}_5}\tilde{h}\left(t\right)\stackrel{\·}{\hat{h}}\left(t\right)\\ =E\left(t\right)(B_p{A}_p-K_e)E\left(t\right)\≤0;\end{array}$

General collection indeterminate:

$h=W^{*T}(T_d^T{d}^{*}+T_v^T{v}^{*}+T_r^T{r}^{*}+N)-{\hat{W}}^T(T_d^T{d}^{*}+T_v^T{v}^{*}+T_r^T{r}^{*})+{\mathrm{\ϵ}}_y-B_p{C}_p(T_L+T_f(v\left)\right);$

The closed loop dynamic equation of supersonic motor drive system:

$B_p\stackrel{\·}{E}\left(t\right)=(B_p{A}_p-K_e)E\left(t\right)+{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})+{\tilde{W}}^T(T_d^T\tilde{d}-T_v^T\tilde{v}-T_r^T\tilde{r})+h-u_r;$

Wherein, η ₁, η ₂, η ₃, η ₄and η ₅for normal number, for the estimation online value of general collection indeterminate h; Error function error e (t)=θ _m(t)-θ _r(t), θ _mt () is control signal, θ _rt () is measuring-signal; A _p=-B/J, B _p=J/K _t>0, C _p=-1/J; B is ratio of damping, and J is moment of inertia, K _tfor current factor, T _fv () is frictional resistance moment, T _lfor loading moment; U (t) is the output torque of described supersonic motor, and k _ebe one normal several, u _rfor controller, for the output of described recursion neural network;

Remember that the unknown kinematic function of described control system is y, estimation error:

$\tilde{y}=y-\hat{y}=W^{*T}T(x,d^{*},v^{*},r^{*})-{\hat{W}}^{T}T(x,\hat{d},\hat{v},\hat{r})+{\mathrm{\ϵ}}_y$

ε _yfor minimum reconstruction error; W ^*for the ideal value of recursion neural network connection weight, for the estimated value of recursion neural network connection weight; d ^*, v ^*and r ^*be respectively the ideal parameters value of d, v and r, wherein d, v are respectively width and the center of recursion neural network Gaussian function used, and r is the feedback gain of recursion neural network inside; ; and for ideal parameters value (d ^*, v ^*and r ^*) estimated value; Make T ^*=T (x, d ^*, v ^*, r ^*), $\hat{T}=(x,\hat{d},\hat{v},\hat{r}),\tilde{W}=W^{*}-\hat{W},\tilde{T}=T^{*}-\hat{T}$ Then:

$\tilde{y}=W^{*T}\tilde{T}+{\hat{W}}^T\hat{T}+{\mathrm{\ϵ}}_y;$

Taylor expansion after the linearization of described recursion part of neural network is:

$\begin{array}{c}\stackrel{:}{T}=\left[\begin{array}{c}{\stackrel{:}{\mathrm{\Θ}}}_1\\ {\stackrel{:}{\mathrm{\Θ}}}_2\\ M\\ {\stackrel{:}{\mathrm{\Θ}}}_k\end{array}\right]={\left[\begin{array}{c}\frac{\∂{\mathrm{\Θ}}_1}{\∂d}\\ \frac{\∂{\mathrm{\Θ}}_2}{\∂d}\\ M\\ \frac{\∂{\mathrm{\Θ}}_k}{\∂d}\end{array}\right]}^T{|}_{d=\hat{d}}(d^{*}-\hat{d})+{\left[\begin{array}{c}\frac{\∂{\mathrm{\Θ}}_1}{\∂v}\\ \frac{\∂{\mathrm{\Θ}}_2}{\∂v}\\ M\\ \frac{\∂{\mathrm{\Θ}}_k}{\∂v}\end{array}\right]}^T{|}_{v=\hat{v}}(v^{*}-\hat{v})+{\left[\begin{array}{c}\frac{\∂{\mathrm{\Θ}}_1}{\∂r}\\ \frac{\∂{\mathrm{\Θ}}_2}{\∂r}\\ M\\ \frac{\∂{\mathrm{\Θ}}_k}{\∂r}\end{array}\right]}^T{|}_{r=\hat{r}}(r^{*}-\hat{r})+N\\ \≡T_d^T\tilde{d}+T_v^T\tilde{v}+T_r^T\tilde{r}+N1\end{array}$

$T_{\mathrm{\δ}}=\[\frac{\∂{\mathrm{\Θ}}_1}{\∂d}\frac{\∂{\mathrm{\Θ}}_2}{\∂d}L\frac{\∂{\mathrm{\Θ}}_k}{\∂d}\]{|}_{d=\hat{d}}\∈R^{j\×k};T_v=\[\frac{\∂{\mathrm{\Θ}}_1}{\∂v}\frac{\∂{\mathrm{\Θ}}_2}{\∂v}L\frac{\∂{\mathrm{\Θ}}_k}{\∂v}\]{|}_{v=\hat{v}}\∈R^{j\×k};$ $T_r=\[\frac{\∂{\mathrm{\Θ}}_1}{\∂r}\frac{\∂{\mathrm{\Θ}}_2}{\∂r}L\frac{\∂{\mathrm{\Θ}}_k}{\∂r}\]{|}_{r=\hat{r}}\∈R^{j\×k};\tilde{d}=d^{*}-\hat{d};\tilde{v}=v^{*}-\hat{v};\tilde{r}=r^{*}-\hat{r};$ N1 is higher order term vector and has dividing value for positive.

In an embodiment of the present invention, the network architecture that described recursion neural network adopts comprises: input layer, hidden layer and output layer, and Gaussian function is the trigger function of hidden layer.

In an embodiment of the present invention, each layer network signal transduction process of described recursion neural network and basic function as follows:

Ground floor: input layer has i neuron node

${\mathrm{net}}_i^1\left(N\right)=x_i\left(N\right);$

$O_i^1\left(N\right)=f_i^1\left({\mathrm{net}}_i^1\right(N\left)\right)={\mathrm{net}}_i^1,i=1,2;$

Wherein, represent the input signal of input layer i-th neuron node; represent the output corresponding to input layer i-th node; represent excitation function; N is the iterations of neural network;

The second layer: hidden layer has m neuron node

${\mathrm{net}}_k^2\left(N\right)=\underset{i=1}{\overset{m}{\Σ}}\frac{{\[x_i\left(N\right)+T_k(N-1)r_k-v_{ik}\]}^2}{{\mathrm{\β}}_{ik}^2};$

Or

${\mathrm{net}}_k^2\left(N\right)=\underset{i=1}{\overset{m}{\Σ}}{\mathrm{\δ}}_{ik}^2{\[x_i\left(N\right)+T_k(N-1)r_k-v_{ik}\]}^2;$

And

$T_k\left(N\right)=f_j^2\left({\mathrm{net}}_k^2\right(N\left)\right)=e^{-{\mathrm{net}}_k^2\left(N\right)},$

Wherein, v _kfor the center of Gaussian function; δ _kfor the width of Gaussian function; Θ _k(N) output corresponding to a hidden layer kth node is represented; represent excitation function; K is natural number;

Third layer: output layer has k node

${\mathrm{net}}^3\left(N\right)=\underset{k}{\Σ}{w}_k{\mathrm{\Θ}}_k\left(N\right);$

Z(N)＝f ³(net ³(N))＝net ³；

Wherein, w _krepresent the link weighted value between hidden layer node k and output layer; Z (N) represents the output corresponding to an output layer kth node; f ³(g) representation unit excitation function.

Compared to prior art, the present invention has following characteristic: not only control accuracy is high for a kind of supersonic motor adaptability recursion nerve network control system proposed by the invention, and structure is simple, compact, and result of use is good.

Accompanying drawing explanation

Fig. 1 is the structural representation of a kind of supersonic motor adaptability of the present invention recursion nerve network control system.

Fig. 2 is control chip circuit theory diagrams in a kind of supersonic motor adaptability of the present invention recursion nerve network control system.

In figure, 1-photoelectric encoder, 2-photoelectric encoder fixed support, 3-supersonic motor output shaft, 4-supersonic motor, 5-supersonic motor fixed support, 6-supersonic motor output shaft, 7-flywheel inertia load, 8-flywheel inertia load output shaft, 9-spring coupling, 10-torque sensor, 11-torque sensor fixed support, 12-pedestal, 13-control chip circuit, 14-driving chip circuit, 15, 16, the A that 17-photoelectric encoder exports, B, Z phase signals, 18, 19, 20, the driving frequency conditioning signal that 21-driving chip circuit produces, the driving half-bridge circuit conditioning signal that 22-driving chip circuit produces, 23, 24, 25, 26, 27, the signal of the driving chip circuit that 28-control chip circuit produces, 29-supersonic motor Drive and Control Circuit.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is specifically described.

The invention provides a kind of supersonic motor adaptability recursion nerve network control system, as shown in Figure 1, comprise: and a pedestal 12 and the supersonic motor 4 that is arranged on this pedestal 12, described supersonic motor 4 side output shaft 3 is connected with a photoelectric encoder 1, and described supersonic motor 4 opposite side output shaft 6 is connected with flywheel inertia load 7 one end; The output shaft 8 of described flywheel inertia load 7 is connected with a torque sensor 10 through a spring coupling 9; The signal output part of described photoelectric encoder 1 and 10 signal output parts of described torque sensor are all connected to a control system; Described supersonic motor 4, described photoelectric encoder 1 and described torque sensor 10 are corresponding to be respectively fixed on described pedestal through supersonic motor fixed support 5, photoelectric encoder fixed support 2 and torque sensor fixed support 11.

Further, in the present embodiment, as shown in Figure 2, described control system comprises a supersonic motor Drive and Control Circuit 29; Described supersonic motor Drive and Control Circuit 29 comprises control chip circuit 13 and a driving chip circuit 14; The signal output part of described photoelectric encoder 4 is connected with the input end of described control chip circuit 13; The output terminal of described control chip circuit 13 is connected with the input end of described driving chip 14 circuit, to drive described driving chip circuit 14; The driving frequency conditioning signal output terminal of described driving chip circuit 14 and driving half-bridge circuit conditioning signal output terminal respectively correspondence are connected with described supersonic motor 4 input end; Described driving chip circuit 14 produces driving frequency conditioning signal and drives half-bridge circuit conditioning signal, control exporting the frequency of described supersonic motor A, B two phase PWM, phase place and break-make to, control the startup of supersonic motor and out of service by the output opening and turn off PWM ripple, regulated the optimal operational condition of motor by the PWM wave frequency of regulation output and the phase differential of two-phase.

Further, in the present embodiment, control chip circuit in described control system estimates the unknown kinematic function of described control system by the recursion neural network estimator be equipped in control chip circuit, and pass through the anglec of rotation of supersonic motor rotor described in recursion ANN (Artificial Neural Network) Control, and obtained the adaptability learning rule of described recursion neural network estimator by Liapunov function, to guarantee the stability of recursion neural network.

Further, in the present embodiment, the dynamic equation of supersonic motor drive system is designated as:

$\stackrel{\·\·}{\mathrm{\θ}}\left(t\right)\stackrel{\mathrm{\Δ}}{=}{A}_p{\stackrel{\·}{\mathrm{\θ}}}_r\left(t\right)+\frac{1}{B_P}U\left(t\right)+C_P(T_L+T_f(v\left)\right)---\left(1\right)$

Wherein A _p=-B/J, B _p=J/K _t>0, C _p=-1/J; B is ratio of damping, and J is moment of inertia, K _tfor current factor, T _fv () is frictional resistance moment, T _lfor loading moment, the output torque that U (t) is supersonic motor.

Error e (t)=θ _m(t)-θ _r(t), θ _mt () is control signal, θ _rt () is measuring-signal.

Choose error function $E\left(t\right)=\stackrel{\·}{e}\left(t\right)+\mathrm{\λ}e\left(t\right),\mathrm{\λ}>0$

Differential is carried out to error function, obtains following formula:

$B_P\stackrel{\·}{E}\left(t\right)=B_P{A}_{p}E\left(t\right)-U\left(t\right)-B_P{C}_P(T_L+T_f(v\left)\right)+y---\left(2\right)$

The nonlinear function y that note is unknown, also namely the unknown kinematic function y of control system is:

$y=B_P\[{\stackrel{\·\·}{\mathrm{\θ}}}_m\left(t\right)+\mathrm{\λ}\stackrel{\·}{e}\left(t\right)\]-B_P{A}_p\[{\stackrel{\·\·}{\mathrm{\θ}}}_m\left(t\right)+\mathrm{\λ}e\left(t\right)\]---\left(3\right)$

Recursion neural network is used for estimating the y of this unknown.By the output of recursion neural network and cannot estimate accurately and y.In the present embodiment, controller u is adopted _rreduce the error of estimation and the interference caused by cross-couplings interference, be the connection weight weight values of on-line tuning recursion neural network and reached follow effect and degree of stability, and control law is designated as:

$U\left(t\right)=K_{e}E\left(t\right)+\hat{y}+u_r---\left(4\right)$

Wherein, K _ebe one normal several.The closed loop dynamic equation of supersonic motor drive system can be expressed as follows:

$B_P\stackrel{\·}{E}\left(t\right)=(B_P{A}_p-K_e)E\left(t\right)+\tilde{y}-B_P{C}_P(T_L+T_f(v\left)\right)-u_r---\left(5\right)$

Estimation error can be expressed as:

$\tilde{y}=y-\hat{y}=W^{*T}T(x,d^{*},v^{*},r^{*})-{\hat{W}}^{T}T(x,\hat{d},\hat{v},\hat{r})+{\mathrm{\ϵ}}_y---\left(6\right)$

ε _yfor minimum reconstruction error; W ^*for the ideal value of recursion neural network connection weight, for the estimated value of recursion neural network connection weight; d ^*, v ^*and r ^*be respectively d, the ideal parameters value of v and r, wherein d, v are respectively width and the center of recursion neural network Gaussian function used, and r is the feedback gain of recursion neural network inside; with for ideal parameters value (d ^*, v ^*and r ^*) estimated value.For convenience's sake, we will T ^*=T (x, d ^*, v ^*, r ^*) and

(6) can be rewritten into:

$\tilde{y}=W^{*T}\tilde{T}+{\hat{W}}^T\hat{T}+{\mathrm{\ϵ}}_y---\left(7\right)$

Wherein, $\tilde{W}=W^{*}-\hat{W}$ With $\tilde{T}=T^{*}-\hat{T}.$

Utilizing linearizing method to convert recursion neural network the form of partial linear to, can Taylor expansion obtained as follows:

$\begin{array}{c}\stackrel{:}{T}=\left[\begin{array}{c}{\stackrel{:}{\mathrm{\Θ}}}_1\\ {\stackrel{:}{\mathrm{\Θ}}}_2\\ M\\ {\stackrel{:}{\mathrm{\Θ}}}_k\end{array}\right]={\left[\begin{array}{c}\frac{\∂{\mathrm{\Θ}}_1}{\∂d}\\ \frac{\∂{\mathrm{\Θ}}_2}{\∂d}\\ M\\ \frac{\∂{\mathrm{\Θ}}_k}{\∂d}\end{array}\right]}^T{|}_{d=\hat{d}}(d^{*}-\hat{d})+{\left[\begin{array}{c}\frac{\∂{\mathrm{\Θ}}_1}{\∂v}\\ \frac{\∂{\mathrm{\Θ}}_2}{\∂v}\\ M\\ \frac{\∂{\mathrm{\Θ}}_k}{\∂v}\end{array}\right]}^T{|}_{v=\hat{v}}(v^{*}-\hat{v})+{\left[\begin{array}{c}\frac{\∂{\mathrm{\Θ}}_1}{\∂r}\\ \frac{\∂{\mathrm{\Θ}}_2}{\∂r}\\ M\\ \frac{\∂{\mathrm{\Θ}}_k}{\∂r}\end{array}\right]}^T{|}_{r=\hat{r}}(r^{*}-\hat{r})+N\\ \≡T_d^T\tilde{d}+T_v^T\tilde{v}+T_r^T\tilde{r}+N1\end{array}---\left(8\right)$

Wherein, $T_{\mathrm{\δ}}=\[\frac{\∂{\mathrm{\Θ}}_1}{\∂d}\frac{\∂{\mathrm{\Θ}}_2}{\∂d}L\frac{\∂{\mathrm{\Θ}}_k}{\∂d}\]{|}_{d=\hat{d}}\∈R^{j\×k};T_v=\[\frac{\∂{\mathrm{\Θ}}_1}{\∂v}\frac{\∂{\mathrm{\Θ}}_2}{\∂v}L\frac{\∂{\mathrm{\Θ}}_k}{\∂v}\]{|}_{v=\hat{v}}\∈R^{j\×k}$

$T_r=\[\frac{\∂{\mathrm{\Θ}}_1}{\∂r}\frac{\∂{\mathrm{\Θ}}_2}{\∂r}L\frac{\∂{\mathrm{\Θ}}_k}{\∂r}\]{|}_{r=\hat{r}}\∈R^{j\×k};\tilde{d}=d^{*}-\hat{d};\tilde{v}=v^{*}-\hat{v};\tilde{r}=r^{*}-\hat{r};$ N1 is higher order term vector and is assumed to be positive have dividing value.

Further, can obtain following formula is:

$\tilde{y}-B_p{C}_p(T_L+T_f(v\left)\right)={\hat{W}}^T\tilde{T}+{\tilde{W}}^T\tilde{T}+{\tilde{W}}^T\hat{T}+{\mathrm{\ϵ}}_y-B_p{C}_p(T_L+T_f(v\left)\right)$

$={\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})+{\hat{W}}^T(T_d^T{d}^{*}+T_v^T{v}^{*}+T_r^T{r}^{*})+h---\left(9\right)$

Wherein, general collection indeterminate

$h=W^{*T}(T_d^T{d}^{*}+T_v^T{v}^{*}+T_r^T{r}^{*}+N)-{\hat{W}}^T(T_d^T{d}^{*}+T_v^T{v}^{*}+T_r^T{r}^{*})+{\mathrm{\ϵ}}_y-B_p{C}_p(T_L+T_f(v\left)\right)$

System closed loop dynamic equation is:

$B_p\stackrel{\·}{E}\left(t\right)=(B_p{A}_p-K_e)E\left(t\right)+{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})+{\tilde{W}}^T(T_d^T\tilde{d}-T_v^T\tilde{v}-T_r^T\tilde{r})+h-u_r---\left(10\right)$

In the present embodiment, supersonic motor drive system control law is such as formula shown in (4), the adaptability study control rule of recursion neural network estimator is such as formula shown in (11) to (14), and the design of robustness controller is such as formula shown in (15), its adaptability general collection indeterminate estimated value such as formula shown in (16), then can ensure the stability of designed adaptability recursion nerve network control system.

$\stackrel{\·}{\hat{W}}={\mathrm{\η}}_1(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})E\left(t\right)---\left(11\right)$

$\stackrel{\·}{\hat{d}}={\mathrm{\η}}_2\hat{W}{T}_{\mathrm{\δ}}E\left(t\right)---\left(12\right)$

$\stackrel{\·}{\hat{v}}={\mathrm{\η}}_3\hat{W}{T}_{v}E\left(t\right)---\left(13\right)$

$\stackrel{\·}{\hat{r}}={\mathrm{\η}}_4\hat{W}{T}_{r}E\left(t\right)---\left(14\right)$

$u_r=\hat{h}---\left(15\right)$

$\stackrel{\·}{\hat{h}}\left(t\right)={\mathrm{\η}}_{5}E\left(t\right)---\left(16\right)$

Wherein, η ₁, η ₂, η ₃, η ₄and η ₅for normal number, for the estimation online value of general collection indeterminate h.Definition Liapunov function:

$V_L\left(E\right(t),\tilde{W},\tilde{d},\tilde{v},\tilde{r},\tilde{h}(t\left)\right)=\frac{B_p}{2}{E}^2\left(t\right)+\frac{1}{2{\mathrm{\η}}_1}{\tilde{W}}^T\tilde{W}+\frac{1}{2{\mathrm{\η}}_2}{\tilde{d}}^T\tilde{d}+\frac{1}{2{\mathrm{\η}}_3}{\tilde{v}}^T\tilde{v}+\frac{1}{2{\mathrm{\η}}_4}{\tilde{r}}^T\tilde{r}+\frac{1}{2{\mathrm{\η}}_5}{\tilde{h}}^2\left(t\right)---\left(17\right)$

Further, estimation error is defined to above formula differential, then:

${\stackrel{\·}{V}}_L=B_{p}E\left(t\right)\stackrel{\·}{E}\left(t\right)-\frac{1}{{\mathrm{\η}}_1}\tilde{W}{\stackrel{\·}{\hat{W}}}^T-\frac{1}{{\mathrm{\η}}_2}{\tilde{d}}^T\stackrel{\·}{\hat{d}}-\frac{1}{{\mathrm{\η}}_3}{\tilde{v}}^T\stackrel{\·}{\hat{v}}-\frac{1}{{\mathrm{\η}}_4}{\tilde{r}}^T\stackrel{\·}{\hat{r}}-\frac{1}{{\mathrm{\η}}_5}\tilde{h}\left(t\right)\stackrel{\·}{\hat{h}}\left(t\right)$

$\begin{array}{c}=E\left(t\right)\[(B_p{A}_p-K_e)E\left(t\right)+{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})+{\hat{W}}^T(T_d^T\tilde{d}+T_v^T\tilde{v}+T_r^{T}r+h-u_r)\]\\ -\frac{1}{{\mathrm{\η}}_1}{\tilde{W}}^T\stackrel{\·}{\hat{W}}-\frac{1}{{\mathrm{\η}}_2}{\tilde{d}}^T\stackrel{\·}{\hat{d}}-\frac{1}{{\mathrm{\η}}_3}{\tilde{v}}^T\stackrel{\·}{\hat{v}}-\frac{1}{{\mathrm{\η}}_4}{\tilde{r}}^T\stackrel{\·}{\hat{r}}-\frac{1}{{\mathrm{\η}}_5}\tilde{h}\left(t\right)\stackrel{\·}{\hat{h}}\left(t\right)\end{array}---\left(18\right)$

If a Design of Neural Network Controller accepted way of doing sth (11), (12), (13) and (14), and strong controller is such as formula designed by (15), the estimation of simultaneous adaptation general collection indeterminate is such as formula (16), and so formula (18) can be rewritten as follows:

$\begin{array}{c}{\stackrel{\·}{V}}_L=E\left(t\right)\[(B_p{A}_p-K_e)E\left(t\right)+{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})+{\hat{W}}^T(T_d^T\tilde{d}+T_v^T\tilde{v}+T_r^{T}r+h-u_r)\]\\ -{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})E\left(t\right)-{\tilde{d}}^T\hat{W}{T}_d^{T}E\left(t\right)-{\tilde{v}}^T\hat{W}{T}_v^{T}E\left(t\right)-{\tilde{r}}^T\hat{W}{T}_v^{T}E\left(t\right)\frac{1}{{\mathrm{\η}}_5}\tilde{h}\left(t\right)\stackrel{\·}{\hat{h}}\left(t\right)\\ =E\left(t\right)(B_p{A}_p-K_e)E\left(t\right)\≤0\end{array}---\left(19\right)$

When ${\stackrel{\·}{V}}_L\left(E\right(t),\tilde{W},\tilde{d},\tilde{v},\tilde{r},\tilde{h}(t\left)\right)\≤0,$ Then ${\stackrel{\·}{V}}_L\left(E\right(t),\tilde{W},\tilde{d},\tilde{v},\tilde{r},\tilde{h}(t\left)\right)\≤0$ Meet negative semidefinite condition, namely ${\stackrel{\·}{V}}_L\left(E\right(t),\tilde{W},\tilde{d},\tilde{v},\tilde{r},\tilde{h}(t\left)\right)\≤{\stackrel{\·}{V}}_L\left(E\right(0),\tilde{W},\tilde{d},\tilde{v},\tilde{r},\tilde{h}(0\left)\right),$ It can thus be appreciated that, E (t), with be limited function.Make function $P_a\left(t\right)=-E\left(t\right)(B_p{A}_p-K_e)E\left(t\right)=-{\stackrel{\·}{V}}_L\left(E\right(t),\tilde{W},\tilde{d},\tilde{v},\tilde{r},\tilde{h}(t\left)\right),$ And function P _at () time differential is as follows:

${\∫}_0^t{P}_a\left(\mathrm{\τ}\right)d\mathrm{\τ}={\stackrel{\·}{V}}_L\left(E\left(0\right),\tilde{W},\tilde{d},\tilde{v},\tilde{r},\tilde{h}\left(0\right)\right)-{\stackrel{\·}{V}}_L\left(E\left(t\right),\tilde{W},\tilde{d},\tilde{v},\tilde{r},\tilde{h}\left(t\right)\right))---\left(20\right)$

Because, for there being dividing value, and for non-increasing limited function, can following results be obtained: $\underset{t\&RightArrow;\mathrm{\&infin;}}{\lim }{\&Integral;}_0^t{P}_a\left(\mathrm{\&tau;}\right)d\mathrm{\&tau;}<\mathrm{\&infin;}---\left(21\right)$

Similarly, for limited function.According to Barbara lemma, can inference namely when the time levels off to infinity, E (t) levels off to zero.So, the stability of designed adaptability recursion nerve network control system can be guaranteed.

Further, in this enforcement, the network architecture that described recursion neural network adopts comprises: input layer, hidden layer and output layer, and Gaussian function is the trigger function of hidden layer.Each layer network signal transduction process of described recursion neural network and basic function as follows:

Ground floor: input layer has i neuron node

${\mathrm{net}}_i^1\left(N\right)=x_i\left(N\right);$

$O_i^1\left(N\right)=f_i^1\left({\mathrm{net}}_i^1\right(N\left)\right)={\mathrm{net}}_i^1,i=1,2;$

Wherein, represent the input signal of input layer i-th neuron node; represent the output corresponding to input layer i-th node; represent excitation function; N is the iterations of neural network;

The second layer: hidden layer has m neuron node

${\mathrm{net}}_k^2\left(N\right)=\underset{i=1}{\overset{m}{\&Sigma;}}\frac{{\&lsqb;x_i\left(N\right)+T_k(N-1)r_k-v_{ik}\&rsqb;}^2}{{\mathrm{\&beta;}}_{ik}^2};$

Or

${\mathrm{net}}_k^2\left(N\right)=\underset{i=1}{\overset{m}{\&Sigma;}}{\mathrm{\&delta;}}_{ik}^2{\&lsqb;x_i\left(N\right)+T_k(N-1)r_k-v_{ik}\&rsqb;}^2;$

And

$T_k\left(N\right)=f_j^2\left({\mathrm{net}}_k^2\right(N\left)\right)=e^{-{\mathrm{net}}_k^2\left(N\right)},$

Wherein, v _kfor the center of Gaussian function; δ _kfor the width of Gaussian function; Θ _k(N) output corresponding to a hidden layer kth node is represented; represent excitation function; K is natural number;

Third layer: output layer has k node

${\mathrm{net}}^3\left(N\right)=\underset{k}{\&Sigma;}{w}_k{\mathrm{\&Theta;}}_k\left(N\right);$

Z(N)＝f ³(net ³(N))＝net ³；

Wherein, w _krepresent the link weighted value between hidden layer node k and output layer; Z (N) represents the output corresponding to an output layer kth node; f ³(g) representation unit excitation function.

Be more than preferred embodiment of the present invention, all changes done according to technical solution of the present invention, when the function produced does not exceed the scope of technical solution of the present invention, all belong to protection scope of the present invention.

Claims (6)

1. a supersonic motor adaptability recursion nerve network control system, comprise: a pedestal and the supersonic motor be arranged on this pedestal, it is characterized in that, described supersonic motor side output shaft is connected with a photoelectric encoder, and described supersonic motor opposite side output shaft is connected with a flywheel inertia load one end; The output shaft of described flywheel inertia load is connected with a torque sensor through a spring coupling; The signal output part of described photoelectric encoder and the signal output part of described torque sensor are all connected to a control system; Described supersonic motor, described photoelectric encoder and described torque sensor are corresponding to be respectively fixed on described pedestal through supersonic motor fixed support, photoelectric encoder fixed support and torque sensor fixed support.

2. a kind of supersonic motor adaptability recursion nerve network control system according to claim 1, it is characterized in that, described control system comprises a supersonic motor Drive and Control Circuit; Described supersonic motor Drive and Control Circuit comprises a control chip circuit and a driving chip circuit; The signal output part of described photoelectric encoder is connected with the input end of described control chip circuit; The output terminal of described control chip circuit is connected with the input end of described driving chip circuit, to drive described driving chip circuit; The driving frequency conditioning signal output terminal of described driving chip circuit and driving half-bridge circuit conditioning signal output terminal respectively correspondence are connected with described supersonic motor input end; Described driving chip circuit produces driving frequency conditioning signal and drives half-bridge circuit conditioning signal, controls exporting the frequency of described supersonic motor A, B two phase PWM, phase place and break-make to.

3. a kind of supersonic motor adaptability recursion nerve network control system according to claim 2, it is characterized in that, control chip circuit in described control system estimates the unknown kinematic function of described control system by recursion neural network estimator, and pass through the anglec of rotation of supersonic motor rotor described in recursion ANN (Artificial Neural Network) Control, and obtained the adaptability learning rule of described recursion neural network estimator by Liapunov function, to guarantee the stability of recursion neural network.

4. a kind of supersonic motor adaptability recursion nerve network control system according to claim 3, it is characterized in that, the adaptability learning rule of described recursion neural network estimator is as follows:

$\stackrel{\&CenterDot;}{\hat{W}}={\mathrm{\&eta;}}_1(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})E\left(t\right),$

$\stackrel{\&CenterDot;}{\hat{d}}={\mathrm{\&eta;}}_2\hat{W}{T}_{\mathrm{\&delta;}}E\left(t\right),$

$\stackrel{\&CenterDot;}{\hat{v}}={\mathrm{\&eta;}}_3\hat{W}{T}_{v}E\left(t\right),$

$\stackrel{\&CenterDot;}{\hat{r}}={\mathrm{\&eta;}}_4\hat{W}{T}_{r}E\left(t\right);$

Robustness controller is:

Adaptability general collection indeterminate estimated value is:

The differential of Liapunov function is:

$\begin{array}{c}{\stackrel{\&CenterDot;}{V}}_L=E\left(t\right)\&lsqb;(B_p{A}_p-K_e)E\left(t\right)+{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})+{\hat{W}}^T(T_d^T\tilde{d}-T_v^T\tilde{v}-T_r^{T}r+h-u_r)\&rsqb;\\ -{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})E\left(t\right)-{\tilde{d}}^T\hat{W}{T}_d^{T}E\left(t\right)-{\tilde{v}}^T\hat{W}{T}_v^{T}E\left(t\right)-{\tilde{r}}^T\hat{W}{T}_v^{T}E\left(t\right)\frac{1}{{\mathrm{\&eta;}}_5}\tilde{h}\left(t\right)\stackrel{\&CenterDot;}{\hat{h}}\left(t\right)\\ =E\left(t\right)(B_p{A}_p-K_e)E\left(t\right)\&le;0\end{array};$

General collection indeterminate:

$h=W^{*T}(T_d^T{d}^{*}+T_v^T{v}^{*}+T_r^T{r}^{*}+N)-{\hat{W}}^T(T_d^T{d}^{*}+T_v^T{v}^{*}+T_r^T{r}^{*})+{\mathrm{\&epsiv;}}_y-B_p{C}_p(T_L+T_f(v\left)\right);$

The closed loop dynamic equation of supersonic motor drive system:

$B_p\stackrel{\&CenterDot;}{E}\left(t\right)=(B_p{A}_p-K_e)E\left(t\right)+{\tilde{W}}^T(\hat{T}-T_d^T\hat{d}-T_v^T\hat{v}-T_r^T\hat{r})+{\tilde{W}}^T(T_d^T\tilde{d}-T_v^T\tilde{v}-T_r^T\tilde{r})+h-u_r;$

Wherein, η ₁, η ₂, η ₃, η ₄and η ₅for normal number, for the estimation online value of general collection indeterminate h; Error function λ >0; Error e (t)=θ _m(t)-θ _r(t), θ _mt () is control signal, θ _rt () is measuring-signal; A _p=-B/J, B _p=J/K _t>0, C _p=-1/J; B is ratio of damping, and J is moment of inertia, K _tfor current factor, T _fv () is frictional resistance moment, T _lfor loading moment; U (t) is the output torque of described supersonic motor, and k _ebe one normal several, u _rfor controller, for the output of described recursion neural network;

Remember that the unknown kinematic function of described control system is y, estimation error:

$\tilde{y}=y-\hat{y}=W^{*T}T(x,d^{*},v^{*},r^{*})-{\hat{W}}^{T}T(x,\hat{d},\hat{v},\hat{r})+{\mathrm{\&epsiv;}}_y$

ε _yfor minimum reconstruction error; W ^*for the ideal value of recursion neural network connection weight, for the estimated value of recursion neural network connection weight; d ^*, v ^*and r ^*be respectively the ideal parameters value of d, v and r, wherein d, v are respectively width and the center of recursion neural network Gaussian function used, and r is the feedback gain of recursion neural network inside; and for ideal parameters value (d ^*, v ^*and r ^*) estimated value; Make T ^*=T (x, d ^*, v ^*, r ^*), $\hat{T}=(x,\hat{d},\hat{v},\hat{r})\tilde{W}=W^{*}-\hat{W},\tilde{T}=T^{*}-\hat{T},$ Then:

$\tilde{y}=W^{*T}\tilde{T}+{\hat{W}}^T\hat{T}+{\mathrm{\&epsiv;}}_y;$

Taylor expansion after the linearization of described recursion part of neural network is:

$\begin{array}{c}\stackrel{\&CenterDot;}{\stackrel{\&CenterDot;}{T}}=\left[\begin{array}{c}{\stackrel{\&CenterDot;}{\stackrel{\&CenterDot;}{\mathrm{\&Theta;}}}}_1\\ {\stackrel{\&CenterDot;}{\stackrel{\&CenterDot;}{\mathrm{\&Theta;}}}}_2\\ M\\ {\stackrel{\&CenterDot;}{\stackrel{\&CenterDot;}{\mathrm{\&Theta;}}}}_k\end{array}\right]={\left[\begin{array}{c}\frac{\&part;{\mathrm{\&Theta;}}_1}{\&part;d}\\ \frac{\&part;{\mathrm{\&Theta;}}_2}{\&part;d}\\ M\\ \frac{\&part;{\mathrm{\&Theta;}}_m}{\&part;d}\end{array}\right]}^T{|}_{d=\hat{d}}(d^{*}-\hat{d}){\left[\begin{array}{c}\frac{\&part;{\mathrm{\&Theta;}}_1}{\&part;v}\\ \frac{\&part;{\mathrm{\&Theta;}}_2}{\&part;v}\\ M\\ \frac{\&part;{\mathrm{\&Theta;}}_m}{\&part;v}\end{array}\right]}^T{|}_{v=\hat{v}}(v^{*}-\hat{v})+{\left[\begin{array}{c}\frac{\&part;{\mathrm{\&Theta;}}_1}{\&part;r}\\ \frac{\&part;{\mathrm{\&Theta;}}_2}{\&part;r}\\ M\\ \frac{\&part;{\mathrm{\&Theta;}}_m}{\&part;r}\end{array}\right]}^T{|}_{r=\hat{r}}(r^{*}-\hat{r})+N\\ \&equiv;T_d^T\tilde{d}+T_v^T\tilde{v}+T_r^T\tilde{r}+N1\end{array}$

$T_{\mathrm{\&delta;}}=\&lsqb;\frac{\&part;{\mathrm{\&Theta;}}_1}{\&part;d}\frac{\&part;{\mathrm{\&Theta;}}_2}{\&part;d}L\frac{\&part;{\mathrm{\&Theta;}}_m}{\&part;d}\&rsqb;{|}_{d=\hat{d}};T_v=\&lsqb;\frac{\&part;{\mathrm{\&Theta;}}_1}{\&part;v}\frac{\&part;{\mathrm{\&Theta;}}_2}{\&part;v}L\frac{\&part;{\mathrm{\&Theta;}}_m}{\&part;v}\&rsqb;{|}_{v=\hat{v}};T_r=\&lsqb;\frac{\&part;{\mathrm{\&Theta;}}_1}{\&part;r}\frac{\&part;{\mathrm{\&Theta;}}_2}{\&part;r}L\frac{\&part;{\mathrm{\&Theta;}}_m}{\&part;r}\&rsqb;{|}_{r=\hat{r}};$

$\tilde{d}=d^{*}-\hat{d};\tilde{v}=v^{*}-\hat{v};\hat{r}=r^{*}-\hat{r};$ N1 is higher order term vector and has dividing value for positive.

5. a kind of supersonic motor adaptability recursion nerve network control system according to claim 4, it is characterized in that, the network architecture that described recursion neural network adopts comprises: input layer, hidden layer and output layer, and Gaussian function is the trigger function of hidden layer.

6. a kind of supersonic motor adaptability recursion nerve network control system according to claim 5, is characterized in that, each layer network signal transduction process of described recursion neural network and basic function as follows:

Ground floor: input layer has i neuron node

${\mathrm{net}}_i^1\left(N\right)=x_i\left(N\right);$

$O_i^1\left(N\right)=f_i^1\left({\mathrm{net}}_i^1\right(N))={\mathrm{net}}_i^1,i=1,2;$

Wherein, represent the input signal of input layer i-th neuron node; represent the output corresponding to input layer i-th node; represent excitation function; N is the iterations of neural network;

The second layer: hidden layer has m neuron node

${\mathrm{net}}_k^2\left(N\right)=\underset{i=1}{\overset{m}{\&Sigma;}}\frac{{\&lsqb;x_i\left(N\right)+T_k(N-1)r_k-v_{ik}\&rsqb;}^2}{{\mathrm{\&beta;}}_{ik}^2};$

Or

${\mathrm{net}}_k^2\left(N\right)=\underset{i=1}{\overset{m}{\&Sigma;}}{\mathrm{\&delta;}}_{ik}^2{\&lsqb;x_i\left(N\right)+T_k(N-1)r_k-v_{ik}\&rsqb;}^2;$

And

$T_k\left(N\right)=f_j^2\left({\mathrm{net}}_k^2\right(N\left)\right)=e^{-{\mathrm{net}}_k^2\left(N\right)},$

Wherein, v _kfor the center of Gaussian function; δ _kfor the width of Gaussian function; Θ _k(N) output corresponding to a hidden layer kth node is represented; represent excitation function; K is natural number;

Third layer: output layer has k node

${\mathrm{net}}^3\left(N\right)=\underset{k}{\&Sigma;}{w}_k{\mathrm{\&Theta;}}_k\left(N\right);$

Z(N)＝f ³(net ³(N))＝net ³；

Wherein, w _krepresent the link weighted value between hidden layer node k and output layer; Z (N) represents the output corresponding to an output layer kth node; f ³(g) representation unit excitation function.