CN104730920A - Adaptive dynamic surface controller structure of neural network and method for designing adaptive dynamic surface controller structure - Google Patents

Abstract

The invention discloses an adaptive dynamic surface controller structure of a neural network and a method for designing the adaptive dynamic surface controller structure. The adaptive dynamic surface controller structure comprises n stages of sub-controllers. The adaptive dynamic surface controller structure and the method have the advantages that predictors are introduced into a controller design, so that online learning on the uncertainty of controlled systems are based on prediction errors instead of tracking errors, the shortcoming of influence of high tracking errors at initial phases on the transient performance of an existing control system can be overcome, and system control signals are not easy to saturate; low-pass filters are introduced into the controller design, so that the problem of high-frequency oscillation of input control signals due to high adaptive parameters can be solved, and the adaptive dynamic surface controller structure and the method are favorable for guaranteeing that the control signals are within execution frequency band ranges of executors; first-order filters utilized in the traditional dynamic surface control are replaced by differential trackers, so that the finite time of the virtual control signals can be assuredly estimated, and the estimation accuracy can be improved; estimation states are fed, and accordingly the adaptive dynamic surface controller structure and the method are favorable for eliminating interference of measurement noise on a control system.

Description

A kind of neural network self-adaptation dynamic surface control device design and construction method

Technical field

The present invention relates to Control of Nonlinear Systems field, particularly relate to neural network self-adaptation dynamic surface control device structure and the method for designing of the uncertain tight Feedback Nonlinear of a class.

Background technology

Uncertain tight Feedback Nonlinear is the nonlinear system of a quasi-representative, and many real systems all meet the form of uncertain tight Feedback Nonlinear, as Marine Autopilot system, Vehicle Active Suspension System, aerocraft system and robot system etc.Therefore to the control of uncertain tight Feedback Nonlinear research, there is important theory value and practical significance widely.

To have design process clear when processing uncertain tight Feedback Nonlinear control problem for Backstepping (Backstepping), and control law such as easily to be derived at the feature, obtains pay attention to widely and develop at industrial control field.But Backstepping is often walking in the process of recursion, needing to carry out differentiate to virtual controlling rule, causing computational complexity can be explosive increase along with the growth of controlled system exponent number, thus constrain the practical application of Backstepping.For overcoming the defect of Backstepping design, the people such as Swaroop propose a kind of dynamic surface control (DynamicSurface Control, DSC) method for designing, by introducing some firstorder filters, the derivative operation of complexity is transformed into simple algebraic operation, thus significantly reduces the complicacy of controller.Dynamic surface combines with Neural Network Adaptive Control technology with Huang Jie etc. by wangdan, significantly relaxes in the past to the constraint condition of the uncertain linear parameterization of controlled system, solves the adaptive control design problem with height Uncertain nonlinear systems.Subsequently, the method is generalized in the design of the various self-adaptation dynamic surface control based on online approximating by scholars.

But in controller architecture and Controller gain variations, still there is following deficiency in existing self-adaptation dynamic surface control device designing technique:

First, prior art all adopts tracking error to carry out on-line study, due to usually comparatively large in starting stage tracking error, thus has a strong impact on the transient state learning performance of neural network, and then it is saturated to make controller be absorbed in, the overall control performance of control system finally can be caused to reduce.

Second, in order to carry out Fast Learning to controlled system uncertainty in prior art, often need to choose larger adaptive control parameter, but large adaptive control parameter can cause the higher-order of oscillation of control signal, robustness and the stability of control system restrict mutually, are difficult to reach desirable control effects.

3rd, usually firstorder filter is adopted to obtain the estimation of dummy pilot signal and derivative thereof in prior art, owing to adopting linear filter form, be difficult to realize the accurate estimation to derivative, and need the bandwidth by increasing wave filter to improve the tracking performance of control system.

4th, all suppose in prior art that controlled system state accurately can be surveyed, but inevitably there is measurement noises in feedback states in actual applications, due to existing controller method for designing cannot stress release treatment on the impact of control system, be thus difficult to ensure desirable control performance.

Summary of the invention

For solving the problems referred to above that prior art exists, the present invention will propose a kind of neural network self-adaptation dynamic surface control device structure and method for designing, not only can significantly improve the transient performance of control system, avoid the higher-order of oscillation of controller input signal, and the accuracy that dummy pilot signal is estimated can be improved, the impact that measurement noises brings can be eliminated simultaneously, make this method for designing more be conducive to actual engineer applied.

To achieve these goals, technical scheme of the present invention is as follows: a kind of neural network self-adaptation dynamic surface control device structure, is made up of n level sub-controller;

The input end of the 1st grade of sub-controller and external reference signal y _rbe connected, also with the output terminal x of measuring mechanism _1m, x _2mbe connected, the output terminal α of the 1st grade of sub-controller ₂be connected with the input end of the 2nd grade of sub-controller, another output terminal of the 1st grade of sub-controller input end respectively with the 1st grade to n level sub-controller is connected;

The input end of i-th grade of sub-controller and the input end α of the i-th-1 grade sub-controller _ibe connected, and with the output terminal of front i level sub-controller be connected, also with the output terminal x of measuring mechanism _im, x _{(i+1) m}be connected, the output terminal α of i-th grade of sub-controller _ibe connected with the input end of the i-th+1 grade sub-controller, another output terminal of i-th grade of sub-controller input end respectively with i-th grade to n level sub-controller is connected;

By that analogy, the input end of n-th grade of sub-controller and the output terminal α of (n-1)th grade of sub-controller _nbe connected, and respectively with the output terminal of whole n level sub-controller be connected, also with the output terminal x of measuring mechanism _nmbe connected, the output terminal u of n-th grade of sub-controller is connected with the input end of controlled system;

The 1st grade of described sub-controller by Nonlinear Tracking Differentiator, comparer 1, comparer 2, prediction device, Linear Control unit, approach device, low-pass filter and summer and form, the input end of Nonlinear Tracking Differentiator and external reference signal y _rbe connected, the output terminal of Nonlinear Tracking Differentiator is connected with the input end of summer with comparer 1 respectively; Another input end of comparer 1 is connected with the output terminal of prediction device, and the output terminal of comparer 1 is connected with the input end of Linear Control unit; Two input ends of comparer 2 are connected with the output terminal of prediction device with measuring mechanism respectively; The input end of prediction device is connected with the output terminal approaching device with measuring mechanism respectively, and the output terminal of prediction device is an output terminal of the 1st grade of sub-controller; The input end approaching device is connected with the output terminal of comparer 2, and another input end is connected with the output terminal of prediction device, and the output terminal approaching device is also connected with the input end of low-pass filter; The output terminal of low-pass filter is connected with the input end of summer; Another input end of summer is connected with the output terminal of Linear Control unit, and the output terminal of summer is another output terminal of the 1st grade of sub-controller;

I-th grade of described sub-controller by Nonlinear Tracking Differentiator, comparer 1, comparer 2, prediction device, Linear Control unit, approach device, low-pass filter and summer and form, the input end of Nonlinear Tracking Differentiator is connected with the output terminal of the i-th-1 grade sub-controller, and the output terminal of Nonlinear Tracking Differentiator is connected with the input end of summer with comparer 1 respectively; Another input end of comparer 1 is connected with the output terminal of prediction device, and the output terminal of comparer 1 is connected with the input end of Linear Control unit; Two input ends of comparer 2 are connected with the output terminal of prediction device with measuring mechanism respectively; The input end of prediction device is connected with the output terminal approaching device with measuring mechanism respectively, and the output terminal of prediction device is an output terminal of i-th grade of sub-controller; The input end approaching device is connected with the output terminal of comparer 2, and another input end is connected with the output terminal of front i level sub-controller, and the output terminal approaching device is also connected with the input end of low-pass filter; The output terminal of low-pass filter is connected with the input end of summer; Another input end of summer is connected with the output terminal of Linear Control unit, and the output terminal of summer is another output terminal of i-th grade of sub-controller;

N-th grade of described sub-controller by Nonlinear Tracking Differentiator, comparer 1, comparer 2, prediction device, Linear Control unit, approach device, low-pass filter and summer and form, the input end of Nonlinear Tracking Differentiator is connected with the output terminal of (n-1)th grade of sub-controller, and the output terminal of Nonlinear Tracking Differentiator is connected with the input end of summer with comparer 1 respectively; Another input end of comparer 1 is connected with the output terminal of prediction device, and the output terminal of comparer 1 is connected with the input end of Linear Control unit; Two input ends of comparer 2 are connected with the output terminal of prediction device with measuring mechanism respectively; The input end of prediction device respectively with measuring mechanism, the output terminal approaching device and sum unit is connected; The input end approaching device is connected with the output terminal of comparer 2, and another input end is connected with the output terminal of all n level sub-controllers, and the output terminal approaching device is also connected with the input end of low-pass filter; The output terminal of low-pass filter is connected with the input end of summer; Another input end of summer is connected with the output terminal of Linear Control unit, and the output terminal of summer is the output terminal of n-th grade of sub-controller, is connected with the input end of controlled system;

Described controlled system is described by the uncertain tight Feedback Nonlinear form in following n rank:

If represent real number set with R, so x in formula _i∈ R represents the state of controlled system i-th grade of subsystem; U ∈ R represents the control inputs of controlled system; for the non-linear continuous function of the unknown, y ∈ R is the output of controlled system.

A kind of neural network self-adaptation dynamic surface control device method for designing, comprises the following steps:

A, the 1st grade of sub-controller design:

A1, the 1st grade of Nonlinear Tracking Differentiator: the 1st grade of Nonlinear Tracking Differentiator receives external reference signal y _r, through lower rank transformation:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{1r}=x_{1r}^d\\ {\stackrel{\·}{x}}_{1r}^d=-{\mathrm{\γ}}_1\mathrm{sign}(x_{1r}-y_r+\frac{x_{1r}^d\left|x_{1r}^d\right|}{{2\mathrm{\γ}}_1})\end{array}\right.---\left(2\right)$

The output signal obtaining the 1st grade of Nonlinear Tracking Differentiator is predictor x _1rand derivative wherein γ ₁> 0 is constant value, be intermediate variable, sign () represents sign function;

A2, the 1st grade of comparer 1: the 1 grade of comparer 1 receive the output signal predictor x of Nonlinear Tracking Differentiator respectively _1rwith the output signal of prediction device the signal received is through lower rank transformation:

${\hat{S}}_1={\hat{x}}_1-x_{1r}---\left(3\right)$

Obtain the output signal of the 1st grade of comparer 1

A3, the 1st grade of comparer 2: the 1 grades of comparers 2 receive the status signal x of controlled system the 1st grade of subsystem exported by measuring mechanism respectively _1mwith the output signal of prediction device the signal received obtains the output end signal of comparer 2 through lower rank transformation

${\tilde{x}}_1={\hat{x}}_1-x_{1m}---\left(4\right)$

Wherein x _1m=x ₁+ w ₁for the status signal of the 1st grade of subsystem containing measurement noises, w ₁for measurement noises;

A4, the 1st grade of prediction device: the 1st grade of prediction device receives the status signal x of controlled system the 1st grade of subsystem exported by measuring mechanism respectively _1mwith the status signal x of the 2nd grade of subsystem _2m, and approach the output signal α of device _w1, the signal received obtains the output signal of prediction device through lower rank transformation

${\stackrel{\·}{\hat{x}}}_1={\mathrm{\α}}_{w1}+x_{2m}-(k_1+{\mathrm{\κ}}_1)({\hat{x}}_1-x_{1m})---\left(5\right)$

Wherein k ₁> 0, κ ₁> 0 is constant; The output signal of prediction device also be an output signal of the 1st grade of sub-controller simultaneously;

A5, the 1st grade of Linear Control unit: the 1st grade of Linear Control unit receives the output signal of comparer 1 control through following ratio:

${\mathrm{\α}}_{k1}={-k}_1{\hat{S}}_1---\left(6\right)$

Obtain the output signal α of the 1st grade of Linear Control unit _k1;

A6, the 1st grade approach device: the 1st grade is approached the output signal that device receives prediction device respectively with the output signal of comparer 2

The effect approaching device is to the unknown nonlinear in controlled system carry out On-line Estimation, the described device that approaches adopts neural network approach method, will be expressed as form, wherein be approximate error, meet it is normal number; W ₁∈ R ^sfor the weight matrix of the unknown, and meet || W ₁|| _f≤ W ₁ ^*, W ₁ ^*it is normal number; for known excitation function matrix, its form is definition w ₁estimation, design turnover rate be:

Wherein Γ _w1∈ R, k _w1∈ R is normal number;

Finally obtain the output signal α that the 1st grade is approached device _w1:

A7, the 1st grade of low-pass filter: the 1st grade of low-pass filter receives the output signal α approaching device _w1, pass through with down conversion:

α _cw1=C (s) α _w1(9) the output signal α of the 1st grade of low-pass filter is obtained _cw1, wherein C (s) represents wave filter;

A8, the 1st grade of summer: the 1st grade of summer receives the output signal α of Linear Control unit respectively _k1, low-pass filter output signal α _cw1with the derivative of the output signal predictor of Nonlinear Tracking Differentiator the signal received is through following read group total:

${\mathrm{\α}}_2={\mathrm{\α}}_{k1}+{\mathrm{\α}}_{\mathrm{cw}1}+{\stackrel{\·}{x}}_{1r}---\left(10\right)$

Obtain another output end signal α of the 1st grade of sub-controller ₂;

B, i-th grade of sub-controller design:

B1, i-th grade of Nonlinear Tracking Differentiator: i-th grade of Nonlinear Tracking Differentiator receives the output signal α of the i-th-1 grade sub-controller _i, through lower rank transformation:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{\mathrm{ir}}=x_{\mathrm{ir}}^d\\ {\stackrel{\·}{x}}_{\mathrm{ir}}^d=-{\mathrm{\γ}}_i\mathrm{sign}(x_{\mathrm{ir}}-{\mathrm{\α}}_i+\frac{x_{\mathrm{ir}}^d\left|x_{\mathrm{ir}}^d\right|}{{2\mathrm{\γ}}_i})\end{array}\right.---\left(11\right)$

The output signal obtaining i-th grade of filter cell is predictor x _irand derivative wherein γ _i> 0 is constant value, it is intermediate variable;

B2, i-th grade of comparer, 1: the i-th grade of comparer 1 receive the output signal predictor x of Nonlinear Tracking Differentiator respectively _irwith the output signal of prediction device the signal received is through lower rank transformation

${\hat{S}}_i={\hat{x}}_i-x_{\mathrm{ir}}---\left(12\right)$

Obtain the output signal of i-th grade of comparer 1

B3, i-th grade of comparer, 2: the i-th grades of comparers 2 receive the status signal x of the controlled system i-th grade of subsystem exported by measuring mechanism respectively _imwith the output signal of prediction device the signal received obtains the output end signal of comparer 2 through lower rank transformation

${\tilde{x}}_i={\hat{x}}_i-x_{\mathrm{im}}---\left(13\right)$

Wherein x _im=x _i+ w _ifor the status signal of i-th grade of subsystem containing measurement noises, w _ifor measurement noises;

B4, i-th grade of prediction device: i-th grade of prediction device receives the status signal x of the controlled system i-th grade of subsystem exported by measuring mechanism respectively _imwith the status signal x of the i-th+1 grade subsystem _{(i+1) m}, and approach the output signal α of device _wi, the signal received obtains the output signal of prediction device through lower rank transformation

${\stackrel{\·}{\hat{x}}}_1={\mathrm{\α}}_{\mathrm{wi}}+x_{(i+1)m}-(k_i+{\mathrm{\κ}}_i)({\hat{x}}_i-x_{\mathrm{im}})---\left(14\right)$

Wherein k _i> 0, κ _i> 0 is constant; The output signal of prediction device also be an output signal of i-th grade of sub-controller simultaneously;

B5, i-th grade of Linear Control unit: i-th grade of Linear Control unit receives the output signal of comparer 1 control through following ratio:

${\mathrm{\α}}_{\mathrm{ki}}={-k}_i{\hat{S}}_i---\left(15\right)$

Obtain the output end signal α of i-th grade of Linear Control unit _ki;

B6, i-th grade approach device: i-th grade is approached the output signal that device receives front i level sub-controller respectively and the output signal of i-th grade of comparer 2

Approaching device effect is to the unknown nonlinear in controlled system carry out On-line Estimation, the described device that approaches adopts neural network approach method, will be expressed as form, wherein be approximate error, meet it is normal number; W _i∈ R ^sfor unknown weight matrix, and meet || W _i|| _f≤ W _i ^*, W _i ^*it is normal number; for known excitation function matrix, its form is definition w _iestimation, design turnover rate be

Wherein Γ _wi∈ R, k _wi∈ R is normal number.

Finally obtain the output signal α that i-th grade is approached device _wi:

B7, i-th grade of low-pass filter: i-th grade of low-pass filter receives the output signal α approaching device _wi, pass through with down conversion:

α _cwi=C (s) α _wi(18) the output signal α of i-th grade of low-pass filter is obtained _cwi;

B8, i-th grade of summer: i-th grade of summer receives the output signal α of Linear Control unit respectively _ki, low-pass filter output signal α _cwiwith the derivative of the output signal predictor of Nonlinear Tracking Differentiator the signal received is through following read group total:

${\mathrm{\α}}_{(i+1)}={\mathrm{\α}}_{\mathrm{ki}}+{\mathrm{\α}}_{\mathrm{cwi}}+{\stackrel{\·}{x}}_{\mathrm{ir}}---\left(19\right)$

Obtain another output end signal α of i-th grade of sub-controller _(i+1);

Repeat step B1-B8 Recursive Design and obtain the 2nd grade to (n-1)th grade sub-controller structures;

C, n-th grade of sub-controller design:

C1, n-th grade of Nonlinear Tracking Differentiator: n-th grade of Nonlinear Tracking Differentiator receives the output signal α of (n-1)th grade of sub-controller _n, through lower rank transformation:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{\mathrm{nr}}=x_{\mathrm{nr}}^d\\ {\stackrel{\·}{x}}_{\mathrm{nr}}^d=-{\mathrm{\γ}}_n\mathrm{sign}(x_{\mathrm{nr}}-{\mathrm{\α}}_n+\frac{x_{\mathrm{nr}}^d\left|x_{\mathrm{nr}}^d\right|}{{2\mathrm{\γ}}_n})\end{array}\right.---\left(20\right)$

The output signal obtaining n-th grade of filter cell is predictor x _nrand derivative wherein γ _n> 0 is constant value, it is intermediate variable;

C2, n-th grade of comparer, 1: the n-th grade of comparer 1 receive the output signal predictor x of Nonlinear Tracking Differentiator respectively _nrwith the output signal of prediction device the signal received is through lower rank transformation:

${\hat{S}}_n={\hat{x}}_n-x_{\mathrm{nr}}---\left(21\right)$

Obtain the output signal of n-th grade of comparer 1

C3, n-th grade of comparer, 2: the n-th grades of comparers 2 receive the status signal x of the controlled system n-th grade of subsystem exported by measuring mechanism respectively _nmwith the output signal of prediction device the signal received obtains the output end signal of comparer 2 through lower rank transformation

${\tilde{x}}_n={\hat{x}}_n-x_{\mathrm{nm}}---\left(22\right)$

Wherein x _nm=x _n+ w _nfor the status signal of n-th grade of subsystem containing measurement noises, w _nfor measurement noises;

C4, n-th grade of prediction device: n-th grade of prediction device receives the status signal x of the controlled system n-th grade of subsystem exported by measuring mechanism respectively _nm, approach the output signal α of device _wnwith the output signal u of summer, the signal received obtains the output signal of prediction device through lower rank transformation

${\stackrel{\·}{\hat{x}}}_n={\mathrm{\α}}_{\mathrm{wn}}+u-(k_n+{\mathrm{\κ}}_n)({\hat{x}}_n-x_{\mathrm{nm}})---\left(23\right)$

Wherein k _n> 0, κ _n> 0 is constant;

C5, n-th grade of Linear Control unit: n-th grade of Linear Control unit receives the output signal of comparer 1 control through following ratio:

${\mathrm{\α}}_{\mathrm{kn}}={-k}_n{\hat{S}}_n---\left(24\right)$

Obtain the output signal α of n-th grade of Linear Control unit _kn;

C6, n-th grade approach device: n-th grade is approached the output signal that device receives all n level sub-controllers respectively be connected and the output signal of n-th grade of comparer 2

Similar with step B6, the signal received approaches device through following:

Obtain the output signal α that n-th grade is approached device _wn;

C7, n-th grade of low-pass filter: n-th grade of low-pass filter receives the output signal α approaching device _wn, pass through with down conversion:

α _cwn=C (s) α _wn(27) the output signal α of n-th grade of low-pass filter is obtained _cwn;

C8, n-th grade of summer: n-th grade of summer unit receives the output signal α of Linear Control unit respectively _kn, low-pass filter output signal α _cwnwith the derivative of the output signal predictor of Nonlinear Tracking Differentiator unit the signal received is through following read group total:

$u={\mathrm{\α}}_{\mathrm{kn}}+{\mathrm{\α}}_{\mathrm{cwn}}+{\stackrel{\·}{x}}_{\mathrm{nr}}---\left(28\right)$

Obtain the control inputs u that controlled system is total; Select suitable parameters, control inputs u can make the external reference signal y of the output y tracing preset of controlled system _r.

Compared with prior art, the invention has the beneficial effects as follows:

The first, the present invention introduces prediction device in Controller gain variations, to the probabilistic on-line study of controlled system no longer based on tracking error, but based on predictor error, by choosing κ _icontrol the speed of convergence of predictor error, can overcome the larger impact on control system transient performance of starting stage tracking error, thus make controlled system have the input of good transient state, control signal is not easy to be absorbed in saturated.

Second, the present invention introduces low-pass filter in Controller gain variations, the higher-order of oscillation problem of the input control signal caused more greatly due to auto-adaptive parameter can be eliminated, therefore effectively can carry out filtering to the high fdrequency component of control signal, be conducive to ensureing that control signal is within the execution frequency band range of actuator.

3rd, firstorder filter during the present invention adopts differential tracker to replace conventional dynamic face to control, while can overcoming " computational complexity " problem in Backstepping, can also ensure to estimate the finite time of dummy pilot signal, improve the accuracy estimated, and firstorder filter needs improve tracking performance shortcoming by increasing bandwidth can be overcome.

4th, the present invention adopts the state estimated to feed back, and eliminates the interference of measurement noises to control system, makes this controller design method be conducive to actual engineer applied.

Accompanying drawing explanation

The present invention has 4, accompanying drawing, wherein:

Fig. 1 is neural network self-adaptation dynamic surface control device structural representation of the present invention.

Fig. 2 to be neural network self-adaptation dynamic surface control device (PNDSC) of the present invention with traditional neural network self-adaptation dynamic surface control device (NDSC) export comparing of responding.

Fig. 3 is neural network self-adaptation dynamic surface control device of the present invention and the comparing of the control inputs signal of traditional neural network self-adaptation dynamic surface control device.

Fig. 4 is neural network self-adaptation dynamic surface control device of the present invention and the comparing of the amplitude spectrum of the control inputs signal of traditional neural network self-adaptation dynamic surface control device.

Embodiment

The present invention is further described for the uncertain tight Feedback Nonlinear of second order below in conjunction with accompanying drawing.

Consider the uncertain tight Feedback Nonlinear of following second order

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=f_1\left({\stackrel{\‾}{x}}_1\right)+x_2\\ {\stackrel{\·}{x}}_2=f_2\left({\stackrel{\‾}{x}}_2\right)+u\\ y=x_1\end{array}\right.---\left(29\right)$

For emulation needs, arrange with for

$\left\{\begin{array}{c}{f}_1\left({\stackrel{\‾}{x}}_1\right)={2x}_1^2\sin \left(x_1\right)\\ f_2\left({\stackrel{\‾}{x}}_2\right)=x_1^2+x_1{x}_2+x_2\cos x_1\end{array}\right.---\left(30\right)$

For this system, neural network self-adaptation dynamic surface control device can be designed according to Fig. 1 as follows:

1st grade of sub-controller:

2nd grade of sub-controller:

Select the parameter of following controller:

k ₁＝k ₂＝5,γ ₁＝γ ₂＝0.005,κ ₁＝κ ₂＝100,Γ _W1＝Γ _W2＝10000,k _W1＝k _W2＝0.001；

As adopted traditional neural network self-adaptation dynamic surface control method for designing, controller architecture is as follows:

1st grade of sub-controller:

2nd grade of sub-controller:

The selection of controller parameter is consistent with neural network self-adaptation dynamic surface control device of the present invention.

Simulation result as in Figure 2-4.Shown in Fig. 2 be control system output response, as seen from the figure, neural network self-adaptation dynamic surface control device (PNDSC) of the present invention and traditional neural network self-adaptation dynamic surface control device (NDSC) all can make the effective tracking reference signal y of the output of controlled system _r.Shown in Fig. 3 be neural network self-adaptation dynamic surface control device of the present invention with traditional neural network self-adaptation dynamic surface control device control inputs signal compare schematic diagram, can find out in figure, control inputs signal based on neural network self-adaptation dynamic surface control device of the present invention is more level and smooth, and the higher-order of oscillation obviously reduces.Shown in Fig. 4 is neural network self-adaptation dynamic surface control device of the present invention and the comparing of the traditional neural network self-adaptation dynamic surface control device control inputs amplitude spectrum of signal under frequency domain, can obviously find out, neural network self-adaptation dynamic surface control device of the present invention significantly improves the control inputs signal of controller.In sum, the control performance of the neural network self-adaptation dynamic surface control algorithm of the present invention's proposition is obviously better than existing traditional neural network self-adaptation dynamic surface control algorithm.

Claims (2)

1. a neural network self-adaptation dynamic surface control device structure, is made up of n level sub-controller; It is characterized in that:

The input end of the 1st grade of sub-controller and external reference signal y _rbe connected, also with the output terminal x of measuring mechanism _1m, x _2mbe connected, the output terminal α of the 1st grade of sub-controller ₂be connected with the input end of the 2nd grade of sub-controller, another output terminal of the 1st grade of sub-controller input end respectively with the 1st grade to n level sub-controller is connected;

The input end of i-th grade of sub-controller and the input end α of the i-th-1 grade sub-controller _ibe connected, and with the output terminal of front i level sub-controller be connected, also with the output terminal x of measuring mechanism _im, x _{(i+1) m}be connected, the output terminal α of i-th grade of sub-controller _ibe connected with the input end of the i-th+1 grade sub-controller, another output terminal of i-th grade of sub-controller input end respectively with i-th grade to n level sub-controller is connected;

By that analogy, the input end of n-th grade of sub-controller and the output terminal α of (n-1)th grade of sub-controller _nbe connected, and respectively with the output terminal of whole n level sub-controller be connected, also with the output terminal x of measuring mechanism _nmbe connected, the output terminal u of n-th grade of sub-controller is connected with the input end of controlled system;

The 1st grade of described sub-controller by Nonlinear Tracking Differentiator, comparer 1, comparer 2, prediction device, Linear Control unit, approach device, low-pass filter and summer and form, the input end of Nonlinear Tracking Differentiator and external reference signal y _rbe connected, the output terminal of Nonlinear Tracking Differentiator is connected with the input end of summer with comparer 1 respectively; Another input end of comparer 1 is connected with the output terminal of prediction device, and the output terminal of comparer 1 is connected with the input end of Linear Control unit; Two input ends of comparer 2 are connected with the output terminal of prediction device with measuring mechanism respectively; The input end of prediction device is connected with the output terminal approaching device with measuring mechanism respectively, and the output terminal of prediction device is an output terminal of the 1st grade of sub-controller; The input end approaching device is connected with the output terminal of comparer 2, and another input end is connected with the output terminal of prediction device, and the output terminal approaching device is also connected with the input end of low-pass filter; The output terminal of low-pass filter is connected with the input end of summer; Another input end of summer is connected with the output terminal of Linear Control unit, and the output terminal of summer is another output terminal of the 1st grade of sub-controller;

I-th grade of described sub-controller by Nonlinear Tracking Differentiator, comparer 1, comparer 2, prediction device, Linear Control unit, approach device, low-pass filter and summer and form, the input end of Nonlinear Tracking Differentiator is connected with the output terminal of the i-th-1 grade sub-controller, and the output terminal of Nonlinear Tracking Differentiator is connected with the input end of summer with comparer 1 respectively; Another input end of comparer 1 is connected with the output terminal of prediction device, and the output terminal of comparer 1 is connected with the input end of Linear Control unit; Two input ends of comparer 2 are connected with the output terminal of prediction device with measuring mechanism respectively; The input end of prediction device is connected with the output terminal approaching device with measuring mechanism respectively, and the output terminal of prediction device is an output terminal of i-th grade of sub-controller; The input end approaching device is connected with the output terminal of comparer 2, and another input end is connected with the output terminal of front i level sub-controller, and the output terminal approaching device is also connected with the input end of low-pass filter; The output terminal of low-pass filter is connected with the input end of summer; Another input end of summer is connected with the output terminal of Linear Control unit, and the output terminal of summer is another output terminal of i-th grade of sub-controller;

N-th grade of described sub-controller by Nonlinear Tracking Differentiator, comparer 1, comparer 2, prediction device, Linear Control unit, approach device, low-pass filter and summer and form, the input end of Nonlinear Tracking Differentiator is connected with the output terminal of (n-1)th grade of sub-controller, and the output terminal of Nonlinear Tracking Differentiator is connected with the input end of summer with comparer 1 respectively; Another input end of comparer 1 is connected with the output terminal of prediction device, and the output terminal of comparer 1 is connected with the input end of Linear Control unit; Two input ends of comparer 2 are connected with the output terminal of prediction device with measuring mechanism respectively; The input end of prediction device respectively with measuring mechanism, the output terminal approaching device and sum unit is connected; The input end approaching device is connected with the output terminal of comparer 2, and another input end is connected with the output terminal of all n level sub-controllers, and the output terminal approaching device is also connected with the input end of low-pass filter; The output terminal of low-pass filter is connected with the input end of summer; Another input end of summer is connected with the output terminal of Linear Control unit, and the output terminal of summer is the output terminal of n-th grade of sub-controller, is connected with the input end of controlled system;

Described controlled system is described by the uncertain tight Feedback Nonlinear form in following n rank:

If represent real number set with R, so x in formula _i∈ R represents the state of controlled system i-th grade of subsystem; U ∈ R represents the control inputs of controlled system; for the non-linear continuous function of the unknown, y ∈ R is the output of controlled system.

2. a neural network self-adaptation dynamic surface control device method for designing, is characterized in that: comprise the following steps:

A, the 1st grade of sub-controller design:

A1, the 1st grade of Nonlinear Tracking Differentiator: the 1st grade of Nonlinear Tracking Differentiator receives external reference signal y _r, through lower rank transformation:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{1r}=x_{1r}^d\\ {\stackrel{\·}{x}}_{1r}^d=-{\mathrm{\γ}}_1\mathrm{sign}(x_{1r}-y_r+\frac{x_{1r}^d\left|x_{1r}^d\right|}{2{\mathrm{\γ}}_1})\end{array}\right.---\left(2\right)$

The output signal obtaining the 1st grade of Nonlinear Tracking Differentiator is predictor x _1rand derivative wherein γ ₁> 0 is constant value, be intermediate variable, sign () represents sign function;

A2, the 1st grade of comparer 1: the 1 grade of comparer 1 receive the output signal predictor x of Nonlinear Tracking Differentiator respectively _1rwith the output signal of prediction device the signal received is through lower rank transformation:

${\hat{S}}_1={\hat{x}}_1-x_{1r}---\left(3\right)$

Obtain the output signal of the 1st grade of comparer 1

A3, the 1st grade of comparer 2: the 1 grades of comparers 2 receive the status signal x of controlled system the 1st grade of subsystem exported by measuring mechanism respectively _1mwith the output signal of prediction device the signal received obtains the output end signal of comparer 2 through lower rank transformation

${\tilde{x}}_1={\hat{x}}_1-x_{1m}---\left(4\right)$

Wherein x _1m=x ₁+ w ₁for the status signal of the 1st grade of subsystem containing measurement noises, w ₁for measurement noises;

A4, the 1st grade of prediction device: the 1st grade of prediction device receives the status signal x of controlled system the 1st grade of subsystem exported by measuring mechanism respectively _1mwith the status signal x of the 2nd grade of subsystem _2m, and approach the output signal α of device _w1, the signal received obtains the output signal of prediction device through lower rank transformation

${\stackrel{\stackrel{\·}{^}}{x}}_1={\mathrm{\α}}_{w1}+x_{2m}-(k_1+{\mathrm{\κ}}_1)({\hat{x}}_1-x_{1m})---\left(5\right)$

Wherein k ₁> 0, κ ₁> 0 is constant; The output signal of prediction device also be an output signal of the 1st grade of sub-controller simultaneously;

A5, the 1st grade of Linear Control unit: the 1st grade of Linear Control unit receives the output signal of comparer 1 control through following ratio:

${\mathrm{\α}}_{k1}=-k_1{\hat{S}}_1---\left(6\right)$

Obtain the output signal α of the 1st grade of Linear Control unit _k1;

A6, the 1st grade approach device: the 1st grade is approached the output signal that device receives prediction device respectively with the output signal of comparer 2

The effect approaching device is to the unknown nonlinear in controlled system carry out On-line Estimation, the described device that approaches adopts neural network approach method, will be expressed as form, wherein be approximate error, meet it is normal number; W ₁∈ R ^sfor the weight matrix of the unknown, and meet it is normal number; for known excitation function matrix, its form is definition w ₁estimation, design turnover rate be:

Wherein Γ _w1∈ R, k _w1∈ R is normal number;

Finally obtain the output signal α that the 1st grade is approached device _w1:

A7, the 1st grade of low-pass filter: the 1st grade of low-pass filter receives the output signal α approaching device _w1, pass through with down conversion:

α _cw1＝C(s)α _w1(9)

Obtain the output signal α of the 1st grade of low-pass filter _cw1, wherein C (s) represents wave filter;

A8, the 1st grade of summer: the 1st grade of summer receives the output signal α of Linear Control unit respectively _k1, low-pass filter output signal α _cw1with the derivative of the output signal predictor of Nonlinear Tracking Differentiator the signal received is through following read group total:

${\mathrm{\α}}_2={\mathrm{\α}}_{k1}+{\mathrm{\α}}_{\mathrm{cw}1}+{\stackrel{\·}{x}}_{1r}---\left(10\right)$

Obtain another output end signal α of the 1st grade of sub-controller ₂;

B, i-th grade of sub-controller design:

B1, i-th grade of Nonlinear Tracking Differentiator: i-th grade of Nonlinear Tracking Differentiator receives the output signal α of the i-th-1 grade sub-controller _i, through lower rank transformation:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{\mathrm{ir}}=x_{\mathrm{ir}}^d\\ {\stackrel{\·}{x}}_{\mathrm{ir}}^d=-{\mathrm{\γ}}_i\mathrm{sign}(x_{\mathrm{ir}}-{\mathrm{\α}}_i+\frac{x_{\mathrm{ir}}^d\left|x_{\mathrm{ir}}^d\right|}{2{\mathrm{\γ}}_i})\end{array}\right.---\left(11\right)$

The output signal obtaining i-th grade of filter cell is predictor x _irand derivative wherein γ _i> 0 is constant value, it is intermediate variable;

B2, i-th grade of comparer, 1: the i-th grade of comparer 1 receive the output signal predictor x of Nonlinear Tracking Differentiator respectively _irwith the output signal of prediction device the signal received is through lower rank transformation

${\hat{S}}_i={\hat{x}}_i-x_{\mathrm{ir}}---\left(12\right)$

Obtain the output signal of i-th grade of comparer 1

B3, i-th grade of comparer, 2: the i-th grades of comparers 2 receive the status signal x of the controlled system i-th grade of subsystem exported by measuring mechanism respectively _imwith the output signal of prediction device the signal received obtains the output end signal of comparer 2 through lower rank transformation

${\tilde{x}}_i={\hat{x}}_i-x_{\mathrm{im}}---\left(13\right)$

Wherein x _im=x _i+ w _ifor the status signal of i-th grade of subsystem containing measurement noises, w _ifor measurement noises;

B4, i-th grade of prediction device: i-th grade of prediction device receives the status signal x of the controlled system i-th grade of subsystem exported by measuring mechanism respectively _imwith the status signal x of the i-th+1 grade subsystem _{(i+1) m}, and approach the output signal α of device _wi, the signal received obtains the output signal of prediction device through lower rank transformation

${\stackrel{\stackrel{\·}{^}}{x}}_i={\mathrm{\α}}_{\mathrm{wi}}+x_{(i+1)m}-(k_i+{\mathrm{\κ}}_i)({\hat{x}}_i-x_{\mathrm{im}})---\left(14\right)$

Wherein k _i> 0, κ _i> 0 is constant; The output signal of prediction device also be an output signal of i-th grade of sub-controller simultaneously;

B5, i-th grade of Linear Control unit: i-th grade of Linear Control unit receives the output signal of comparer 1 control through following ratio:

${\mathrm{\α}}_{\mathrm{ki}}=-k_i{\hat{S}}_i---\left(15\right)$

Obtain the output end signal α of i-th grade of Linear Control unit _ki;

B6, i-th grade approach device: i-th grade is approached the output signal that device receives front i level sub-controller respectively and the output signal of i-th grade of comparer 2

Approaching device effect is to the unknown nonlinear in controlled system carry out On-line Estimation, the described device that approaches adopts neural network approach method, will be expressed as form, wherein be approximate error, meet it is normal number; W _i∈ R ^sfor unknown weight matrix, and meet it is normal number; for known excitation function matrix, its form is definition w _iestimation, design turnover rate be

Wherein Γ _wi∈ R, k _wi∈ R is normal number;

Finally obtain the output signal α that i-th grade is approached device _wi:

B7, i-th grade of low-pass filter: i-th grade of low-pass filter receives the output signal α approaching device _wi, pass through with down conversion:

α _cwi＝C(s)α _wi(18)

Obtain the output signal α of i-th grade of low-pass filter _cwi;

B8, i-th grade of summer: i-th grade of summer receives the output signal α of Linear Control unit respectively _ki, low-pass filter output signal α _cwiwith the derivative of the output signal predictor of Nonlinear Tracking Differentiator the signal received is through following read group total:

${\mathrm{\α}}_{(i+1)}={\mathrm{\α}}_{\mathrm{ki}}+{\mathrm{\α}}_{\mathrm{cwi}}+{\stackrel{\·}{x}}_{\mathrm{ir}}---\left(19\right)$

Obtain another output end signal α of i-th grade of sub-controller _(i+1);

Repeat step B1-B8 Recursive Design and obtain the 2nd grade to (n-1)th grade sub-controller structures;

C, n-th grade of sub-controller design:

C1, n-th grade of Nonlinear Tracking Differentiator: n-th grade of Nonlinear Tracking Differentiator receives the output signal α of (n-1)th grade of sub-controller _n, through lower rank transformation:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_{\mathrm{nr}}=x_{\mathrm{nr}}^d\\ {\stackrel{\·}{x}}_{\mathrm{nr}}^d=-{\mathrm{\γ}}_n\mathrm{sign}(x_{\mathrm{nr}}-{\mathrm{\α}}_n+\frac{x_{\mathrm{nr}}^d\left|x_{\mathrm{nr}}^d\right|}{2{\mathrm{\γ}}_n})\end{array}\right.---\left(20\right)$

The output signal obtaining n-th grade of filter cell is predictor x _nrand derivative wherein γ _n> 0 is constant value, it is intermediate variable;

C2, n-th grade of comparer, 1: the n-th grade of comparer 1 receive the output signal predictor x of Nonlinear Tracking Differentiator respectively _nrwith the output signal of prediction device the signal received is through lower rank transformation:

${\hat{S}}_n={\hat{x}}_n-x_{\mathrm{nr}}---\left(21\right)$

Obtain the output signal of n-th grade of comparer 1

C3, n-th grade of comparer, 2: the n-th grades of comparers 2 receive the status signal x of the controlled system n-th grade of subsystem exported by measuring mechanism respectively _nmwith the output signal of prediction device the signal received obtains the output end signal of comparer 2 through lower rank transformation

${\tilde{x}}_n={\hat{x}}_n-x_{\mathrm{nm}}---\left(22\right)$

Wherein x _nm=x _n+ w _nfor the status signal of n-th grade of subsystem containing measurement noises, w _nfor measurement noises;

C4, n-th grade of prediction device: n-th grade of prediction device receives the status signal x of the controlled system n-th grade of subsystem exported by measuring mechanism respectively _nm, approach the output signal α of device _wnwith the output signal u of summer, the signal received obtains the output signal of prediction device through lower rank transformation

${\stackrel{\stackrel{\·}{^}}{x}}_n={\mathrm{\α}}_{\mathrm{wn}}+u-(k_n+{\mathrm{\κ}}_n)({\hat{x}}_n-x_{\mathrm{nm}})---\left(23\right)$

Wherein k _n> 0, κ _n> 0 is constant;

C5, n-th grade of Linear Control unit: n-th grade of Linear Control unit receives the output signal of comparer 1 control through following ratio:

${\mathrm{\α}}_{\mathrm{kn}}=-k_n{\hat{S}}_n---\left(24\right)$

Obtain the output signal α of n-th grade of Linear Control unit _kn;

C6, n-th grade approach device: n-th grade is approached the output signal that device receives all n level sub-controllers respectively be connected and the output signal of n-th grade of comparer 2

Similar with step B6, the signal received approaches device through following:

Obtain the output signal α that n-th grade is approached device _wn;

C7, n-th grade of low-pass filter: n-th grade of low-pass filter receives the output signal α approaching device _wn, pass through with down conversion:

α _cwn＝C(s)α _wn(27)

Obtain the output signal α of n-th grade of low-pass filter _cwn;

C8, n-th grade of summer: n-th grade of summer unit receives the output signal α of Linear Control unit respectively _kn, low-pass filter output signal α _cwnwith the derivative of the output signal predictor of Nonlinear Tracking Differentiator unit the signal received is through following read group total:

$u={\mathrm{\α}}_{\mathrm{kn}}+{\mathrm{\α}}_{\mathrm{cwn}}+{\stackrel{\·}{x}}_{\mathrm{nr}}---\left(28\right)$

Obtain the control inputs u that controlled system is total; Select suitable parameters, control inputs u can make the external reference signal y of the output y tracing preset of controlled system _r.