CN106078741A - Based on a determination that the limited performance flexible mechanical arm control method of theory of learning - Google Patents

Abstract

The invention discloses a kind of based on a determination that the limited performance flexible mechanical arm control method of theory of learning, the method, for the uncertainty of flexible mechanical arm dynamic model, design tracking error, is allowed to meet constraints and limits, and constitute error controller.Step of the present invention includes: set up flexible mechanical arm dynamic model；Set up State Observer；Design tracking error performance constraints；Based on a determination that theory of learning design nerve network controller；Utilize Heuristics modifier controller.Control method designed by the present invention can realize Fast Convergent, the dynamic property of low overshoot, meets the constraints set and limits, avoids neural network weight on-line control simultaneously, shorten the control time.It addition, the method can utilize the Heuristics learnt that identical control task afterwards is directly realized by quick control.

Description

Based on a determination that the limited performance flexible mechanical arm control method of theory of learning

Technical field

The invention belongs to the Trajectory Tracking Control field of flexible mechanical arm, especially for flexible mechanical arm system dynamics mould The uncertainty of type, designs tracking error, is allowed to meet constraints and limits.Be given a kind of based on a determination that the performance of theory of learning Limited flexible mechanical arm control method.

Background technology

Nowadays, along with robot develops towards high accuracy, quick direction, mechanical part increasingly tends to lightness.Phase Ratio is in traditional Rigid Robot Manipulator, and flexible mechanical arm has the advantages that structure is light, work space is big and efficiency is high, so flexible unit Part is in manufacturing industry, and the application in the fields such as Aero-Space is increasingly wider, but the flexible effect that flexible armed lever brings, machinery can be caused Vibration, this stationarity that TRAJECTORY CONTROL can be made to require is more difficult to reach with accuracy, the track following control of flexible mechanical arm end System difficulty all the more.And in practical application in industry, due to the constrained of industrial environment, the such as limit of motor maximum output torque The restriction of system, steady-state process end orbit tracking error, the maximum overshoot of initial movement segment tracking error and convergence rate Limiting, the control performance often also needing to system meets certain constraints, and this makes the control program of design not only ensure Track following error system is stable, and the tracking performance of tracking error be also satisfied the constraint under practical situation, and this gives and controls The design of scheme brings the biggest challenge.

For intelligence controls such as the Trajectory Tracking Control of flexible mechanical arm system, the control of back stepping control, sliding formwork, dynamic surface controls Method processed combines ANN Control, it is possible to solve the stationarity that TRAJECTORY CONTROL requires in the case of system model Dynamic Uncertain And accuracy problem.But in the case of having concrete constraint for tracking performance, the uncontrollable tracking error of these control methods Meet the requirement that particular characteristic is limited.A kind of performance error conversion adaptive neural network control method, is subject to by introducing performance Limit function, is specially the tracking error limited performance condition in actual environment mathematical functional expression and expresses, pass through performance further Error is changed, and original affined tracking error control problem is converted to unconfinement transformed error stability control problem, pin Unconfinement transformed error is designed neural network control, and for Design of State state observation immeasurablel in system Device, final unconfinement convert error stablize enable to end orbit follow the tracks of meet limited performance condition limit.Therefore pass through Introduce the performance error conversion adaptive neural network control method of Performance Constraints function, it is possible to according to concrete actual performance about Bundle, designs corresponding limited performance function, it is achieved the Trajectory Tracking Control under the conditions of flexible mechanical arm limited performance.

Existing utilize neutral net to Unknown Model dynamically approaches in flexible mechanical arm system during, need Constantly on-line tuning, every time during start operation system, controller needs to readjust neural network weight, at weighed value adjusting Starting stage, neutral net approximate error dynamic for Unknown Model is bigger, and the process adjusted is the most time-consuming, This makes the control effect of entirety be affected.For identical control task, the Unknown Model that neutral net is approached is dynamically base This is consistent, so the neural network weight adjustment repeated is the operation of redundancy.In order to solve the time-consuming redundancy of neutral net Line adjusts process, needs the weights of neutral net finally to restrain, but this is extremely difficult reaching.Determine theory of learning (Wang C.and Hill D.J..Learning From Neural Control[J].IEEE Transactions OnNeural Networks, 2006,17 (1): 130-145) having turned out the track for cycle or class cycle carries out nerve When network approaches, neural network weight can finally be restrained.Based on a determination that the rail of the limited performance flexible mechanical arm of theory of learning Mark tracking and controlling method, the neural network weight after storage convergence, in the most identical upper control task, directly utilize storage Neural network weight, it is to avoid the on-line tuning process of the neutral net of repetition, it is achieved constant value nerve net based on Heuristics Network controls.

Summary of the invention

Present invention is primarily targeted at and overcome the shortcoming of prior art with not enough, propose a kind of based on a determination that theory of learning The Trajectory Tracking Control method of limited performance flexible mechanical arm, it is to avoid for the most identical control task, meet reality simultaneously Control the Trajectory Tracking Control task in the case of concrete tracking error Performance Constraints in environment.

In order to achieve the above object, the present invention is by the following technical solutions:

The present invention's, based on a determination that the limited performance flexible mechanical arm control method of theory of learning, comprises the steps of:

Step (1): set up flexible mechanical arm dynamic model: by state transformation, sets up single flexibility of linking rod mechanical arm decoupling The dynamic model of the quadravalence canonical system form closed；

Step (2): set up State Observer: to the system mode design point observation not directly measured in model Device:

Wherein, p and r_iFor design parameter, i=1 ..., 4,Immeasurability shape in the system of being respectively State [υ₂ υ₃ υ₄] state observer；

Step (3): design tracking error performance constraints: to connecting rod output angle and cycle reference track output angle Between tracking error, transient state and the steady-state behaviour of tracking error are retrained by design performance function, particularly as follows:

$\left\{\begin{array}{c}{e}_1=x_1-x_d\\ -\underset{\&OverBar;}{\mathrm{\&sigma;}}\mathrm{\&rho;}\left(t\right)<e_1\left(t\right)<\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\mathrm{\&rho;}\left(t\right)\\ \mathrm{\&rho;}\left(t\right)=({\mathrm{\&rho;}}_0-{\mathrm{\&rho;}}_{\mathrm{\&infin;}})e^{-st}+{\mathrm{\&rho;}}_{\mathrm{\&infin;}}\end{array}\right.$

Wherein, ρ (t) is performance function, ρ₀、ρ_∞、s、σ、For design constant, x_dFor joint link lever angle reference periodically Track, e₁For track following error；

Design a strictly monotone increasing smooth function Ψ (ε₁), by limited tracking error e₁T () is converted to transformed error ε₁ (t):

$\left\{\begin{array}{c}{e}_1\left(t\right)=\mathrm{\&rho;}\left(t\right)\mathrm{\&Psi;}\left({\mathrm{\&epsiv;}}_1\right)\\ \mathrm{\&Psi;}\left({\mathrm{\&epsiv;}}_1\right)=\frac{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\exp \left({\mathrm{\&epsiv;}}_1\right)-\underset{\&OverBar;}{\mathrm{\&sigma;}}}{1+\exp \left({\mathrm{\&epsiv;}}_1\right)}\\ {\mathrm{\&epsiv;}}_1\left(t\right)={\mathrm{\&Psi;}}^{-1}(e_1/\mathrm{\&rho;})=In\&lsqb;\underset{\&OverBar;}{\mathrm{\&sigma;}}\mathrm{\&rho;}\left(t\right)+e_1\left(t\right)\&rsqb;-In\&lsqb;\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\mathrm{\&rho;}\left(t\right)-e_1\left(t\right)\&rsqb;\end{array}\right.$

Step (4): based on a determination that theory of learning design nerve network controller: utilize and determine theory of learning, design adaptive Answer RBF neural learning controller:

$u=-k_4{\mathrm{\&epsiv;}}_4-{\hat{W}}^{T}S\left(X\right)$

Wherein,Export for neutral net, k₄For the controller gain constant of design, ε₄For by following design The median error amount that process calculates:

The state observer output set up according to step (2)With step (3) in conversion after non- Limited transformed error ε₁, design Virtual Controller α₁, α₂, α₃:

Wherein k_i(i=1,2,3) is the Virtual Controller gain constant of design, x_dFor joint link lever angle reference periodically Track, γ, B are the middle control variable related in virtual controlling；

The median error amount occurred in controller u

Step (5): utilize Heuristics modifier controller: according to determining theory of learning, weighs neutral net in step (4) ValueConvergency value save asRealize utilizing the constant value RBF neural expressing HeuristicsModifier controller, I.e. controller form is:

$u=-k_4{\mathrm{\&epsiv;}}_4-{\stackrel{\&OverBar;}{W}}^{T}S\left(X\right).$

As preferred technical scheme, in step (1), described flexible mechanical arm uncoupled quadravalence canonical system form Dynamic model be:

$\left\{\begin{array}{c}{\mathrm{\&upsi;}}_1=x_1,{\mathrm{\&upsi;}}_2={\stackrel{\&CenterDot;}{x}}_1,{\mathrm{\&upsi;}}_3={\stackrel{\&CenterDot;\&CenterDot;}{x}}_1,{\mathrm{\&upsi;}}_4={\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_1\\ {\stackrel{\&CenterDot;}{\mathrm{\&upsi;}}}_i={\mathrm{\&upsi;}}_{i+1},i=1,2,3\\ {\stackrel{\&CenterDot;}{\mathrm{\&upsi;}}}_4=f(x_1,{\stackrel{\&CenterDot;}{x}}_1,x_2,{\stackrel{\&CenterDot;}{x}}_2)+\frac{K}{IJ}u\\ f(x_1,{\stackrel{\&CenterDot;}{x}}_1,x_2,{\stackrel{\&CenterDot;}{x}}_2)=\frac{MgL{\stackrel{\&CenterDot;}{x}}_1^2}{I}\sin \left(x_1\right)+\frac{MgL\cos \left(x_1\right)+K}{I^2}\left(MgL\sin \right(x_1)+K(x_1-x_2\left)\right)+\frac{K^2(x_1-x_2)}{IJ}\end{array}\right.$

Wherein, x₁And x₂Being respectively joint link lever angle and electric machine rotation angle, I and J is respectively the used of connecting rod and motor Amount, M is the quality of connecting rod, and L is the length of connecting rod, and g is acceleration of gravity, and K is the coefficient of elasticity of flexible portion spring, and u is control The control output of device processed, i.e. motor.

As preferred technical scheme, in step (3), described limited tracking error e₁T () is strict by design one Monotonic increase smooth function Ψ (ε₁) be converted to transformed error ε₁T (), by controlling ε₁T stablizing of (), makes e₁T () meets constraint ConditionThus the Trajectory Tracking Control under realizing constraints.

As preferred technical scheme, in step (4), M signal variable γ, the B tool that described Virtual Controller relates to Body is:Neutral net exportsFor approaching mechanical arm system Unknown multidate information, the input of neutral net isNeural network weight for online updating Vector.

As preferred technical scheme, in step (4), described neural network weight is convergence, based on a determination that study Theory, the neutral net of tracking cycle track input, neural net regression vector S (X) meets persistent excitation condition, finally god Through network weightConverge to optimal value

As preferred technical scheme, in step (5), the controller of described correction contains and determines in learning process HeuristicsMake the controller can be for the most identical control task, it is achieved Fast Convergent, low overshoot dynamic State property energy.

The present invention compared with prior art, has the advantage that and beneficial effect:

1 compared with the flexible mechanical arm Trajectory Tracking Control method that presently, there are, the control method energy that the present invention proposes Enough realize track following error and meet specific performance constraints, and not only realize what track following error finally went to zero Inside one neighborhood, moreover it is possible to realize overshoot and the convergence rate of error are limited.

2, the method for the present invention passes through design performance function, the parameter of regulation performance function, it is possible to by performance constraints Embody by the way of mathematical function such that it is able to further design controller.

3, the method for the present invention is by one strictly monotone increasing smooth function Ψ (ε of design₁), by limited tracking error e₁T () is converted to transformed error ε₁T (), its essence is that limited tracking error control problem is converted into the steady of untethered error Qualitative question, it is simple to controller designs.

4, the method for the present invention can utilize and determine that the ambiguous model of system is dynamically learnt by theory of learning, and will Learn to Heuristics store with the form of constant value neural network weight, when carrying out identical control task after being allowed to, The knowledge that can directly utilize storage is controlled, it is to avoid the on-line tuning process of redundancy, it is achieved neutral net Off-line control, joint The performance of dynamic tracking in the starting stage is improved while making an appointment.

Accompanying drawing explanation

Fig. 1 is flexible mechanical arm system schematic of the present invention.

Fig. 2 is the overall control block diagram of flexible mechanical arm of the present invention.

Fig. 3 is the convergence situation analogous diagram of neural network learning stage tracking error of the present invention.

Fig. 4 is error analogous diagram between state observer of the present invention and institute's observer state.

Fig. 5 is that neural network weight of the present invention restrains analogous diagram.

Fig. 6 is the controller Output simulation figure in neural network learning stage of the present invention.

Fig. 7 is that the present invention uses constant value neutral net that system the unknown is approached analogous diagram dynamically.

Fig. 8 is neural network learning stage of the present invention and knowledge recycling control stage tracking error convergence contrast simulation Figure.

Detailed description of the invention

Below in conjunction with embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention do not limit In this.

Embodiment

The present embodiment mainly studies flexible mechanical arm Trajectory Tracking Control under tracking performance limited situation, and Fig. 1 is soft The schematic diagram of property mechanical arm system.

Based on a determination that the overall control block diagram of the limited performance flexible mechanical arm control method of theory of learning as in figure 2 it is shown, Its detailed implementation process includes:

Step (1): set up flexible mechanical arm dynamic model.

Flexible mechanical arm system model according to following:

$\left\{\begin{array}{c}I{\stackrel{\&CenterDot;\&CenterDot;}{x}}_1+MgL\sin x_1+K(x_1-x_2)=0\\ J{\stackrel{\&CenterDot;\&CenterDot;}{x}}_2-K(x_1-x_2)=u\end{array}\right.$

The dynamic model form being converted into the quadravalence canonical system form after decoupling is as follows:

$\left\{\begin{array}{c}{\mathrm{\&upsi;}}_1=x_1,{\mathrm{\&upsi;}}_2={\stackrel{\&CenterDot;}{x}}_1,{\mathrm{\&upsi;}}_3={\stackrel{\&CenterDot;\&CenterDot;}{x}}_1,{\mathrm{\&upsi;}}_4={\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_1\\ {\stackrel{\&CenterDot;}{\mathrm{\&upsi;}}}_i={\mathrm{\&upsi;}}_{i+1},i=1,2,3\\ {\stackrel{\&CenterDot;}{\mathrm{\&upsi;}}}_4=f(x_1,{\stackrel{\&CenterDot;}{x}}_1,x_2,{\stackrel{\&CenterDot;}{x}}_2)+\frac{K}{IJ}u\\ f(x_1,{\stackrel{\&CenterDot;}{x}}_1,x_2,{\stackrel{\&CenterDot;}{x}}_2)=\frac{MgL{\stackrel{\&CenterDot;}{x}}_1^2}{I}\sin \left(x_1\right)+\frac{MgL\cos \left(x_1\right)+K}{I^2}\left(MgL\sin \right(x_1)+K(x_1-x_2\left)\right)\\ +K^2(x_1-x_2)/\left(IJ\right)\end{array}\right.$

Wherein, x₁And x₂Being respectively joint link lever angle and electric machine rotation angle, I and J is respectively the used of connecting rod and motor Amount, M is the quality of connecting rod, and L is the length of connecting rod, and g is acceleration of gravity, and K is the coefficient of elasticity of flexible portion spring, and u is electricity The control output of machine；

In this example, the systematic parameter choosing flexible mechanical arm is respectively as follows:

M=0.2kg, L=1m, I=2.3kg m², K=15N m/rad, J=0.5kg m², g=9.8m/s²

Step (2): set up State Observer.

Owing to the state that can measure in system is x₁, and υ₂, υ₃, υ₄Being immesurable in system, design point is observed Device is as follows:

Wherein p=1250, r₁=r₃=-2p, r₂=-3p, r₄=-p,Can not in the system of being respectively Measuring state [υ₂ υ₃ υ₄] state observer.

Step (3): design tracking error performance constraints.

Select the reference locus in following cycle:

$x_d=\frac{80\mathrm{\&pi;}}{360}sin\left(\frac{2\mathrm{\&pi;}}{7}t\right)$

Wherein, x_dFor the reference angle track of joint link lever angle at the end, and there is continuous print derivativee₁= x₁-x_dTrack following error for connecting rod end.

This example requiring, tracking error meets following limited performance constraints: e₁The maximum overshoot upper limit and under Limit is respectively 1.44 and-1.2, e₁Convergence rate cannot be below e^-t, e₁Steady-state error constrain between-0.05 and 0.05, As follows according to the above-mentioned limited function of constraints design performance:

$\left\{\begin{array}{c}-\mathrm{\&rho;}\left(t\right)<e_1\left(t\right)<1.2\mathrm{\&rho;}\left(t\right)\\ \mathrm{\&rho;}\left(t\right)=(1.2-0.05)e^{-t}+0.05\end{array}\right.$

According to limited performance function, design a strictly monotone increasing smooth function Ψ (ε₁), by limited track following Error e₁Be converted to the transformed error ε of untethered₁:

$\left\{\begin{array}{c}{e}_1\left(t\right)=\mathrm{\&rho;}\left(t\right)\mathrm{\&Psi;}\left({\mathrm{\&epsiv;}}_1\right)\\ -1\&le;\mathrm{\&Psi;}\left({\mathrm{\&epsiv;}}_1\right)=\frac{1.2\exp \left({\mathrm{\&epsiv;}}_1\right)-1}{1+\exp \left({\mathrm{\&epsiv;}}_1\right)}\&le;1.2\\ {\mathrm{\&epsiv;}}_1\left(t\right)={\mathrm{\&Psi;}}^{-1}(e_1/\mathrm{\&rho;})=In\&lsqb;\mathrm{\&rho;}\left(t\right)+e_1\left(t\right)\&rsqb;-In\&lsqb;1.2\mathrm{\&rho;}\left(t\right)-e_1\left(t\right)\&rsqb;\end{array}\right.$

Step (4): based on a determination that theory of learning design nerve network controller.

Transformed error ε is ensured by design controller₁Stablize, thus realize limited error e₁Meet wanting of constraints Ask, particularly as follows:

First designVirtual Controller α₁, and and state observerConstitute error variance ε₂:

Wherein, k₁=1,

Design furtherVirtual Controller α₂, and and state observerConstitute error variance ε₃:

Wherein, k₂=4, γ=1/ (ρ+e₁)+1/(1.2ρ-e₁)。

Design furtherVirtual Controller α₃, and and state observerConstitute error variance ε₄:

Wherein, k₃=10,

In this example, the system model of flexible mechanical arm is the most totally unknown, utilizes neutral netApproach the unknown Dynamic:The wherein input of neutral netAdaptive neural network The e-learning controller following form of design:

$u=-k_4{\mathrm{\&epsiv;}}_4-{\hat{W}}^{T}S\left(X\right)$

Wherein, selection control gain k₄=20.

Select neural network weightOnline updating regulation is:

$\stackrel{\&CenterDot;}{\hat{W}}=\mathrm{\&Gamma;}S\left(X\right)z_4-\mathrm{\&Gamma;}o\hat{W}$

The selection of system initial state and neural network parameter is as follows:

The initial condition of system:

Neural network parameter selects: neural network node number N=9 × 9 × 11 × 11, weights initial value Central point is evenly distributed on [-0.9,0.9] × [-0.9,0.9] × [-1.5,1.5] × [-1.5,1.5], neutral net turnover rate Parameter Γ=12, o=0.0001.

According to nerve network controllerControl transformed error ε₁Stable, ε₁Stablize so that limited Tracking error e₁Meet constraints-ρ (t) ＜ e₁(t) ＜ 1.2 ρ (t), thus realize the track following control under Performance Constraints System.

Fig. 3 shows study stage tracking error e₁The analogous diagram of convergence, final tracking error e₁In constraints-ρ (t) ＜ e₁Fluctuation in (t) ＜ 1.2 ρ (t), and converge within the limited time inside the small neighbourhood of zero, thus meet and set Constraints requirement, it is achieved the Trajectory Tracking Control under performance constraints.Fig. 4 is state observer and the system of design Observation error change analogous diagram between middle institute observer state.Fig. 5 is the study weights of neutral net F dynamic to unknown system (X) Convergence analogous diagram.Fig. 6 is the wave simulation figure of neural network learning phase controller output u.According to Fig. 5, at Neural Network Science In the habit stage, the weights of neutral net finally converge to constant value, store the weights constant value of these neutral nets, as system not Know the expression of multidate information.

Step (5): utilize Heuristics modifier controller.

In this example, constant value is calculated by the weights of convergence in the time period [400s, 500s] are averaged neural Network weight:

$\stackrel{\&OverBar;}{W}=\underset{t\&Element;\&lsqb;400s,500s\&rsqb;}{mean}\hat{W}\left(t\right)$

Design nerve network controller based on Heuristics:

$\stackrel{\&OverBar;}{u}=-k_4{\mathrm{\&epsiv;}}_4-{\stackrel{\&OverBar;}{W}}^{T}S\left(X\right)$

Wherein, the control parameter in controller is chosen consistent with the neural network learning stage.

Fig. 7 is constant value neutral netAnd the Approximation effect analogous diagram between the dynamic F of unknown system (X), storage Constant value neutral net can approach the system of the unknown, thus realize neutral net study dynamic to unknown system and recycled Journey, it is to avoid the process of readjusting online of redundancy.Fig. 8 is neural network learning stage and experience recycling control stage tracking mistake Difference convergence contrast effect analogous diagram, for identical control task, nerve network controller based on Heuristics has less Overshoot, the dynamic characteristic in the starting stage is better than the neural network learning stage, shortens regulating time.

Above-described embodiment is the present invention preferably embodiment, but embodiments of the present invention are not by above-described embodiment Limit, the change made under other any spirit without departing from the present invention and principle, modify, substitute, combine, simplify, All should be the substitute mode of equivalence, within being included in protection scope of the present invention.

Claims (6)

1. based on a determination that the limited performance flexible mechanical arm control method of theory of learning, it is characterised in that comprise the steps of:

Step (1): set up flexible mechanical arm dynamic model: by state transformation, sets up single flexibility of linking rod mechanical arm uncoupled The dynamic model of quadravalence canonical system form；

Step (2): set up State Observer: the system mode design point observer to not directly measuring in model:

Wherein, p and r_iFor design parameter, i=1 ..., 4,Unmeasured state [υ in the system of being respectively₂ υ₃ υ₄] state observer；

Step (3): design tracking error performance constraints: between connecting rod output angle and cycle reference track output angle Tracking error, transient state and the steady-state behaviour of tracking error are retrained by design performance function, particularly as follows:

$\left\{\begin{array}{c}{e}_1=x_1-x_d\\ -\underset{\&OverBar;}{\mathrm{\&sigma;}}\mathrm{\&rho;}\left(t\right)<e_1\left(t\right)<\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\mathrm{\&rho;}\left(t\right)\\ \mathrm{\&rho;}\left(t\right)=\left({\mathrm{\&rho;}}_0-{\mathrm{\&rho;}}_{\mathrm{\&infin;}}\right)e^{-st}+{\mathrm{\&rho;}}_{\mathrm{\&infin;}}\end{array}\right.$

Wherein, ρ (t) is performance function, ρ₀、ρ_∞、s、σ、For design constant, x_dFor joint link lever angle reference periodically track, e₁For track following error；

Design a strictly monotone increasing smooth function Ψ (ε₁), by limited tracking error e₁T () is converted to transformed error ε₁(t):

$\left\{\begin{array}{c}{e}_1\left(t\right)=\mathrm{\&rho;}\left(t\right)\mathrm{\&Psi;}\left({\mathrm{\&epsiv;}}_1\right)\\ \mathrm{\&Psi;}\left({\mathrm{\&epsiv;}}_1\right)=\frac{\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\exp \left({\mathrm{\&epsiv;}}_1\right)-\underset{\&OverBar;}{\mathrm{\&sigma;}}}{1+\exp \left({\mathrm{\&epsiv;}}_1\right)}\\ {\mathrm{\&epsiv;}}_1\left(t\right)={\mathrm{\&Psi;}}^{-1}(e_1/\mathrm{\&rho;})=In\&lsqb;\underset{\&OverBar;}{\mathrm{\&sigma;}}\mathrm{\&rho;}\left(t\right)+e_1\left(t\right)\&rsqb;-In\&lsqb;\stackrel{\&OverBar;}{\mathrm{\&sigma;}}\mathrm{\&rho;}\left(t\right)-e_1\left(t\right)\&rsqb;\end{array}\right.$

Step (4): based on a determination that theory of learning design nerve network controller: utilize and determine theory of learning, design self_adaptive RBF Neural network learning controller:

$u=-k_4{\mathrm{\&epsiv;}}_4-{\hat{W}}^{T}S\left(X\right)$

Wherein,Export for neutral net, k₄For the controller gain constant of design, ε₄For by following design process meter The median error amount calculated:

The state observer output set up according to step (2)Turn with the untethered after conversion in step (3) Change error ε₁, design Virtual Controller α₁, α₂, α₃:

Wherein k_i(i=1,2,3) is the Virtual Controller gain constant of design, x_dFor joint link lever angle reference periodically track, γ, B are the middle control variable related in virtual controlling；

Median error amount ε occurred in controller u₄:

Step (5): utilize Heuristics modifier controller: according to determining theory of learning, by neural network weight in step (4) Convergency value save asRealize utilizing the constant value RBF neural expressing HeuristicsModifier controller, i.e. controls Device form processed is:

$u=-k_4{\mathrm{\&epsiv;}}_4-{\stackrel{\&OverBar;}{W}}^{T}S\left(X\right).$

The most according to claim 1 based on a determination that the limited performance flexible mechanical arm control method of theory of learning, its feature Being, in step (1), the dynamic model of described flexible mechanical arm uncoupled quadravalence canonical system form is:

$\left\{\begin{array}{c}{\mathrm{\&upsi;}}_1=x_1,{\mathrm{\&upsi;}}_2={\stackrel{\&CenterDot;}{x}}_1,{\mathrm{\&upsi;}}_3={\stackrel{\&CenterDot;\&CenterDot;}{x}}_1,{\mathrm{\&upsi;}}_4={\stackrel{\&CenterDot;\&CenterDot;\&CenterDot;}{x}}_1\\ \begin{array}{cc}{\stackrel{\&CenterDot;}{\mathrm{\&upsi;}}}_i={\mathrm{\&upsi;}}_{i+1}& i=1,2,3\end{array}\\ {\stackrel{\&CenterDot;}{\mathrm{\&upsi;}}}_4=f\left(x_1,{\stackrel{\&CenterDot;}{x}}_1,x_2,{\stackrel{\&CenterDot;}{x}}_2\right)+\frac{K}{IJ}u\\ f\left(x_1,{\stackrel{\&CenterDot;}{x}}_1,x_2,{\stackrel{\&CenterDot;}{x}}_2\right)=\frac{MgL{\stackrel{\&CenterDot;}{x}}_1^2}{I}\sin \left(x_1\right)+\frac{MgL\cos \left(x_1\right)+K}{I^2}\left(MgL\sin \left(x_1\right)+K\left(x_1-x_2\right)\right)+\frac{K^2\left(x_1-x_2\right)}{IJ}\end{array}\right.$

Wherein, x₁And x₂Being respectively joint link lever angle and electric machine rotation angle, I and J is respectively the inertia of connecting rod and motor, and M is The quality of connecting rod, L is the length of connecting rod, and g is acceleration of gravity, and K is the coefficient of elasticity of flexible portion spring, and u is controller, i.e. The control output of motor.

The most according to claim 1 based on a determination that the limited performance flexible mechanical arm control method of theory of learning, its feature It is, in step (3), described limited tracking error e₁T () is by one strictly monotone increasing smooth function Ψ (ε of design₁) turn It is changed to transformed error ε₁T (), by controlling ε₁T stablizing of (), makes e₁T () meets constraints Thus the Trajectory Tracking Control under realizing constraints.

It is the most according to claim 1 based on a determination that the limited performance flexible mechanical arm control method of theory of learning, it is characterised in that In step (4), M signal variable γ, B that described Virtual Controller relates to particularly as follows: Neutral net exportsFor approaching the unknown multidate information of mechanical arm system, the input of neutral net is Neural network weight vector for online updating.

The most according to claim 1 based on a determination that the limited performance flexible mechanical arm control method of theory of learning, its feature Being, in step (4), described neural network weight is convergence, based on a determination that theory of learning, tracking cycle track inputs Neutral net, neural net regression vector S (X) meets persistent excitation condition, final neural network weightConverge to optimum Value

The most according to claim 1 based on a determination that the limited performance flexible mechanical arm control method of theory of learning, its feature Being, in step (5), the controller of described correction contains the Heuristics determining in learning processMake Controller can be for the most identical control task, it is achieved Fast Convergent, the dynamic property of low overshoot.