CN105739310A - Multi-model-based servo system adaptive control system - Google Patents

Abstract

The present invention discloses a multi-model-based servo system adaptive control system which belongs to the electromechanical control field. The system comprises a multi-mode parameter estimation module, a switching mechanism module and an adaptive controller, wherein a servo system is controlled by the adaptive control system. The multi-mode parameter estimation module comprises n fixing modules, an identification model and an adaptive model, and each module in the multi-mode parameter estimation module outputs a set of model parameters aiming at the servo system and inputs to the switching mechanism module. The switching mechanism module selects a set of model parameters making a cost function to be minimum from the multiple sets of model parameters as the optimal model parameters, and inputs to the adaptive controller, and the adaptive controller carriers out the adaptive control law calculation on the inputted optimal model parameters to obtain an adaptive controlled quantity, and inputs to the controlled object. The system can obtain the estimation parameters which can represent the system dynamic characteristics best without needing to obtain the priori knowledge about the system uncertainty.

Description

A kind of servo system self-adaptive based on multi-model controls system

Technical field

The present invention relates to direct current generator servo-control system, belong to electromechanical control field, be specifically related to a kind of servo system self-adaptive based on multi-model and control system.

Background technology

In servo system control, due to the existence of the uncertain factors such as dynamic friction, load change and external disturbance, often there is saltus step in the parameter of system model, the control performance such as response speed, precision and stability is produced a very large impact.If additionally, control system exists unknown parameter, it is likely to differ bigger with its actual value to the initial estimate of these parameters.Therefore, if can not accurately obtain the parameter of system model in control process, it is difficulty with desirably controlling effect.

Parameter can be estimated in real time by tradition adaptive approach by adaptive law, it is achieved quickly follows the tracks of.But, under complex environment, the time making Automatic adjusument is lengthened by parameter sudden change significantly, causes that mapping worsens.Increase self adaptation proportional gain and can add the convergence of fast parameter, but also can increase the system sensitivity to noise simultaneously, make steady-state behaviour be deteriorated.

Summary of the invention

In view of this, the invention provides a kind of servo system self-adaptive based on multi-model and control system, this system can know that the priori about systematic uncertainty can obtain the estimation parameter that can characterize system dynamic characteristic.

In order to achieve the above object, the technical scheme is that a kind of servo system self-adaptive based on multi-model controls system, this system includes multi-model parameter estimation module, handover mechanism module and adaptive controller, and wherein said servosystem is the controlled device of this adaptive control system.

Described multi-model parameter estimation module includes n fixed model, 1 identification model and an adaptive model.

Each model in described multi-model parameter estimation module exports one group of model parameter for described servosystem, and input is described handover mechanism module extremely.

Described handover mechanism module selects one group of model parameter making cost function minimum as optimal models parameter from many group models parameter, is input to adaptive controller.

The optimal models parameter of input is calculated acquisition Self Adaptive Control amount u, Self Adaptive Control amount u by adaptive control laws and inputs to controlled device by described adaptive controller；The input parameter of adaptive controller includes: the desired throughput of controlled device, optimal models parameter, output feedback amount and can not survey the filtering observation of parameter；The desired throughput of described controlled device includes angle and the angular velocity of expectation controlled device output.

Wherein output feedack amount is the real-time output of controlled device.

The described filtering observation that can not survey parameter is obtained by filtering observer, described filtering observer obtains the real-time output of controlled device, parameter of can not surveying in adaptive controller is once estimated by the closed loop observer in filtering observer, in accessory filter in filtering observer, the error once estimated is carried out quadratic estimate, then by twice, the filtering observation that can not survey parameter estimates that signal compound obtains；The filtering observation that can not survey parameter is inputted to adaptive controller.

Described fixed model is fixed the estimation of model parameter in the following way:

Static parameter first with servosystem mathematical model calculates the preset value obtaining a model parameter, and the excursion according to each model parameter of default settings, excursion is carried out point process such as m, each Along ent is to should an estimated value of parameter, the fixed model parameter of one fixed model output is that each parameter appoints the combination taking an Along ent estimated value, total n=(m-1)^aIndividual fixed model.

Described identification model includes low pass filter, discernibility matrixes module and recognition module, carries out the estimation of identification model parameter in identification model in the following way:

Described low pass filter with the output u of adaptive controller, controlled device real-time output x and can not survey parameter filtering observation composition input vector, wherein x includes real-time angular and the angular velocity of controlled device；Switching instant set in advance in low pass filter, low pass filter is filtered at each switching instant and exports the Real-Time Filtering value of above-mentioned input vector.

Described discernibility matrixes module includes discernibility matrixes P (t), Q (t) and preset initial value P thereof₀And Q₀, wherein P₀And Q₀Meet P₀ ^-1Q₀Bounded, and P (t) is reversible all the time；Discernibility matrixes P (t), Q (t) value real-time update: P (t) be the product of low pass filter output vector and its transposition from a upper switching instant to the integration of current time t, Q (t) is that the low pass filter output vector product with the angular velocity in x is from a upper switching instant to the integration of current time t.

Described recognition module is utilized as P^-1T the product of () and Q (t) instantaneous value is as identification model parameterInput is to described handover mechanism module.

Described adaptive model, with identification model parameter and optimal models parameter for reference, carries out the estimation of adaptive mode shape parameter in the following way:

Adaptive model arranges marking variable sw, if P (t) is reversible, andWithin the model parameter span set, then sw=1；Otherwise sw=0.

With the output x of the output u of adaptive controller and controlled device for input, at switching instant: when marking variable sw=1 and a upper switching instant handover mechanism module are output as identification model parameter, then adaptive mode shape parameterWhen a upper switching instant handover mechanism module is output as fixed model parameter, then adaptive mode shape parameterFor the output of a upper switching instant handover mechanism module, adaptive mode shape parameter in other situationsAdopt discontinuous projection operator；The parameter estimation result input of output adaptive model is to described handover mechanism module alternately.

Further, servosystem is direct current generator servosystem, and its state space form being obtained direct current generator servo system models by LuGre model is $\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2={\mathrm{\θ}}_{1}u+{\mathrm{\θ}}_2{x}_2+{\mathrm{\θ}}_3\frac{\left|x_2\right|}{g\left(x_2\right)}z-{\mathrm{\θ}}_{4}z-d\\ y=x_1\end{array}\right.;$

Wherein, state variable x₁And x₂It is Angle Position and the angular velocity of servosystem respectively,WithIt is x respectively₁And x₂First derivative；θ₁, θ₂, θ₃And θ₄Being the unknown parameter characterizing system dynamic characteristic, u is the output of adaptive controller, and x is the output of controlled device, and x includes angle x₁With angular velocity x₂, z is average bristle amount of deflection,For the accessory filter estimated value to z；D is integrated disturbance, bounded and average is zero；G () is this Trebek friction model function；

The then input vector of low pass filter ${\mathrm{\φ}}_0\left(t\right)={\[u,x_2,\frac{\left|x_2\right|}{g\left(x_2\right)}(\hat{z}+{\mathrm{\ξ}}_0),-(\hat{z}+{\mathrm{\ξ}}_1)\]}^T;$

The adaptive law that the filtering being exports in described adaptive model is:

Wherein,For adaptive mode shape parameter,For identification model parameter,Optimal models parameter for a upper switching instant handover mechanism module output；Γ is the adaptive learning factor, is a positive definite diagonal matrix；For auto-adaptive function；For φ₀Low-pass filter value, γ filter tracking error；J^*For the optimal value of performance index function, $J^{*}=\min \{J\left({\widehat{\mathrm{\θ}}}_{f1}\right),J\left({\widehat{\mathrm{\θ}}}_{f2}\right),...,J\left({\widehat{\mathrm{\θ}}}_{fn}\right),J\left({\widehat{\mathrm{\θ}}}_{ident}\right),J\left({\widehat{\mathrm{\θ}}}_a\right)\};$ Parameter estimation result for n fixed model；J () is performance index function.

Further, filtering observer is:

$\hat{z}=x_2-\frac{\left|x_2\right|}{g\left(x_2\right)}\hat{z}$

WhereinIt it is the estimated value to z；Described accessory filter is

${\stackrel{\·}{\mathrm{\ξ}}}_0=-\frac{\left|x_2\right|}{g\left(x_2\right)}{\mathrm{\ξ}}_0-k_0\frac{\left|x_2\right|}{g\left(x_2\right)}\mathrm{\γ}$

${\stackrel{\·}{\mathrm{\ξ}}}_1=-\frac{\left|x_2\right|}{g\left(x_2\right)}{\mathrm{\ξ}}_1+k_1\mathrm{\γ}$

Wherein ξ₀And ξ₁It is to observer estimation differenceObservation,WithIt is ξ₀And ξ₁First derivative, k₀And k₁It it is adjustable gain.

Beneficial effect:

The present invention adopts a kind of adaptive approach based on multi-model to improve adaptive process.Whole control strategy includes multi-model, handover mechanism and the adaptive controller based on filtering observer.Filtering observer can obtain immesurable state parameter in system model；Multi-model is made up of fixed model, identification model and adaptive model；Handover mechanism can pass through a certain performance index function of relatively above-mentioned each model, and therefrom selecting can of characterization control system dynamic characteristic.The method requires no knowledge about the priori about systematic uncertainty.

Accompanying drawing explanation

Fig. 1 is the adaptive control system structure chart based on multi-model.

Fig. 2 is identification model structure chart.

Fig. 3 is parameter adjustment flow chart.

Fig. 4 is that MATLAB emulates tracking effect comparison diagram (Stepped Impedance Resonators).

Fig. 5 is semi-physical simulation experiment system structure chart.

Fig. 6 is HWIL simulation experimental result comparison diagram (sinusoidal input).

Detailed description of the invention

Develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

Embodiment 1, a kind of servo system self-adaptive based on multi-model control system, and this system includes multi-model parameter estimation module, handover mechanism module and adaptive controller, and wherein servosystem is the controlled device of this adaptive control system.

Multi-model parameter estimation module includes n fixed model, 1 identification model and an adaptive model.

Each model in multi-model parameter estimation module exports one group of model parameter for servosystem, inputs to handover mechanism module.

Handover mechanism module selects one group of model parameter making cost function minimum as optimal models parameter from many group models parameter, is input to adaptive controller.

The optimal models parameter of input is calculated acquisition Self Adaptive Control amount u, Self Adaptive Control amount u by adaptive control laws and inputs to controlled device by adaptive controller；The input parameter of adaptive controller includes: the desired throughput of controlled device, optimal models parameter, output feedback amount and can not survey the filtering observation of parameter；The desired throughput of controlled device includes angle and the angular velocity of expectation controlled device output.

Wherein output feedack amount is the real-time output of controlled device.

The filtering observation that can not survey parameter is obtained by filtering observer, filtering observer obtains the real-time output of controlled device, parameter of can not surveying in adaptive controller is once estimated by the closed loop observer in filtering observer, in accessory filter in filtering observer, the error once estimated is carried out quadratic estimate, then by twice, the filtering observation that can not survey parameter estimates that signal compound obtains；The filtering observation that can not survey parameter is inputted to adaptive controller.

Fixed model is fixed the estimation of model parameter in the following way:

Static parameter first with servosystem mathematical model calculates the preset value obtaining a model parameter, and the excursion according to each model parameter of default settings, excursion is carried out point process such as m, each Along ent is to should an estimated value of parameter, the fixed model parameter of one fixed model output is that each parameter appoints the combination taking an Along ent estimated value, total n=(m-1)^aIndividual fixed model.

Identification model includes low pass filter, discernibility matrixes module and recognition module, carries out the estimation of identification model parameter in identification model in the following way:

Low pass filter with the output u of adaptive controller, controlled device real-time output x and can not survey parameter filtering observation composition input vector, wherein x includes real-time angular and the angular velocity of controlled device；Switching instant set in advance in low pass filter, low pass filter is filtered at each switching instant and exports the Real-Time Filtering value of above-mentioned input vector.

Discernibility matrixes module include discernibility matrixes P (t), Q (t) and preset initial value P₀And Q₀, wherein P₀And Q₀Meet P₀ ^-1Q₀Bounded, and P (t) is reversible all the time；Discernibility matrixes P (t), Q (t) value real-time update: P (t) be the product of low pass filter output vector and its transposition from a upper switching instant to the integration of current time t, Q (t) is that the low pass filter output vector product with the angular velocity in x is from a upper switching instant to the integration of current time t.

Recognition module is utilized as p^-1T the product of () and Q (t) instantaneous value is as identification model parameter Input is to described handover mechanism module.

Adaptive model, with identification model parameter and optimal models parameter for reference, carries out the estimation of adaptive mode shape parameter in the following way:

Adaptive model arranges marking variable sw, if P (t) is reversible, andWithin the model parameter span set, then sw=1；Otherwise sw=0.

With the output x of the output u of adaptive controller and controlled device for input, at switching instant: when marking variable sw=1 and a upper switching instant handover mechanism module are output as identification model parameter, then adaptive mode shape parameterWhen a upper switching instant handover mechanism module is output as fixed model parameter, then adaptive mode shape parameterFor the output of a upper switching instant handover mechanism module, adaptive mode shape parameter in other situationsAdopt discontinuous projection operator；The parameter estimation result of output adaptive model inputs to handover mechanism module alternately.

Embodiment 2, the nonlinear dynamic friction considering system and external disturbance, utilize LuGre model to obtain the state space form of certain direct current generator servo system models

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2={\mathrm{\θ}}_{1}u+{\mathrm{\θ}}_2{x}_2+{\mathrm{\θ}}_3\frac{\left|x_2\right|}{g\left(x_2\right)}z-{\mathrm{\θ}}_{4}z-d\\ y=x_1\end{array}\right.---\left(1\right)$

Wherein, state variable x₁And x₂It is Angle Position and angular velocity respectively, θ₁, θ₂, θ₃And θ₄It is the unknown parameter characterizing system dynamic characteristic, it is possible to saltus step, and at t ∈ [t_k, t_k+1) (k=0,1,2 ...) in, θ_i(t)=θ_i(k) (i=1,2,3,4).Without loss of generality, make the following assumptions:

Assume 1: θ_i∈[θ_imin, θ_imax], i=1,2,3,4.Wherein θ_iminAnd θ_imaxIt is known that and θ_imax> θ_imin> O.This hypothesis ensure that unknown parameter changes in the scope of bounded, i.e. θ ∈ Ω_θ。

Assume 2: integrated disturbance d bounded and average are zero.

Assume 3: reference input Angle Position track x_dSmooth enough, to ensure that its second order can micro-and bounded.

Based on multi-model adaptive control system structure as it is shown in figure 1, by multi-model, handover mechanism and based on filtering observer adaptive controller three part form, be specifically addressed separately below.

1. based on the adaptive controller of filtering observer.When direct current generator servo-control system is modeled, the non-linear friction state parameter z in LuGre model is immesurable.Traditional method is with closed loop observer, it to be estimated.The proportional gain in closed loop observer is replaced with accessory filter.Unknown parameter is once estimated by observer part, and the error of above-mentioned estimation is carried out quadratic estimate by filter segment, then by twice, the estimated value of unknown parameter estimates that signal compound obtains.Thus accelerate the convergence rate of estimated value, reduce the impact on system of the observer error.

Filter tracking error is defined as

$\mathrm{\γ}=\stackrel{\·}{e}+\mathrm{\λ}e---\left(2\right)$

Wherein e=x_d-x₁, λ > 0.Owing to G (s)=E (s)/R (s)=1/ (s+ λ) is stable biography letter, if γ (t) restrains, e (t) must restrain.Therefore, to x_dTracking problem be just reduced to the problem making γ minimize.

Observer partial design is

$\stackrel{\·}{\hat{z}}=x_2-\frac{\left|x_2\right|}{g\left(x_2\right)}\hat{z}---\left(3\right)$

WhereinIt it is the estimated value to z.Filter segment is designed as

${\stackrel{\·}{\mathrm{\ξ}}}_0=-\frac{\left|x_2\right|}{g\left(x_2\right)}{\mathrm{\ξ}}_0-k_0\frac{\left|x_2\right|}{g\left(x_2\right)}\mathrm{\γ}---\left(4\right)$

${\stackrel{\·}{\mathrm{\ξ}}}_1=-\frac{\left|x_2\right|}{g\left(x_2\right)}{\mathrm{\ξ}}_1+k_1\mathrm{\γ}---\left(5\right)$

Wherein ξ₀And ξ₁It is to observer estimation differenceEstimated value, k₀And k₁It it is adjustable gain.

Consider the derivative of γ

$\stackrel{\·}{\mathrm{\γ}}=({\stackrel{\·\·}{x}}_d+\mathrm{\λ}\stackrel{\·}{e})-{\mathrm{\θ}}_{1}u-{\mathrm{\θ}}_2{x}_2-{\mathrm{\θ}}_3\frac{\left|x_2\right|}{g\left(x_2\right)}z+{\mathrm{\θ}}_{4}z+d---\left(6\right)$

Adaptive controller is designed as

$\left\{\begin{array}{c}{u}_1=h\mathrm{\γ}\\ u_2=\frac{1}{{\widehat{\mathrm{\θ}}}_1}\[({\stackrel{\·\·}{x}}_d+\mathrm{\λ}\stackrel{\·}{e})-{\widehat{\mathrm{\θ}}}_2{x}_2-{\widehat{\mathrm{\θ}}}_3\frac{\left|x_2\right|}{g\left(x_2\right)}(\hat{z}+{\mathrm{\ξ}}_0)+{\widehat{\mathrm{\θ}}}_4(\hat{z}+{\mathrm{\ξ}}_1)\]\\ u=u_1+u_2\end{array}\right.---\left(7\right)$

WhereinWithIt is the estimation to unknown parameter respectively, u₁It is ratio control item, u₂Being Self Adaptive Control item, h is adjustable proportion gain, it is possible to take

$h=\mathrm{\ρ}\frac{\left|x_2\right|}{g\left(x_2\right)}+h_0---\left(8\right)$

Wherein, p > 0, h₀> 0.Obtained by (6) and (7)

Whereinθ=[θ₁, θ₂, θ₃, θ₄]^T,It it is the estimation difference of θ.

2. the foundation of multi-model.Fixed model need not regulate and reset, and coverage is relatively big, accelerates control speed, but accuracy is difficult to ensure that, model gap size to be compromised between degree of accuracy and operand.Identification model is equivalent to numerous fixed model, it is possible to on-line checking parameter saltus step, decreases the quantity of fixed model, improves dynamic stability simultaneously.Adaptive model adopts discontinuous projection operator as adaptive law, it is ensured that the estimated value of parameter is change in the interval of definition, it is ensured that control accuracy.

I () fixed model: consider to assume closure and the boundedness in unknown parameter space in 1, these models are uniformly distributed in parameter space by a most straightforward procedure determining fixed model.Unknown parameter θ=[θ_1,θ₂, θ₃, θ₄]^TBeing the vector of one 4 dimension, wherein each unit have the restriction of minima and maximum, i.e. θ_i∈[θ_imin, θ_imax], i=1 ..., 4.Definition θ_iWidth be W_i=θ_imax-θ_imin, each width is divided into m_iEqual portions, i=1 ..., 4.Take the fixed model that Along ent is candidate in interval.Give an example, for θ₁∈[θ_1min, θ_1max], its width is W₁=θ_1max-θ_1min, at parameter space 4 decile, namely take m₁=4, then decile is spaced apartThe set of middle Along ent is It is to say, at θ_iClosed interval in have m₁-1=3 fixed estimation value.The corresponding fixed value of other parameter can in like manner obtain.Therefore, the quantity of whole system fixed model is:

$R={\Π}_{i=1}^4(m_i-1)---\left(10\right)$

The position Ω of fixed model_fFor:

$\begin{array}{c}{\mathrm{\Ω}}_f=\{{\widehat{\mathrm{\θ}}}_{f1},{\widehat{\mathrm{\θ}}}_{f2},\mathrm{...},{\widehat{\mathrm{\θ}}}_{fn}\}\\ =\{{\mathrm{\θ}}_{1\min }+\frac{1}{m_1}{W}_1,{\mathrm{\θ}}_{1\min }+\frac{2}{m_1}{W}_1,\mathrm{...},{\mathrm{\θ}}_{1\min }+\frac{m_1-1}{m_1}{W}_1\}\\ \×\{{\mathrm{\θ}}_{2\min }+\frac{1}{m_2}{W}_1,{\mathrm{\θ}}_{2\min }+\frac{2}{m_2}{W}_2,\mathrm{...},{\mathrm{\θ}}_{2\min }+\frac{m_2-1}{m_2}{W}_2\}\\ \×\mathrm{...}\×\{{\mathrm{\θ}}_{4\min }+\frac{1}{m_4}{W}_1,{\mathrm{\θ}}_{4\min }+\frac{2}{m_4}{W}_4,\mathrm{...},{\mathrm{\θ}}_{4\min }+\frac{m_4-1}{m_4}{W}_4\}\end{array}---\left(11\right)$

Thus obtain quantity and the distributing position of fixed model.Theoretically, on the one hand, if the decile interval of each parameter is sufficiently small, divide more thin, then the fixed model obtained has the probability close to realistic model more big；On the other hand, along with parameter divides the refinement of degree, the quantity of fixed model can become geometric growth with computation complexity.In actual application, it should empirically rationally select to wait point interval.

(ii) identification model: the building process of identification model is as shown in Figure 2.

In order to obtain identification model, the low pass filter that first one parameter of structure can reset is:

$\left\{\begin{array}{cc}\mathrm{\φ}\left(t\right)=0& t=t_i\\ \stackrel{\·}{\mathrm{\φ}}\left(t\right)+k\mathrm{\φ}\left(t\right)={\mathrm{\φ}}_0\left(t\right)& t\≠t_i\end{array}\right.,(i=0,1,\mathrm{...})---\left(12\right)$

Wherein, ${\mathrm{\φ}}_0={\[u,x_2,\frac{\left|x_2\right|}{g\left(x_2\right)}(\hat{z}+{\mathrm{\ξ}}_0),-(\hat{z}+{\mathrm{\ξ}}_1)\]}^T$ It is the recurrence input quantity of wave filter, φ=[g₁, g₂, g₃, g₄]^TIt it is the output of wave filter；t₀=0, t_i(i=0,1 ...) referring to select the switching time of optimal models, estimated value is reset at this moment；K is positive function, is used for ensureing that φ can with sufficiently fast speed Tracking φ₀.According to model (7) and formula (12), [t between two adjacent switching instants_i, t_i+1], have

φ^Tθ-g₅=g₆(13)

Wherein, g₅And g₆Be respectively d andFiltering output, can be provided by following formula:

$\left\{\begin{array}{cc}{g}_5\left(t\right)=0& t=t_i\\ {\stackrel{\·}{g}}_5\left(t\right)+{\mathrm{kg}}_5\left(t\right)=d& t\≠t_i\end{array}\right.,(i=0,1,...)---\left(14\right)$

$\left\{\begin{array}{cc}{g}_6\left(t\right)=0& t=t_i\\ {\stackrel{\·}{g}}_6\left(t\right)+{\mathrm{kg}}_6\left(t\right)={\stackrel{\·}{x}}_2\left(t\right)& t\≠t_i\end{array}\right.,(i=0,1,...)---\left(15\right)$

By assuming that 2 know, g₅Bounded and average are zero.Obtain from formula (13) and (15):

$g_6={\stackrel{\·}{g}}_2=x_2-{\mathrm{kg}}_2---\left(16\right)$

From formula (12):

${\∫}_{t_i}^{t_{i+1}}{\mathrm{\φ\φ}}^{T}dr\mathrm{\θ}={\∫}_{t_i}^{t_{i+1}}\mathrm{\φ}(g_5+g_6)dr---\left(17\right)$

In order to adapt to the saltus step of parameter, define discernibility matrixes:

$P\left(t\right)=\left\{\begin{array}{cc}{P}_0& t=t_0\\ {\&Integral;}_{t_i}^t{\mathrm{\&phi;\&phi;}}^{T}dr& t_i<t\&le;t_{i+1},(i=0,1,...)\end{array}\right.---\left(18\right)$

$Q\left(t\right)=\left\{\begin{array}{cc}{Q}_0& t=t_0\\ {\&Integral;}_{t_i}^t{\mathrm{\&phi;g}}_{6}dr& t_i<t\&le;t_{i+1},(i=0,1,...)\end{array}\right.---\left(19\right)$

Wherein P₀And Q₀Meet

${P_0}^{-1}{Q}_0\&Element;{\mathrm{\&Omega;}}_{\mathrm{\&theta;}}---\left(20\right)$

Then can build identifier

${\widehat{\mathrm{\&theta;}}}_{ident}\left(t\right)=P{\left(t_i\right)}^{-1}Q\left(t_i\right)t_i<t\&le;t_{i+1},(i=0,1,...)---\left(21\right)$

Wherein,It it is the parameter estimation of identification model.By (19) it can be seen that P (t) is a positive semidefinite matrix, so its eigenvalue is nonnegative value.A known determinant of a matrix is equal to the product of its all eigenvalues, and therefore, P (t) is reversible, and and if only if that its determinant is just.In order to avoid the problem that quantizes in matrix calculus, introduce a little positive number ε_PThreshold value as determinant judges reversibility, thus obtaining the reversible Rule of judgment of P (t) is:

det(P(t))≥ε_P(22)

By regulating parameter ε_PThe calculating frequency of parameter identification, less ε can be regulated_PMake more frequently to update identification model, but very big amount of calculation can be brought, and bigger ε_PCan cause that identification model can not follow the tracks of real system model in time.Therefore, it should select ε according to practical situation compromise_P。

To sum up, estimated value resets moment t_iJointly determined by condition (20) and (22).Reset moment sparse distribution on a timeline.By P (t) and Q (t) is reset, the estimated value of identifier will be only dependent upon current data.For identifier, when image parameter is undergone mutation, the data recorded before sudden change are by parameter estimation later for first replacement after not affecting sudden change, here it is identification model can effectively cope with the reason of parameter sudden change.Here one indexed variable sw of definition carrys out the replacement of labelling P (t) and Q (t):

$sw=\left\{\begin{array}{cc}1,& \begin{array}{cc}if& \det \left(P\right(t\left)\right)\&GreaterEqual;{\mathrm{\&epsiv;}}_{P}andP{\left(t\right)}^{-1}Q\left(t\right)\&Element;{\mathrm{\&Omega;}}_{\mathrm{\&theta;}}\end{array}\\ 0,& otherwise\end{array}\right.---\left(23\right)$

(iii) adaptive model: adopt discontinuous projection operator as adaptive law here, because it is able to ensure that estimates of parameters change in the interval of definition, definition

${\mathrm{Proj}}_{{\widehat{\mathrm{\&theta;}}}_a}\left(\mathrm{\&Delta;}\right)={\&lsqb;{\mathrm{Proj}}_{{\widehat{\mathrm{\&theta;}}}_{a1}}\left({\mathrm{\&Delta;}}_1\right),\mathrm{...},{\mathrm{Proj}}_{{\widehat{\mathrm{\&theta;}}}_{a4}}\left({\mathrm{\&Delta;}}_4\right)\&rsqb;}^T---\left(24\right)$

Wherein

${\mathrm{Proj}}_{{\widehat{\mathrm{\&theta;}}}_{ai}}\left({\mathrm{\&Delta;}}_i\right)=\left\{\begin{array}{cc}0,& if{\widehat{\mathrm{\&theta;}}}_{ai}={\mathrm{\&theta;}}_{imax}{\mathrm{and\&Delta;}}_i>0\\ 0,& if{\widehat{\mathrm{\&theta;}}}_{ai}={\mathrm{\&theta;}}_{imax}{\mathrm{and\&Delta;}}_i<0\\ {\mathrm{\&Delta;}}_i& otherwise\end{array}\right.---\left(25\right)$

Wherein, Δ_iIt it is the i-th element of vector Δ.So adaptive law is designed as

Wherein,For adaptive mode shape parameter,For identification model parameter；Γ is the adaptive learning factor, is a positive definite diagonal matrix,For auto-adaptive function.The parameter estimation of such adaptive law is improved.

3. handover mechanism and adjustable strategies.Matching system dynamic characteristic is carried out in order to select optimal models, need handover mechanism reasonable in design, it is mainly by selecting reasonably to switch index, adaptive model in system and discernibility matrixes are reset in real time, parameter is made to produce desirable saltus step in learning process, accelerate the learning process of adaptive law, follow the tracks of system model in time.

Define following performance index function

$J({\mathrm{\&Delta;}}^T,t)={\mathrm{\&mu;}}_{1}e{({\mathrm{\&Delta;}}^T,t)}^2+{\mathrm{\&mu;}}_2{\&Integral;}_{t-t_{\mathrm{\&epsiv;}}}^{t}e{({\mathrm{\&Delta;}}^T,t)}^{2}dr---\left(27\right)$

Wherein, t_εIt is the time period length of this target function, μ₁And μ₂It is positive number to be designed, e (Δ^T, t) it is estimation difference, is defined as

e(Δ^T, t)=Δ^Tφ(t)-g₆(t)(28)

The target function that formula (26) defines can react the estimation model degree of approximation to true model, if a model makes target function minimum, then representing in this moment, this model is optimal models, namely

$J^{*}=\min \{J\left({\widehat{\mathrm{\&theta;}}}_{f1}\right),J\left({\widehat{\mathrm{\&theta;}}}_{f2}\right),...,J\left({\widehat{\mathrm{\&theta;}}}_{fn}\right),J\left({\widehat{\mathrm{\&theta;}}}_{ident}\right),J\left({\widehat{\mathrm{\&theta;}}}_a\right)\}---\left(29\right)$

Wherein,It is the performance indications of each fixed model respectively,WithIt is the performance indications of identification model and adaptive model respectively, therefore, obtains optimized parameter and estimate

$\left\{\begin{array}{cc}\widehat{\mathrm{\&theta;}}\left(t\right)={\widehat{\mathrm{\&theta;}}}^{*}\left(t\right)& t=t_i\\ \stackrel{\&CenterDot;}{\widehat{\mathrm{\&theta;}}}\left(t\right)={\mathrm{Proj}}_{\widehat{\mathrm{\&theta;}}}\left({\mathrm{\&Gamma;}}_{\mathrm{\&tau;}}\right)& t_i<t\&le;t_{i+1},(i=0,1,\mathrm{...})\end{array}\right.---\left(30\right)$

Wherein,It is minimum target function J^*Corresponding model parameter.The flow process that parameter regulates is as shown in Figure 3.

Utilize MATLAB/Simulink that said method is emulated.The model parameter of system is set to a=-3.15, b=0.35, B=0.8, σ₀=11, σ₁=8.6, T_c=3, T_s=5,Being computed, the true value obtaining parameter is θ₁=2.86, θ₂=-35.86, θ₃=24.57, θ₄=31.43.The excursion assuming parameter is θ₁∈[1,51,θ₂∈[-37,-34],θ₃∈[22,26],θ₄∈ [30,33], by each parameter area trisection, the Along ent taking centre is fixed model, is therefore θ to its fixed model of each parameter₁=2.3,3.6}, θ₂=-36, and-35}, θ₃=23.3,24.6}, θ₄={ 31,32}, the fixed model of system has 16.The initial value being selected from adaptive model and identification model is all θ₁(0)=1, θ₂(0)=-37, θ₃(0)=26, θ₄(0)=30.State variable x in system₁(0)=x₂(0)=z (0)=ξ₁(0)=ξ₁(0).Controller parameter is chosen as λ=30, ρ=1, h₀=10, k₀=k₁=1, k=0.001, the adaptive learning factor is Γ=diag (15,500,6000,3000), and the reversible critical parameter of discernibility matrixes is ε_P=10^-12, the parameter of target function is μ₁=1, μ₂=5.

Assume that the unknown parameter of system exists following saltus step:

$\mathrm{\&theta;}=\left\{\begin{array}{cc}{\&lsqb;2.4,-35,25,30.5\&rsqb;}^T& t\&le;3\\ {\&lsqb;2.4,-35,23,32.5\&rsqb;}^T& 3<t\&le;6\\ {\&lsqb;2.4,-36,25,30.5\&rsqb;}^T& 6<t\&le;1\end{array}\right.$

Namely in the 3rd, 3s place parameter toward little saltus step, the 4th parameter toward big saltus step, other parameter constants；At 6s place, first parameter toward big saltus step, second parameter toward little saltus step, other parameter constants.This simulation algorithm adopts ode4, fixed step size 0.1ms.Under Stepped Impedance Resonators based on the contrast of the Self Adaptive Control of multi-model and tradition Self Adaptive Control tracking error as shown in Figure 4.

As can be seen from Figure 4, when there is saltus step in the location parameter in system, traditional Self Adaptive Control can not meet the requirement of Fast Convergent and less steady-state error, and the Self Adaptive Control based on multi-model can by the switching of model, effectively cope with the impact that system is caused by the sudden change of parameter, it is ensured that system has good transient state constringency performance and steady-state tracking precision.

Finally build the semi-matter simulating system based on RTW and xPCTarget, by experiment above-mentioned control algolithm is verified.Experimental system includes hardware components and software section.Hardware components has simulation computer, controlled material object and I/O interface.Simulation computer system adopts the structure of host target machine, is made up of two PC computers, and controlled material object is certain double axle table, and I/O interface includes measuring sensor and data transmission.Software section has MicrosoftWindowsXP, MATLAB, Simulink, RTW and xPCTarget.System hardware attachment structure is as shown in Figure 5.

Through parameter tuning repeatedly, choose one group of comparatively ideal parameter: controller parameter is λ=30, ρ=1, h₀=10, sliding formwork filtering observer parameter is k₀=k₁=1, the parameter of performance index function is μ₁=1, μ₂=2, parameter learning matrix is Γ=diag (0.5,0.7,1,0.3), and filter parameter is k=0.001, and it is ε that matrix sentences inverse parameter_P=10^-9.The same step signal that desired trajectory respectively desired trajectory is 0.2 selecting turntable and sinusoidal signal 0.2sin (π t).The experimental result obtained is as shown in Figure 6.

Contrast by experiment and analysis, it will be seen that, and general Self Adaptive Control contrasts, and the adaptive control system mapping based on multi-model is good, simultaneously less steady-state error, has reached to improve the purpose of turntable low-speed performance.

To sum up, these are only presently preferred embodiments of the present invention, be not intended to limit protection scope of the present invention.All within the spirit and principles in the present invention, any amendment of making, equivalent replacement, improvement etc., should be included within protection scope of the present invention.

Claims (3)

1. the servo system self-adaptive based on multi-model controls system, it is characterised in that this system includes multi-model parameter estimation module, handover mechanism module and adaptive controller, and wherein said servosystem is the controlled device of this adaptive control system；

Described multi-model parameter estimation module includes n fixed model, 1 identification model and an adaptive model；

Each model in described multi-model parameter estimation module exports one group of model parameter for described servosystem, and input is described handover mechanism module extremely；

Described handover mechanism module selects one group of model parameter making cost function minimum as optimal models parameter from many group models parameter, is input to adaptive controller；

The optimal models parameter of input is calculated acquisition Self Adaptive Control amount u, Self Adaptive Control amount u by adaptive control laws and inputs to controlled device by described adaptive controller；The input parameter of adaptive controller includes: the desired throughput of controlled device, optimal models parameter, output feedback amount and can not survey the filtering observation of parameter；The desired throughput of described controlled device includes angle and the angular velocity of expectation controlled device output；

Wherein output feedack amount is the real-time output of controlled device；

The described filtering observation that can not survey parameter is obtained by filtering observer, described filtering observer obtains the real-time output of controlled device, parameter of can not surveying in adaptive controller is once estimated by the closed loop observer in filtering observer, in accessory filter in filtering observer, the error once estimated is carried out quadratic estimate, then by twice, the filtering observation that can not survey parameter estimates that signal compound obtains；The filtering observation that can not survey parameter is inputted to adaptive controller；

Described fixed model is fixed the estimation of model parameter in the following way:

Static parameter first with servosystem mathematical model calculates the preset value obtaining a model parameter, and the excursion according to each model parameter of default settings, excursion is carried out point process such as m, each Along ent is to should an estimated value of parameter, the fixed model parameter of one fixed model output is that each parameter appoints the combination taking an Along ent estimated value, total n=(m-1)^aIndividual fixed model；

Described identification model includes low pass filter, discernibility matrixes module and recognition module, carries out the estimation of identification model parameter in identification model in the following way:

Described low pass filter with the output u of adaptive controller, controlled device real-time output x and can not survey parameter filtering observation composition input vector, wherein x includes real-time angular and the angular velocity of controlled device；Switching instant set in advance in low pass filter, low pass filter is filtered at each switching instant and exports the Real-Time Filtering value of above-mentioned input vector；

Described discernibility matrixes module includes discernibility matrixes P (t), Q (t) and preset initial value P thereof₀And Q₀, wherein P₀And Q₀Meet P₀ ^-1Q₀Bounded, and P (t) is reversible all the time；Discernibility matrixes P (t), Q (t) value real-time update: P (t) be the product of low pass filter output vector and its transposition from a upper switching instant to the integration of current time t, Q (t) is that the low pass filter output vector product with the angular velocity in x is from a upper switching instant to the integration of current time t；

Described recognition module is utilized as P^-1T the product of () and Q (t) instantaneous value is as identification model parameterInput is to described handover mechanism module；

Described adaptive model, with identification model parameter and optimal models parameter for reference, carries out the estimation of adaptive mode shape parameter in the following way:

Adaptive model arranges marking variable sw, if P (t) is reversible, andWithin the model parameter span set, then sw=1；Otherwise sw=0；

With the output x of the output u of adaptive controller and controlled device for input, at switching instant: when marking variable sw=1 and a upper switching instant handover mechanism module are output as identification model parameter, then adaptive mode shape parameterWhen a upper switching instant handover mechanism module is output as fixed model parameter, then adaptive mode shape parameterFor the output of a upper switching instant handover mechanism module, adaptive mode shape parameter in other situationsAdopt discontinuous projection operator；The parameter estimation result input of output adaptive model is to described handover mechanism module alternately.

2. a kind of servo system self-adaptive based on multi-model controls system as claimed in claim 1, it is characterised in that described servosystem is direct current generator servosystem, and its state space form being obtained direct current generator servo system models by LuGre model is $\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2={\mathrm{\&theta;}}_{1}u+{\mathrm{\&theta;}}_2{x}_2+{\mathrm{\&theta;}}_3\frac{\left|x_2\right|}{g\left(x_2\right)}z-{\mathrm{\&theta;}}_{4}z-d\\ y=x_1\end{array}\right.;$

Wherein, state variable x₁And x₂It is Angle Position and the angular velocity of servosystem respectively,WithIt is x respectively₁And x₂First derivative；θ₁, θ₂, θ₃And θ₄Being the unknown parameter characterizing system dynamic characteristic, u is the output of adaptive controller, and x is the output of controlled device, and x includes angle x₁With angular velocity x₂, z is average bristle amount of deflection,For the accessory filter estimated value to z；D is integrated disturbance, bounded and average is zero；G () is this Trebek friction model function；

The then input vector of low pass filter ${\mathrm{\&phi;}}_0\left(t\right)={\&lsqb;u,x_2,\frac{\left|x_2\right|}{g\left(x_2\right)}(\hat{z}+{\mathrm{\&xi;}}_0),-(\hat{z}+{\mathrm{\&xi;}}_1)\&rsqb;}^T;$

The adaptive law that the filtering being exports in described adaptive model is:

Wherein,For adaptive mode shape parameter,For identification model parameter,Optimal models parameter for a upper switching instant handover mechanism module output；Γ is the adaptive learning factor, is a positive definite diagonal matrix；For auto-adaptive function；For φ₀Low-pass filter value, γ filter tracking error；J^*For the optimal value of performance index function, $J^{*}=\min \{J\left({\widehat{\mathrm{\&theta;}}}_{f1}\right),J\left({\widehat{\mathrm{\&theta;}}}_{f2}\right),...,J\left({\widehat{\mathrm{\&theta;}}}_{fn}\right),J\left({\widehat{\mathrm{\&theta;}}}_{ident}\right),J\left({\widehat{\mathrm{\&theta;}}}_a\right)\};$ Parameter estimation result for n fixed model；J () is performance index function.

3. a kind of servo system self-adaptive based on multi-model controls system as claimed in claim 2, it is characterised in that described filtering observer is:

$\hat{z}=x_2-\frac{\left|x_2\right|}{g\left(x_2\right)}\hat{z}$

WhereinIt it is the estimated value to z；Described accessory filter is

${\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_0=-\frac{\left|x_2\right|}{g\left(x_2\right)}{\mathrm{\&xi;}}_0-k_0\frac{\left|x_2\right|}{g\left(x_2\right)}\mathrm{\&gamma;}$

${\stackrel{\&CenterDot;}{\mathrm{\&xi;}}}_1=-\frac{\left|x_2\right|}{g\left(x_2\right)}{\mathrm{\&xi;}}_1+k_1\mathrm{\&gamma;}$

Wherein ξ₀And ξ₁It is to observer estimation differenceObservation,WithIt is ξ₀And ξ₁First derivative, k₀And k₁It it is adjustable gain.