CN104614984A - High-precision control method of motor position servo system - Google Patents

Abstract

The invention provides a high-precision control method of motor position servo system; the implementation of the system comprises the following steps: step 1, establishing a motor position servo system model; step 2, designing a high-precision motor controller based on limited time interference estimation; and step 3, adjusting parameters of the high-precision motor control law based on limited time interference estimation, so as to make the system satisfy the control performance index. The provided high-precision control method of motor position servo system establishes the motor position servo system model aiming at the features of the motor position servo system, and designs the high-precision motor controller based on the limited time interference estimation, so as to estimate and compensate unmodeled interference of the system at real time; the total disturbance of the system can be well estimated by adjusting the parameters of the control law, thereby being effectively solving the uncertain nonlinear problem of the motor servo system; the integral robust item ensures the overall stability of the system.

Description

A kind of high-accuracy control method of electric machine position servo system

Technical field

The present invention relates to electric machine position servo control system technical field, in particular to a kind of high-accuracy control method of electric machine position servo system.

Background technology

Because widespread use in the industry, the high performance control of motor-driven kinematic system has caused the extensive concern comprising slip-stick artist and scientist.But, be not easy for the high performance controller of Servo System Design, due to the cause of working condition variation, external disturbance and modeling error, the accurate model of actual industrial process is difficult to obtain, and the various faults of system also will cause the uncertainty of model, that is the uncertainty of model extensively exists in the controls, and therefore designer runs into the non-linear of non-modeling such as a lot of model uncertainties, particularly unstructured uncertainty etc. possibly.These uncertain factors may the severe exacerbation control performance that can obtain, thus causes low control accuracy, and limit cycle is shaken, not even stability.For known non-linear, feedback linearization technical finesse can be passed through.But how accurately the mathematical model of no matter kinematic nonlinearity identification, all can not obtain the whole non-linear behavior of actual nonlinear system, and then perfectly compensate.All the time there is the non-modeling can not simulated with clear and definite function non-linear.

Traditional control method is difficult to the tracking accuracy requirement meeting Uncertain nonlinear, therefore needs study simple and practical and meet the control method of performance requirements.In recent years, various Advanced Control Strategies is applied to motor servo system, as Sliding mode variable structure control, Robust Adaptive Control, ADAPTIVE ROBUST etc.But the equal more complicated of above-mentioned control strategy Controller gain variations, is not easy to Project Realization

For the feature of Uncertain nonlinear in motor servo, establish the model of system, and devising electric machine position servo system finite time interference observer and rise integration Robust Control Law on this basis respectively, the non-modeling interference of estimating system is also compensated in control inputs.

Summary of the invention

The present invention for solving Uncertain nonlinear problem in electric machine position servo system, and then proposes a kind of high-accuracy control method of electric machine position servo system.

Above-mentioned purpose of the present invention is realized by the technical characteristic of independent claims, and dependent claims develops the technical characteristic of independent claims with alternative or favourable mode.

For reaching above-mentioned purpose, the technical solution adopted in the present invention is as follows:

A high-accuracy control method for electric machine position servo system, comprises the following steps:

Step 1, set up electric machine position servo system model;

Step 2, design motor high-precision controller based on finite time Interference Estimation; And

Step 3, the parameter of the high-precision control law of motor based on a kind of finite time Interference Estimation is regulated to make system meet Control performance standard.

In a further embodiment, the high-accuracy control method of the electric machine position servo system proposed in previous embodiment of the present invention, for the feature of Uncertain nonlinear in motor servo, establish the model of system, and devising electric machine position servo system finite time interference observer and rise integration Robust Control Law on this basis respectively, the non-modeling interference of estimating system is also compensated in control inputs.

Have above embodiment of the present invention known, the high-accuracy control method of electric machine position servo system of the present invention, its beneficial effect is:

1, for the feature of electric machine position servo system, establish electric machine position servo system model, and design is based on the motor high-precision controller of finite time Interference Estimation, estimation is carried out and real-Time Compensation to the non-modeling interference of system, total disturbance of energy good estimation system is regulated by control law parameter, effectively can solve motor servo system Uncertain nonlinear problem, integration robust wants the stability that ensure that overall system;

2, under above-mentioned disturbed condition, Systematical control precision meets performance index;

3, this invention simplifies Controller gain variations, simulation result indicates its validity.

As long as should be appreciated that aforementioned concepts and all combinations of extra design described in further detail below can be regarded as a part for subject matter of the present disclosure when such design is not conflicting.In addition, all combinations of theme required for protection are all regarded as a part for subject matter of the present disclosure.

The foregoing and other aspect of the present invention's instruction, embodiment and feature can be understood by reference to the accompanying drawings from the following description more all sidedly.Feature and/or the beneficial effect of other additional aspect of the present invention such as illustrative embodiments will be obvious in the following description, or by learning in the practice of the embodiment according to the present invention's instruction.

Accompanying drawing explanation

Accompanying drawing is not intended to draw in proportion.In the accompanying drawings, each identical or approximately uniform ingredient illustrated in each figure can represent with identical label.For clarity, in each figure, not each ingredient is all labeled.Now, the embodiment of various aspects of the present invention also will be described with reference to accompanying drawing by example, wherein:

Fig. 1 is typical motor actuating unit schematic diagram.

Fig. 2 is the control strategy figure of the high-accuracy control method of electric machine position servo system disclosed by the invention.

Fig. 3 is the schematic diagram of expectation trace command disclosed by the invention.

Fig. 4 is controller input voltage u-curve under interference effect, and controller input voltage meets the input range of-10V ~+10V, realistic application, large interference during the added interference of the system that it can also be seen that in addition.

Fig. 5 is Interference Estimation and Interference Estimation graph of errors.

Fig. 6 is tracking error curve.

Embodiment

In order to more understand technology contents of the present invention, institute's accompanying drawings is coordinated to be described as follows especially exemplified by specific embodiment.

Each side with reference to the accompanying drawings to describe the present invention in the disclosure, shown in the drawings of the embodiment of many explanations.Embodiment of the present disclosure must not be intended to comprise all aspects of the present invention.Be to be understood that, multiple design presented hereinbefore and embodiment, and those designs described in more detail below and embodiment can in many ways in any one is implemented, this should be design disclosed in this invention and embodiment is not limited to any embodiment.In addition, aspects more disclosed by the invention can be used alone, or otherwisely anyly appropriately combinedly to use with disclosed by the invention.

Shown in composition graphs 1, Fig. 2, according to asked price embodiment of the present invention, a kind of high-accuracy control method of electric machine position servo system, its realization comprises the following steps:

Step 1, set up electric machine position servo system model;

Step 2, design motor high-precision controller based on finite time Interference Estimation; And

Step 3, the parameter of the high-precision control law of motor based on a kind of finite time Interference Estimation is regulated to make system meet Control performance standard.

Be to be understood that, shown in composition graphs 2, the high-accuracy control method of the electric machine position servo system that this embodiment proposes, for the feature of Uncertain nonlinear in motor servo, establish the model of system, and devising electric machine position servo system finite time interference observer and rise integration Robust Control Law on this basis respectively, the non-modeling interference of estimating system is also compensated in control inputs.

Shown in accompanying drawing, exemplary explanation is done to the specific implementation of These steps.

Step 1, set up electric machine position servo system model

Figure 1 shows that typical motor actuating unit is illustrated, according to Newton second law, the kinetic model equation of motor inertia load can be expressed as:

$m\stackrel{\·\·}{y}=k_{f}u-b\stackrel{\·}{y}-f(y,\stackrel{\·}{y},t)---\left(1\right)$

In formula, y represents angular displacement, and m represents inertia load, k _frepresent torque coefficient, u is Systematical control input, and b represents viscosity friction coefficient, and f represents other non-modeling interference, such as non-linear friction, external disturbance and Unmarried pregnancy.

Convert aforementioned (1) formula to state space form, as follows:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=\frac{k_f}{m}u-\frac{b}{m}{x}_2-d(x,t)\end{array}\right.---\left(2\right)$

Wherein x=[x ₁, x ₂] ^trepresent the state vector of position and speed; represent and concentrate interference.

To be illustrated by the typical electric machine actuating mechanism shown in earlier figures 1, generally, the unstructured uncertainty d (x, t) of system, obviously it can not specify modeling, but the Unmarried pregnancy of system and disturb always bounded.Thus, below suppose always to set up:

Suppose that 1:d (x, t) is smooth enough, namely

$\begin{array}{ccc}\left|d(x,t)\right|\≤{\mathrm{\δ}}_1& \left|\stackrel{\·}{d}(x,t)\right|\≤{\mathrm{\δ}}_2& \left|\stackrel{\·\·}{d}(x,t)\right|\≤{\mathrm{\δ}}_3\end{array}---\left(3\right)$

Wherein δ ₁, δ ₂, δ ₃known.

Step 2, design motor high-precision controller based on finite time Interference Estimation

Concrete steps are as follows:

Step 2-1, build the finite time interference observer of motor according to formula (2)

The interference observer of the finite time of a d (x, t) is designed by (2) formula, as follows:

$\begin{array}{c}{\stackrel{\·}{e}}_0=v_0+\frac{k_f}{m}u-\frac{b}{m}{x}_2,\\ {\stackrel{\·}{e}}_1=v_1=\stackrel{\·}{\hat{d}},{\stackrel{\·}{e}}_2=v_2=\stackrel{\·}{\widehat{\stackrel{\·}{d}}}\\ v_0={-\mathrm{\λ}}_0{|e_0-x_2|}^{2/3}\mathrm{sgn}(e_0-x_2)+e_1\\ v_1={-\mathrm{\λ}}_1{|e_1-v_0|}^{1/2}\mathrm{sgn}(e_0-v_0)+e_2\\ v_2={-\mathrm{\λ}}_2\mathrm{sgn}(e_2-v_1)\end{array}---\left(4\right)$

There is a time T ₁, when time t is greater than time constant T ₁time, wherein λ ₀, λ ₁, λ ₂for design parameter.

Define one group of saturation function:

$\mathrm{sat}\left(\tilde{d}\right)=\left\{\begin{array}{cc}{\mathrm{\δ}}_1& \mathrm{if}\left|\tilde{d}\right|>{\mathrm{\δ}}_1\\ \tilde{d}& \mathrm{if}\left|\tilde{d}\right|\≤{\mathrm{\δ}}_1\end{array}\right.\mathrm{sat}\left(\stackrel{\·}{\tilde{d}}\right)=\left\{\begin{array}{cc}{\mathrm{\δ}}_2& \mathrm{if}\left|\stackrel{\·}{\tilde{d}}\right|>{\mathrm{\δ}}_2\\ \stackrel{\·}{\tilde{d}}& \mathrm{if}\left|\stackrel{\·}{\tilde{d}}\right|\≤{\mathrm{\δ}}_2\end{array}\right.\mathrm{sat}\left(\stackrel{\·\·}{\tilde{d}}\right)=\left\{\begin{array}{cc}{\mathrm{\δ}}_3& \mathrm{if}\left|\stackrel{\·\·}{\tilde{d}}\right|>{\mathrm{\δ}}_3\\ \stackrel{\·\·}{\tilde{d}}& \mathrm{if}\left|\stackrel{\·\·}{\tilde{d}}\right|\≤{\mathrm{\δ}}_3\end{array}\right.---\left(5\right)$

By formula (5) and aforesaid time T ₁can obtain:

$\begin{array}{ccc}\begin{array}{cc}\tilde{d}\&le;{\mathrm{\&delta;}}_1& \&Exists;T_1,\&ForAll;t<T_1\\ \tilde{d}=0& \&Exists;T_1,\&ForAll;t\&GreaterEqual;T_1.\end{array}& \begin{array}{cc}\stackrel{\&CenterDot;}{\tilde{d}}\&le;{\mathrm{\&delta;}}_2& \&Exists;T_1,\&ForAll;t<T_1\\ \stackrel{\&CenterDot;}{\tilde{d}}=0& \&Exists;T_1,\&ForAll;t\&GreaterEqual;T_1.\end{array}& \begin{array}{cc}\stackrel{\&CenterDot;\&CenterDot;}{\tilde{d}}{\&le;\mathrm{\&delta;}}_3& \&Exists;T_1,\&ForAll;t<T_1\\ \stackrel{\&CenterDot;\&CenterDot;}{\tilde{d}}=0& \&Exists;T_1,\&ForAll;t\&GreaterEqual;T_1.\end{array}\end{array}---\left(6\right)$

Step 2-2, design motor high-precision controller based on finite time Interference Estimation

Specifically comprise the following steps:

Define one group of function as follows:

$z_2={\stackrel{\&CenterDot;}{z}}_1+k_1{z}_1=x_2-x_{2\mathrm{eq}},x_{2\mathrm{eq}}={\stackrel{\&CenterDot;}{x}}_{1d}-k_1{z}_1---\left(7\right)$

$\mathrm{\&gamma;}={\stackrel{\&CenterDot;}{z}}_2+k_2{z}_2$

Wherein z ₁=x ₁-x _1dt () is output tracking error, k ₁>0 and k ₂>0 is feedback gain;

Due to G (s)=z ₁(s)/z ₂(s)=1/ (s+k ₁) be a stable transport function, allow z ₁very little or to level off to zero be exactly allow z ₂very little or level off to zero;

Therefore, Controller gain variations is transformed into and allows z ₂little as far as possible or level off to zero;

Can be obtained by formula (7):

$\mathrm{\&gamma;}={\stackrel{\&CenterDot;}{x}}_2-{\stackrel{\&CenterDot;}{x}}_{2\mathrm{eq}}+k_2{z}_2---\left(8\right)$

Wushu (2) substitutes into and can obtain:

$\mathrm{\&gamma;}=\frac{k_f}{m}u-\frac{b}{m}{x}_2-d(x,t)-{\stackrel{\&CenterDot;}{x}}_{2\mathrm{eq}}+k_2{z}_2---\left(9\right)$

Based on Interference Estimation , the robust controller merging FTDO is as follows:

$\begin{array}{c}u=\frac{m}{k_f}(u_a+u_s)u_s=u_{s1}+u_{s2}\\ u_a={\stackrel{\&CenterDot;}{x}}_{2\mathrm{eq}}+\frac{b}{m}{x}_2+\hat{d}-k_2{z}_2\\ u_{s1}=-k_r{z}_2\end{array}---\left(10\right)$

Wherein k _r>0 is a feedback gain.

Wushu (10) substitutes into formula (9), can obtain the dynamic equation of γ:

$\mathrm{\&gamma;}={-k}_r{z}_2+u_{s2}+\tilde{d}---\left(11\right)$

In order to eliminate the impact of Interference Estimation error, design the integration robust item based on rise, as follows:

$u_{s2}=-{\&Integral;}_0^t[k_r{k}_2{z}_2+\mathrm{\&beta;sign}\left(z_2\right)]\mathrm{d\&tau;}---\left(12\right)$

Wherein β >0 is designing gain.

Can be obtained by formula (11) and formula (12):

$\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}=-k_r{\stackrel{\&CenterDot;}{z}}_2+{\stackrel{\&CenterDot;}{u}}_{s2}+\stackrel{\&CenterDot;}{\tilde{d}}\\ ={-k}_r{\stackrel{\&CenterDot;}{z}}_2+\stackrel{\&CenterDot;}{\tilde{d}}-k_r{k}_2{z}_2-\mathrm{\&beta;sign}\left(z_2\right)\end{array}---\left(13\right)$

As auxiliary function L (t) of giving a definition:

$L\left(t\right)=\mathrm{\&gamma;}[\stackrel{\&CenterDot;}{\tilde{d}}-\mathrm{\&beta;sign}\left(z_2\right)]---\left(14\right)$

If gain beta meets following condition:

$\mathrm{\&beta;}\&GreaterEqual;{\mathrm{\&delta;}}_2+\frac{1}{k_2}{\mathrm{\&delta;}}_3---\left(15\right)$

Then as undefined function P (t) is just always:

$P\left(t\right)=\mathrm{\&beta;}\left|z_2\left(0\right)\right|-z_2\left(0\right)\stackrel{\&CenterDot;}{d}\left(0\right)-{\&Integral;}_0^{t}L\left(v\right)\mathrm{dv}---\left(16\right)$

Step 3, regulate the parameter k of the high-precision control law u of motor based on finite time Interference Estimation ₁, k ₂, k _r, λ ₀, λ ₁, λ ₂, beta system meets Control performance standard.

Lyapunov function is selected to verify the stable of the system of previous designs in the present embodiment.

Theorem 1: finite time interference observer (4) and saturation function (8), β meets formula (15), selects enough large k ₂, k _r, make as undefined matrix A positive definite

$A=\left[\begin{array}{cc}-k_r& \frac{1}{2}\\ \frac{1}{2}& -k_2\end{array}\right]---\left(17\right)$

The high-precision controller based on finite time Interference Estimation (10) then designed can ensure all signal boundeds of system, and can ensure the progressive tracking performance of output signal, namely as t → ∞, and z ₂(t) → 0, z ₁(t) → 0.

Prove: definition Lyapunov function is as follows:

$V=\frac{1}{2}{z}_2^2+\frac{1}{2}{\tilde{d}}^2+\frac{1}{2}{\mathrm{\&gamma;}}^2+P\left(t\right)---\left(18\right)$

Differential (18), substitute into (7), (13), (14) can obtain

$\stackrel{\&CenterDot;}{V}=-\left[\begin{array}{cc}\mathrm{\&gamma;}& z_2\end{array}\right]A\left[\begin{array}{c}\mathrm{\&gamma;}\\ z_2\end{array}\right]+\tilde{d}\stackrel{\&CenterDot;}{\tilde{d}}---\left(19\right)$

Work as 0<t<T ₁time

$\begin{array}{c}\stackrel{\&CenterDot;}{V}=-\left[\begin{array}{cc}\mathrm{\&gamma;}& z_2\end{array}\right]A\left[\begin{array}{c}\mathrm{\&gamma;}\\ z_2\end{array}\right]+\tilde{d}\stackrel{\&CenterDot;}{\tilde{d}}\&le;-\left[\begin{array}{cc}\mathrm{\&gamma;}& z_2\end{array}\right]A\left[\begin{array}{c}\mathrm{\&gamma;}\\ z_2\end{array}\right]+{\mathrm{\&delta;}}_1{\mathrm{\&delta;}}_2\\ \&le;{-\mathrm{\&lambda;}}_{\min }\left(A\right)({\mathrm{\&gamma;}}^2+z_2^2)+\mathrm{\&epsiv;}\end{array}---\left(20\right)$

As t>=T ₁time

$\stackrel{\&CenterDot;}{V}=-\left[\begin{array}{cc}\mathrm{\&gamma;}& z_2\end{array}\right]A\left[\begin{array}{c}\mathrm{\&gamma;}\\ z_2\end{array}\right]+\tilde{d}\stackrel{\&CenterDot;}{\tilde{d}}\&le;-\left[\begin{array}{cc}\mathrm{\&gamma;}& z_2\end{array}\right]A\left[\begin{array}{c}\mathrm{\&gamma;}\\ z_2\end{array}\right]\&le;-{\mathrm{\&lambda;}}_{\min }\left(A\right)({\mathrm{\&gamma;}}^2+z_2^2)=-W---\left(21\right)$

As t → ∞, z ₂(t) → 0, z ₁(t) → 0.

Therefore controller is convergence, and system is stable.

Below in conjunction with concrete example and parameter definition, the realization of the high-accuracy control method of the electric machine position servo system of previous embodiment and effect are described further.

Get following parameter in simulations and modeling carried out to system:

m＝0.01kg·m ²,k _f＝5,b＝1.25N·s/m。

Get controller parameter k ₁=100, k ₂=200, λ ₀=100, λ ₁=400, λ ₂=1500; k _r=175; β=20.

PID controller parameter is k _p=90, k _i=70, k _d=0.3.

Position angle input signal unit rad.

Add one when 20s and disturb f=2.5cos (π t) Nm outward.

Control law action effect schematically as follows, wherein: Fig. 3 be expect trace command signal; Fig. 4 is controller input voltage u-curve under interference effect, and controller input voltage meets the input range of-10V ~+10V, realistic application; Fig. 5 is the contrast of Interference Estimation and Interference Estimation graph of errors; Fig. 6 is the signal of tracking error curve.

From above-mentioned graphic comparison, the algorithm that the present invention proposes can estimate interference value accurately under simulated environment, and compared to traditional PID control, the controller of the present invention's design can greatly improve the control accuracy that there is system under large disturbed condition.Result of study shows that method in this paper can meet performance index under Uncertain nonlinear impact.

Although the present invention with preferred embodiment disclose as above, so itself and be not used to limit the present invention.Persond having ordinary knowledge in the technical field of the present invention, without departing from the spirit and scope of the present invention, when being used for a variety of modifications and variations.Therefore, protection scope of the present invention is when being as the criterion depending on those as defined in claim.

Claims (4)

1. a high-accuracy control method for electric machine position servo system, is characterized in that, the realization of this high-accuracy control method comprises the following steps:

Step 1, set up electric machine position servo system model;

Step 2, design motor high-precision controller based on finite time Interference Estimation; And

Step 3, the parameter of the high-precision control law of motor based on finite time Interference Estimation is regulated to make system meet Control performance standard.

2. the high-accuracy control method of electric machine position servo system according to claim 1, is characterized in that, the realization of abovementioned steps 1 comprises:

According to Newton second law, by the kinetic model the Representation Equation of motor inertia load be:

$m\stackrel{\&CenterDot;\&CenterDot;}{y}=k_{f}u-b\stackrel{\&CenterDot;}{y}-f(y,\stackrel{\&CenterDot;}{y},t)---\left(1\right)$

In formula, y represents angular displacement, and m represents inertia load, k _frepresent torque coefficient, u is Systematical control input, and b represents viscosity friction coefficient, and f represents other non-modeling interference, comprises non-linear friction, external disturbance and Unmarried pregnancy;

Convert aforementioned (1) formula to state space form, as follows:

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_1=x_2\\ {\stackrel{\&CenterDot;}{x}}_2=\frac{k_f}{m}u-\frac{b}{m}{x}_2-d(x,t)\end{array}\right.---\left(2\right)$

Wherein x=[x ₁, x ₂] ^trepresent the state vector of position and speed; represent and concentrate interference;

Due to system Unmarried pregnancy and disturb always bounded, thus, below suppose always to set up:

Suppose that 1:d (x, t) is smooth enough, namely

$\begin{array}{ccc}\left|d(x,t)\right|\&le;{\mathrm{\&delta;}}_1& \left|\stackrel{\&CenterDot;}{d}(x,t)\right|\&le;{\mathrm{\&delta;}}_2& |\stackrel{\&CenterDot;\&CenterDot;}{d}\end{array},(x,t)|\&le;{\mathrm{\&delta;}}_3---\left(3\right)$

Wherein δ ₁, δ ₂, δ ₃known.

3. the high-accuracy control method of electric machine position servo system according to claim 2, is characterized in that, abovementioned steps 2 designs the realization of the motor high-precision controller based on finite time Interference Estimation, and it comprises the following steps:

Step 2-1, build the finite time interference observer of motor according to formula (2)

The interference observer of the finite time of a d (x, t) is designed by (2) formula, as follows:

${\stackrel{\&CenterDot;}{e}}_0=v_0+\frac{k_f}{m}u-\frac{b}{m}{x}_2,$

${\stackrel{\&CenterDot;}{e}}_1=v_1=\stackrel{\&CenterDot;}{\hat{d}},{\stackrel{\&CenterDot;}{e}}_2=v_2=\stackrel{\&CenterDot;}{\widehat{\stackrel{\&CenterDot;}{d}}}$

v ₀＝-λ ₀|e ₀-x ₂| ^2/3sgn(e ₀-x ₂)+e ₁(4)

v ₁＝-λ ₁|e ₁-v ₀| ^1/2sgn(e ₀-v ₀)+e ₂

v ₂＝-λ ₂sgn(e ₂-v ₁)

There is a time T ₁, when time t is greater than time constant T ₁time, wherein λ ₀, λ ₁, λ ₂for design parameter;

Then, one group of saturation function is defined:

$\mathrm{sat}\left(\tilde{d}\right)=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_1& \mathrm{if}\left|\tilde{d}\right|>{\mathrm{\&delta;}}_1\\ \tilde{d}& \mathrm{if}\left|\tilde{d}\right|\&le;{\mathrm{\&delta;}}_1\end{array}\right.\mathrm{sat}\left(\stackrel{\&CenterDot;}{\tilde{d}}\right)=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_2& \mathrm{if}\left|\stackrel{\&CenterDot;}{\tilde{d}}\right|>{\mathrm{\&delta;}}_2\\ \stackrel{\&CenterDot;}{\tilde{d}}& \mathrm{if}\left|\stackrel{\&CenterDot;}{\tilde{d}}\right|\&le;{\mathrm{\&delta;}}_2\end{array}\right.\mathrm{sat}\left(\stackrel{\&CenterDot;\&CenterDot;}{\tilde{d}}\right)=\left\{\begin{array}{cc}{\mathrm{\&delta;}}_3& \mathrm{if}\left|\stackrel{\&CenterDot;\&CenterDot;}{\tilde{d}}\right|>{\mathrm{\&delta;}}_3\\ \stackrel{\&CenterDot;\&CenterDot;}{\tilde{d}}& \mathrm{if}\left|\stackrel{\&CenterDot;\&CenterDot;}{\tilde{d}}\right|\&le;{\mathrm{\&delta;}}_3\end{array}\right.---\left(5\right)$

By formula (5) and aforesaid time T ₁can obtain:

$\begin{array}{cccccc}\tilde{d}\&le;{\mathrm{\&delta;}}_1& \&Exists;T_1,\&ForAll;t<T_1& \stackrel{\&CenterDot;}{\tilde{d}}\&le;{\mathrm{\&delta;}}_2& \&Exists;T_1,\&ForAll;t<T_1& \stackrel{\&CenterDot;\&CenterDot;}{\tilde{d}}\&le;{\mathrm{\&delta;}}_3& \&Exists;T_1,\&ForAll;t<T_1\\ \tilde{d}=0& \&Exists;T_1,\&ForAll;t\&GreaterEqual;T_1.& \stackrel{\&CenterDot;}{\tilde{d}}=0& \&Exists;T_1,\&ForAll;t\&GreaterEqual;T_1.& \stackrel{\&CenterDot;\&CenterDot;}{\tilde{d}}=0& \&Exists;T_1,\&ForAll;t\&GreaterEqual;T_1.\end{array}---\left(6\right)$

Step 2-2, design motor high-precision controller based on finite time Interference Estimation

First one group of function is defined as follows:

$z_2={\stackrel{\&CenterDot;}{z}}_1+k_1{z}_1=x_2-x_{2\mathrm{eq}},x_{2\mathrm{eq}}={\stackrel{\&CenterDot;}{x}}_{1d}-k_1{z}_1---\left(7\right)$

$\mathrm{\&gamma;}={\stackrel{\&CenterDot;}{z}}_2+k_2{z}_2$

Wherein z ₁=x ₁-x _1dt () is output tracking error, k ₁>0 and k ₂>0 is feedback gain;

Due to G (s)=z ₁(s)/z ₂(s)=1/ (s+k ₁) be a stable transport function, allow z1 is very little or to level off to zero be exactly allow z ₂very little or level off to zero;

Therefore, Controller gain variations is transformed into and allows z ₂little as far as possible or level off to zero;

Can be obtained by formula (7):

$\mathrm{\&gamma;}={\stackrel{\&CenterDot;}{x}}_2-{\stackrel{\&CenterDot;}{x}}_{2\mathrm{eq}}+k_2{z}_2---\left(8\right)$

Wushu (2) substitutes into and can obtain:

$\mathrm{\&gamma;}=\frac{k_f}{m}u-\frac{b}{m}{x}_2-d(x,t)-{\stackrel{\&CenterDot;}{x}}_{2\mathrm{eq}}+k_2{z}_2---\left(9\right)$

Based on Interference Estimation the robust controller merging FTDO is as follows:

$u=\frac{m}{k_f}(u_a+u_s)u_s=u_{s1}+u_{s2}$

$u_a={\stackrel{\&CenterDot;}{x}}_{2\mathrm{eq}}+\frac{b}{m}{x}_2+\hat{d}-k_2{z}_2---\left(10\right)$

u _s1＝-k _rz ₂

Wherein k _r>0 is a feedback gain;

Wushu (10) substitutes into formula (9), can obtain the dynamic equation of γ:

$\mathrm{\&gamma;}=-k_r{z}_2+u_{s2}+\tilde{d}---\left(11\right)$

In order to eliminate the impact of Interference Estimation error, design the integration robust item based on rise, as follows:

$u_{s2}=-{\&Integral;}_0^t[k_r{k}_2{z}_2+\mathrm{\&beta;sign}\left(z_2\right)]\mathrm{d\&tau;}---\left(12\right)$

Wherein β >0 is designing gain;

Can be obtained by formula (11) and formula (12):

$\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&gamma;}}=-k_r{\stackrel{\&CenterDot;}{z}}_2+{\stackrel{\&CenterDot;}{u}}_{s2}+\stackrel{\&CenterDot;}{\tilde{d}}\\ =-k_r{\stackrel{\&CenterDot;}{z}}_2+\stackrel{\&CenterDot;}{\tilde{d}}-k_r{k}_2{z}_2-\mathrm{\&beta;sign}\left(z_2\right)\end{array}---\left(13\right)$

Then, auxiliary function L (t) is defined:

$L\left(t\right)=\mathrm{\&gamma;}[\stackrel{\&CenterDot;}{\tilde{d}}-\mathrm{\&beta;sign}\left(z_2\right)]---\left(14\right)$

If gain beta meets following condition:

$\mathrm{\&beta;}\&GreaterEqual;{\mathrm{\&delta;}}_2+\frac{1}{k_2}{\mathrm{\&delta;}}_3---\left(15\right)$

Then as undefined function P (t) is just always:

$P\left(t\right)=\mathrm{\&beta;}\left|z_2\left(0\right)\right|-z_2\left(0\right)\stackrel{\&CenterDot;}{d}\left(0\right)-{\&Integral;}_0^{t}L\left(v\right)\mathrm{dv}.---\left(16\right)$

4. the high-accuracy control method of electric machine position servo system according to claim 3, is characterized in that, in abovementioned steps 3, by regulating the parameter k based on the high-precision control law u of motor of finite time Interference Estimation ₁, k ₂, k _r, λ ₀, λ ₁, λ ₂, β makes system meet Control performance standard.