CN104614984B - 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 motor position servo system

Technical field

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

Background technology

Because extensive application in the industry, the high performance control of motor-driven motor system has been caused including work Cheng Shi and scientist are in interior extensive concern.However, be not easy to for the high performance controller of Servo System Design, due to work The reason of situation variation, external disturbance and modeling error, the accurate model of actual industrial process is hardly resulted in, and system is each Plant the uncertainty that failure also leads to model, that is to say, that the uncertainty of model is widely present in the controls, therefore It is non-linear that designer is likely to encounter that many model uncertainties, particularly unstructured uncertainty etc. do not model. These uncertain factors may the control performance that can obtain of severe exacerbation, so as to cause low control accuracy, limit cycle shake Swing, or even unstability.It is non-linear for known, feedback linearization technical finesse can be passed through.But, no matter dynamic non-thread Property identification how accurate mathematical model, be impossible to obtain the whole non-linear behavior of actual nonlinear system, Jin Erjin The perfect compensation of row.All the time there is not modeling of can not being simulated with clear and definite function non-linear.

Traditional control method is difficult to meet the tracking accuracy of Uncertain nonlinear and requires, it is therefore desirable to study it is simple and practical and Meet the control method of performance requirements.In recent years, various Advanced Control Strategies are applied to motor servo system, and such as sliding formwork becomes Structure control, Robust Adaptive Control, ADAPTIVE ROBUST etc..But above-mentioned control strategy controller design is more complicated, is difficult In Project Realization

For the characteristics of Uncertain nonlinear, establishing the model of system in motor servo, and set respectively on this basis Motor position servo system finite time interference observer and rise integration Robust Control Laws are counted, estimating system does not model interference And be compensated by control input.

The content of the invention

The present invention proposes that a kind of motor position is watched to solve the problems, such as Uncertain nonlinear in motor position servo system The high-accuracy control method of dress system.

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

A kind of high-accuracy control method of motor position servo system, comprises the following steps：

Step 1, set up motor position servo system model；

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

Step 3, regulation cause system based on a kind of parameter of the high-precision control law of motor of finite time Interference Estimation Meet Control performance standard.

In a further embodiment, the high accuracy of the motor position servo system for proposing in previously described embodiments of the present invention Control method, for the characteristics of Uncertain nonlinear, establishing the model of system in motor servo, and sets respectively on this basis Motor position servo system finite time interference observer and rise integration Robust Control Laws are counted, estimating system does not model interference And be compensated by control input.

There is above embodiment of the present invention to understand, the high-accuracy control method of the motor position servo system of the present invention, Its advantage is：

1st, for motor position servo system the characteristics of, motor position servo system model is established, and design is based on and has The motor high-precision controller of Interference Estimation between in limited time, interference is not modeled to system to be carried out estimating and real-Time Compensation, by control Total disturbance of rule parameter regulation energy good estimation system, energy effectively solving motor servo system Uncertain nonlinear problem, integration Robust is wanted to ensure that the stability that system is overall；

2nd, system control accuracy meets performance indications under above-mentioned disturbed condition；

3rd, this invention simplifies controller design, simulation result indicates its effectiveness.

As long as it should be appreciated that all combinations of aforementioned concepts and the extra design for describing in greater detail below are at this A part for the subject matter of the disclosure is can be viewed as in the case that the design of sample is not conflicting.In addition, required guarantor All combinations of the theme of shield are considered as a part for the subject matter of the disclosure.

Can be more fully appreciated with from the following description with reference to accompanying drawing present invention teach that foregoing and other aspect, reality Apply example and feature.The feature and/or beneficial effect of other additional aspects such as illustrative embodiments of the present invention will be below Description in it is obvious, or by according to present invention teach that specific embodiment practice in learn.

Description of the drawings

Accompanying drawing is not intended to drawn to scale.In the accompanying drawings, identical or approximately uniform group of each for illustrating in each figure Can be indicated by the same numeral into part.For clarity, in each figure, not each ingredient is labeled. Now, by example and the embodiment of various aspects of the invention will be described in reference to the drawings, wherein：

Fig. 1 is typical motor performs device schematic diagram.

Fig. 2 is the control strategy figure of the high-accuracy control method of motor 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 of -10V～+10V Scope, meets practical application, in addition it can also be seen that big interference during interference added by system.

Fig. 5 is Interference Estimation and Interference Estimation curve of error.

Fig. 6 is tracking error curve.

Specific embodiment

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

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 disclosure must not be intended to include all aspects of the invention.It should be appreciated that various designs presented hereinbefore and reality Apply example, and those designs for describing in more detail below and embodiment can in many ways in any one come real Apply, this is to should be design disclosed in this invention to be not limited to any embodiment with embodiment.In addition, disclosed by the invention one A little aspects can be used alone, or otherwise any appropriately combined using with disclosed by the invention.

With reference to shown in Fig. 1, Fig. 2, specific embodiment of the invention, a kind of high accuracy of motor position servo system Control method, its realization is comprised the following steps：

Step 1, set up motor position servo system model；

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

Step 3, regulation cause system based on a kind of parameter of the high-precision control law of motor of finite time Interference Estimation Meet Control performance standard.

It should be appreciated that with reference to shown in Fig. 2, the high-accuracy control method of the motor position servo system that the embodiment is proposed, For the characteristics of Uncertain nonlinear, establishing the model of system in motor servo, and motor has been separately designed on this basis Positional servosystem finite time interference observer and rise integration Robust Control Laws, estimating system does not model interference and in control It is compensated by input.

It is shown below in conjunction with the accompanying drawings, exemplary explanation is done to implementing for These steps.

Step 1, set up motor position servo system model

Fig. 1 show typical motor performs device and illustrates, according to Newton's second law, the kinetics of motor inertia load Model equation is represented by：

Y represents angular displacement in formula, and m represents inertia load, k_fTorque coefficient is represented, u is system control input, and b represents viscous Frottage coefficient, f represents other and does not model interference, such as non-linear friction, external disturbance and Unmarried pregnancy.

Aforementioned (1) formula is converted into into state space form, it is as follows：

WhereinX=[x₁,x₂]^TRepresent the state vector of position and speed； Represent and concentrate interference.

Typical electric machine actuating mechanism by shown in aforementioned Fig. 1 is illustrated, generally, the unstructured uncertainty of system D (x, t), it is clear that what it can not clearly be modeled, but the Unmarried pregnancy of system and interference always bounded.Thus, it is assumed hereinafter that Always set up：

Assume 1：D (x, t) be it is smooth enough, i.e.,

Wherein δ₁, δ₂,δ₃It is known.

The motor high-precision controller of step 2, design based on finite time Interference Estimation

Comprise the following steps that：

Step 2-1, the finite time interference observer that motor is built according to formula (2)

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

There is a time T₁, when time t is more than time constant T₁When,Wherein λ₀, λ₁, λ₂For design parameter.

Define one group of saturation function：

By formula (5) and aforesaid time T₁Can obtain：

The motor high-precision controller of step 2-2, design based on finite time Interference Estimation

Specifically include following steps：

Define one group of function as follows：

Wherein z₁=x₁-x_1dT () is output tracking error, k₁＞ 0 and k₂＞ 0 is feedback oscillator；

Due to G (s)=z₁(s)/z₂(the s+k of (s)=1/₁) it is a stable transmission function, allow z₁Very little levels off to zero Exactly allow z₂Very little levels off to zero；

Therefore, controller design is transformed into and allows z₂It is as little as possible or level off to zero；

Can be obtained by formula (7)：

Wushu (2) is substituted into and can obtained：

Based on Interference EstimationThe robust controller of fusion FTDO is as follows：

Wherein k_r＞ 0 is a feedback oscillator.

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

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

Wherein β ＞ 0 are designing gain.

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

Auxiliary function L (t) is defined as below：

If gain beta meets following condition：

Function P (t) being then defined as below is always just：

Step 3, parameter k for adjusting the high-precision control law u of motor for being based on finite time Interference Estimation₁,k₂,k_r, λ₀, λ₁, λ₂, beta system meets Control performance standard.

In the present embodiment the stablizing for system of previous designs is verified from liapunov function.

Theorem 1：Finite time interference observer (4) and saturation function (8), β meets formula (15), selects sufficiently large k_2,, k_r, make the matrix A positive definite being defined as below

The high-precision controller (10) based on finite time Interference Estimation for then designing ensure that all signals of system Bounded, and can guarantee that the progressive tracking performance of output signal, i.e., as t → ∞, z₂(t) → 0, z₁(t)→0。

Prove：Define liapunov function as follows：

Differential (18), substitutes into (7), and (13), (14) can obtain

As 0 ＜ t ＜ T₁When

As t >=T₁When

As t → ∞, z₂(t) → 0, z₁(t)→0。

Therefore controller is convergence, and system is stable.

Define with reference to specific example and parameter, the high accuracy control to the motor position servo system of previous embodiment The realization of method processed and effect are described further.

Take following parameter in simulations to be modeled system：

M=0.01kgm²,k_f=5, b=1.25Ns/m.

Take controller parameter k₁=100, k₂=200, λ₀=100, λ₁=400, λ₂=1500；k_r=175；β=20.

PID controller parameter is k_p=90, k_i=70, k_d=0.3.

Position angle input signalUnit rad.

One is added to disturb f=2.5cos (π t) Nm outward in 20s.

Control law action effect schematically as follows, wherein：Fig. 3 is to expect that trace command is illustrated；Fig. 4 is controlled under interference effect Device input voltage u-curve processed, controller input voltage meets the input range of -10V～+10V, meets practical application；Fig. 5 is dry Disturb the contrast estimated with Interference Estimation curve of error；Fig. 6 is the signal of tracking error curve.

From above-mentioned graphic comparison, algorithm proposed by the present invention can accurately estimate interference under simulated environment Value, compared to traditional PID control, the controller of present invention design can greatly improve the control that there is system under big disturbed condition Precision processed.Result of study shows under the influence of Uncertain nonlinear, set forth herein method disclosure satisfy that performance indications.

Although the present invention is disclosed above with preferred embodiment, so it is not limited to the present invention.Skill belonging to of the invention Has usually intellectual in art field, without departing from the spirit and scope of the present invention, when can be used for a variety of modifications and variations.Cause This, protection scope of the present invention ought be defined depending on those as defined in claim.

Claims (2)

1. a kind of high-accuracy control method of motor position servo system, it is characterised in that the realization of the high-accuracy control method Comprise the following steps：

Step 1, set up motor position servo system model；Its realization includes：

According to Newton's second law, the kinetic model equation of motor inertia load is expressed as：

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

Y represents angular displacement in formula, and m represents inertia load, k_fTorque coefficient is represented, u is system control input, and b represents viscous friction Coefficient, f represents other and does not model interference, including non-linear friction, external disturbance and Unmarried pregnancy；

Aforementioned (1) formula is converted into into state space form, it is as follows：

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

WhereinX=[x₁,x₂]^TRepresent the state vector of position and speed；Represent Concentrate interference；

Due to the Unmarried pregnancy and interference always bounded of system, thus, it is assumed hereinafter that always set up：

Assume 1：D (x, t) be it is smooth enough, i.e.,

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

Wherein δ₁, δ₂,δ₃It is known；

The motor high-precision controller of step 2, design based on finite time Interference Estimation；

It is comprised the following steps：

Step 2-1, the finite time interference observer that motor is built according to formula (2)

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

There is a time T₁, when time t is more than time constant T₁When,Whereinλ₀, λ₁, λ₂For design parameter, e₀, e₁, e₂Respectively x₂, d,Estimation；v₀, v₁, v₂For intermediate variable,For Interference Estimation error,For Interference Estimation；

Then, one group of saturation function is defined：

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

By formula (5) and aforesaid time T₁Can obtain：

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

The motor high-precision controller of step 2-2, design based on finite time Interference Estimation

It is as follows that one group of function is defined first：

$\begin{array}{c}{z}_2={\stackrel{\&CenterDot;}{z}}_1+k_1{z}_1=x_2-x_{2eq},x_{2eq}={\stackrel{\&CenterDot;}{x}}_{1d}-k_1{z}_1\\ \mathrm{\&gamma;}={\stackrel{\&CenterDot;}{z}}_2+k_2{z}_2\end{array}---\left(7\right)$

Wherein z₁=x₁-x_1dT () is output tracking error, k₁＞ 0 and k₂＞ 0 is feedback oscillator；

Due to G (s)=z₁(s)/z₂(the s+k of (s)=1/₁) it is a stable transmission function, allow z₁Very little levels off to and zero is exactly Allow z₂Very little levels off to zero；

Therefore, controller design is transformed into and allows z₂It is as little as possible or level off to zero；

Can be obtained by formula (7)：

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

Wushu (2) is substituted into and can obtained：

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

Based on Interference EstimationThe robust controller of fusion FTDO is as follows：

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

Wherein k_r＞ 0 is a feedback oscillator, u_aFor model compensation item, u_sFor robust feedback term, u_s1For linear feedback item, u_s2For Integration robust feedback term；

Wushu (10) substitutes into formula (9), can obtain the dynamical 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, integration robust item of the design based on rise is as follows：

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

Wherein β ＞ 0 are 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：

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

If gain beta meets following condition：

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

Function P (t) being then defined as below is always just：

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

And

Step 3, regulation cause system to meet control based on the parameter of the high-precision control law of motor of finite time Interference Estimation Performance indications.

2. the high-accuracy control method of motor position servo system according to claim 1, it is characterised in that abovementioned steps In 3, by adjusting parameter k based on the high-precision control law u of motor of finite time Interference Estimation₁,k₂,k_r, λ₀, λ₁, λ₂, β So that system meets Control performance standard.