CN109740110A - The generation method of the sampling observer of multiple-input and multiple-output Nonlinear Differential Algebraic Systems - Google Patents
The generation method of the sampling observer of multiple-input and multiple-output Nonlinear Differential Algebraic Systems Download PDFInfo
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Abstract
The invention discloses a kind of sampling observer generation methods of multiple-input and multiple-output Nonlinear Differential Algebraic Systems, comprising: S1: creation multiple-input and multiple-output Nonlinear Differential Algebraic Systems；S2: vector relative degree is calculated, so that multiple-input and multiple-output Nonlinear Differential Algebraic Systems equivalence is converted to multiple-input and multiple-output nonlinear ordinary differential systems by seeking differomorphism；S3: using output signal sampled value to construct sampling observer；S4: by construction systematic observation proportional error equation and liapunov function, to determine system communication cycle.The present invention can utilize the sampled value and Lipschitz condition of output signal, construct the sampling observer of multiple-input and multiple-output Nonlinear Differential Algebraic Systems, so that the controlled device range of system has more popularity, it is easier to the realization of digital computer, the generation method of the sampling observer of multiple-input and multiple-output Nonlinear Differential Algebraic Systems mentioned by the present invention, it is simple and practical, computational accuracy is high.
Description
Technical field
The present invention relates to multiple-input and multiple-output Nonlinear Differential Algebraic Systems technical fields, in particular to a kind of how defeated
Enter the generation method of the sampling observer of multi output Nonlinear Differential Algebraic Systems.
Background technique
Observer is then to need original system output to generate as feedback control since built-in system state can not directly acquire
Unique measuring signal realize state reconstruction new system, substitute into Nonlinear Differential Algebraic Systems in, in many practical application systems
In system, such as electric system, biosystem, robot system play the role of it is vital.However existing research achievement
It is and to be all based on continuous time model about single-input single-output Nonlinear Differential Algebraic Systems model and seen mostly
Survey what device generated.However the controlled device of many real application systems is often by multiple-input and multiple-output non-linear differential algebraic system
It unites to describe, and with the extensive use of digital computer, data are to realize transmission in digital form.Multi input
The sampling observer of multi output Nonlinear Differential Algebraic Systems has the following advantages: 1, system form is with more generality；2, it generates
State observer be discrete, it is easier to the realization of digital computer.
Summary of the invention
It is an object of that present invention to provide a kind of lifes of the sampling observer of multiple-input and multiple-output Nonlinear Differential Algebraic Systems
Multiple-input and multiple-output Nonlinear Differential Algebraic Systems are constructed using the sampled value and Lipschitz condition of output signal at method
The sampling observer of model, so that the controlled device range of system has more popularity, it is easier to the realization of digital computer, this
The generation method of the sampling observer of the mentioned multiple-input and multiple-output Nonlinear Differential Algebraic Systems of invention, simple and practical, meter
It is high to calculate precision.
To reach above-mentioned purpose, in conjunction with Fig. 1, the present invention proposes a kind of multiple-input and multiple-output Nonlinear Differential Algebraic Systems
Sample observer generation method, the sampling observer generation method the following steps are included:
S1: creation multiple-input and multiple-output Nonlinear Differential Algebraic Systems.
S2: the vector relative degree of the multiple-input and multiple-output Nonlinear Differential Algebraic Systems created in step S1 is calculated, is passed through
Seeking differomorphism makes multiple-input and multiple-output Nonlinear Differential Algebraic Systems equivalence be converted to the non-linear Chang Wei of multiple-input and multiple-output
Subsystem.
S3: it according to the multiple-input and multiple-output nonlinear ordinary differential systems for converting generation in step S2, is adopted using output signal
Sample value is to construct sampling observer.
S4: by construction systematic observation proportional error equation and liapunov function, to determine system communication cycle.
In further embodiment, in step S1, the mathematics of the multiple-input and multiple-output Nonlinear Differential Algebraic Systems of creation
Model are as follows:
Wherein x ∈ Rn,z∈RlRespectively differential variable, algebraic variable, ui∈R,yi∈ R, (i=1,2 ..., m) be respectively
Control input and control output, f1、gi∈Rn、f2∈RlIt is Smooth Maps, and algebraic equation f2() is about algebraic variable z
Jacobian matrix be normal full rank.
In further embodiment, in step S2, the multiple-input and multiple-output non-linear differential generation created in step S1 is calculated
The vector relative degree of number system is converted to multiple-input and multiple-output Nonlinear Differential Algebraic Systems equivalence by seeking differomorphism
The methods of multiple-input and multiple-output nonlinear ordinary differential systems the following steps are included:
S21: calculating the vector relative degree of multiple-input and multiple-output Nonlinear Differential Algebraic Systems, specifically, defining symbol F
(x, z), i.e.,
If rightAnd i, j=1,2 ..., m, k=0,1 ..., ri- 2 meet following two condition:
(I)
(II)It is nonsingular matrix.
Then by (r1,r2,…,rm) vector relative degree as multiple-input and multiple-output Nonlinear Differential Algebraic Systems.
S22: when there are vector relative degree (r for multiple-input and multiple-output Nonlinear Differential Algebraic Systems1,r2,…,rm) and meet Under conditions of, the differomorphism being calculated corresponding to it is as follows:
To convert the non-linear Chang Wei of multiple-input and multiple-output for multiple-input and multiple-output Nonlinear Differential Algebraic Systems equivalence
Subsystem, i.e.,
Wherein, nonlinear terms φi,j() (i=1,2 ..., m；J=1,2 ..., ri) meet Lipschitz condition
It is non-linear often according to the multiple-input and multiple-output for converting generation in step S2 in step S3 in further embodiment
Differential system, using output signal sampled value with construct sampling observer method include:
On the basis of multiple-input and multiple-output Nonlinear Ordinary Differential equivalent system, y (t is sampled using output signalk) value,
Construction sampling observer is as follows:
Wherein, θ1,θ2,…,θm>=1 is gain parameter, It is simultaneously Hurwitz polynomialCoefficient.
The sampling observer is init state, samples the initial estimated state of observer by algebraic equation f2(x,z)
=0 constraint, then haveIt sets up.
In further embodiment, in step S4, systematic observation proportional error equation and liapunov function is constructed, is asked
The method for sampling the system communication cycle of observer is obtained after solution includes:
S41: construction system proportional observation error equation is as follows:
Comparative example observation error equation carries out derivation, can obtain
Wherein,
Obtain HiThatch matrix is tieed up for Hull, further calculates to obtain symmetric positive definite matrix Pi, so that equationIt sets up.
S42: construction liapunov function is as follows:
To liapunov function derivation, following formula are obtained:
S43: determining sampling period T, and sampling period T meets:
Wherein, θi>=1 is observation gain, γi> 0 is constant, c*> 0 is system generation option.
The present invention is based on multiple-input and multiple-output Nonlinear Differential Algebraic Systems to realize construction one using the sampled value of output
The sampling observer of kind multiple-input and multiple-output Nonlinear Differential Algebraic Systems, to guarantee to realize to the accurate of the data of system
Estimation, achievees the effect that system stable.Primary structure step includes: the life of multiple-input and multiple-output Nonlinear Differential Algebraic Systems
At the generation of, multiple-input and multiple-output nonlinear ordinary differential systems, sample the generation of observer.
A kind of generation method of multiple-input and multiple-output Nonlinear Differential Algebraic Systems sampling observer mentioned by the present invention
In, the effect of multiple-input and multiple-output Nonlinear Differential Algebraic Systems is the definition using vector relative degree, and same by differential
Embryo makes multiple-input and multiple-output Nonlinear Differential Algebraic Systems equivalence be converted into multiple-input and multiple-output nonlinear ordinary differential systems module.
A kind of generation method of multiple-input and multiple-output Nonlinear Differential Algebraic Systems sampling observer mentioned by the present invention
In, the effect of multiple-input and multiple-output nonlinear ordinary differential systems is to utilize the sampling of output based on nonlinear ordinary differential systems
Value generates sampling observer.
A kind of generation method of multiple-input and multiple-output Nonlinear Differential Algebraic Systems sampling observer mentioned by the present invention
In, the effect for sampling observer is to guarantee that system data is accurately estimated in realization, passes through construction systematic observation ratio and misses
Eikonal equation and liapunov function determine system communication cycle, guarantee that observation proportional error is asymptotic goes to zero.
In conjunction with Fig. 2, a kind of life of multiple-input and multiple-output Nonlinear Differential Algebraic Systems sampling observer proposed by the present invention
At method, including following groundwork step:
Step 1. establishes model: establishing the model of multiple-input and multiple-output Nonlinear Differential Algebraic Systems, i.e.,
Wherein x ∈ Rn,z∈RlRespectively differential variable, algebraic variable, ui∈R,yi∈ R, (i=1,2 ..., m) be respectively
Control input and control output, f1、gi∈Rn、f2∈RlIt is Smooth Maps.Multiple-input and multiple-output non-linear differential is required simultaneously
The index of algebra system is 1, i.e. algebraic equation f2() is normal full rank about the Jacobian matrix of algebraic variable z.
Step 2. calculates vector relative degree: defining symbol F (x, z), i.e.,
If rightAnd i, j=1,2 ..., m, k=0,1 ..., ri- 2 meet following two condition:
(I)
(II)It is nonsingular matrix.
Then (r1,r2,…,rm) be multiple-input and multiple-output Nonlinear Differential Algebraic Systems vector relative degree.
Step 3. carries out conversion of equal value: when there are vector relative degree (r for multiple-input and multiple-output Nonlinear Differential Algebraic Systems1,
r2,…,rm) and meetUnder conditions of, then there are a differomorphisms
So that big system equivalence is converted into multiple-input and multiple-output nonlinear ordinary differential systems, i.e.,
Nonlinear terms φ is required simultaneouslyi,j() (i=1,2 ..., m；J=1,2 ..., ri) meet Lipschitz condition
The sampling observer of step 4. generation system: the basis based on multiple-input and multiple-output Nonlinear Ordinary Differential equivalent system
On, y (t is sampled using output signalk) value, structural regime observer is as follows:
Wherein, θ1,θ2,…,θm>=1 is gain parameter, It and is Hurwitz polynomialCoefficient.Requiring observer simultaneously is initialization
, i.e., the initial estimation initial value of observer is by algebraic equation f2The constraint of (x, z)=0, then have It sets up.
It is as follows that step 4.1. constructs system proportional observation error equation:
Comparative example observation error equation carries out derivation, can obtain
Wherein
Be easy to get HiThatch matrix is tieed up for Hull.Therefore there are symmetric positive definite matrix Pi, so that equation
It is to set up.
It is as follows that step 4.2. constructs liapunov function:
To liapunov function derivation, can obtain
The sampling observer of step 4.3. in step 3 can be sampled according to output valve, and it is full to define sampling period T
Foot:
Wherein, θi>=1 is observation gain, γi> 0 is constant, c*> 0 is system generation option, guarantees that ratio observation misses with this
Difference is asymptotic goes to zero.
The above technical solution of the present invention, compared with existing, significant beneficial effect is that the present invention is based on existing
The generation method of single-input single-output Nonlinear Differential Algebraic Systems continuous time observer, it is non-thread to propose multiple-input and multiple-output
Property differential-algebraic systems sampling observer generation method so that the range of controlled device is more extensive, it is easier to numerical calculation
The realization of machine.The present invention carries out structural regime observer using the sampled value and Lipschitz condition of output signal, realizes pair
The accurate estimation of system data, there is good effect in the real application systems such as electric system, so that the ratio of system is observed
Error asymptotic can go to zero.
It should be appreciated that as long as aforementioned concepts and all combinations additionally conceived described in greater detail below are at this
It can be viewed as a part of the subject matter of the disclosure 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 of the subject matter of the disclosure.
Can be more fully appreciated from the following description in conjunction with attached drawing present invention teach that the foregoing and other aspects, reality
Apply example and feature.The features and/or benefits of other additional aspects such as illustrative embodiments of the invention will be below
Description in it is obvious, or learnt in practice by the specific embodiment instructed according to the present invention.
Detailed description of the invention
Attached drawing is not intended to drawn to scale.In the accompanying drawings, identical or nearly identical group each of is shown in each figure
It can be indicated by the same numeral at part.For clarity, in each figure, not each component part is labeled.
Now, example will be passed through and the embodiments of various aspects of the invention is described in reference to the drawings, in which:
Fig. 1 is the generation method process of the sampling observer of multiple-input and multiple-output Nonlinear Differential Algebraic Systems of the invention
Figure.
Fig. 2 is the generation method flow chart of the sampling observer of one of example of the invention.
Fig. 3 is differential variable ξ in Numerical examples1,1And estimated valueProportional error value schematic diagram.
Fig. 4 is differential variable ξ in Numerical examples1,2And estimated valueProportional error value schematic diagram.
Fig. 5 is differential variable ξ in Numerical examples2,1And estimated valueProportional error value schematic diagram.
Fig. 6 is differential variable ξ in Numerical examples2,2And estimated valueProportional error value schematic diagram.
Fig. 7 is algebraic variable z and estimated value in Numerical examplesError amount schematic diagram.
Specific embodiment
In order to better understand the technical content of the present invention, special to lift specific embodiment and institute's accompanying drawings is cooperated to be described as follows.
Below by taking two two output nonlinear differential-algebraic systems of input as an example, to multiple-input and multiple-output mentioned by the present invention
The generation method of the sampling observer of Nonlinear Differential Algebraic Systems elaborates.
The generation method of the sampling observer of two two output nonlinear differential-algebraic systems of input includes the following steps:
Step 1. establishes model: establishing the model of multiple-input and multiple-output Nonlinear Differential Algebraic Systems, i.e.,
Wherein x ∈ Rn,z∈RlRespectively differential variable, algebraic variable, ui∈R,yi∈ R, (i=1,2 ..., m) be respectively
Control input and control output, f1、gi∈Rn、f2∈RlIt is Smooth Maps.Multiple-input and multiple-output non-linear differential is required simultaneously
The index of algebra system is 1, i.e. algebraic equation f2() is normal full rank about the Jacobian matrix of algebraic variable z.
In this Numerical examples, the Nonlinear Differential Algebraic Systems model of two inputs two output is established, i.e.,
(x in formula1,x2,x3,x4) be system differential variable, the algebraic variable of z system, u1,u2It is defeated for the control of system
Enter, y1,y2It is exported for the control of system.
Step 2. calculates vector relative degree: defining symbol F (x, z), i.e.,
If rightAnd i, j=1,2 ..., m, k=0,1 ..., ri- 2 meet following two condition:
(I)
(II)It is nonsingular matrix.
Then (r1,r2,…,rm) be multiple-input and multiple-output Nonlinear Differential Algebraic Systems vector relative degree.
In this Numerical examples, the Relative order of the Nonlinear Differential Algebraic Systems model of two inputs, two output is (2,2).
Step 3. carries out conversion of equal value: when there are vector relative degree (r for multiple-input and multiple-output Nonlinear Differential Algebraic Systems1,
r2,…,rm) and meetUnder conditions of, then there are a differomorphisms
So that big system equivalence is converted into multiple-input and multiple-output nonlinear ordinary differential systems, i.e.,
Nonlinear terms φ is required simultaneouslyi,j() (i=1,2 ..., m；J=1,2 ..., ri) meet Lipschitz condition
In this Numerical examples, the differomorphism that the Nonlinear Differential Algebraic Systems model of two inputs, two output is chosen is
The Nonlinear Differential Algebraic Systems model equivalency for exporting two inputs two is converted to
Obviously have That is nonlinear terms φi,j() meets Lipchitz assumed condition, constant c=1.
The sampling observer of step 4. generation system: the basis based on multiple-input and multiple-output Nonlinear Ordinary Differential equivalent system
On, y (t is sampled using output signalk) value, structural regime observer is as follows:
Wherein, θ1,θ2,…,θm>=1 is gain parameter,AndIt is simultaneously Hurwitz polynomial
Coefficient.Requiring observer simultaneously is initialization, the i.e. initial estimated state of observer By algebraic equation f2The limitation of (x, z)=0, then haveIt sets up.
In this Numerical examples, the sampling observer that the Nonlinear Differential Algebraic Systems model of two inputs, two output generates is
Wherein choose L1.1=5, L1.2=6, L2.1=2, L2.2=0.5.
In this Numerical examples, input takes u1=3t, u2=sin (1.5t), observer gain parameter value are as follows: θ1=6,
θ2=13, T=0.01s.The original state of emulation are as follows:
(x1(0),x2(0),x3(0),x4(0), (0) z)=(1, -1,0,0,0),
In this Numerical examples, observation proportional error equation construction is as follows
Simulation result is as shown in Fig. 3 to Fig. 7, as can be seen from Fig. between the state variable and its estimated value of sampling observer
Proportional error value, zero is gradually leveled off within a certain period of time, to verify multiple-input and multiple-output non-linear differential algebra original system
The estimated state (x, z) of system is asymptotically stable in origin.
Various aspects 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 need not be defined on including all aspects of the invention.It should be appreciated that a variety of designs and reality presented hereinbefore
Those of apply example, and describe in more detail below design and embodiment can in many ways in any one come it is real
It applies, this is because conception and embodiment disclosed in this invention are not limited to any embodiment.In addition, disclosed by the invention one
A little aspects can be used alone, or otherwise any appropriately combined use with disclosed by the invention.
Although the present invention has been disclosed as a preferred embodiment, however, it is not to limit the invention.Skill belonging to the present 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, the scope of protection of the present invention is defined by those of the claims.
Claims (5)
1. a kind of sampling observer generation method of multiple-input and multiple-output Nonlinear Differential Algebraic Systems, which is characterized in that described
Sample observer generation method the following steps are included:
S1: creation multiple-input and multiple-output Nonlinear Differential Algebraic Systems；
S2: the vector relative degree of the multiple-input and multiple-output Nonlinear Differential Algebraic Systems created in step S1 is calculated, by seeking
Differomorphism makes multiple-input and multiple-output Nonlinear Differential Algebraic Systems equivalence be converted to multiple-input and multiple-output Nonlinear Ordinary Differential system
System；
S3: according to the multiple-input and multiple-output nonlinear ordinary differential systems for converting generation in step S2, output signal sampled value is utilized
Observer is sampled with building；
S4: by construction systematic observation proportional error equation and liapunov function, to determine system communication cycle.
2. the sampling observer generation method of multiple-input and multiple-output Nonlinear Differential Algebraic Systems according to claim 1,
It is characterized in that, in step S1, the mathematical model of the multiple-input and multiple-output Nonlinear Differential Algebraic Systems of creation are as follows:
Wherein x ∈ Rn,z∈RlRespectively differential variable, algebraic variable, ui∈R,yi∈ R, (i=1,2 ..., m) it is respectively to control
Input and control output, f1、gi∈Rn、f2∈RlIt is Smooth Maps, and algebraic equation f2() is refined about algebraic variable z's
It is normal full rank than matrix.
3. the sampling observer generation method of multiple-input and multiple-output Nonlinear Differential Algebraic Systems according to claim 1,
It is characterized in that, calculating the vector phase of the multiple-input and multiple-output Nonlinear Differential Algebraic Systems created in step S1 in step S2
To rank, by seeking differomorphism, so that multiple-input and multiple-output Nonlinear Differential Algebraic Systems equivalence is converted to multiple-input and multiple-output non-
The method of linear ordinary differential system the following steps are included:
S21: calculating the vector relative degree of multiple-input and multiple-output Nonlinear Differential Algebraic Systems, specifically, symbol F (x, z) is defined,
I.e.
If rightAnd i, j=1,2 ..., m, k=0,1 ..., ri- 2 meet following two condition:
(I)
(II)It is nonsingular matrix,
Then by (r1,r2,…,rm) vector relative degree as multiple-input and multiple-output Nonlinear Differential Algebraic Systems.
S22: when there are vector relative degree (r for multiple-input and multiple-output Nonlinear Differential Algebraic Systems1,r2,…,rm) and meet Under conditions of, the differomorphism being calculated corresponding to it is as follows:
To convert multiple-input and multiple-output Nonlinear Ordinary Differential system for multiple-input and multiple-output Nonlinear Differential Algebraic Systems equivalence
System, i.e.,
Wherein, nonlinear terms φi,j() (i=1,2 ..., m；J=1,2 ..., ri) meet Lipschitz condition
4. the sampling observer generation method of multiple-input and multiple-output Nonlinear Differential Algebraic Systems according to claim 1,
It is characterized in that, according to the multiple-input and multiple-output nonlinear ordinary differential systems for converting generation in step S2, utilization is defeated in step S3
Signal sampling value includes: out in the method for constructing sampling observer
On the basis of multiple-input and multiple-output Nonlinear Ordinary Differential equivalent system, y (t is sampled using output signalk) value, construction
It is as follows to sample observer:
Wherein, θ1,θ2,…,θm>=1 is gain parameter,It is simultaneously Hurwitz polynomialCoefficient；
The sampling observer is init state, samples the initial estimated state of observer by algebraic equation f2(x's, z)=0
Constraint, then haveIt sets up.
5. the sampling observer generation method of multiple-input and multiple-output Nonlinear Differential Algebraic Systems according to claim 1,
It is characterized in that, constructing systematic observation proportional error equation and liapunov function in step S4, sampling is obtained after solution and is seen
The method of system communication cycle for surveying device includes:
S41: construction system proportional observation error equation is as follows:
Comparative example observation error equation carries out derivation, can obtain
Wherein,
Obtain HiThatch matrix is tieed up for Hull, further calculates to obtain symmetric positive definite matrix Pi, so that equation
It sets up；
S42: construction liapunov function is as follows:
To liapunov function derivation, following formula are obtained:
S43: determining sampling period T, and sampling period T meets:
Wherein, θi>=1 is observation gain, γi> 0 is constant, c*> 0 is system generation option.
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| CN106547207A (en) * | 2016-10-13 | 2017-03-29 | 浙江理工大学 | A kind of hybrid observer construction method of non-linear multi-input multi-output system |
| CN107203139A (en) * | 2017-07-06 | 2017-09-26 | 南京信息工程大学 | The stabilized control method of multiple-input and multiple-output non-linear differential algebraic subsystem |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106547207A (en) * | 2016-10-13 | 2017-03-29 | 浙江理工大学 | A kind of hybrid observer construction method of non-linear multi-input multi-output system |
| CN107203139A (en) * | 2017-07-06 | 2017-09-26 | 南京信息工程大学 | The stabilized control method of multiple-input and multiple-output non-linear differential algebraic subsystem |
Non-Patent Citations (1)
| Title |
|---|
| 臧强等: "MIMO非线性DAE***的采样输出反馈观测器设计", 《中国科技论文》 * |
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