CN110377928A - The design method of ancillary input signals based on state set-member estimation - Google Patents
The design method of ancillary input signals based on state set-member estimation Download PDFInfo
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Abstract
The invention discloses the design methods of the ancillary input signals based on state set-member estimation, including indicating the range of the uncertain factors such as the process interference of system, measurement noise with zonotopes.It is system design point observer using the thought that zonotopes theory and Kalman filtering combine, real-time estimation obtains the state of system.In order to recognize to multiple approximate models, in the smallest situation of systematic influence, the intersection by the zonotopes where the real-time status difference of each model is empty Design assistant input signal.By the ancillary input signals injected system, abundant excitation system realizes the separation of multiple models.The present invention reduces the conservative in ancillary input signals design process from the angle of system mode, gives a kind of simple, effective ancillary input signals design method.
Description
Technical field
The present invention is the method in multi-model identification field, and in particular to a kind of auxiliary input based on state set-member estimation
Signal computational algorithm.
Background technique
Multi-model based on ancillary input signals is recognized generally by Design assistant input signal, guarantees that the auxiliary is defeated
Under the premise of entering signal and capable of separating multiple approximate models, while the influence to system is smaller.Currently, being estimated based on collection person
The research of the ancillary input signals design method of meter is concentrated mainly on through the set where the output of analysis system, Lai Jinhang
Ancillary input signals design.But since the process for not only containing system in the set where the measured value that system exports is dry
Disturb that also contain measurement uncertain factors, the conservative such as noise larger.And where the collection composition and division in a proportion where the state of system exports
Set lacked the measurement noise of subsequent time, therefore be that empty Design assistant input signal can using set intersection where state
A part of conservative is reduced, so that the ancillary input signals that design obtains are smaller.For this purpose, this method is based primarily upon system mode
The zonotopes at place, give a kind of ancillary input signals design method, and this method is observed using observer
Set where system mode is obtained in the case where guaranteeing the smallest situation of ancillary input signals by each model real-time estimation
The intersection of zonotopes where state is sky, obtains optimal ancillary input signals.
Multi-model identification process is as shown in Figure 2.Wherein, Fig. 2 (a) is model 1 and model 2 when not adding ancillary input signals
Output set, it can be seen that two zonotopes intersection at this time, can not when the output of system belongs to intersection
Which model judgement belongs to.Therefore, in order to pick out which model the output of system belongs to, optimal ancillary input signals are designed,
By the ancillary input signals injected system, so that two models separate, as shown in Fig. 2 (b).
Existing method is that the intersection of output set is used to obtain ancillary input signals for sky design.By linear system mould
Type can obtain, and the set where system output can indicate are as follows:
Y=CX+FV (1)
X, Y, V are respectively the set where state, output and measurement noise, and C, F are respectively the parameter square of appropriate dimension
Battle array.
As shown in (a) in Fig. 2, the set where 2 state of model 1 and model is made by Design assistant input signal
It is just tangent.At this point, will not influence the positional relationship of two models since CX is linear change, such as (b) in Fig. 2.When drawing
When entering FV, so that originally tangent two and intersection, intersecting area is related with the measurement size of noise introduced, in Fig. 2
(c) shown in.It therefore, is that the ancillary input signals ratio that empty design obtains is using state set intersection by output set intersection
The ancillary input signals that sky design obtains are big.
The uncertain factors such as the process interference of system, measurement noise are indicated with zonotopes.It retouches for convenience
It states, next introduces defined below and property first.
The expression formula of r rank zonotopes are as follows:
Wherein, -1≤αj≤ 1, oeprator ⊕ are Minkowski and hypercube Br=[- 1 ,+1]r, c is in Z
The heart,For the generator matrix of Z, g1, g2,…,grRespectively generate vector.
Zonotopes meet following computation rule:
- Z=<-c, G>(5)
Wherein, M is the constant matrices of appropriate dimension, and zonotopes Z ' is that can surround zonotopes Z most
Etui, rs (G) are diagonal matrix, are met:
Lemma 1: known zonotopes Z1=< a1+b1,G1> and Z2=< a2+b2,G2>, then's
Sufficient and necessary condition are as follows:
Wherein, (a1+b1) and (a2+b2) it is respectively zonotopes Z1And Z2Center, G1、G2Respectively Z1、Z2's
Generator matrix.
Summary of the invention
It is an object of the invention to overcome auxiliary signal conservative in the existing multi-model identification based on output set-member estimation
Larger problem provides a kind of ancillary input signals calculation method based on state set-member estimation.From the angle of state,
Under the premise of guaranteeing that multiple models can separate, so that it is smaller to systematic influence.
The purpose of the present invention is what is be achieved through the following technical solutions: filtering first with zonotopes and Kalman
Wave combines, and design obtains the state observer of system, and estimation obtains the zonotopes where the state of subsequent time.
The zonotopes intersection estimated where obtaining state using model is sky, and design obtains ancillary input signals.By the auxiliary
Input signal injected system, excitation system, the separation of implementation model.
Specifically, in technical solution of the present invention, the design side of the ancillary input signals based on state set-member estimation
Method includes the following steps:
Step 1: by the range zonotopes table of the uncertain factors such as the process interference of system, measurement noise
Show；
Step 2: the thought design point observer combined using zonotopes theory and Kalman filtering, it is real
When estimate to obtain the state of system；
Step 3: in order to be recognized to multiple approximate models, in the smallest situation of systematic influence, by each
The intersection of zonotopes where the real-time status difference of model is empty Design assistant input signal；
Step 4: by the ancillary input signals injected system, abundant excitation system, the separation of implementation model.
The range of the process interference of system, measurement incorrect noise factor is indicated with zonotopes.
The thought design point observer combined using zonotopes theory and Kalman filtering, real-time estimation
Obtain the state of system.
In order to recognize to multiple approximate models, in the smallest situation of systematic influence, pass through the reality of each model
When state respectively where the intersections of zonotopes be empty Design assistant input signal.
By the ancillary input signals injected system, abundant excitation system, the separation of implementation model.
Flow chart of the invention as shown in figure 3, the ancillary input signals based on state set-member estimation design method, tool
Steps are as follows for body:
Step 1: the uncertainties such as measurement noise and the process interference of system are described with zonotopes:
Assuming that the original state x of system0, measurement noise ωkυ is interfered with processkMeet:
Wherein, X0, W, V be respectively system initial state, process interference and measurement noise where zonotopes,
G0、Gω、GυRespectively zonotopes X0, W, V center.
Step 2: the thought design point observer combined using zonotopes theory and Kalman filtering, it is real
When estimate to obtain the state of system.
For following linear discrete time-invariable system:
Wherein, m is Number of Models,The respectively state and output of k moment model j, ukFor k moment model
Input, υk,ωkRespectively process interference and measurement noise, A[j]、B[j]、C[j]、E[j]F[j]The parameter square of respectively appropriate dimension
Battle array.
Estimation, which is combined, with zonotopes and Kalman filtering thought obtains the state at k+1 moment:
WhereinIt is the state estimation of k moment model j,It is the state estimation of k+1 moment model j,
For the gain matrix of the filter of k moment model j.In the method,It is designed by the thought of Kalman filter
It obtains.
Assuming that the state that the k moment is estimated isThen by the more cell spaces of central symmetry
The state of property, k+1 moment obtains:
Wherein
WithThe respectively center of zonotopes where k+1 moment model j state and generator matrix.
By obtaining optimal observer gain to each modelling using zonotopes theory and Kalman filtering
Matrix
Wherein,Intermediate variable respectively during solving optimal observer gain,For
The generator matrix of zonotopes where k moment model j state multiplied by the generator matrix transposition.For model j
Parameter matrix F[j]Multiplied by F[j]Transposition.
Step 3: in order to realize that multi-model recognizes, in the smallest situation of systematic influence, pass through the real-time of each model
The intersection of zonotopes where state difference is empty Design assistant input signal.
For the expression formula of the calculating process after simplification, define:
For system (10), so that the intersection of the zonotopes where the state that each model is estimated is sky:
WhereinWithRespectively k+1 moment model l and model j estimates obtained state.
It is obtained by lemma 1, the sufficient and necessary condition that (16) are set up are as follows:
Wherein Δ[lj]=B[j]-B[l],
In order to enable designed ancillary input signals are minimum, optimal auxiliary input letter is obtained by following optimization problem
Number:
Wherein matrix R is positive semidefinite matrix.
Work as Δ[lj]uk∈Zq,kWhen (l, j):
Wherein | | ξ '[lj]||∞≤1。
Therefore, whenWhen:
Wherein | | ξ[lj]||∞≤1+δ[lj], δ[lj]For constant, work as δ[lj]When≤0, | | ξ[lj]||∞≤ 1, then it is unsatisfactory forCondition, only work as δ[lj]When > 0, it is just able to satisfy the condition.
Therefore, optimization problem (18) is reconstructed into following linear problem:
Constraint condition inIt can be seen that the feasible set of optimization problem is a unbounded set, because
U may be not present during solving optimization in thiskUp to infimum, therefore effective feasible solution in order to obtain, it enables
WhereinFor the smallest separation threshold value,For maximum separation threshold value.
Therefore, optimization problem is further converted to:
Since optimization problem is dual-layer optimization problem, it is difficult to obtain optimal solution, therefore will by construction Lagrangian
The double-deck problem is converted into single layer problem.
Therefore, optimization problem converts are as follows:
s.t.
Wherein, λ[lj],For Lagrange multiplier, r is generator matrixColumn
Number,For binary variable, vector 1=[1 1 ... 1]T。
Step 4: by the ancillary input signals injected system, abundant excitation system realizes the separation of multiple models.
Optimal ancillary input signals u is obtained by optimization problemk, by ukInjection, the separation of implementation model.
The invention has the following advantages over the prior art:
Ancillary input signals design method proposed by the present invention is the more born of the same parents of holohedral symmetry where the state obtained using estimation
Shape intersection is empty to be obtained.Probabilistic ranges such as measurement noise and the process interference by system utilize zonotopes
It indicates.Real-time observer gain is obtained by the thought of Extended Kalman filter, estimation obtains real-time status.
Angle design ancillary input signals of the invention from state, the collection at the collection composition and division in a proportion output place as where state
The measurement noise for having lacked a moment is closed, therefore the ancillary input signals that design obtains are smaller, it is auxiliary to reduce conventional method design
Help the conservative of input signal.
Detailed description of the invention
Fig. 1 is the influence that ancillary input signals are added and ancillary input signals are not added to export model.
Fig. 2 is influence of the ancillary input signals to model state and output.
Fig. 3 is the design method flow chart of the ancillary input signals based on state set-member estimation.
Fig. 4 is set when not adding ancillary input signals where model state.
Fig. 5 is ancillary input signals.
Fig. 6 is set where model state after ancillary input signals are added.
Fig. 7 is the influence exported after ancillary input signals are added to model 1.
Fig. 8 is the influence exported after ancillary input signals are added to model 2.
Specific embodiment
Below with reference to the low frequency model and Detailed description of the invention a specific embodiment of the invention of permanent magnet direct current motor.This is forever
The low frequency model of magnetic dc motor are as follows:
Wherein, u, i, Ra, L, Ke, Kt, J1, frRespectively armature voltage, electric current, resistance, inductance, torque constant, anti-electronic
Potential constant, motor inertia and coefficient of friction, torque constant Kt=1.0005Ke.U=uc+ua, ucIt is inputted for the control of system, ua
It is inputted for the auxiliary of system.The parameter of model 1 is respectively as follows:
Ra=1.2030 Ω, L=5.5840*10-3H, Ke=8.1876*10-2V rad/s
J1=1.3528*10-4J s2/ rad, fr=2.3396*10-4J s2/ rad,
When motor inductances change, i.e. L=8.7548 × 10-3It is at this time model 2 when H.
According to the mechanism process of motor, for the revolving speed of motor is maintained 70.3rad/s, the control input of system
uc=6V.Using it is preceding to Euler's difference method by motor model discretization, wherein the sampling time is 5 ms.Due to the discrete mistake of system
It is uncertain that journey can make parameter introduce, therefore the state of discretization increases uncertain item E ωk, wherein
It executes step 1: the uncertainties such as measurement noise and the process interference of system is retouched with the more cell spaces of central symmetry
State probabilistic range:
Wherein
It executes step 2: being observed using the thought design point that zonotopes theory and Kalman filtering combine
Device, real-time estimation obtain the state of system.
By observer, real-time observer gain is obtained, real-time estimation obtains the state of model 1 and model 2.
It executes step 3: in order to be recognized to multiple approximate models, in the smallest situation of systematic influence, leading to
The intersection of the zonotopes where the real-time status difference of each model is crossed as empty Design assistant input signal.
Fig. 4 is the set where the state of model 1 and model 2 not plus when ancillary input signals, at this time two models
Intersection of sets where state can not judge which system belongs at this time when the state that systematic observation obtains is in intersection
A model.Real-time ancillary input signals, such as Fig. 5 are obtained by optimization problem, wherein solid line is to design to obtain by state set
Ancillary input signals, dotted line is the ancillary input signals designed by output set, it can thus be seen that passing through
The ancillary input signals auxiliary that set design where state obtains is smaller.
Execute step 4: by the ancillary input signals injected system, abundant excitation system, the separation of implementation model.
After ancillary input signals input system, model 1 and model 2 observe the set separation where obtained state, such as
Fig. 6.Fig. 7, Fig. 8 are respectively the influence of output of the ancillary input signals to model 1 and model 2, mould when solid line is indicated not plus inputted
Model 1 and model 2 after the ancillary input signals obtained by state set is added in the output of type 1 and model 2, chain-dotted line expression
Output, dotted line indicates the output of model 1 and model 2 after the ancillary input signals obtained by output set.It is possible thereby to see
Out, the conservative of the ancillary input signals designed based on state set-member estimation is small, and the influence to system is small.
The present embodiment conclusion: using the present invention to the low frequency model ancillary input signals of permanent magnet direct current motor, by system
Original state, the range of process interference and measurement noise indicated using zonotopes, utilize zonotopes theoretical
And Extended Kalman filter designs to obtain state observer, real-time estimation obtains state, estimates to obtain by model l and model j
State where zonotopes intersection obtain ancillary input signals for empty design, it is by the auxiliary injected system, this is auxiliary
Input signal injected system is helped, abundant excitation system realizes the separation of two models.Using zonotopes to system not
Determination is described, and by Design assistant input signal, realizes multi-model separation, is that a kind of lower auxiliary of conservative is defeated
Enter Design of Signal method.
Claims (5)
1. the design method of the ancillary input signals based on state set-member estimation, characterized by the following steps:
Step 1: the process interference of system, measurement incorrect noise are indicated with zonotopes；
Step 2: the thought design point observer combined using zonotopes theory and Kalman filtering is estimated in real time
The state of meter systems；
Step 3: in order to be recognized to multiple approximate models, in the smallest situation of systematic influence, Design assistant input
Signal, so that the intersection of the zonotopes where the real-time status of each model is sky；
Step 4: by the ancillary input signals injected system, abundant excitation system, the separation of implementation model.
2. the design method of the ancillary input signals according to claim 1 based on state set-member estimation, it is characterised in that:
The process interference of system, measurement incorrect noise are indicated with zonotopes.
3. the design method of the ancillary input signals according to claim 1 based on state set-member estimation, it is characterised in that:
The thought design point observer combined using zonotopes theory and Kalman filtering, real-time estimation obtain system
State.
4. the design method of the ancillary input signals according to claim 1 based on state set-member estimation, it is characterised in that:
In order to recognize to multiple approximate models, in the smallest situation of systematic influence, pass through the real-time status point of each model
The intersection of zonotopes where not is empty Design assistant input signal.
5. the design method of the ancillary input signals according to claim 1 based on state set-member estimation, it is characterised in that:
By the ancillary input signals injected system, abundant excitation system, the separation of implementation model.
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