CN111856933A - Design method of self-adaptive controller of aircraft engine considering uncertainty - Google Patents

Design method of self-adaptive controller of aircraft engine considering uncertainty Download PDF

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CN111856933A
CN111856933A CN202010640775.0A CN202010640775A CN111856933A CN 111856933 A CN111856933 A CN 111856933A CN 202010640775 A CN202010640775 A CN 202010640775A CN 111856933 A CN111856933 A CN 111856933A
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CN111856933B (en
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杜宪
石岩
杨林翰
吴玉虎
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Dalian University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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Abstract

The invention belongs to the field of design of control algorithms of aero-engines, and provides a design method of an aero-engine self-adaptive controller considering uncertainty. The method is designed aiming at the multivariable self-adaptive controller of the aero-engine under the uncertainty of performance degradation, manufacturing tolerance, unmodeled dynamics and the like, and comprises a new identification model selection mechanism, so that the set reference model state is tracked under the premise, and the requirement of multivariable control of the aero-engine is met. Meanwhile, the unknown parameters with more dimensions can be processed in the design of the filter. In addition, two performance indexes with different priorities are selected in the identification model selection mechanism, and the first-level index can better reflect the information of the system model, so the transient performance of the system can be improved. Finally, the Simulink simulation structure built by the invention is convenient to add and modify the identification model or change the system parameters, and is suitable for simulation verification of other systems with unmodeled dynamic and affine items.

Description

Design method of self-adaptive controller of aircraft engine considering uncertainty
Technical Field
The invention provides a method for designing and verifying a self-adaptive controller aiming at uncertainty of an aero-engine due to performance degradation, manufacturing tolerance, unmodeled dynamics and the like, and belongs to the field of design of aero-engine control algorithms.
Background
The invention relies on the background of a certain type of aeroengine control system, and aims at the influence of performance degradation, manufacturing tolerance and unmodeled system dynamics of the aeroengine to design and verify a multivariable adaptive controller meeting the system performance.
Aircraft engines are important components of aircraft, and they greatly affect the performance and safety of the aircraft. When the engine runs for a long time, the performance of the engine can be gradually reduced, and the problem that the thrust of the engines on two sides of the airplane is not matched in practice can be caused, so that the airplane has yaw or other serious problems. In addition, the balance point of the system operation is also shifted due to errors caused during the manufacturing of the engine. Meanwhile, because the structure of the aircraft engine is very complex, the operation dynamics of the aircraft engine cannot be accurately expressed, so that the influence of unmodeled dynamics of the system needs to be considered. In addition, since whether the aircraft engine operating state is good depends on the combined action of a plurality of parameters, the design of the aircraft engine controller also needs to meet the requirement of multivariable control.
Aiming at the uncertainty of performance degradation, manufacturing tolerance, unmodeled dynamics and the like in the design of an engine control system, the invention provides and designs a multivariable self-adaptive controller to meet various performance requirements of an engine. Adaptive control is an important method for solving the problem that the system contains unknown parameters and uncertainty. Compared with other methods, the adaptive control can adapt to the change of the system and the external environment, and other methods rely on the stability margin or other indexes considered before the design to solve the control problem. However, adaptive control also has the problems of slow system response rate, etc. In recent years, in order to improve the transient characteristics of a control system, multi-model adaptive control has gained more and more attention, and the structure of the multi-model adaptive control generally comprises three basic parts: the recognition model set, the controller and the recognition model selection mechanism, and the adaptive recognition model and the fixed recognition model can be included in the recognition model. In addition, each recognition model in the traditional multi-model adaptive control method has a corresponding controller, but the number of the recognition models is increased, and the number of the controllers is also increased correspondingly. Since the conventional controller is similar in structure, there is a related research to set the controller part in the multi-model adaptation to a parameter resettable form, thereby avoiding the problem of an excessive number of controllers. In addition, regarding the selection problem of the multi-recognition model, the existing research mainly uses the performance index with forgetting factor as the basis for selecting the recognition model, but under the selection mechanism, the limited time recognition model constructed by using the filter is only used for resetting the real parameters of the system to the fixed recognition model with one resettable parameter, and the acquired unknown parameters of the system are not related to the selection mechanism of the recognition model. Meanwhile, the performance index of the traditional identification model switching only considers the identification error at the current moment and the identification error accumulated in a period of time before, but the accuracy of the identification model is not only reflected in the state error, and the derivative of the state can more reflect the information of the model, so the invention provides the performance index of the derivative term by using the identification error so as to better reflect the information of the model.
In summary, the invention provides a method for describing and modeling an aircraft engine with manufacturing process errors, performance degradation and unmodeled dynamics by using an affine system, and designs a multivariable adaptive controller with resettable parameters and an identification model selection mechanism based on a multi-identification model and a model reference adaptive method, so that the system dynamics can track an upper reference model, improve the transient performance of the system, and finally verify the relevant design on MATLAB/Simulink.
Disclosure of Invention
In order to solve the problem of balance point movement caused by uncertainty existing in an engine system due to performance degradation, manufacturing tolerance, unmodeled dynamics and the like and improve the transient performance of an engine control system, the invention provides a design and verification method of a multivariable adaptive controller with resettable parameters and a multi-identification model selection mechanism.
The technical scheme of the invention is as follows:
an adaptive controller design method for an aircraft engine considering uncertainty comprises the following steps:
s1, abstracting an aircraft engine dynamic system into an affine system containing unknown constant terms, and setting expected reference model dynamics and applicable conditions;
the steps of carrying out abstract modeling on the system and determining the applicable conditions are as follows:
S1.1, firstly, considering a certain type of aeroengine, determining a dynamic system model of the aeroengine, wherein a continuous state space expression of the aeroengine is as follows:
Figure BDA0002571382890000032
wherein x (t) e RnIs a state vector, u (t) e RmFor control vectors, and m > 1, A ═ θ1,θ2,…,θn]T∈Rn×nFor system matrices containing unknown constant parameters, θi＝[ai1,ai2,…,ain]TI e {1,2 …, n }, where any element may be unknown, B e Rn×mAs an input matrix, d ∈ RnIs an unknown affine constant vector;
s1.2 consider the reference model dynamic system expression as:
Figure BDA0002571382890000031
wherein xm(t) is the reference model state vector, r (t) is the reference input, AmHurwitz matrix co-dimensional with A, BmAnd B is the input matrix of the same dimension. dmA constant vector representing an ideal balance point of the system;
applicable conditions for S1.3 are as follows:
s1.31 Condition 1
The range of unknown parameters is known, i.e.:
θi∈Ωi＝{θi∈Rn|θimin≤θi≤θimax}
d∈Φ＝{d∈Rn|dmin≤d≤dmax}
wherein theta isimin＝[θi1min,θi2min,...,θinmin],θimax＝[θi1max,θi2max,...,θinmax]，
dmin＝[d1min,d2min,...,dnmin],dmax＝[d1max,d2max,...,dnmax]；
S1.32 Condition 2
The presence matrix M ∈ Rm×nB × M is an invertible matrix, i.e.:
|B×M|≠0；
s2, designing a parameter-resettable multivariable adaptive controller, a filter containing multidimensional unknown parameters and an identification model selection mechanism according to a system dynamic equation and reference model dynamics;
the specific design steps are as follows:
s2.1, setting the tracking error as e and setting the control target as e as x-xmApproaching 0, then
Figure BDA0002571382890000041
S2.2, according to the change rate of the tracking error and depending on the adaptive control theory, the design parameter-resettable multivariable adaptive controller is in the following form:
Figure BDA0002571382890000042
where N is the inverse of the matrix BM,
Figure BDA0002571382890000043
for the estimated value of unknown affine vector d, A ═ θ1θ2...θn]TIn the case of an unknown matrix, the matrix,
Figure BDA0002571382890000044
an estimation matrix of A, and setting
Figure BDA0002571382890000045
Figure BDA0002571382890000046
Order to
Figure BDA0002571382890000047
Thus, can obtain
Figure BDA0002571382890000048
S2.3 in order to make the system tracking error approach to 0, an estimation matrix needs to be designed
Figure BDA0002571382890000049
And estimating affine vectors
Figure BDA00025713828900000410
The adaptive law of (1) is as follows:
Figure BDA00025713828900000411
Figure BDA00025713828900000412
wherein1And beta1Programmable matrices and parameters, respectively, P, Q is a positive definite matrix, and satisfies:
Am TP+PAm≤-Q；
s2.4, in order to improve the transient performance of system control, a filter and a multi-identification model need to be designed, wherein the filter is used for calculating the actual unknown parameters of the system and participating in an identification model selection mechanism, and the multi-identification model is used for ensuring that one identification model is closest to the dynamic state of a controlled system object at any moment, so that the estimation parameters of the identification model can be reset to the self-adaptive controller so as to improve the response speed of the system;
s2.41, further dynamically listing the aircraft engine system into two parts, wherein one part comprises unknown parameters, and the other part does not comprise system unknown items, namely:
Figure BDA0002571382890000051
Wherein
Figure BDA0002571382890000052
Figure BDA0002571382890000053
g＝Bu∈Rn；
S2.42 constructs a filter containing multidimensional unknown parameters as follows:
Figure BDA0002571382890000054
Figure BDA0002571382890000055
wherein ω is0∈Rn,
Figure BDA0002571382890000056
Is the filter state, A0Is a Hurwitz matrix and satisfies
Figure BDA0002571382890000057
While keeping the variable ζ ═ x- ω0-ωη；
S2.43 in order to obtain system unknown parameters, the following reasoning is utilized:
lesion 1, for k ∈ N, there are
Figure BDA0002571382890000058
Figure BDA0002571382890000059
Where τ is the integrated time variable, assuming there is a time tkcSuch that P (t)kc) Is reversible, i.e.
Figure BDA00025713828900000510
And is
P-1(tkc)Q(tkc)∈{Ωi,Φ}
Then
η＝[θ1 T,θ2 T,...,θn Td1d2...,dn]T＝P-1(t)Q(t)；
S2.5 in order to ensure that the identification model closest to the controlled object can be selected at any time, an identification model set needs to be designed, wherein the identification model set comprises N fixed identification models, 1 fixed identification model capable of resetting parameters and 1 self-adaptive identification model, and the model expression is as follows:
Figure BDA0002571382890000061
Figure BDA0002571382890000062
to estimate the system state x, where p ∈ {0,1,2 … N +1},
Figure BDA0002571382890000063
in order to fix the parameters of the recognition model,
Figure BDA0002571382890000064
to adaptively identify the parameter estimates of the model,
Figure BDA0002571382890000065
parameter estimation values of a fixed model which can be subjected to parameter resetting;
s2.6 after N +2 identification models are determined, switching selection is carried out on the identification models by means of a model selection mechanism, the selection mechanism comprises two switching indexes with different priorities, one switching index utilizes real parameters calculated by a filter, and the other switching index continues to use the traditional hysteresis switching index, and the specific form is as follows:
Figure BDA0002571382890000066
Figure BDA0002571382890000067
Wherein
Figure BDA0002571382890000068
κ＞0,p∈P,k∈N,c1,c2Are all constant, and phip(t) has a higher priority than Ψp(t)；
S2.6.1 construction of the recognition model selection algorithm
Initialization: initially selecting a normal number h and randomly selecting an identification model in an initial state, i.e.
Figure BDA0002571382890000069
Setting P, Q as 0;
step 1: firstly, resetting parameters to a self-adaptive controller by using an identification model at an initial moment, adjusting the parameters by the controller according to a self-adaptive law corresponding to S2.3 and acting the parameters to an aircraft engine controller, and meanwhile, starting to calculate the parameters of the two limited time identification models P and Q;
step 2: judging whether the current time S2.43 theorem is satisfied, if so, resetting the real parameters to the (N + 1) th identification model, and simultaneously utilizing the first-level index phi in S2.6p(t), i.e. the square of the sum of the square of the recognition error and the absolute value of the derivative of the recognition error at the current time, is given by phi at the current timep(t) minimum parameters of the identification model
Figure BDA0002571382890000071
Taking out and entering step 4; if the conditions for leading are not satisfiedIf yes, entering step 3;
and step 3: holding
Figure BDA0002571382890000077
Fixed until tkl＞tkSo that
Figure BDA0002571382890000072
At this time, let
Figure BDA0002571382890000073
And 4, step 4: resetting the parameters of the adaptive controller to
Figure BDA0002571382890000074
And 5: the controller controls by using the updated value of the step 4, and repeatedly calculates from the step 2 until the system tracks the dynamic state of the reference model;
S3, building a control system simulation in the Simulink, and verifying the designed controller and the identification model selection mechanism;
s3.1, building a state space description of a controlled object and a state space description of a reference model by using a built-in mathematical module of Simulink, and building a control vector according to the theoretical control law; secondly, an improved filter model is built, the filter model can process multidimensional unknown parameters, after the filter is built, an identification model set is selected and built, and finally the modules are connected;
s3.2, constructing an identification model selection mechanism module, wherein the input is P, Q matrix in the S2.43 lemma 1 and identification error of the identification model and corresponding identification error
Figure BDA0002571382890000075
Outputting the identification model parameter with the minimum identification error at the current moment
Figure BDA0002571382890000076
S3.3, connecting the selected parameters with an adaptive controller so as to reset the parameters;
and S3.3, given a reference signal vector, operating the simulation model, and checking the tracking effect of the system, the selection index change of the identification model and the switching condition of the identification model.
The invention has the following beneficial results: the invention provides a design of a multivariable self-adaptive controller aiming at the uncertainty of the aeroengine such as performance degradation, manufacturing tolerance, unmodeled dynamic state and the like, and comprises a new identification model selection mechanism, so that the state of a set reference model can be tracked on the premise of existence of the unfavorable conditions, and the requirement of multivariable control of the aeroengine is met. Meanwhile, compared with the past related research on the design of the filter, the method can process more multidimensional unknown parameters. In addition, two performance indexes with different priorities are selected in the identification model selection mechanism, and the first-level index can better reflect the information of the system model, so the transient performance of the system can be improved. Finally, the Simulink simulation structure built by the invention is convenient to add and modify the identification model or change the system parameters, and is suitable for simulation verification of other systems with unmodeled dynamic and affine items.
Drawings
FIG. 1 is a block diagram of an aircraft engine control system
FIG. 2 is a diagram of an identification model selection strategy
FIG. 3 is a system state tracking error diagram
FIG. 4 is a diagram of identification model switching signals
FIG. 5 is a graph of one-level performance indicators for switching of identification models
Detailed Description
The invention will be further explained with reference to the drawings.
A design and verification method of a multivariable adaptive controller of an aeroengine considering uncertainty of performance degradation, manufacturing tolerance, unmodeled dynamics and the like comprises the following steps:
s1, modeling an aircraft engine system with uncertainties such as performance degradation, manufacturing tolerance, unmodeled dynamic state and the like into an affine system in a dynamic abstract mode, and setting reference model dynamics and corresponding applicable conditions;
s2, designing a parameter-resettable adaptive controller, a filter containing multidimensional unknown parameters and an identification model selection mechanism according to a system dynamic equation and reference model dynamics;
s3, building a control system simulation in MATLAB/Simulink, and verifying the designed controller and the identification model selection mechanism;
the method comprises the following steps of modeling an aircraft engine dynamic abstraction into an affine system and setting dynamic and applicable conditions of a reference model:
S1, for the dynamic state of a certain type of aeroengine, an abstract modeling is performed to form an affine system as follows:
Figure BDA0002571382890000091
wherein the engine system state is x ═ Δ NfΔNc]TI.e., low and high rotor speeds, with a system input of u ═ Δ WFΔVSV]TI.e. fuel flow and adjustable stator vane angle, given the current
Figure BDA0002571382890000092
In order for the system matrix to be unknown,
Figure BDA0002571382890000093
in order to input the matrix, the input matrix is,
Figure BDA0002571382890000094
is an unknown affine term;
s2, setting the ideal reference model dynamics as follows:
Figure BDA0002571382890000095
wherein
Figure BDA0002571382890000096
Figure BDA0002571382890000097
S3, considering the following applicable conditions:
s3.1 condition 1:
the unknown parameters are bounded, i.e.:
θ1∈Ω1＝{θ1∈Rn|-5≤θ1≤2}
θ2∈Ω2＝{θ2∈Rn|-6≤θ2≤1}；
d∈Φ＝{d∈Rn|0≤d≤0.6}
s3.2 Condition 2
The aero-engine input matrix satisfies:
|B×M|≠0
namely, selection
Figure BDA0002571382890000098
The specific process of designing the parameter-resettable adaptive controller, the filter containing the multidimensional unknown parameters, and the identification model selection mechanism according to the system dynamic equation and the reference model dynamics is as follows:
s1, according to the conditions, recording the tracking error as e, and setting a control target as e-xmApproaching 0, the tracking error satisfies:
Figure BDA0002571382890000101
the multivariable adaptive controller with resettable parameters can thus be designed in the form of:
Figure BDA0002571382890000102
where N is the inverse of the matrix BM,
Figure BDA0002571382890000103
for the estimated value of unknown affine vector d, A ═ θ1θ2...θn]TIn the case of an unknown matrix, the matrix,
Figure BDA0002571382890000104
an estimation matrix of A, and setting
Figure BDA0002571382890000105
Order to
Figure BDA0002571382890000106
Thus, can obtain
Figure BDA0002571382890000107
Figure BDA0002571382890000108
S2, in order to ensure state tracking, corresponding self-adaptive law is designed to
Figure BDA0002571382890000109
Wherein
Figure BDA00025713828900001010
S3, constructing a filter containing multidimensional unknown parameters, and firstly, arranging the dynamic state of an aircraft engine system into two parts, wherein one part contains the unknown parameters, and the other part is a known part:
Figure BDA00025713828900001011
wherein
Figure BDA00025713828900001012
η＝[θ1 T,θ2 T,d1,d2]T∈R6，g＝Bu∈R2；
S4, further taking the f, the g and the system state as filter input, and constructing a filter form as follows:
Figure BDA0002571382890000111
Figure BDA0002571382890000112
wherein ω is0∈R2,
Figure BDA0002571382890000113
In order to be a state of the filter,
Figure BDA0002571382890000114
and satisfy
Figure BDA0002571382890000115
Then select
Figure BDA0002571382890000116
While keeping the variable ζ ═ x- ω0-ωη；
S5, in order to obtain real parameters of the system and participate in an identification model selection mechanism, the following lemma is required;
lemma 1 for k ∈ N, let
Figure BDA0002571382890000117
Figure BDA0002571382890000118
Where τ is the integrated time variable, assuming there is a time tkcSuch that P (t)kc) Is reversible, i.e.
Figure BDA0002571382890000119
And is
P-1(tkc)Q(tkc)∈{Ωi,Φ},i∈{1,2}
Then
η＝[θ1 T,θ2 T,...,θn Td1d2...dn]T＝P-1(t)Q(t)；
S6, in order to improve the transient performance of the system, a plurality of identification models need to be added, and the identification models are selected as follows:
Figure BDA00025713828900001110
Figure BDA00025713828900001111
Figure BDA00025713828900001112
wherein the content of the first and second substances,
Figure BDA00025713828900001113
s7, after the identification model set is introduced, selecting a model closest to the current state of the aircraft engine at the current moment by using an identification model selection mechanism, and resetting parameters to the controller, so that the following performance indexes are utilized:
Figure BDA0002571382890000121
Figure BDA0002571382890000122
wherein
Figure BDA0002571382890000123
And phip(t) has a higher priority than Ψp(t)；
S8, selecting the identification model by using an identification model selection mechanism as follows:
Initialization: initially selecting a normal number h equal to 0.1, and randomly selecting an initial shapeThe identification model in the state, i.e. σ (t)0) 1, while setting P, Q to an initial value of 0;
step 1: firstly, resetting parameters to a self-adaptive controller by using an identification model at an initial moment, adjusting the parameters by the controller according to a self-adaptive law corresponding to S2.3 and acting the parameters to an aircraft engine controller, and meanwhile, starting to calculate the parameters of the two limited time identification models P and Q;
step 2: judging whether the theorem 1 of S2.43 at the current moment is met, if so, resetting the real parameters to the (N + 1) th identification model, and simultaneously utilizing the first-level index phi in S2.6p(t), i.e. the square of the sum of the square of the recognition error and the absolute value of the derivative of the recognition error at the current time, is given by phi at the current timep(t) minimum parameters of the identification model
Figure BDA0002571382890000124
Taking out and entering step 4; if the lemma is not satisfied, entering step 3;
and step 3: hold σ (t)k) Fixed 1 up to tkl＞tkSo that
Figure BDA0002571382890000125
At this time, let
Figure BDA0002571382890000126
And 4, step 4: resetting the parameters of the adaptive controller to
Figure BDA0002571382890000127
And 5: the controller controls by using the updated value of the step 4, and repeatedly calculates from the step 2 until the system tracks the dynamic state of the reference model;
according to the theoretical conditions, a Simulink simulation structure is built by referring to a structure diagram shown in FIG. 1, and the specific steps are as follows:
S1, building a controlled object dynamic state, a reference model dynamic state, a multi-dimensional filter, an identification model set and a controller by utilizing various built-in mathematical modules of Simulink;
s2, as shown in the flow of FIG. 2, an identification model selection mechanism module is set up, three output interfaces of the module are respectively selected identification model parameters, the change condition of the performance index at the current moment and identification model switching signals;
s3, connecting the identification model parameters at the output end of the identification model selection mechanism module with an integrator with unknown parameters in the controller, setting the initial value of the integrator as external signal trigger, and setting the trigger form as rising edge trigger, so as to reset the corresponding parameters selected by the identification model to the parameters in the corresponding controller;
s4, after connection is finished, connecting a given reference input signal at the input end of the reference model, setting the simulation time to be 20s, and setting the initial value of the state of the aircraft engine to be x ═ 0.5,0.2]T(ii) a After the system operates, as shown in fig. 3, the tracking error between the state of the aircraft engine and the reference model approaches to 0, and the control target is reached; in addition, in order to illustrate the switching of the identification models during the operation of the system, fig. 4 and 5 respectively show an identification model switching selection signal and switching performance index states corresponding to different identification models, wherein 0 to 6s are taken as an example, as shown in fig. 4, the switching signal is equal to 1 in the initial condition, but P and Q are equal to 0 at this time, so that the identification model is selected by using the secondary performance index Ψ, and at this time, the parameters of the identification model 1 are reset to the controller; after that, since P is 1.0049 × 10 -31If the comparison result is more than 0, and P is more than 0 afterwards, therefore, the lemma condition is met, and the system adopts a first-level performance index phi as the identification model for switching; as can be seen from fig. 5, the first-level performance index value of the identification model 3 in the first 0.2s is the minimum, so the model is selected, the parameters are reset to the controller, the first-level performance index value of the identification model 2 in the period of 0.2s to 2.1s is the minimum, so the parameters of the identification model 2 are reset to the adaptive controller, and the last-level performance index value of the identification model 1 in the period of 2.1s to 6s is the minimum, so the parameters of the identification model 3 are reset to the controller. The subsequent time is repeated until the state tracking error approaches 0.
In conclusion, the design and verification method of the adaptive controller and the identification model switching mechanism aiming at the uncertainty of the aero-engine, such as performance degradation, manufacturing tolerance, unmodeled dynamic state and the like, is feasible, and can ensure the dynamic state of the corresponding reference model on system tracking and improve the transient performance.

Claims (1)

1. An adaptive controller design method for an aircraft engine considering uncertainty is characterized by comprising the following steps:
s1, abstracting an aircraft engine dynamic system into an affine system containing unknown constant terms, and setting expected reference model dynamics and applicable conditions;
The steps of carrying out abstract modeling on the system and determining the applicable conditions are as follows:
s1.1, firstly, considering a certain type of aeroengine, determining a dynamic system model of the aeroengine, wherein a continuous state space expression of the aeroengine is as follows:
Figure FDA0002571382880000011
wherein x (t) e RnIs a state vector, u (t) e RmFor control vectors, and m > 1, A ═ θ1,θ2,…,θn]T∈Rn×nFor system matrices containing unknown constant parameters, θi＝[ai1,ai2,…,ain]TI e {1,2 …, n }, where any element may be unknown, B e Rn×mAs an input matrix, d ∈ RnIs an unknown affine constant vector;
s1.2 consider the reference model dynamic system expression as:
Figure FDA0002571382880000012
wherein xm(t) is the reference model state vector, r (t) is the reference input, AmHurwitz matrix co-dimensional with A, BmAn input matrix co-dimensional with B; dmA constant vector representing an ideal balance point of the system;
applicable conditions for S1.3 are as follows:
s1.31 Condition 1
The range of unknown parameters is known, i.e.:
θi∈Ωi＝{θi∈Rn|θimin≤θi≤θimax}
d∈Φ＝{d∈Rn|dmin≤d≤dmax}
wherein theta isimin＝[θi1min,θi2min,...,θinmin],θimax＝[θi1max,θi2max,...,θinmax]，
dmin＝[d1min,d2min,...,dnmin],dmax＝[d1max,d2max,...,dnmax]；
S1.32 Condition 2
The presence matrix M ∈ Rm×nB × M is an invertible matrix, i.e.:
|B×M|≠0；
s2, designing a parameter-resettable multivariable adaptive controller, a filter containing multidimensional unknown parameters and an identification model selection mechanism according to a system dynamic equation and reference model dynamics;
the specific design steps are as follows:
s2.1, setting the tracking error as e and setting the control target as e as x-x mApproaching 0, then
Figure FDA0002571382880000021
S2.2, according to the change rate of the tracking error and depending on the adaptive control theory, the design parameter-resettable multivariable adaptive controller is in the following form:
Figure FDA0002571382880000022
where N is the inverse of the matrix BM,
Figure FDA0002571382880000023
for the estimated value of unknown affine vector d, A ═ θ1θ2...θn]TIn the case of an unknown matrix, the matrix,
Figure FDA0002571382880000024
an estimation matrix of A, and setting
Figure FDA0002571382880000025
Figure FDA0002571382880000026
Order to
Figure FDA0002571382880000027
Thus, can obtain
Figure FDA0002571382880000028
S2.3 in order to make the system tracking error approach to 0, an estimation matrix needs to be designed
Figure FDA0002571382880000029
And estimating affine vectors
Figure FDA00025713828800000210
The adaptive law of (1) is as follows:
Figure FDA00025713828800000211
Figure FDA00025713828800000212
wherein1And beta1Programmable matrices and parameters, respectively, P, Q is a positive definite matrix, and satisfies:
Am TP+PAm≤-Q；
s2.4, in order to improve the transient performance of system control, a filter and a multi-identification model need to be designed, wherein the filter is used for calculating the actual unknown parameters of the system and participating in an identification model selection mechanism, and the multi-identification model is used for ensuring that one identification model is closest to the dynamic state of a controlled system object at any moment, so that the estimation parameters of the identification model can be reset to the self-adaptive controller so as to improve the response speed of the system;
s2.41, further dynamically listing the aircraft engine system into two parts, wherein one part comprises unknown parameters, and the other part does not comprise system unknown items, namely:
Figure FDA0002571382880000031
Wherein
Figure FDA0002571382880000032
g＝Bu∈Rn；
S2.42 constructs a filter containing multidimensional unknown parameters as follows:
Figure FDA0002571382880000033
Figure FDA0002571382880000034
wherein ω is0∈Rn,
Figure FDA0002571382880000035
Is the filter state, A0Is a Hurwitz matrix and satisfies
Figure FDA0002571382880000036
While keeping the variable ζ ═ x- ω0-ωη；
S2.43 in order to obtain system unknown parameters, the following reasoning is utilized:
lesion 1, for k ∈ N, there are
Figure FDA0002571382880000037
Figure FDA0002571382880000038
Where τ is the integrated time variable, assuming there is a time tkcSuch that P (t)kc) Is reversible, i.e.
Figure FDA0002571382880000039
And is
P-1(tkc)Q(tkc)∈{Ωi,Φ}
Then
η＝[θ1 T,θ2 T,...,θn Td1d2...,dn]T＝P-1(t)Q(t)；
S2.5 in order to ensure that the identification model closest to the controlled object can be selected at any time, an identification model set needs to be designed, wherein the identification model set comprises N fixed identification models, 1 fixed identification model with resettable parameters and 1 self-adaptive identification model, and the model expression is as follows:
Figure FDA0002571382880000041
Figure FDA0002571382880000042
to estimate the system state x, where p ∈ {0,1,2 … N +1},
Figure FDA0002571382880000043
in order to fix the parameters of the recognition model,
Figure FDA0002571382880000044
to adaptively identify the parameter estimates of the model,
Figure FDA0002571382880000045
parameter estimation values of a fixed model which can be subjected to parameter resetting;
s2.6 after N +2 identification models are determined, switching selection is carried out on the identification models by means of a model selection mechanism, the selection mechanism comprises two switching indexes with different priorities, one switching index utilizes real parameters calculated by a filter, and the other switching index continues to use the traditional hysteresis switching index, and the specific form is as follows:
Figure FDA0002571382880000046
Figure FDA0002571382880000047
Wherein
Figure FDA0002571382880000048
κ＞0,p∈P,k∈N,c1,c2Are all constant, and phip(t) has a higher priority than Ψp(t)；
S2.6.1 construction of the recognition model selection algorithm
Initialization: initially selecting a normal number h and randomly selecting an identification model in an initial state, i.e.
Figure FDA0002571382880000049
Setting P, Q as 0;
step 1: firstly, resetting parameters to a self-adaptive controller by using an identification model at an initial moment, adjusting the parameters by the controller according to a self-adaptive law corresponding to S2.3 and acting the parameters to an aircraft engine controller, and meanwhile, starting to calculate the parameters of the two limited time identification models P and Q;
step 2: judging whether the current time S2.43 theorem is satisfied, if so, resetting the real parameters to the (N + 1) th identification model, and simultaneously utilizing one of S2.6Grade index phip(t), i.e. the square of the sum of the square of the recognition error and the absolute value of the derivative of the recognition error at the current time, is given by phi at the current timep(t) minimum parameters of the identification model
Figure FDA00025713828800000410
Taking out and entering step 4; if the guiding condition is not met, entering the step 3;
and step 3: holding
Figure FDA00025713828800000411
Fixed until tkl＞tkSo that
Figure FDA00025713828800000412
At this time, let
Figure FDA0002571382880000051
And 4, step 4: resetting the parameters of the adaptive controller to
Figure FDA0002571382880000052
And 5: the controller controls by using the updated value of the step 4, and repeatedly calculates from the step 2 until the system tracks the dynamic state of the reference model;
S3, building a control system simulation in the Simulink, and verifying the designed controller and the identification model selection mechanism;
s3.1, building a state space description of a controlled object and a state space description of a reference model by using a built-in mathematical module of Simulink, and building a control vector according to the theoretical control law; secondly, an improved filter model is built, the filter model can process multidimensional unknown parameters, after the filter is built, an identification model set is selected and built, and finally the modules are connected;
s3.2, constructing an identification model selection mechanism module, wherein the input is P, Q matrix in the S2.43 lemma 1 and identification error of the identification model and corresponding identification error
Figure FDA0002571382880000053
Outputting the identification model parameter with the minimum identification error at the current moment
Figure FDA0002571382880000054
S3.3, connecting the selected parameters with an adaptive controller so as to reset the parameters;
and S3.3, given a reference signal vector, operating the simulation model, and checking the tracking effect of the system, the selection index change of the identification model and the switching condition of the identification model.
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