CN106959613A - Dynamical linearization adaptive control laws algorithm of the SISO systems based on recent renewal information - Google Patents

Dynamical linearization adaptive control laws algorithm of the SISO systems based on recent renewal information Download PDF

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Publication number
CN106959613A
CN106959613A CN201710236885.9A CN201710236885A CN106959613A CN 106959613 A CN106959613 A CN 106959613A CN 201710236885 A CN201710236885 A CN 201710236885A CN 106959613 A CN106959613 A CN 106959613A
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algorithm
adaptive control
pseudo
dynamical linearization
partial derivative
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吴爱国
胡志勇
张颖
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Shenzhen Graduate School Harbin Institute of Technology
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Shenzhen Graduate School Harbin Institute 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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  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
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Abstract

The present invention propose it is a kind of be directed to dynamical linearization adaptive control laws algorithm of the single-input single-output system based on recent renewal information, the purpose of the algorithm be solve Self Adaptive Control identification algorithm tracking accuracy it is not high, the problem of convergence is not strong.The algorithm is using matrix inversion principle and passs rank discrimination method, on-line identification and nearest information updating are carried out to the pseudo- partial derivative of dynamical linearization parameter of nonlinear system, and set pseudo- partial derivative reset condition, then in conjunction with MFA control rule, so as to form dynamical linearization adaptive control laws algorithm of the single-input single-output system of a series of new based on recent renewal information.Adaptive control algorithm is run by adjusting weight factor, the stepping factor, primary condition, reset condition.Compared with prior art, convergence of the present invention is stronger, to overshoot, concussion situations such as there is more preferable rejection ability；Possess higher output accuracy and more preferable regulating power, parameter regulation mode is more enriched flexible.

Description

Dynamical linearization adaptive control laws algorithm of the SISO systems based on recent renewal information
Technical field
Single-input single-output system base is directed to the present invention relates to MFA control technical field, more particularly to one kind In dynamical linearization adaptive control algorithm.
Background technology
The tracking trajectory capacity of traditional MFA control (MFAC) algorithm is not strong, and precision is not high, and convergence is bad, Regulative mode is simple.
The content of the invention
In order to overcome the deficiencies in the prior art, the invention provides a kind of dynamical linearization based on recent renewal information certainly Suitable solution restrains algorithm.For up to above-mentioned purpose, the present invention is achieved through the following technical solutions：
A kind of dynamical linearization adaptive control laws algorithm of SISO systems based on recent renewal information, the algorithm will be single The pseudo- partial derivative identification model of dynamical linearization parameter of the single output SISO systems of input resolves into two and is directed to input respectively and defeated The sub- identification model of dynamical linearization parameter gone outWithIt is as follows：
Recognize the two sub- identification models decomposed above respectively using projecting methodWithAnd obtain it and estimate Calculating methodWith
Wherein, μ1、μ2It is weight factor, η1、η2It is step series, Ly、LuIt is the exponent number of pseudo- partial derivative, #(*)TIt is Matrix transposition, Δ y (k)=y (k)-y (k-1), Δ μ (k)=μ (k)-μ (k-1)；
Then, handled using recent renewal information approach by projection identificationWithBetween associations, In dynamical linearization parameter Estimation formulaIn, use estimateInstead ofThen in estimator In, use estimateInstead of
Further, handled using recent renewal information approach by projection identificationWithBetween pass Copula, in dynamical linearization parameter Estimation formulaIn, use estimateReplaceTo updateEstimate EvaluationThen in estimatorMiddle use estimateReplace
Further, defineα is weight factor in formula, meet α ∈ (0, 1), then in estimatorIt is middle to useReplace
Further, defineβ is weight factor in formula, meet β ∈ (0, 1), then in estimatorIt is middle to useReplace
Further, full format adaptive control laws are：
Wherein, ρiIt is weight factor, ρ with λi∈ (0,1], η1∈ (0,2], η2∈ (0,2], μ1＞ 0, μ2＞ 0, λ ＞ 0.
Further, pseudo- partial derivative reset condition is set as follows：
In formulaIt isReset values,It isReset values, ε is to reset the factor, and ε is individual very small Constant.
The beneficial effects of the invention are as follows：Compared with prior art, convergence of the present invention is stronger, to overshoot, concussion situations such as With more preferable rejection ability；Possess higher output accuracy, overall precision is greatly improved；Possess more preferable regulation Ability, parameter regulation mode more enriches flexible, by joining to weight factor, the stepping factor, pseudo- partial derivative initial value and reset values Several various combinations, can be obtained and the more preferable ability of tracking of desired trajectory.
Brief description of the drawings
Fig. 1 is the dynamical linearization adaptive control algorithm FB(flow block) of the invention based on recent renewal information；
Fig. 2 is that the control output of inventive algorithm and desired output track oscillogram；
Fig. 3 is control output and the desired output tracking error figure of inventive algorithm.
Specific embodiment
The present invention is described in further detail below by embodiment combination accompanying drawing.
General nonlinear discrete time system can be expressed as：
Wherein,Y (k-1) ... y (k-n) },μ (k-2) ... μ (k-m) }, μ (k), y (k) The respectively input and output of system, f (*) is Any Nonlinear Function, and m, n are respectively the unknown exponent number of system.In accompanying drawing 1, y*(k+1) it is the desired tracking signal of system.
The pseudo- partial derivative identification model of the dynamical linearization parameter of single-input single-output SISO systems is resolved into two difference For the sub- identification model of dynamical linearization parameter for inputting and exportingWithIt is as follows：
Recognize the two sub- identification models decomposed above respectively using projecting methodWithAnd obtain it and estimate Calculating methodWith
As shown in Figure 1, algorithm of the invention passes through projection identification algorithm using the processing of recent renewal information approach WithBetween associations, first in dynamical linearization parameter Estimation formulaIn, use estimateInstead ofThen in estimatorIn, use estimateInstead ofDynamical linearization parametric scheme 1 is as follows：
Wherein, μ1、μ2It is weight factor, η1、η2It is step series, (*)TIt is matrix transposition, Ly、LuIt is the exponent number of pseudo- partial derivative, Δ y (k) =y (k)-y (k-1), Δ μ (k)=μ (k)-μ (k-1).
Handled using recent renewal information approach by projection identification algorithmWithBetween associations, Dynamical linearization parameter Estimation formulaIn, use estimateReplaceTo updateEstimateThen in estimatorMiddle use estimateReplaceDynamical linearization parametric scheme 2 is as follows：
The pseudo- partial derivative of definition weighting previous moment is as follows：
α is weight factor in formula, α ∈ (0,1) is met, then in estimatorIt is middle to useReplaceIt is dynamic State linear parameter scheme 3 is as follows：
The pseudo- partial derivative for defining another weighting previous moment is as follows：
β is weight factor in formula, β ∈ (0,1) is met, then in estimatorIt is middle to useReplaceIt is dynamic State linear parameter scheme 4 is as follows：
Set as follows by pseudo- partial derivative reset condition：
The MFA control rule of the present invention is as follows：
In formula, ρiIt is weight factor, L with λy、LuIt is the exponent number of pseudo- partial derivative.
The pseudo- partial derivative with reference to more thanWithEstimation scheme 1-4 and its reset condition (9)-(10) and self adaptation Control law (11), can obtain 4 groups of dynamic linears based on recent renewal information for single-input single-output system completely Change adaptive control laws scheme, wherein accompanying drawing 1 contains the main contents of the algorithm,WithBefore Dotted line represent they be array input, dynamical linearization estimator dotted line input be to represent estimation scheme 2.It is good in order to obtain Good tracking trajectory capacity, convergence and stability, user is needed according to parameter setting requirement and simulation data waveform come rationally The stepping factor, weight factor are set, factor ε, input and output initial value, pseudo- partial derivative initial value and reset values are resetted, otherwise as moment k When reaching some value, control output can not effectively track desired output track.Wherein ε is a very small positive number, ρi∈ (0,1], η1∈ (0,2], η2∈ (0,2], μ1＞ 0, μ2＞ 0, λ ＞ 0.
The effect of the dynamical linearization adaptive control laws based on recent renewal information will be illustrated by specific embodiment below Really.The exponent number of the pseudo- partial derivative of nonlinear system in specific embodiment is set as Ly=1, Lu=2, algorithm selects dynamic linear Change parametric scheme 1, i.e. formula (1)-(2) and formula (9)-(11).Consider that single-input single-output system nonlinear system is as follows：
Desired output signal is：
The primary condition of input and output is set to：
U (1)=u (2)=0, y (1)=y (2)=0
The stepping factor is set to
ρ1=ρ2=1, μ1=μ2=1
Weight factor is set to
η1=η2=1, λ=0.1
PG initial values are set to
Reset parameter and the reset factor are set to
Dynamical linearization adaptive control laws based on recent renewal information output and desired output of the accompanying drawing 2 for lower example Track following figure, accompanying drawing 3 be algorithm keeps track Error Graph, from accompanying drawing 2 we can be found that the algorithm have good track with Spike in track effect, accompanying drawing 3 is due to the influence that the algorithm that desired output track mutation is caused controls lag output, but whole Body output error is smaller and smoother.
Above content is to combine specific preferred embodiment further description made for the present invention, it is impossible to assert The specific implementation of the present invention is confined to these explanations.For general technical staff of the technical field of the invention, On the premise of not departing from present inventive concept, some simple deduction or replace can also be made, should all be considered as belonging to the present invention's Protection domain.

Claims (6)

1. a kind of dynamical linearization adaptive control laws algorithm of SISO systems based on recent renewal information, it is characterised in that：Institute State algorithm and the pseudo- partial derivative identification model of the dynamical linearization parameter of single-input single-output SISO systems is resolved into two difference pins To the sub- identification model of dynamical linearization parameter for inputting and exportingWithIt is as follows：
Recognize the two sub- identification models decomposed above respectively using projecting methodWithAnd obtain its estimation calculation MethodWith
Wherein, μ1、μ2It is weight factor, η1、η2It is step series, Ly、LuIt is the exponent number of pseudo- partial derivative, #(*)TIt is Matrix transposition, Δ y (k)=y (k)-y (k-1), Δ μ (k)=μ (k)-μ (k-1)；
Then, handled using recent renewal information approach by projection identificationWithBetween associations, dynamic State linear parameter estimatorIn, use estimateInstead ofThen in estimatorIn, use EstimateInstead of
2. algorithm according to claim 1, it is characterised in that：Handled using recent renewal information approach by projection identification 'sWithBetween associations, in dynamical linearization parameter Estimation formulaIn, use estimateReplace ChangeTo updateEstimateThen in estimatorMiddle use estimateReplace
3. algorithm according to claim 1, it is characterised in that：DefinitionFormula Middle α is weight factor, α ∈ (0,1) is met, then in estimatorIt is middle to useReplace
4. algorithm according to claim 3, it is characterised in that：DefinitionFormula Middle β is weight factor, β ∈ (0,1) is met, then in estimatorIt is middle to useReplace
5. the algorithm according to claim any one of 1-4, it is characterised in that full format adaptive control laws are：
Wherein, ρiIt is weight factor, L with λy、LuIt is the exponent number of pseudo- partial derivative, ρi∈ (0,1], η1∈ (0,2], η2∈ (0,2], μ1 ＞ 0, μ2＞ 0, λ ＞ 0.
6. the algorithm according to claim any one of 1-4, it is characterised in that：The pseudo- partial derivative reset condition of setting is as follows：
In formulaIt isReset values,It isReset values, ε is to reset the factor, and ε is very small normal Number.
CN201710236885.9A 2017-04-12 2017-04-12 Dynamical linearization adaptive control laws algorithm of the SISO systems based on recent renewal information Pending CN106959613A (en)

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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108154231A (en) * 2017-12-12 2018-06-12 浙江大学 Methods of self-tuning of the MISO full format Non-Model Controller based on systematic error
CN108287467A (en) * 2018-01-18 2018-07-17 河南理工大学 Model-free adaption data drive control method based on event triggering
CN110376901A (en) * 2019-08-19 2019-10-25 哈尔滨工业大学（深圳） A kind of iterative learning control method based on dynamic controller
CN110376879A (en) * 2019-08-16 2019-10-25 哈尔滨工业大学（深圳） A kind of PID type iterative learning control method neural network based
CN111913391A (en) * 2020-08-12 2020-11-10 深圳职业技术学院 Method for stabilizing self-adaptive control discrete time non-minimum phase system
CN112402732A (en) * 2020-10-10 2021-02-26 广东食品药品职业学院 Insulin infusion amount control method based on adaptive control weighting factor strategy

Cited By (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108154231A (en) * 2017-12-12 2018-06-12 浙江大学 Methods of self-tuning of the MISO full format Non-Model Controller based on systematic error
CN108154231B (en) * 2017-12-12 2021-11-26 浙江大学 System error-based parameter self-tuning method for MISO full-format model-free controller
CN108287467A (en) * 2018-01-18 2018-07-17 河南理工大学 Model-free adaption data drive control method based on event triggering
CN110376879A (en) * 2019-08-16 2019-10-25 哈尔滨工业大学（深圳） A kind of PID type iterative learning control method neural network based
CN110376901A (en) * 2019-08-19 2019-10-25 哈尔滨工业大学（深圳） A kind of iterative learning control method based on dynamic controller
CN110376901B (en) * 2019-08-19 2022-09-02 哈尔滨工业大学（深圳） Iterative learning control method based on dynamic controller
CN111913391A (en) * 2020-08-12 2020-11-10 深圳职业技术学院 Method for stabilizing self-adaptive control discrete time non-minimum phase system
CN111913391B (en) * 2020-08-12 2022-05-24 深圳职业技术学院 Method for stabilizing self-adaptive control discrete time non-minimum phase system
CN112402732A (en) * 2020-10-10 2021-02-26 广东食品药品职业学院 Insulin infusion amount control method based on adaptive control weighting factor strategy

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