CN113625563A - DC motor quantization iterative learning fault-tolerant control method - Google Patents

DC motor quantization iterative learning fault-tolerant control method Download PDF

Info

Publication number
CN113625563A
CN113625563A CN202110900739.8A CN202110900739A CN113625563A CN 113625563 A CN113625563 A CN 113625563A CN 202110900739 A CN202110900739 A CN 202110900739A CN 113625563 A CN113625563 A CN 113625563A
Authority
CN
China
Prior art keywords
input
quantization
fault
output
motor
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110900739.8A
Other languages
Chinese (zh)
Other versions
CN113625563B (en
Inventor
陶洪峰
黄彦德
庄志和
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Jiangnan University
Original Assignee
Jiangnan University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Jiangnan University filed Critical Jiangnan University
Priority to CN202110900739.8A priority Critical patent/CN113625563B/en
Publication of CN113625563A publication Critical patent/CN113625563A/en
Application granted granted Critical
Publication of CN113625563B publication Critical patent/CN113625563B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P7/00—Arrangements for regulating or controlling the speed or torque of electric DC motors
    • H02P7/06—Arrangements for regulating or controlling the speed or torque of electric DC motors for regulating or controlling an individual dc dynamo-electric motor by varying field or armature current
    • H02P7/18—Arrangements for regulating or controlling the speed or torque of electric DC motors for regulating or controlling an individual dc dynamo-electric motor by varying field or armature current by master control with auxiliary power

Abstract

The invention discloses a direct current motor quantization iterative learning fault-tolerant control method, which relates to the field of direct current motor fault-tolerant control, and is characterized in that a repeatedly-operated direct current motor is converted into a time-series input-output matrix model based on a lifting technology, a coder-decoder is designed based on the property of a logarithmic quantizer, and the influence of quantization errors on the tracking performance of a system is reduced; modifying a traditional norm optimization framework, designing a performance index function in a mathematical expectation meaning, and further obtaining a quantitative iterative learning fault-tolerant control algorithm; an actuator fault model is established, and a compression mapping method is utilized to prove that the designed quantitative iterative learning fault-tolerant control law can solve the problem of track tracking of a direct current motor with limited network communication bandwidth when the actuator fails.

Description

DC motor quantization iterative learning fault-tolerant control method
Technical Field
The invention relates to the field of fault-tolerant control of direct-current motors, in particular to a quantitative iterative learning fault-tolerant control method for a direct-current motor.
Background
The electric motor is an important device for completing the conversion between electric energy and mechanical energy as the core of an electric drive system. The direct current motor has the characteristics of simple converter, good speed regulation performance, capability of realizing excellent running performance and the like, and is widely applied to the field of industrial manufacturing.
With the rapid development of computers and communication technologies, input and output signals between the direct current motor and the controller can be transmitted by adopting a network, so that field wiring is reduced, allocation of control resources is improved, and remote control of the motor is realized. Due to the limited communication bandwidth of the network and reliability considerations, the signals need to be quantized to reduce the amount of information transmitted, reduce the transmission burden, and improve the system operating efficiency. On the other hand, for a direct current motor executing a repeated operation task, iterative learning control can achieve a good control effect and complete accurate tracking of an expected track, because an actuator usually reciprocates at a high frequency in the iterative learning control process and mechanical fatigue and loss of the actuator are easily generated, the influence of actuator faults on control performance and safety needs to be considered, and the designed iterative learning control law is expected to have certain fault-tolerant performance, so that the system output can track the expected track as much as possible under the condition that the actuator has faults. Therefore, for the direct current motor which adopts a network communication scheme and has the repeated operation characteristic, the design of the iterative learning fault-tolerant controller under the condition of quantitative data is a research with practical significance.
In the context of network control, quantization error exists in a transmission signal due to quantization, which makes the control effect of a conventional iterative learning fault-tolerant control algorithm not ideal, and therefore a corresponding mechanism is required to eliminate the influence caused by the quantization error, so as to achieve the purpose of accurately tracking a desired track.
Disclosure of Invention
The invention provides a quantization iterative learning fault-tolerant control method for a direct-current motor aiming at the problems and the technical requirements, a quantization codec is designed by combining a logarithmic quantizer and a coding and decoding mechanism, accurate signal transmission is realized in an iterative mode, a quantization iterative learning fault-tolerant control algorithm is built by adopting a norm optimization algorithm frame, and a robust bounded convergence condition of a system is obtained according to a compression mapping method.
The technical scheme of the invention is as follows:
a DC motor quantization iterative learning fault-tolerant control comprises the following steps:
firstly, establishing a dynamic model of a direct current motor:
the dynamic model is expressed by a dynamic equation and describes the conversion relation between the input voltage and the rotating speed of the motor; according to the relation between the motor rotating speed and the electrical parameter, an actual physical model shown in the formula (1) is established:
Figure BDA0003199693020000021
wherein R isaRepresenting armature resistance, LaRepresenting armature inductance, CeRepresenting the back electromotive force coefficient, CfIndicating mechanical damping of the motor, JrRepresenting the moment of inertia of the rotor, CMRepresenting the torque coefficient, ω representing the motor speed, e representing the input voltage, iaRepresents armature current;
secondly, constructing a discrete state space equation of the direct current motor:
defining the armature current and the rotating speed of the direct current motor as state variables: x ═ ia ω]TWhen the input variable is defined as the input voltage e and the output is defined as the motor speed ω, the dc motor represented by equation (1) is described as:
Figure BDA0003199693020000022
y＝[0 1]x
discretizing the model formula (2) of the continuous system, and selecting a sampling period T meeting the Shannon sampling theoremsObtaining a discrete state space model of the direct current motor as follows:
Figure BDA0003199693020000023
wherein T and k respectively represent sampling time and batch, and the operation period of the batch process is T; within each cycle of the repetitive process, for a point in time T e 0, T]Taking N sampling points; u. ofk(t)、yk(t) and xk(t) input, output and state vectors at time t of the kth lot of the system, respectively; A. b, C is the parameter matrix of the discrete system in equation (3), and it satisfies CB ≠ 0, and it is assumed that the initial state of each batch of the system is consistent, i.e. xk(0)＝x0；
Thirdly, establishing a track tracking model:
for a linear discrete system in the form of equation (3), converting a state space expression of the system into a time-series input-output matrix model:
yk＝Guk+dk (4)
wherein:
Figure BDA0003199693020000031
dk＝[CA CA2 CA3 ... CAN]Txk(0)
uk＝[uk(0),uk(1),...,uk(N-1)]T
yk＝[yk(1),yk(2),...,yk(N)]T
g is an input-output transfer matrix on a time series; dkIs the effect of the initial state of the system on the output, assuming xk(0)＝0,
Figure BDA0003199693020000039
Then dk＝0；
Step four, designing a quantization codec:
in a system using network transmission signals, because the network bandwidth is limited, the goal of accurately tracking the track needs to be realized under the condition of reducing the amount of transmitted information, so the signals can be quantized, and an input end quantization codec is designed as follows:
Figure BDA0003199693020000032
Figure BDA0003199693020000033
where 0 represents a zero vector having the same dimensions as the system input, uk(t)、
Figure BDA0003199693020000034
And
Figure BDA0003199693020000035
are respectively an encoder E1Input, output and internal states of;
Figure BDA0003199693020000036
is a decoder D1I.e. the controller output uk(t) an estimate of; q (-) is a logarithmic quantizer defined by equation (7):
Figure BDA0003199693020000037
where v represents the input to the log quantizer;
Figure BDA0003199693020000038
μ is the selected quantization density, and the quantization levels are as follows:
Z＝{±zi|zi＝μiz0,i＝0,±1,±2,…}∪{0},0<μ<1,z0>0
the output side quantization codec is designed as follows:
Figure BDA0003199693020000041
Figure BDA0003199693020000042
where 0 represents a zero vector having the same dimensions as the system output, yk(t)、
Figure BDA0003199693020000043
And
Figure BDA0003199693020000044
are respectively an encoder E2Input, output and internal states of;
Figure BDA0003199693020000045
is a decoder D2I.e. the system output yk(t) an estimate of;
fifthly, establishing a relational expression of signals before and after quantization:
the input v of the logarithmic quantizer and the output q (v) have a quantization error Δ v, which is processed by a fan-bounded method, and for k batches of signals at time t:
q(vk(t))＝(1+ηk(t))vk(t) (10)
wherein eta isk(t) represents a relative quantization error, and satisfies
Figure BDA0003199693020000046
From the input quantization codec definition and equation (10), we obtain:
Figure BDA0003199693020000047
by using the mathematical induction method of
Figure BDA0003199693020000048
Is established so that
Figure BDA0003199693020000049
And uk+1(t) ofThe relation is as follows:
Figure BDA00031996930200000410
lifting the formula (12) into a vector form to obtain
Figure BDA00031996930200000411
And uk+1The vector relationship of (a) is:
Figure BDA00031996930200000412
wherein:
Figure BDA00031996930200000413
by quantizing the codec definition at the output
Figure BDA00031996930200000414
And yk+1The vector relationship of (a) is:
Figure BDA00031996930200000415
wherein:
Figure BDA00031996930200000416
the relative quantization error is independent of the quantizer input, so there is E v for any k batches at time tk(t)ηk(t)]0; the relative quantization errors produced by the different quantizers are also independent of each other, i.e.
Figure BDA0003199693020000051
i ≠ j and i, j ∈ {1,2 }; while in the same quantizer, the relative quantization error etak(t) in the interval [ - δ, δ]Inner uniform distribution and for arbitrary k1，k2And t1，t2Satisfies the following conditions:
Figure BDA0003199693020000052
wherein the content of the first and second substances,
Figure BDA0003199693020000053
thus, cancel by taking the mathematically expected way
Figure BDA0003199693020000054
And
Figure BDA0003199693020000055
the actual tracking error e exists in the systemk+1＝yd-yk+1And correcting errors with assistance
Figure BDA0003199693020000056
The actual tracking error really reflects the tracking performance of the system, and the controller corrects the input signals of the current batch by using the auxiliary correction error; according to
Figure BDA0003199693020000057
Obtaining:
Figure BDA0003199693020000058
therefore, a relation between the current actual error sequence and the auxiliary correction error sequence of the previous batch is established:
Figure BDA0003199693020000059
sixthly, designing a quantitative iterative learning fault-tolerant control trajectory tracking optimization algorithm:
considering a norm optimal iterative learning control framework, the control input of each batch is obtained by optimizing a performance index function, and the general form of the performance index function is as follows:
Figure BDA00031996930200000510
the performance index function comprises actual tracking error, control oscillation and control energy; in the optimization process, each part is represented by symmetrical positive definite weight matrixes Q and R and a symmetrical non-negative definite weight matrix S respectively, namely Q is QT>0,R＝RT>0,S＝STNot less than 0; taking the weight matrix Q-qI, R-rI, S-sI, and the induction norm is defined as follows:
Figure BDA00031996930200000511
Figure BDA00031996930200000512
Figure BDA00031996930200000513
and
Figure BDA00031996930200000514
none contain a random variable, so its expectation is equal to itself;
definition of
Figure BDA00031996930200000515
Ξ＝σ2diag(γ11,γ22,…,γNN) Obtained according to formula (17):
Figure BDA00031996930200000516
xi and sigma2I are all symmetric positive definite matrixes; substituting equation (19) into the performance indicator function (18) yields:
Figure BDA0003199693020000061
solving a quadratic optimal solution of the formula (20) to obtain:
Figure BDA0003199693020000062
due to (G)TQG + xi + R + S) is reversible, and the quantized iterative learning fault-tolerant control law obtained by sorting the formula (21) is as follows:
Figure BDA0003199693020000063
wherein:
Figure BDA0003199693020000064
step seven, establishing an actuator fault model:
input for actually controlling DC motor
Figure BDA0003199693020000065
Order to
Figure BDA0003199693020000066
An output signal representing an actuator fault, defining an actuator fault model:
Figure BDA0003199693020000067
wherein:
Figure BDA0003199693020000068
actuator failure coefficient alphaiUnknown, but in range
Figure BDA0003199693020000069
In a change of alphai(αiNot more than 1) with
Figure BDA00031996930200000610
Are all known scalars; alpha is alpha i1 indicates that the actuator is normal; alpha is alphai>0 represents partial actuator failure due to mechanical wear, aging conditions; alpha is alpha i0 represents complete failure of the actuator due to damage and falling off; therefore, only a needs to be consideredi>0 in this case;
converting the actuator fault model into a time series form:
Figure BDA00031996930200000611
wherein:
Figure BDA00031996930200000612
Figure BDA00031996930200000613
α＝diag[α1,α2…,αN]T
thus, the following results:
Figure BDA00031996930200000614
there is a desired input udIn the event of a fault α, there is
Figure BDA00031996930200000615
So that
Figure BDA00031996930200000616
Let Δ α represent a system fault tolerance indicator, defined as follows:
α＝I+Δα,Δα＝diag[Δα1,Δα2…ΔαN]T (27)
eighthly, analyzing the convergence of the fault-tolerant control trajectory tracking optimization algorithm of quantitative iterative learning:
for theDesired tracking trajectory ydThere is an ideal input udSatisfy the requirement of
Figure BDA00031996930200000617
Definition of
Figure BDA00031996930200000618
Then for the k +1 batch:
Figure BDA0003199693020000071
substituting a quantitative iterative learning fault-tolerant control law (22) into an equation (28) to obtain:
Figure BDA0003199693020000072
according to the relation of the input end signals, the equivalent form of the auxiliary correction error is obtained as follows:
Figure BDA0003199693020000073
due to the fact that
Figure BDA0003199693020000074
Is a reversible matrix in accordance with
Figure BDA0003199693020000075
Comprises the following steps:
Figure BDA0003199693020000076
the compound is obtained by substituting formula (30) and formula (31) into formula (29):
Figure BDA0003199693020000077
taking expectations for both sides of equation (32):
E(Δuk+1)＝(I-Ku-Kζ)E(ud)+(Ku-KeGα+Kζ)E(Δuk) (33)
taking norm on both sides of formula (33) to obtain E (Δ u)k+1) The inequality of (a) is:
||E(Δuk+1)||≤||I-Ku-Kζ||||E(ud)||+||Ku-KeGα+Kζ||||E(Δuk)|| (34)
after k iterations of the system, E (Δ u)k+1) The inequality of (d) translates into:
Figure BDA0003199693020000078
if the selected weight matrix and quantization density are such that the constraint condition is
Figure BDA0003199693020000079
If true, we get:
Figure BDA00031996930200000710
namely: i Ku-KeGα+Kζ||≤ρ<1 (37)
Derived from the compressed mapping theorem
Figure BDA00031996930200000711
Equation (35) is simplified to:
Figure BDA0003199693020000081
wherein | | | I-Ku-Kζ||||E(ud)||≤b；
Remember that | | G α | | | is less than or equal to | | G | | (1+ | Δ α |) < d, according to E (E)k)＝GαE(Δuk) Obtaining:
Figure BDA0003199693020000082
i.e. the error norm E (E) in the expected sensek) | | converge to a bounded value; when S is 0 matrix, then have | | | I-Ku-Kζ||||E(ud) I.e. 0
Figure BDA0003199693020000083
The method shows that the quantitative iterative learning fault-tolerant control algorithm can make the norm of the tracking error in the expected meaning of the system converge to 0;
ninth, track tracking of the direct current motor is realized by using the quantization signals of the quantization coder-decoder:
and determining a generated input vector of each iteration batch of the direct current motor according to a quantization iteration learning fault-tolerant control law, obtaining an actual input vector under the action of a quantization coder-decoder, performing trajectory tracking control on the direct current motor by using the actual input vector, and when an actuator fails, tracking the expected output by the direct current motor under the control action of the actual input vector.
The beneficial technical effects of the invention are as follows:
the application discloses a linear system with repetitive motion characteristics, such as a direct current motor, a direct current motor with actuator faults is used as a controlled object, a quantization coder-decoder is designed aiming at the condition that the bandwidth of network transmission signals is limited, and a logarithmic quantizer and a signal coding mechanism are combined, so that the influence of quantization errors on tracking performance is gradually reduced in the iteration process, and the precision of the transmission signals is improved. The method is based on a norm optimization iterative learning framework, a quantitative iterative learning fault-tolerant control algorithm is designed, and the convergence of system tracking errors in a mathematical expectation meaning is guaranteed.
Drawings
Fig. 1 is a model block diagram of a dc motor provided in the present application.
Fig. 2 is a graph of the actual output of the dc motor when no actuator failure has occurred as provided herein.
Fig. 3 is a graph of the actual output of the dc motor after an actuator failure as provided herein.
Fig. 4 is a graph of 2-norm convergence of the actual tracking error of the system provided by the present application.
FIG. 5 is a graph of a performance indicator function provided herein.
Detailed Description
The following further describes the embodiments of the present invention with reference to the drawings.
Referring to fig. 1, a block diagram of a dc motor model disclosed in the present application is shown in conjunction with fig. 1-5. Controller output of kth lot is ukVia an encoder E1After encoding, transmitted over a network by a decoder D1Receiving and decoding to obtain the actual control vector
Figure BDA0003199693020000091
The actual output y of the k-th batch of the system can be obtained by acting on the direct current motorkWith a set desired value y stored in a desired track memorydComparing to obtain the actual tracking error ek. Comparing the actual tracking error precision with the set precision value, if the error precision does not reach the set precision, outputting the actual ykVia encoder E2After encoding, transmitted over a network by a decoder D2Receiving and decoding to obtain estimated output value
Figure BDA0003199693020000092
Which is compared with the set expected value stored in the expected track memory to obtain the auxiliary correction error
Figure BDA0003199693020000093
Will assist in correcting errors
Figure BDA0003199693020000094
Current controller input ukAnd an encoder E1Internal state quantity of
Figure BDA0003199693020000095
Passing to optimized iterative learning controller generationController output u of the next batchk+1And the iteration is stopped when the error between the actual output and the expected value of the system reaches the precision requirement in the circulating operation, and the input of the controller at the moment is the optimal control input.
For the actual physical model of the direct current motor shown in the formula (1), the variable parameters are respectively set as:
Ce＝0.18V/(rad/s),Cf＝1.07×10-3Nm/(rad/s),
Jr＝1kgm2,CM＝0.646Nm/A,Ra＝2.1Ω,La＝0.8H
the system simulation time is set to be T-20 s, and the sampling time is set to be Ts0.1s, the parameter matrices of the discrete state space expression of the system are respectively:
Figure BDA0003199693020000096
in the present embodiment, the desired trajectory of the dc motor is set as follows:
Figure BDA0003199693020000097
in units of rad/s while making the initial state satisfy xk(0) 0. With network transmission signals, quantization codecs are designed due to the limited bandwidth, where the parameter of the log quantizer is set to μ 0.7.
Assume that the actuator-dependent fault α is 0.8+0.4sin (0.5t) at batch 16, when | | | Δ α | | | is 0.2. The weight matrix Q ═ I, R ═ 0.08I, and S ═ 0.02I were selected, and formula (37) was satisfied. When the weight matrices Q, R and S are determined with the quantization density μ, the quantization iteration learns K in the fault-tolerant control lawu,Ke,KζAs determined accordingly. The above-mentioned quantification iteration learning fault-tolerant controller of this application is realized based on STM32F103RCT6 chip, and the input of chip is motor control voltage u to obtain through voltage sensor collection. The input signal enters an STM32F103RCT6 chip through a conditioning circuit to be stored and countedCalculating and constructing an iterative learning updating law, and generating an input signal u by a signal obtained after the calculation of the CPUk+1Via an encoder E1After encoding, transmitted over a network by a decoder D1Receiving and decoding to obtain actual control signal
Figure BDA0003199693020000098
The actual control signal is applied to the DC motor to continuously correct the output trajectory until the desired trajectory is tracked.
When the dynamic model (1) of the dc motor is running, please refer to fig. 2 and fig. 3, which respectively show the trace tracking effect diagram of the dc motor applying the quantized iterative learning fault-tolerant control law (22). In 15 batches before the actuator fails, the output of the dc motor gradually tracks the desired trajectory as the batches increase. After 16 th batch of actuator faults occur, the tracking performance of the system is reduced, and after several batches of iterations, the output of the direct current motor retraces to a desired track. Fig. 4 shows that after a fault occurs, the quantized iterative learning fault-tolerant control algorithm reaches an ideal level again through a certain iterative batch tracking performance, so that bounded convergence is realized, and the rationality and the effectiveness of the algorithm are verified. Fig. 5 shows that in the quantized iterative learning fault-tolerant control algorithm, after the 16 th batch of actuators have failed, the performance index function gradually decreases with the increase of the iterative batches.
What has been described above is only a preferred embodiment of the present application, and the present invention is not limited to the above embodiment. It is to be understood that other modifications and variations directly derivable or suggested by those skilled in the art without departing from the spirit and concept of the present invention are to be considered as included within the scope of the present invention.

Claims (1)

1. A method for controlling the fault tolerance of a DC motor through quantitative iterative learning is characterized by comprising the following steps:
firstly, establishing a dynamic model of a direct current motor:
the dynamic model is expressed by a dynamic equation and describes a conversion relation between the input voltage and the rotating speed of the motor; according to the relation between the motor rotating speed and the electrical parameter, an actual physical model shown as the formula (1) is established:
Figure FDA0003199693010000011
wherein R isaRepresenting armature resistance, LaRepresenting armature inductance, CeRepresenting the back electromotive force coefficient, CfIndicating mechanical damping of the motor, JrRepresenting the moment of inertia of the rotor, CMRepresenting the torque coefficient, ω representing the motor speed, e representing the input voltage, iaRepresents armature current;
secondly, constructing a discrete state space equation of the direct current motor:
defining the armature current and the rotating speed of the direct current motor as state variables: x ═ ia ω]TWhen the input variable is defined as the input voltage e and the output is defined as the motor speed ω, the dc motor represented by equation (1) is described as:
Figure FDA0003199693010000012
discretizing the model formula (2) of the continuous system, and selecting a sampling period T meeting the Shannon sampling theoremsObtaining a discrete state space model of the direct current motor as follows:
Figure FDA0003199693010000013
wherein T and k respectively represent sampling time and batch, and the operation period of the batch process is T; within each cycle of the repetitive process, for a point in time T e 0, T]Taking N sampling points; u. ofk(t)、yk(t) and xk(t) input, output and state vectors at time t of the kth lot of the system, respectively; A. b, C is the parameter matrix of the discrete system in equation (3), and satisfies CB ≠ 0, and assumes the initial of each batch of the systemThe states being identical, i.e. xk(0)＝x0；
Thirdly, establishing a track tracking model:
for a linear discrete system in the form of equation (3), converting a state space expression of the system into a time-series input-output matrix model:
yk＝Guk+dk (4)
wherein:
Figure FDA0003199693010000021
dk＝[CA CA2 CA3 … CAN]Txk(0)
uk＝[uk(0),uk(1),...,uk(N-1)]T
yk＝[yk(1),yk(2),...,yk(N)]T
g is an input-output transfer matrix on a time series; dkIs the influence of the initial state of the system on the output, assuming
Figure FDA0003199693010000022
Then dk＝0；
Step four, designing a quantization codec:
in a system using network transmission signals, the signals are quantized, and an input end quantization codec is designed as follows:
Figure FDA0003199693010000023
Figure FDA0003199693010000024
where 0 represents a zero vector having the same dimensions as the system input, uk(t)、
Figure FDA0003199693010000025
And
Figure FDA0003199693010000026
are respectively an encoder E1Input, output and internal states of;
Figure FDA0003199693010000027
is a decoder D1I.e. the controller output uk(t) an estimate of; q (-) is a logarithmic quantizer defined by equation (7):
Figure FDA0003199693010000028
wherein v represents the input of the log quantizer;
Figure FDA0003199693010000029
μ is the selected quantization density, and the quantization levels are as follows:
Z＝{±zi|zi＝μiz0,i＝0,±1,±2,…}∪{0},0<μ<1,z0>0
the output side quantization codec is designed as follows:
Figure FDA0003199693010000031
Figure FDA0003199693010000032
where 0 represents a zero vector having the same dimensions as the system output, yk(t)、
Figure FDA0003199693010000033
And
Figure FDA0003199693010000034
are respectively an encoder E2Input, output and internal states of;
Figure FDA0003199693010000035
is a decoder D2I.e. the system output yk(t) an estimate of;
fifthly, establishing a relational expression of signals before and after quantization:
the logarithmic quantizer input v and the output q (v) have a quantization error Δ v, which is processed by a fan-bounded method, for k batches of signals at time t:
q(vk(t))＝(1+ηk(t))vk(t) (10)
wherein eta isk(t) represents a relative quantization error, and satisfies
Figure FDA0003199693010000036
From the input quantization codec definition and equation (10), we obtain:
Figure FDA0003199693010000037
by using the mathematical induction method of
Figure FDA0003199693010000038
Is established so that
Figure FDA0003199693010000039
And uk+1(t) is given by:
Figure FDA00031996930100000310
general formula(12) Lifting to vector form to obtain
Figure FDA00031996930100000311
And uk+1The vector relationship of (a) is:
Figure FDA00031996930100000312
Figure FDA00031996930100000313
wherein:
Figure FDA00031996930100000314
according to the definition of the output end quantization coding decoder
Figure FDA00031996930100000315
And yk+1The vector relationship of (a) is:
Figure FDA00031996930100000316
Figure FDA00031996930100000317
wherein:
Figure FDA00031996930100000318
the relative quantization error is independent of the quantizer input, so for any k batches at time t there is E vk(t)ηk(t)]0; the relative quantization errors produced by the different quantizers are also independent of each other, i.e.
Figure FDA0003199693010000041
i ≠ j and i, j ∈ {1,2 }; while in the same quantizer, the relative quantization error etak(t) in the interval [ - δ, δ]Inner uniform distribution and for arbitrary k1，k2And t1，t2Satisfies the following conditions:
Figure FDA0003199693010000042
wherein the content of the first and second substances,
Figure FDA0003199693010000043
thus, cancel by taking the mathematically expected way
Figure FDA0003199693010000044
And
Figure FDA0003199693010000045
the actual tracking error e exists in the systemk+1＝yd-yk+1And correcting errors with assistance
Figure FDA0003199693010000046
The actual tracking error really reflects the tracking performance of the system, and the controller corrects the input signals of the current batch by using the auxiliary correction error; according to
Figure FDA0003199693010000047
Obtaining:
Figure FDA0003199693010000048
therefore, a relation between the current actual error sequence and the auxiliary correction error sequence of the previous batch is established:
Figure FDA0003199693010000049
sixthly, designing a quantitative iterative learning fault-tolerant control trajectory tracking optimization algorithm:
considering a norm optimal iterative learning control framework, the control input of each batch is obtained by optimizing a performance index function, and the general form of the performance index function is as follows:
Figure FDA00031996930100000410
the performance indicator function includes the actual tracking error, control oscillation, and control energy; in the optimization process, each part is represented by symmetrical positive definite weight matrixes Q and R and a symmetrical non-negative definite weight matrix S respectively, namely Q is QT>0,R＝RT>0,S＝STNot less than 0; taking the weight matrix Q-qI, R-rI, S-sI, and the induction norm is defined as follows:
Figure FDA00031996930100000411
Figure FDA00031996930100000412
Figure FDA00031996930100000413
and
Figure FDA00031996930100000414
none contain a random variable, so its expectation is equal to itself;
definition of
Figure FDA00031996930100000415
Obtained according to equation (17):
Figure FDA00031996930100000416
xi and sigma2I are all symmetric positive definite matrixes; substituting equation (19) into the performance indicator function (18) yields:
Figure FDA0003199693010000051
solving a quadratic optimal solution of the formula (20) to obtain:
Figure FDA0003199693010000052
due to (G)TQG + xi + R + S) is reversible, and the quantized iterative learning fault-tolerant control law obtained by sorting the formula (21) is as follows:
Figure FDA0003199693010000053
wherein:
Figure FDA0003199693010000054
step seven, establishing an actuator fault model:
input for actually controlling DC motor
Figure FDA0003199693010000055
Order to
Figure FDA0003199693010000056
An output signal representing an actuator fault, defining an actuator fault model:
Figure FDA0003199693010000057
wherein:
Figure FDA0003199693010000058
actuator failure coefficient alphaiUnknown, but in range
Figure FDA0003199693010000059
In the case of (a) to (b), iα( iαnot more than 1) with
Figure FDA00031996930100000510
Are all known scalars; alpha is alphai1 indicates that the actuator is normal; alpha is alphai>0 represents partial actuator failure due to mechanical wear, aging conditions; alpha is alphai0 represents complete failure of the actuator due to damage and falling off; therefore, only a needs to be consideredi>0 in this case;
converting the actuator fault model into a time series form:
Figure FDA00031996930100000511
wherein:
Figure FDA00031996930100000512
Figure FDA00031996930100000513
α＝diag[α1,α2…,αN]T
thus, the following results:
Figure FDA00031996930100000514
there is a desired input udIn the event of a fault α, there is
Figure FDA00031996930100000515
So that
Figure FDA00031996930100000516
Let Δ α represent a system fault tolerance indicator, defined as follows:
α＝I+Δα,Δα＝diag[Δα1,Δα2…ΔαN]T (27)
eighthly, analyzing the convergence of the fault-tolerant control trajectory tracking optimization algorithm of quantitative iterative learning:
for the desired tracking trajectory ydThere is an ideal input udSatisfy the requirement of
Figure FDA00031996930100000517
Definition of
Figure FDA00031996930100000518
Then for the k +1 batch:
Figure FDA0003199693010000061
substituting a quantitative iterative learning fault-tolerant control law (22) into an equation (28) to obtain:
Figure FDA0003199693010000062
according to the relation of the input end signals, obtaining the equivalent form of the auxiliary correction error as follows:
Figure FDA0003199693010000063
due to the fact that
Figure FDA0003199693010000064
Is a reversible matrix in accordance with
Figure FDA0003199693010000065
Comprises the following steps:
Figure FDA0003199693010000066
the compound is obtained by substituting formula (30) and formula (31) into formula (29):
Figure FDA0003199693010000067
taking expectations for both sides of equation (32):
E(Δuk+1)＝(I-Ku-Kζ)E(ud)+(Ku-KeGα+Kζ)E(Δuk) (33)
taking norm on both sides of formula (33) to obtain E (Δ u)k+1) The inequality of (a) is:
||E(Δuk+1)||≤||I-Ku-Kζ||||E(ud)||+||Ku-KeGα+Kζ||||E(Δuk)|| (34)
after k iterations of the system, E (Δ u)k+1) The inequality of (d) translates into:
Figure FDA0003199693010000068
if the selected weight matrix and quantization density are such that the constraint condition is
Figure FDA0003199693010000069
If true, we get:
Figure FDA00031996930100000610
namely: i Ku-KeGα+Kζ||≤ρ<1 (37)
Derived from the compressed mapping theorem
Figure FDA00031996930100000611
Equation (35) is simplified to:
Figure FDA0003199693010000071
wherein | | | I-Ku-Kζ||||E(ud)||≤b；
Remember that | | G α | | | is less than or equal to | | G | | (1+ | Δ α |) < d, according to E (E)k)＝GαE(Δuk) Obtaining:
Figure FDA0003199693010000072
i.e. the error norm E (E) in the expected sensek) | | converge to a bounded value; when S is 0 matrix, then have | | | I-Ku-Kζ||||E(ud) I.e. 0
Figure FDA0003199693010000073
The method shows that the quantitative iterative learning fault-tolerant control algorithm can make the norm of the tracking error in the expected meaning of the system converge to 0;
ninth, track following of the DC motor is realized by using the quantized signal of the quantized coder-decoder:
and determining a generated input vector of each iteration batch of the direct current motor according to the quantization iteration learning fault-tolerant control law, obtaining an actual input vector under the action of the quantization codec, performing trajectory tracking control on the direct current motor by using the actual input vector, and tracking expected output of the direct current motor under the control action of the actual input vector when an actuator fails.
CN202110900739.8A 2021-08-06 2021-08-06 DC motor quantization iteration learning fault-tolerant control method Active CN113625563B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110900739.8A CN113625563B (en) 2021-08-06 2021-08-06 DC motor quantization iteration learning fault-tolerant control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110900739.8A CN113625563B (en) 2021-08-06 2021-08-06 DC motor quantization iteration learning fault-tolerant control method

Publications (2)

Publication Number Publication Date
CN113625563A true CN113625563A (en) 2021-11-09
CN113625563B CN113625563B (en) 2024-03-15

Family

ID=78383078

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110900739.8A Active CN113625563B (en) 2021-08-06 2021-08-06 DC motor quantization iteration learning fault-tolerant control method

Country Status (1)

Country Link
CN (1) CN113625563B (en)

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115107034A (en) * 2022-07-18 2022-09-27 江南大学 Quantitative iterative learning control method for single mechanical arm
CN115437238A (en) * 2022-10-21 2022-12-06 江南大学 Variable-length PD type iterative learning control method of direct-current motor-driven single-rod system
CN116048085A (en) * 2023-02-03 2023-05-02 江南大学 Fault estimation and fault-tolerant iterative learning control method for mobile robot
CN116893619A (en) * 2023-08-29 2023-10-17 江南大学 Industrial robot quantization iterative learning control method

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6064997A (en) * 1997-03-19 2000-05-16 University Of Texas System, The Board Of Regents Discrete-time tuning of neural network controllers for nonlinear dynamical systems
WO2017114001A1 (en) * 2015-12-28 2017-07-06 中南大学 Predictive control-based open-circuit fault diagnosis method for matrix converter switch
CN108227494A (en) * 2018-01-05 2018-06-29 海南师范大学 The fuzzy fault tolerant control method of the non-linear optimal constraints of batch process 2D
CN110815225A (en) * 2019-11-15 2020-02-21 江南大学 Point-to-point iterative learning optimization control method of motor-driven single mechanical arm system
CN111650837A (en) * 2020-06-19 2020-09-11 哈尔滨理工大学 Second-order preset performance fault-tolerant control method for track tracking of surface ship during propeller failure

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6064997A (en) * 1997-03-19 2000-05-16 University Of Texas System, The Board Of Regents Discrete-time tuning of neural network controllers for nonlinear dynamical systems
WO2017114001A1 (en) * 2015-12-28 2017-07-06 中南大学 Predictive control-based open-circuit fault diagnosis method for matrix converter switch
CN108227494A (en) * 2018-01-05 2018-06-29 海南师范大学 The fuzzy fault tolerant control method of the non-linear optimal constraints of batch process 2D
CN110815225A (en) * 2019-11-15 2020-02-21 江南大学 Point-to-point iterative learning optimization control method of motor-driven single mechanical arm system
CN111650837A (en) * 2020-06-19 2020-09-11 哈尔滨理工大学 Second-order preset performance fault-tolerant control method for track tracking of surface ship during propeller failure

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
ALI MOHAMMADPOUR 等: "Fault-Tolerant Operation of Multiphase Permanent-Magnet Machines Using Iterative Learning Control", 《IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS》, vol. 2, no. 2, XP011544575, DOI: 10.1109/JESTPE.2013.2295537 *
YANDE HUANG 等: "Optimal Iterative Learning Control of Quantized Signals Based on Encoding-Decoding Method", 《2021 IEEE 10TH DATA DRIVEN CONTROL AND LEARNING SYSTEMS CONFERENCE》 *

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115107034A (en) * 2022-07-18 2022-09-27 江南大学 Quantitative iterative learning control method for single mechanical arm
CN115437238A (en) * 2022-10-21 2022-12-06 江南大学 Variable-length PD type iterative learning control method of direct-current motor-driven single-rod system
CN115437238B (en) * 2022-10-21 2023-12-22 江南大学 Variable-length PD type iterative learning control method for direct-current motor driven single-rod system
CN116048085A (en) * 2023-02-03 2023-05-02 江南大学 Fault estimation and fault-tolerant iterative learning control method for mobile robot
CN116048085B (en) * 2023-02-03 2023-11-07 江南大学 Fault estimation and fault-tolerant iterative learning control method for mobile robot
CN116893619A (en) * 2023-08-29 2023-10-17 江南大学 Industrial robot quantization iterative learning control method
CN116893619B (en) * 2023-08-29 2024-04-09 江南大学 Industrial robot quantization iterative learning control method

Also Published As

Publication number Publication date
CN113625563B (en) 2024-03-15

Similar Documents

Publication Publication Date Title
CN113625563A (en) DC motor quantization iterative learning fault-tolerant control method
US9294113B2 (en) Energy-efficient time-stampless adaptive nonuniform sampling
US8700190B2 (en) Method for generating trajectories for motor controlled actuators
Amann et al. An H∞ approach to linear iterative learning control design
CN112882391B (en) Double-end event triggered nonlinear control method
CN111381501B (en) Fault-tolerant control method of asynchronous system based on event trigger
Norouzi et al. Robotic manipulator control using PD-type fuzzy iterative learning control
CN111769544B (en) Multi-machine electric power system distributed digital controller equipped with SVC
CN112327810A (en) Fault estimation method of dynamic event triggered transmission Markov jump system
CN113644857B (en) Finite-stage quantization iterative learning control method for permanent magnet linear motor
CN104022701A (en) Method for controlling internal model speed of permanent magnet synchronous linear motor through Newton method
CN114499755B (en) Geometric and probability combined constellation shaping method and system based on mutual information quantity estimation
CN113900377B (en) Point-to-point iterative learning minimum energy control method for double-rotor pneumatic system
CN115204057A (en) Digital twin multi-level model construction method for power transmission and transformation equipment
CN110531625B (en) Finite frequency range iterative learning fault-tolerant control method of active electronic ladder circuit
CN116893619B (en) Industrial robot quantization iterative learning control method
Hsu et al. Fuzzy PI controller tuning for a linear permanent magnet synchronous motor drive
Marumo et al. Intelligent modeling and control of a pneumatic motor
CN115107034B (en) Quantization iterative learning control method for single mechanical arm
CN116865532B (en) Control method of AC-DC converter adopting model predictive control
Goyal et al. Transform coding using adaptive bases and quantization
Xu et al. Quantized Distributed Nonconvex Optimization Algorithms with Linear Convergence under the Polyak--${\L} $ ojasiewicz Condition
Villarroel et al. A new discretization method of model equations for predictive power converter control applications based on input-state linearization
Tao et al. Gradient-Based Iterative Learning Control for Signal Quantization with Encoding-Decoding Mechanism
CN115730701B (en) Load prediction method and system suitable for power dispatching equipment in small energy consumption place

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant