CN109995290A - The control method and system of open loop iterative learning based on Fractional Calculus - Google Patents
The control method and system of open loop iterative learning based on Fractional Calculus Download PDFInfo
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Abstract
The invention discloses the control methods and system of the open loop iterative learning based on Fractional Calculus, and wherein method is the following steps are included: establish Discrete Fractional Open-loop iterative learning control device；The permanent magnetism synchronous electric machine position servo system based on vector controlled is established, to fractional calculus iterative learning controller equivalence transformation；By iq、idWithThe difference compared, is respectively fed to current regulator, obtains voltage control quantity u by current regulatordAnd uq；udAnd uqThe voltage control quantity u under α β coordinate system is transformed by PARK inverse transformationαAnd uβ, then according to uαAnd uβImpulse modulation pwm signal is generated, and three-phase inverter is controlled by SVPWM principle and generates three-phase voltage signal.The present invention has higher control precision, has combined practicability and accuracy.
Description
Technical Field
The invention belongs to the technical field of motor control, and relates to a control method and a system for open-loop iterative learning based on fractional calculus.
Background
In actual industrial production, systems including a plurality of repetitive or periodic motion processes, such as various industrial production lines including robot welding, mobile phones and the like, textile industry and the like, have a common characteristic that the devices have repetitive motion and production processes. The existing control algorithms generally adopt PID, sliding mode, self-adaption and other control algorithms, the algorithms generally adopt a single feedback or feedforward technology, and although satisfactory precision can be obtained for a single product, the problem of product consistency cannot be well solved.
Iterative learning control is a control algorithm for systems with repetitive motion that can achieve accurate control by using data information from previous control and by iteratively finding appropriate control inputs on-line. The fractional calculus has good memory function and genetic characteristic, and the combination of the fractional calculus and iterative learning control is a feasible control algorithm. However, the fractional calculus is difficult to implement by using microprocessors such as a DSP in industrial control due to a large calculation amount.
Disclosure of Invention
In order to solve the above problems, an object of the present invention is to provide a method for controlling a position servo of a Permanent Magnet Synchronous Motor (PMSM) based on fractional order open loop iterative learning. The invention applies discrete fractional order iterative learning to the position control design and designs the fractional order calculus engineering realization, and the introduction of the fractional order leads the system to have higher control precision. The method has the advantages of both practicability and accuracy and higher application value.
In order to achieve the purpose, the technical scheme of the invention is a control method of open-loop iterative learning based on fractional calculus, which comprises the following steps:
s10, establishing a discrete fractional order open-loop iterative learning controller, wherein the iterative learning control law adopts PDαPerforming position control by using a type iterative learning control law;
s20, establishing a vector control-based permanent magnet synchronous motor position servo system, and improving the performance of the controller by combining fractional calculus, wherein learning gain and the fractional calculus factor are adjusted according to the dynamic performance and the steady-state performance of the system;
s30, carrying out equivalent transformation on the fractional calculus iterative learning controller;
s40, controlling the motor position uk(i) Carrying out convergence certification on the obtained productq、idAndcomparing the obtained difference values, respectively sending into current regulators to obtain voltage control values udAnd uq；
S50, after the motor position control quantity is obtained, a position loop and current loop control strategy is adopted, the control quantity is converted into a current control quantity under a q coordinate system through a position regulator, and the given reference of a d axis is 0;
S60，udand uqVoltage control quantity u converted into αβ coordinate system by PARK inverse transformationαAnd uβThen according to uαAnd uβAnd generating a pulse modulation PWM signal, and controlling a three-phase inverter to generate a three-phase voltage signal by an SVPWM principle.
Preferably, the S10 includes the steps of:
s11, under the dq coordinate system, the discrete mechanical dynamic equation of the permanent magnet synchronous motor is as follows:
where, x (t) ═ θ (t) ω (t)]T，u(t)＝Te(t)＝kTiq(t)，B＝[0 1/J]TC＝[1 0]Theta (T) and omega (T) respectively represent the position and rotation speed signals at the time T of the system, Te(t) is an electromagnetic torqueInput, kTIs the torque coefficient, iq(t) is the q-axis current, BfIs a friction coefficient, J is a moment of inertia, d (t) is interference information including a load;
s12, adopting discrete fractional order open loop iterative learning control to give a given position theta*The difference between the position theta fed back by the position sensor and the position theta is sent to a discrete fractional order open-loop iterative learning controller, the output of the discrete fractional order open-loop iterative learning controller is a torque command signal, and the output of the discrete fractional order open-loop iterative learning controller is
uk+1(t)＝uk(t)+Kpek(t)+KDΔαek(t) (2)
Wherein u isk(t) the kth iterative controlled variable at time t, uk+1(t) is the (k + 1) th iteration control quantity at the time t, ekThe kth iteration error at time (t) t, i.e. ek(t)＝yd(t)-yk(t)，KpTo scale factor, KDThe differential adjustment coefficient, Δ, representing a discrete differential operator, ΔαIs a derivative of α order, α epsilon (0, 1);
the discrete fractional calculus is defined as follows,
wherein h is the sampling time, and m is the discrete time.
P is defined as follows,
preferably, the S30 includes the steps of:
s31, let the sampling time h → 0, thenFrom equations (3) and (4), the α order differential of the kth error at time t can be obtained as
S32, orderTransforming equation (5) into:
s33, discrete fractional order open-loop iterative learning controller transformation in S12 according to equation (6)
Wherein,
preferably, the S40 includes the steps of:
s41, obtained by the formula (1),
let Yk＝[yk(1)yk(2),...yk(N)]T(10)
xk＝[xk(0)xk(1),...xk(N-1)]T(11)
Uk＝[δuk(0)δuk(1),...δuk(N-1)]T(12)
δuk(i)＝ud(i)-uk(i) (13)
Wherein u isk(i) Is the motor control quantity ud(i) To expect, ekAnd (t) is the kth iteration error at the time t.
S42, according to the formula (13), u is subtracted from both sides of the formula (7) at the same timed(i) Then taking the inverse, and then bringing t to 0 into a discrete fractional order open-loop iterative learning controller,
wherein
The formula (15) is simplified according to the formula (14), and the formula (14) is brought into
＝δuk(0)-kpCBδuk(0)
Extracting the formula to obtain
δuk+1(0)＝(I-kpCB)δuk(0)
δuk+1(0) The difference between the expected value and the control quantity of the k +1 th iteration at the moment when t is 0;
s43, according to the formulas (13) and (14), subtracting u from both sides of the formula (7) at the same timed(i) Then taking the inverse, and then bringing t to 1 into a discrete fractional order open-loop iterative learning controller,
δuk+1(1)＝δuk(1)-kpCABδuk(0)-kpCBδuk(1)+kpc1ek(0) (16)
wherein k ispc1ek(0)＝0；
Simplifying the formula (16), extracting a formula to obtain,
δuk+1(1)＝(I-kpcB)δuk(1)-kpCABδuk(0) (17)
s44, according to the formulas (13) and (14), subtracting u from both sides of the formula (7) at the same timed(i) Then taking the inverse, and then bringing t to 2 into a discrete fractional order open-loop iterative learning controller,
the formula (18) is simplified according to the formula (14), and a formula is extracted to obtain,
δuk+1(2)＝(I-kpcB)δuk(2)+Δ (19)
wherein, is ═ kpek(c1-c3)；
S45, finishing to obtain,
i.e. delta Uk+1＝QδUk
Wherein,
the invention also provides a system of the control method of the open-loop iterative learning based on the fraction calculus, which comprises a discrete fraction order open-loop iterative learning controller, a current regulator, a DSP microprocessor, an inverter circuit and a position sensor, wherein,
the position sensor collects the position information of the permanent magnet synchronous motor and gives a position theta*The difference between the position theta fed back by the position sensor and the position theta is input into the discrete fractional order open-loop iterative learning controller, and the output of the discrete fractional order open-loop iterative learning controller is a torque, namely a current command signalAnd
the current regulator comprises a q-axis current regulator and a d-axis current regulatorq、idAnd comparing the obtained difference values, respectively inputting the q-axis current regulator and the d-axis current regulator, and outputting a voltage control quantity udAnd uq；
The DSP microprocessor comprises a PARK inverter, a PARK converter, a CLARK converter, an SVPWM generator, a q-axis current regulator, a d-axis current regulator, and an output voltage control quantity udAnd uqInputting PARK inverse transformer, converting to voltage control amount u under αβ coordinate systemαAnd uβAnd then the SVPWM generator generates the signal according to uαU β generates pulse modulation PWM signal to control the inverter circuit to generate three-phase voltage signal Va、Vb、VcControlling the permanent magnet synchronous motor; to Va、VbIs converted into a current signal ia、ibObtaining current i under αβ coordinate system through CLARK converterαAnd iβThen is transformed by PARKThe converter obtains iq、id。
The invention has the following beneficial effects: the invention adds the adjustable factor of the position controller by introducing the fractional order differential operator in the position control, also ensures the monotonous convergence of the control rate of the position controller aiming at the time-varying nonlinearity of the system, and leads the position controller to have better stability and adaptability. The invention effectively utilizes the fractional order DαCompared with the traditional iterative learning, the type learning law has the unique advantage of adjusting the monotonous convergence of tracking learning, the tracking performance is improved by combining the P type learning law and the added adjustable parameter fractional order, and the convergence speed is increased.
Drawings
FIG. 1 is a flowchart of the steps of a control method of open-loop iterative learning based on fractional calculus in embodiment 1 of the method of the present invention;
FIG. 2 is a system block diagram of a control method for open-loop iterative learning based on fractional calculus according to an embodiment of the present invention;
fig. 3 is a schematic diagram of control logic of open-loop iterative learning based on fractional calculus according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
On the contrary, the invention is intended to cover alternatives, modifications, equivalents and alternatives which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. It will be apparent to one skilled in the art that the present invention may be practiced without these specific details.
Method example 1
Referring to fig. 1, a technical solution of the present invention, which is an embodiment of the present invention, is a flowchart of steps of a control method of open-loop iterative learning based on fractional calculus, including the following steps:
s10, establishing a discrete fractional order open-loop iterative learning controller, wherein the iterative learning control law adopts PDαPerforming position control by using a type iterative learning control law;
s20, establishing a vector control-based permanent magnet synchronous motor position servo system, and improving the performance of the controller by combining fractional calculus, wherein learning gain and the fractional calculus factor are adjusted according to the dynamic performance and the steady-state performance of the system;
s30, carrying out equivalent transformation on the fractional calculus iterative learning controller;
s40, controlling the motor position uk(i) Carrying out convergence certification on the obtained productq、idAndcomparing the obtained difference values, respectively sending into current regulators to obtain voltage control values udAnd uq；
S50, after the motor position control quantity is obtained, a position loop and current loop control strategy is adopted, the control quantity is converted into a current control quantity under a q coordinate system through a position regulator, and the given reference of a d axis is 0;
S60，udand uqVoltage control quantity u converted into αβ coordinate system by PARK inverse transformationαAnd uβThen according to uαAnd uβAnd generating a pulse modulation PWM signal, and controlling a three-phase inverter to generate a three-phase voltage signal by an SVPWM principle.
In the above method, the iterative learning control law adopts PDαThe reason why the position control is carried out by the type iterative learning control law is that due to the introduction of a fractional order differential operator in the position control, an adjustable factor of the position controller is increased, and the monotonic convergence of the control rate of the position controller aiming at the time-varying nonlinearity of the system is also ensured, so that the position controller has better stability and adaptability.
In a specific embodiment, S10 includes the following steps:
s11, under the dq coordinate system, the discrete mechanical dynamic equation of the permanent magnet synchronous motor is as follows:
where, x (t) ═ θ (t) ω (t)]T，u(t)＝Te(t)＝kTiq(t)，B＝[0 1/J]TC＝[1 0]Theta (T) and omega (T) respectively represent the position and rotation speed signals at the time T of the system, Te(t) electromagnetic torque input, kTIs the torque coefficient, iq(t) is the q-axis current, BfIs a friction coefficient, J is a moment of inertia, d (t) is interference information including a load;
s12, adopting discrete fractional order open loop iterative learning control to give a given position theta*The difference between the position theta fed back by the position sensor and the position theta is sent to a discrete fractional order open-loop iterative learning controller, the output of the discrete fractional order open-loop iterative learning controller is a torque command signal, and the output of the discrete fractional order open-loop iterative learning controller is
uk+1(t)＝uk(t)+Kpek(t)+KDΔαek(t) (2)
Wherein u isk(t) the kth iterative controlled variable at time t, uk+1(t) is the (k + 1) th iteration control quantity at the time t, ekThe kth iteration error at time (t) t, i.e. ek(t)＝yd(t)-yk(t)，KpTo scale factor, KDThe differential adjustment coefficient, Δ, representing a discrete differential operator, ΔαIs a derivative of α order, α epsilon (0, 1);
the discrete fractional calculus is defined as follows,
wherein h is the sampling time, and m is the discrete time.
P is defined as follows,
s30 includes the steps of:
s31, let the sampling time h → 0, thenFrom equations (3) and (4), the α order differential of the kth error at time t can be obtained as
S32, orderTransforming equation (5) into:
s33, discrete fractional order open-loop iterative learning controller transformation in S12 according to equation (6)
Wherein,
s40 includes the steps of:
s41, obtained by the formula (1),
let Yk＝[yk(1)yk(2),...yk(N)]T(10)
xk＝[xk(0)xk(1),...xk(N-1)]T(11)
Uk＝[δuk(0)δuk(1),...δuk(N-1)]T(12)
δuk(i)＝ud(i)-uk(i) (13)
Wherein u isk(i) Is the motor control quantity ud(i) To expect, ek(t) the kth iteration error at time t;
s42, according to the formula (13), u is subtracted from both sides of the formula (7) at the same timed(i) And then the process is carried out by taking the inverse,then the discrete fractional order open loop iterative learning controller is substituted with t being 0,
wherein
The formula (15) is simplified according to the formula (14), and the formula (14) is brought into
＝δuk(0)-kpCBδuk(0)
Extracting the formula to obtain
δuk+1(0)＝(I-kpCB)δuk(0)
δuk+1(0) The difference between the expected value and the control quantity of the k +1 th iteration at the moment when t is 0;
s43, according to the formulas (13) and (14), subtracting u from both sides of the formula (7) at the same timed(i) Then taking the inverse, and then bringing t to 1 into a discrete fractional order open-loop iterative learning controller,
δuk+1(1)＝δuk(1)-kpCABδuk(0)-kpCBδuk(1)+kpc1ek(0) (16)
wherein k ispc1ek(0)＝0；
Simplifying the formula (16), extracting a formula to obtain,
δuk+1(1)＝(I-kpcB)δuk(1)-kpCABδuk(0) (17)
s44, according to the formulas (13) and (14), subtracting u from both sides of the formula (7) at the same timed(i) Then taking the inverse, and then bringing t to 2 into a discrete fractional order open-loop iterative learning controller,
the formula (18) is simplified according to the formula (14), and a formula is extracted to obtain,
δuk+1(2)＝(I-kpcB)δuk(2)+Δ (19)
wherein, is ═ kpek(c1-c3)；
S45, finishing to obtain,
i.e. delta Uk+1＝QδUk
Wherein,
system embodiment
Referring to fig. 2, the present invention further provides a system of a control method of open-loop iterative learning based on fractional calculus, which includes a discrete fractional order open-loop iterative learning controller 10, a current regulator, a DSP microprocessor, an inverter circuit 40 and a position sensor 50, wherein,
the position sensor 50 collects the position information of the permanent magnet synchronous motor 60 and gives a position theta*The difference between the position θ fed back by the position sensor 50 and the input of the discrete fractional order open-loop iterative learning controller 10, and the output of the discrete fractional order open-loop iterative learning controller 10 is a torque, i.e., a current command signalAnd
the current regulators include a q-axis current regulator 21 and a d-axis current regulator 22, will iq、idAnd comparing the obtained difference values, inputting the difference values into a q-axis current regulator 21 and a d-axis current regulator 22, and outputting a voltage control quantity udAnd uq；
The DSP microprocessor comprises a PARK inverter 31, a PARK converter 32, a CLARK converter 33, an SVPWM generator 34, a q-axis current regulator 21, a d-axis current regulator 22 and an output voltage control quantity udAnd uqInputting the PARK inverse transformer 31, converting to the voltage control quantity u under the αβ coordinate systemαAnd uβAnd then by the SVPWM generator 34 according to uαAnd uβGenerates pulse modulation PWM signal, controls inverter circuit 40 to generate three-phase voltage signal Va、Vb、VcControlling the permanent magnet synchronous motor 60; to Va、VbIs converted into a current signal ia、ibThe current i under αβ coordinate system is obtained through the CLARK converter 33αAnd iβThen, i is obtained through the PARK converter 32q、id。
In a specific embodiment, referring to FIG. 3, to reduce the computational burden of the DSP microprocessor on multiplication, it will be appreciated thatPerforming off-line operation to obtain a result table, and quickly obtaining c by looking up the table in the operation processjThe value of (c).
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. The control method of the open-loop iterative learning based on the fraction calculus is characterized by comprising the following steps:
s10, establishing a discrete fractional order open-loop iterative learning controller, wherein the iterative learning control law adopts PDαPerforming position control by using a type iterative learning control law;
s20, establishing a vector control-based permanent magnet synchronous motor position servo system, and improving the performance of the controller by combining fractional calculus, wherein learning gain and the fractional calculus factor are adjusted according to the dynamic performance and the steady-state performance of the system;
s30, carrying out equivalent transformation on the fractional calculus iterative learning controller;
s40, controlling the motor position uk(i) Carrying out convergence certification on the obtained productq、idAndcomparing the obtained difference values, respectively sending into current regulators to obtain voltage control values udAnd uq；
S50, after the motor position control quantity is obtained, a position loop and current loop control strategy is adopted, the control quantity is converted into a current control quantity under a q coordinate system through a position regulator, and the given reference of a d axis is 0;
S60，udand uqVoltage control quantity u converted into αβ coordinate system by PARK inverse transformationαAnd uβThen according to uαAnd uβAnd generating a pulse modulation PWM signal, and controlling a three-phase inverter to generate a three-phase voltage signal by an SVPWM principle.
2. The method according to claim 1, wherein the S10 comprises the following steps:
s11, under the dq coordinate system, the discrete mechanical dynamic equation of the permanent magnet synchronous motor is as follows:
where, x (t) ═ θ (t) ω (t)]T，u(t)＝Te(t)＝kTiq(t)，B＝[0 1/J]TC＝[1 0]Theta (T) and omega (T) respectively represent the position and rotation speed signals at the time T of the system, Te(t) electromagnetic torque input, kTIs the torque coefficient, iq(t) is the q-axis current, BfIs coefficient of friction, J is moment of inertia, d (t) is dry including loadDisturbing the information;
s12, adopting discrete fractional order open loop iterative learning control to give a given position theta*The difference between the position theta fed back by the position sensor and the position theta is sent to a discrete fractional order open-loop iterative learning controller, the output of the discrete fractional order open-loop iterative learning controller is a torque command signal, and the output of the discrete fractional order open-loop iterative learning controller is
uk+1(t)＝uk(t)+Kpek(t)+KDΔαek(t) (2)
Wherein u isk(t) the kth iterative controlled variable at time t, uk+1(t) is the (k + 1) th iteration control quantity at the time t, ekThe kth iteration error at time (t) t, i.e. ek(t)＝yd(t)-yk(t)，KpTo scale factor, KDThe differential adjustment coefficient, Δ, representing a discrete differential operator, ΔαIs a derivative of α order, α epsilon (0, 1);
the discrete fractional calculus is defined as follows,
wherein h is sampling time, and m is discrete time;
p is defined as follows,
3. the method according to claim 2, wherein the S30 comprises the steps of:
s31, let the sampling time h → 0, thenFrom equations (3) and (4), the α order differential of the kth error at time t can be obtained as
S32, orderTransforming equation (5) into:
s33, discrete fractional order open-loop iterative learning controller transformation in S12 according to equation (6)
Wherein,
4. the method according to claim 3, wherein the S40 comprises the following steps:
s41, obtained by the formula (1),
let Yk＝[yk(1)yk(2),...yk(N)]T(10)
xk＝[xk(0)xk(1),...xk(N-1)]T(11)
Uk＝[δuk(0)δuk(1),...δuk(N-1)]T(12)
δuk(i)＝ud(i)-uk(i) (13)
Wherein u isk(i) Is the motor control quantity ud(i) To expect, ek(t) the kth iteration error at time t;
s42, according to the formula (13), u is subtracted from both sides of the formula (7) at the same timed(i) Then taking the inverse, and then bringing t to 0 into a discrete fractional order open-loop iterative learning controller,
wherein
The formula (15) is simplified according to the formula (14), and the formula (14) is brought into
＝δuk(0)-kpCBδuk(0)
Extracting the formula to obtain
δuk+1(0)＝(I-kpCB)δuk(0)
δuk+1(0) The difference between the expected value and the control quantity of the k +1 th iteration at the moment when t is 0;
s43, according to the formulas (13) and (14), subtracting u from both sides of the formula (7) at the same timed(i) Then taking the inverse, and then bringing t to 1 into a discrete fractional order open-loop iterative learning controller,
δuk+1(1)＝δuk(1)-kpCABδuk(0)-kpCBδuk(1)+kpc1ek(0) (16)
wherein k ispc1ek(0)＝0；
Simplifying the formula (16), extracting a formula to obtain,
δuk+1(1)＝(I-kpcB)δuk(1)-kpCABδuk(0) (17)
s44, according to the formulas (13) and (14), subtracting u from both sides of the formula (7) at the same timed(i) Then taking the inverse, and then bringing t 2 into the discrete fractional order open loop iterationThe learning controller is used for learning the data,
the formula (18) is simplified according to the formula (14), and a formula is extracted to obtain,
δuk+1(2)＝(I-kpcB)δuk(2)+Δ (19)
wherein, is ═ kpek(c1-c3)；
S45, finishing to obtain,
i.e. delta Uk+1＝QδUk
Wherein,
5. a system employing the control method of fractional calculus based open-loop iterative learning of any of claims 1-4, comprising a discrete fractional order open-loop iterative learning controller, a current regulator, a DSP microprocessor, an inverter circuit, and a position sensor, wherein,
the position sensor collects the position information of the permanent magnet synchronous motor and gives a position theta*The difference between the position theta fed back by the position sensor and the position theta is input into the discrete fractional order open-loop iterative learning controller, and the output of the discrete fractional order open-loop iterative learning controller is a torque, namely a current command signalAnd
the current regulator comprises a q-axis current regulator and a d-axis current regulatorFlow regulator ofq、idAnd comparing the obtained difference values, respectively inputting the q-axis current regulator and the d-axis current regulator, and outputting a voltage control quantity udAnd uq；
The DSP microprocessor comprises a PARK inverter, a PARK converter, a CLARK converter, an SVPWM generator, a q-axis current regulator, a d-axis current regulator, and an output voltage control quantity udAnd uqInputting PARK inverse transformer, converting to voltage control amount u under αβ coordinate systemαAnd uβAnd then the SVPWM generator generates the signal according to uαAnd uβGenerating pulse modulation PWM signal, controlling the inverter circuit to generate three-phase voltage signal Va、Vb、VcControlling the permanent magnet synchronous motor; to Va、VbIs converted into a current signal ia、ibObtaining current i under αβ coordinate system through CLARK converterαAnd iβAnd then obtaining i through PARK converterq、id。
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| CN112720244A (en) * | 2020-12-18 | 2021-04-30 | 杭州电子科技大学 | Crystal grinding control method and system based on open-loop cross-coupling iterative learning |
| CN115556103A (en) * | 2022-10-11 | 2023-01-03 | 华中科技大学 | Fractional order impedance controller based on dynamics feedforward and design method thereof |
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| CN115556103A (en) * | 2022-10-11 | 2023-01-03 | 华中科技大学 | Fractional order impedance controller based on dynamics feedforward and design method thereof |
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