CN118068043A - Repeated control method and device for multi-shaft precise centrifugal machine system - Google Patents
Repeated control method and device for multi-shaft precise centrifugal machine system Download PDFInfo
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Abstract
The invention discloses a repeated control method and a device for a multi-shaft precise centrifuge system, wherein the method comprises the following steps: modeling the multi-axis precision centrifuge, establishing a main shaft closed loop transfer function and a secondary shaft closed loop transfer function of the multi-axis precision centrifuge, analyzing periodic interference of the secondary shaft, and determining to adopt repeated control based on a position domain; constructing a finite time error constraint performance function irrelevant to an initial state, defining an error conversion function based on coordinate transformation, and ensuring finite time convergence of tracking errors of the multi-axis precision centrifuge; based on a finite time error constraint performance function, designing a position domain repetitive controller by utilizing the error converted by the error conversion function; and a smooth transition function is introduced into the position domain repetitive controller, so that overshoot of the dynamic adjustment process of the system is reduced. The dynamic and steady control performance of the multi-axis precision centrifuge system can be improved on the premise of restraining periodic interference.
Description
Technical Field
The invention belongs to the technical field of electromechanical control, and relates to a repeated control method and device for a multi-shaft precision centrifuge system.
Background
Precision centrifuges are used as an important electromechanical device for testing and calibrating accelerometers and other inertial instruments, and are widely used in inertial navigation systems in the aerospace field due to their precise calibration capabilities. Compared with static calibration of an accelerometer by a single-axis precise centrifuge system, the multi-axis precise centrifuge system can be used for calibrating dynamic characteristics of the accelerometer, such as sinusoidal acceleration, step acceleration and the like, and provides guarantee for development of a thrust vector technology in the field of aerospace. However, in multi-axis precision centrifuge systems, periodic disturbances are a major factor affecting system performance. Due to the centrifugal effect and the uneven movement, the auxiliary shaft can carry larger periodic interference when the main shaft moves, so that the control precision of the system can be reduced, and the stable operation of the multi-shaft precise centrifugal machine can be seriously influenced.
Therefore, in order to suppress the influence of the periodic disturbance on the precision centrifuge system, many scholars have adopted a repetitive control method. The method is developed from the internal model principle, and can effectively inhibit periodic interference. A scholars put forward a repetitive control method based on a time-lag internal model to solve the tracking problem of periodic reference and disturbance signals. Its highly accurate tracking performance is achieved by repeating a periodic signal generator in the controller. However, the periodic signal generated by the positive feedback loop decreases the stability of the system. In order to solve this problem, a learner proposes a method of connecting a low-pass filter in series before a time lag link to shift a high-frequency pole on a virtual axis of a system, but this definitely sacrifices the high-frequency tracking performance of the system to improve the stability of the system. Although the above repetitive control method is studied deeply in the steady state of the system, the transient performance of the system is not considered, even because of the existence of a delay link, the repetitive controller can act at least after one period, so that the transient response of the system is poor, and the overall control performance and safe and stable operation of the system can be seriously affected by the poor transient performance.
Disclosure of Invention
The invention aims to provide a repeated control method and a device for a multi-axis precise centrifugal machine system, which can improve the dynamic and steady control performance of the multi-axis precise centrifugal machine system on the premise of inhibiting periodic interference.
One aspect of the present invention provides a repetitive control method for a multi-axis precision centrifuge system, comprising:
step S1: modeling the multi-axis precision centrifuge, establishing a main shaft closed loop transfer function and a secondary shaft closed loop transfer function of the multi-axis precision centrifuge, analyzing periodic interference of the secondary shaft, and determining to adopt repeated control based on a position domain;
step S2: constructing a finite time error constraint performance function irrelevant to an initial state, defining an error conversion function based on coordinate transformation, and ensuring finite time convergence of tracking errors of the multi-axis precision centrifuge;
Step S3: based on a finite time error constraint performance function, designing a position domain repetitive controller by utilizing the error converted by the error conversion function;
Step S4: and a smooth transition function is introduced into the position domain repetitive controller, so that overshoot of the dynamic adjustment process of the system is reduced.
Preferably, in step S1, the closed loop transfer functions of the main shaft and the auxiliary shaft of the multi-shaft precision centrifuge are:
Wherein K T1 and K Ti are torque coefficients of a main shaft and a secondary shaft respectively, K e1 and K ei are counter potential coefficients of the main shaft and the secondary shaft respectively, J 1 and J i are motor load total inertia of the main shaft and the secondary shaft respectively, L 1 and L i are inductances of armature windings of the main shaft and the secondary shaft respectively, R 1 and R i are resistances of the armature windings of the main shaft and the secondary shaft respectively, K s1 and K si are gain coefficients of a current loop controller of the main shaft and the secondary shaft respectively, k 1(s) and K i(s) are the primary and secondary shaft controller gains, respectively, and U 1(s) and U i(s) are the primary and secondary shaft control outputs, respectively. T fi and T ri are periodic disturbance moments converted onto the auxiliary shafts, T ri is electromagnetic wave power moment, T fi is periodic disturbance moment caused by friction force, i=2, 3 … n is the ith auxiliary shaft coefficient, and n is the number of auxiliary shafts.
Preferably, in step S1, a frequency domain analysis is performed on the periodic interference of the multi-axis precision centrifuge by using a spectrum analysis method, a corresponding control output curve is obtained by setting different speed reference instructions, and a fast fourier transform diagram of a time domain and a position domain thereof is drawn to analyze the characteristics of the periodic interference, thereby determining that the interference period in the position domain is fixed.
Preferably, in step S2, the finite time error constraint performance function η (t) is:
Wherein T f is the rest time, η 0 and For the preset condition, eta 0 is not less than 1,/>T f > 0, and the initial value of the function
Preferably, in step S2, the error transfer function is: The coordinate transformation is as follows: z=tan (pi e/2 eta), where e is the control error.
Preferably, in step S3, the position domain repetitive controller for a single frequency point of periodic interference is calculated as follows:
Wherein omega n is the angular frequency of the position domain of the periodic disturbance moment, the first parameter ζ and the second parameter ζ are two parameters of the repetitive controller, and 1 > ζ > 0, Is a position domain Laplace transform operator.
Preferably, the values of the first parameter ζ and the second parameter ζ are in the range of the first parameterThe second parameter ζ ε [00.1].
Preferably, in step S4, the smooth transition function is a nonlinear fal function, and the expression is:
Where ε is the input error, α and δ are constants, α determines the nonlinearity of the fal function, smaller α is the nonlinearity, larger δ determines the linear segment interval length.
Preferably, δ=0.25, α=0.5.
Another aspect of the present invention provides a repetitive control device for a multi-axis precision centrifuge system, comprising:
the position domain repetitive control determining module is used for modeling the multi-axis precision centrifuge, establishing a main shaft closed loop transfer function and a secondary shaft closed loop transfer function of the multi-axis precision centrifuge, analyzing periodic interference of the secondary shaft, and determining to adopt the repetitive control based on the position domain;
The finite time error constraint performance function construction module is used for constructing a finite time error constraint performance function irrelevant to an initial state, defining an error conversion function based on coordinate transformation and ensuring finite time convergence of tracking errors of the multi-axis precision centrifuge;
The position domain repetitive controller design module designs the position domain repetitive controller by utilizing the error converted by the error conversion function based on the limited time error constraint performance function;
and the smooth transition function introduction module introduces a smooth transition function into the position domain repetitive controller, so that overshoot of the dynamic adjustment process of the system is reduced.
According to the repetitive control method and the repetitive control device for the multi-axis precision centrifuge system, the improved repetitive controller is designed by introducing a limited time constraint performance function and a coordinate transformation mechanism, constraint control on transient and steady state performance of the system is realized, and system errors can be ensured to be converged in a given range in a given time, so that the defect of slow response of the repetitive control is overcome.
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For a clearer description of the technical solutions of the present invention, the following description will be given with reference to the attached drawings used in the description of the embodiments of the present invention, it being obvious that the attached drawings in the following description are only some embodiments of the present invention, and that other attached drawings can be obtained by those skilled in the art without the need of inventive effort:
FIG. 1 is a flow chart of a repetitive control method for a multi-axis precision centrifuge system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the repetitive control of a multi-axis precision centrifuge according to an embodiment of the present invention;
FIG. 3 is a time domain FFT and position domain FFT contrast plot output by the controller;
FIG. 4 is a Bode plot of R(s) for different zeta and zeta compositions;
FIG. 5 is a graph comparing repetitive control tracking performance with or without finite time error constraints;
Fig. 6 is a configuration diagram of a repetitive control device for a multi-axis precision centrifuge system according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiment of the invention is based on repeated control research of a multi-axis precise centrifuge system, takes the transient control performance requirement of the multi-axis precise centrifuge system as a background, aims at the time delay problem of repeated control in the process of restraining periodic interference, and provides a repeated control method for the multi-axis precise centrifuge system around the limited time error constraint repeated control of the multi-axis precise centrifuge system. FIG. 1 is a flow chart of a repetitive control method for a multi-axis precision centrifuge system according to an embodiment of the present invention. As shown in fig. 1, the repetitive control method for a multi-axis precision centrifuge system according to an embodiment of the present invention includes steps S1 to S4. Fig. 2 is a schematic diagram of repetitive control of a multi-axis precision centrifuge according to an embodiment of the present invention. The steps in fig. 1 are described in detail below with reference to fig. 2.
In step S1, modeling is carried out on the multi-axis precision centrifuge, a main shaft closed loop transfer function and a secondary shaft closed loop transfer function of the multi-axis precision centrifuge are established, periodic interference of the secondary shaft is analyzed, and repeated control based on a position domain is determined to be adopted.
The multi-shaft precision centrifugal machine of the embodiment of the invention is a permanent magnet synchronous motor driving system. Simplifying motor driving system by moving back electromotive force feedback item of motor, and then obtaining transfer function of the system as
Wherein s is a Laplacian factor, K s is an equivalent gain of a current regulator and an inverter, K T is a motor moment coefficient, K e is a motor counter potential coefficient, ω(s) is a centrifuge rotating speed, i cmd(s) is a control current, R is an armature resistance of the motor, L is an armature inductance of the motor, J is a rotational inertia of a load, and D is a windage coefficient.
Since the windage is small, the windage coefficient D is negligible, and d=0 is substituted into formula (1)
For the multi-axis precision centrifuge control system of the invention, a position sensor is adopted to measure a position signal for position feedback to form a closed loop, and a speed signal is used as an integral function to the position signal, so that an integral link is introduced into an object shown in a formula (2), and a final model of a controlled object of the vector control type permanent magnet synchronous motor system is as follows:
Order the Then
Where τ m is the electromechanical time constant of the motor and τ e is the electromagnetic time constant of the motor. Typically τ m＞10τe.
At this time, the formula (4) can be written as
The formula is a mechanism model of a controlled object of an actual multi-axis precision centrifuge.
Based on the formula (5) of the multi-shaft precision centrifuge, the method comprisesAnd ω(s) =su(s) is substituted into equation (5) and the secondary axis disturbances are taken into account, then a closed loop transfer function of the primary and secondary axis can be established as follows:
Wherein K T1 and K Ti are torque coefficients of a main shaft and a secondary shaft respectively, K e1 and K ei are counter potential coefficients of the main shaft and the secondary shaft respectively, J1 and Ji are motor load total inertia of the main shaft and the secondary shaft respectively, L 1 and L i are inductances of armature windings of the main shaft and the secondary shaft respectively, R 1 and R i are resistances of the armature windings of the main shaft and the secondary shaft respectively, K s1 and K si are gain coefficients of a current loop controller of the main shaft and the secondary shaft respectively, k 1(s) and K i(s) are the primary and secondary shaft controller gains, respectively, and U 1(s) and U i(s) are the primary and secondary shaft control outputs, respectively. T fi and T ri are periodic disturbance moments converted onto the layshafts, T ri is electromagnetic wave power moment, T fi is periodic disturbance moment caused by friction force, i=2, 3..n, i-th layshaft coefficient, n is the number of layshafts.
The periodic disturbance of the multi-axis precision centrifuge can be subjected to frequency domain analysis by adopting a frequency spectrum analysis method, and the characteristics of the periodic disturbance can be analyzed by setting different speed reference instructions, such as 20deg/sec, 50deg/sec and 100deg/sec, obtaining corresponding controller output curves, and drawing a Fast Fourier Transform (FFT) graph of a time domain and a position domain of the output curves. FIG. 3 is a comparison of the controller output time domain FFT and position domain FFT, where (a) is the time domain FFT and position domain FFT at 20 deg/sec; (b) is a time domain FFT and a location domain FFT at 50 deg/sec; (c) is a time domain FFT and a position domain FFT at 100 deg/sec. As can be seen from fig. 3, the period of the disturbance is not fixed in the time domain, that is, the disturbance is not periodic when the system is moving at variable speeds; but in the position domain the period of the disturbance is fixed, i.e. the layshaft periodic disturbance is a time-varying periodic disturbance. Thus, the present invention designs a tracking controller using repetitive control based on a location field, i.e., designs a repetitive controller of a location field.
In step S2, a finite time error constraint performance function unrelated to the initial state is constructed from the coordinate transformation avoiding the inversion of the function, and an error conversion function based on the coordinate transformation is defined, so that finite time convergence of tracking errors of the multi-axis precision centrifuge is realized.
In the existing control method, repeated control is adopted for inhibiting periodic interference, but due to the introduction of a delay link, the control only acts after at least one period, the transient performance of the system is affected, and the control precision is reduced. In order to overcome the inherent defect of repetitive control, the embodiment of the invention avoids the problem of slow transient response of repetitive control by introducing a finite time constraint performance function and a coordinate transformation mechanism.
In order to construct a finite time constraint performance function, the following finite time stabilization concept is introduced:
definition: for systems containing unknown nonlinearities, if for any state x (T 0)＝x0, there is a normal number y and a rest time T < + -infinity, has the following components
Where E (-) is an average, the system is a practically finite time stable in the mean-square sense. Since the rest time T is a design parameter in the equation (8), it is independent of the initial state. The finite time constraint performance function designed below is independent of the initial state and needs to satisfy the following conditions
1)η(t)＞0；2)3)/>And/>Is an arbitrary positive constant, and T f is the rest time.
Therefore, the finite time error constraint performance function η (t) selected by the embodiment of the invention is
Wherein: eta 0 is more than or equal to 1,T f > 0 is a design parameter, η 0 and/>Is a preset condition. It can be seen that the above-described function satisfies three conditions defining a finite time constraint performance function, and that the initial value of the function/>
As the traditional error conversion function mostly adopts hyperbolic functions, the problem of singularity can be generated in inversion. Therefore, the invention adopts a coordinate transformation method to avoid function inversion.
The following error transfer function is definedWhere e is the control error. Unlike the previous preset performance function, the error transfer function is only used for variable substitution in the derivation process, and no inversion is needed. And the following coordinate transformation z=tan (pi e/2 eta) is adopted, and in combination with a finite time error constraint function, it can be seen that when stability analysis is performed, a new variable z is derived, and a conversion function P can appear, so that finite time stability conditions can be met without performing function inversion, the problem of singularity is avoided, and the error constraint of the whole system state can be realized.
In step S3, a position domain repetitive controller is designed by utilizing the error converted by the error conversion function based on the limited time error constraint performance function, so that the transient performance of the control system is improved, and the high-precision tracking control of the multi-axis precision centrifuge is realized.
The repeated control is an effective method for inhibiting periodic interference, and can better realize the high-precision tracking control of the multi-shaft precision centrifugal machine. The proposal of the method of repetitive control is derived from the internal model principle. The basic idea of the internal mold principle is as follows: for a stable closed loop system, if the model of the input signal is connected in series in the feedforward loop, the tracking error of the system for the signal is theoretically 0, and if the signal is an interference signal, the complete suppression of the signal can be realized. Since the time-varying periodic disturbance of the multi-axis precision centrifuge is of a position domain nature, the most suitable method is to suppress it by using a position domain repetitive control method.
For the limited frequency points of the interference signals, the embodiment of the invention adopts a limited-dimensional repetitive control strategy, and the calculation formula of the position domain repetitive controller for a single frequency point is as follows:
where ω n is the position domain angular frequency of the periodic disturbance moment. ζ and ζ are two parameters to be selected (first parameter and second parameter) of the repetitive controller and 1 > ζ > 0, Is a position domain Laplace transform operator and is applied to a signal/>Lawster's transformation with position domain
Obtaining a state space expression by the repetitive controller:
Wherein the method comprises the steps of
To better analyze the effect of this location domain finite dimension in-mold repetitive controller, equation (12) is converted to a form of transfer function
Let ω n ω (t) be 1 without loss of generality, fig. 4 is a Bode diagram (Bode diagram) of R(s) composed of different ζ and ζ. It can be seen from the figure that the effect of this repetitive controller and its effect on system stability are both dependent on the design of the repetitive controller parameters ζ and ζ. The following conclusions can be drawn:
1. Zeta/zeta represents the amplitude of the repetitive controller at the action frequency point, when zeta/zeta is larger, the amplitude of the repetitive controller at the action frequency point is larger, and at this time, the suppression effect of the repetitive controller on the periodic interference is better;
2.ζ affects the width of the repetitive controller near the action frequency point, and the width of the repetitive controller directly affects the robustness of the repetitive controller to the uncertainty of acquiring the speed signal, namely, when the speed signal has an acquisition error, the suppression effect of the repetitive controller to the periodic interference can be reduced, and when the width of the repetitive controller is widened, the effect can be reduced;
3. The stability of the closed loop of the system is jointly influenced by ζ and ζ, because the repetitive controller has phase angle loss after the action frequency point, the stability of the system can be influenced, and factors in the aspect are considered in the design process.
In view of the above-mentioned, it is desirable,Zeta is preferably a value in the range/>ζ∈[00.1]。
In step S4, a smooth transition function is introduced into the design of the position domain repetitive control, so that the problem of excessive overshoot of the dynamic adjustment process of the system caused by the traditional repetitive controller is solved.
The amplitude of the resonance controller is suddenly changed near the resonance frequency, so that a Nyquist curve is easy to approach a critical point, the sensitivity function of the system is increased, the oscillation of the dynamic adjustment process of the system is aggravated, the overshoot large-scale repetitive controller can be regarded as a series of superposition of the resonance controllers, and the problem that the overshoot of the system is too large caused after the repetitive controller is added is solved.
In order to solve the problem of excessive overshoot caused by the addition of the repetitive controller, the fal function is introduced into the repetitive controller, and the overshoot of the dynamic motor adjusting process can be effectively reduced by utilizing the characteristics of small gain with large error and small gain with small error. The nonlinear fal function has fast convergence characteristic and is expressed as
Where ε is the input error, α and δ are constants, α determines the nonlinearity of the fal function, and δ determines the linear segment interval length as smaller α is more nonlinear. In order to reduce the problem of excessive rotational speed overshoot in the dynamic system adjustment process caused by the addition of the repetitive controllers, the embodiment of the invention selects delta=0.25 and alpha=0.5. Smoothing the fal function to smooth the curve of the reference signal can greatly improve the dynamic performance of the repetitive controller.
FIG. 5 shows a graph of repetitive control tracking performance with or without error constraints, where (a) shows tracking error without error constraint function; (b) shows tracking errors with the addition of error constraints. It can be seen from fig. 5 (a) that the transient response of the system is slow with repeated control without error constraints, and the controller will not start to function until approximately 0.3 seconds later. This is because repeated control requires one cycle of learning of periodic disturbance at the initial stage of the system, resulting in a decrease in transient performance of the system; in fig. 5 (b), it is shown that after adding an error constraint in the repetitive control, the transient performance of the system is improved, and the controller starts to operate almost at the beginning of the system. It can be seen that the added finite time constraint performance function can improve the transient performance of the system to a greater extent and ensure the stability of the system. Therefore, the limited time error constraint repetitive control of the embodiment of the invention can well solve the time delay problem existing in the traditional repetitive control and realize the precise control of the multi-axis centrifugal machine system.
In summary, according to the repetitive control method for a multi-axis precision centrifuge system according to the embodiment of the present invention, aiming at the periodic interference problem existing in the multi-axis precision centrifuge system, a frequency spectrum analysis method is adopted to perform frequency domain analysis on the periodic interference, and repetitive control based on a location domain is designed to suppress the influence of the periodic interference; in order to solve the delay problem of repeated control, a finite time error constraint performance function irrelevant to an initial state is constructed, and an error constraint repeated control method based on finite time is designed through error transformation, so that the transient control performance of the multi-axis precision centrifuge system is improved; a smooth transition function with large error and small gain is introduced in the design of the position domain repetitive control, so that the problem of overlarge system dynamic adjustment process caused by the traditional repetitive controller is solved.
The embodiment of the invention also provides a repetitive control device for the multi-shaft precision centrifuge system. Fig. 6 is a configuration diagram of a repetitive control device for a multi-axis precision centrifuge system according to an embodiment of the present invention. As shown in fig. 6, the repetitive control device for a multi-axis precision centrifuge system according to an embodiment of the present invention includes:
The position domain repetitive control determining module 101 is used for modeling the multi-axis precision centrifuge, establishing a main shaft closed loop transfer function and a secondary shaft closed loop transfer function of the multi-axis precision centrifuge, analyzing periodic interference of the secondary shaft, and determining to adopt the repetitive control based on the position domain;
The finite time error constraint performance function construction module 102 is used for constructing a finite time error constraint performance function irrelevant to an initial state, defining an error conversion function based on coordinate transformation and ensuring finite time convergence of tracking errors of the multi-axis precision centrifuge;
The position domain repetitive controller design module 103 designs the position domain repetitive controller by using the error converted by the error conversion function based on the finite time error constraint performance function;
the smooth transition function introduction module 104 introduces a smooth transition function into the position domain repetitive controller to reduce overshoot of the system dynamic adjustment process.
Specific examples of the repetitive control device for a multi-axis precision centrifuge system according to the present embodiment may be found in the above limitation of the repetitive control method for a multi-axis precision centrifuge system, and will not be described herein. The respective modules in the repetitive control device for a multi-axis precision centrifuge system described above may be implemented in whole or in part by software, hardware, and combinations thereof. The above modules may be embedded in hardware or may be independent of a processor in the computer device, or may be stored in software in a memory in the computer device, so that the processor may call and execute operations corresponding to the above modules.
While certain exemplary embodiments of the present invention have been described above by way of illustration only, it will be apparent to those of ordinary skill in the art that modifications may be made to the described embodiments in various different ways without departing from the spirit and scope of the invention. Accordingly, the drawings and description are to be regarded as illustrative in nature and not as restrictive of the scope of the invention, which is defined by the appended claims.
Claims (10)
1. A repetitive control method for a multi-axis precision centrifuge system, comprising:
step S1: modeling the multi-axis precision centrifuge, establishing a main shaft closed loop transfer function and a secondary shaft closed loop transfer function of the multi-axis precision centrifuge, analyzing periodic interference of the secondary shaft, and determining to adopt repeated control based on a position domain;
step S2: constructing a finite time error constraint performance function irrelevant to an initial state, defining an error conversion function based on coordinate transformation, and ensuring finite time convergence of tracking errors of the multi-axis precision centrifuge;
Step S3: based on a finite time error constraint performance function, designing a position domain repetitive controller by utilizing the error converted by the error conversion function;
Step S4: and a smooth transition function is introduced into the position domain repetitive controller, so that overshoot of the dynamic adjustment process of the system is reduced.
2. The method of claim 1, wherein in step S1, the main and auxiliary shaft closed loop transfer functions of the multi-shaft precision centrifuge are:
Wherein K T1 and K Ti are torque coefficients of a main shaft and a secondary shaft respectively, K e1 and K ei are counter potential coefficients of the main shaft and the secondary shaft respectively, J 1 and J i are motor load total inertia of the main shaft and the secondary shaft respectively, L 1 and L i are inductances of armature windings of the main shaft and the secondary shaft respectively, R 1 and R i are resistances of the armature windings of the main shaft and the secondary shaft respectively, K s1 and K si are gain coefficients of a current loop controller of the main shaft and the secondary shaft respectively, k 1(s) and K i(s) are the primary and secondary shaft controller gains, respectively, and U 1(s) and U i(s) are the primary and secondary shaft control outputs, respectively. T fi and T ri are periodic disturbance moments converted onto the auxiliary shafts, T ri is electromagnetic wave power moment, T fi is periodic disturbance moment caused by friction force, i=2, 3 … n is the ith auxiliary shaft coefficient, and n is the number of auxiliary shafts.
3. The method according to claim 1 or 2, wherein in step S1, frequency domain analysis is performed on the periodic disturbance of the multi-axis precision centrifuge by using a spectrum analysis method, corresponding control output curves are obtained by setting different speed reference instructions, and the characteristics of the periodic disturbance are analyzed by drawing a fast fourier transform diagram of a time domain and a position domain thereof, so as to determine that the disturbance period in the position domain is fixed.
4. A method according to any one of claims 1-3, characterized in that in step S2 the finite time error constraint performance function η (t) is:
Wherein T f is the rest time, η 0 and For the preset condition, eta 0 is not less than 1,/>T f > 0, and the initial value of the function
5. The method according to any one of claims 1-4, wherein in step S2, the error transfer function is: The coordinate transformation is as follows: z=tan (pi e/2 eta), where e is the control error.
6. The method according to any one of claims 1-5, wherein in step S3, the position domain repetitive controller formula for a single frequency point of periodic interference is as follows:
Wherein omega n is the angular frequency of the position domain of the periodic disturbance moment, the first parameter ζ and the second parameter ζ are two parameters of the repetitive controller, and 1 > ζ > 0, Is a position domain Laplace transform operator.
7. The method of claim 6, wherein the first parameter ζ and the second parameter ζ are in a range of values for the first parameterThe second parameter ζ ε [ 0.1].
8. The method according to any one of claims 1 to 7, wherein in step S4, the smooth transition function is a nonlinear fal function expressed as:
Where ε is the input error, α and δ are constants, α determines the nonlinearity of the fal function, smaller α is the nonlinearity, larger δ determines the linear segment interval length.
9. The method of claim 8, wherein δ=0.25 and α=0.5.
10. A repetitive control device for a multi-axis precision centrifuge system, comprising:
the position domain repetitive control determining module is used for modeling the multi-axis precision centrifuge, establishing a main shaft closed loop transfer function and a secondary shaft closed loop transfer function of the multi-axis precision centrifuge, analyzing periodic interference of the secondary shaft, and determining to adopt the repetitive control based on the position domain;
The finite time error constraint performance function construction module is used for constructing a finite time error constraint performance function irrelevant to an initial state, defining an error conversion function based on coordinate transformation and ensuring finite time convergence of tracking errors of the multi-axis precision centrifuge;
The position domain repetitive controller design module designs the position domain repetitive controller by utilizing the error converted by the error conversion function based on the limited time error constraint performance function;
and the smooth transition function introduction module introduces a smooth transition function into the position domain repetitive controller, so that overshoot of the dynamic adjustment process of the system is reduced.
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