Adaptive sinusoidal control method, apparatus and medium

Abstract

The application discloses a kind of self-adapting sinusoidal control method, device and medium, according to the real part of original acceleration by discrete fourier transform, the imaginary part of original acceleration by discrete fourier transform, reference sine gain coefficient, reference cosine gain coefficient, period count, each control period sine coefficient increment, each control period cosine coefficient increment are calculated;In each self-adapting sinusoidal control coefficient update period, the value of each control period sine coefficient increment and each control period cosine coefficient increment is unchanged, period count is constantly reduced, reference sine gain coefficient and reference cosine gain coefficient are updated;According to reference sine gain coefficient and reference cosine gain coefficient, self-adapting sinusoidal control displacement excitation is calculated;According to pose excitation and response, control output is calculated.The application can quickly converge, so that the acceleration of corresponding axis quickly reaches target value, can be applied to multi-degree-of-freedom vibration table, and can effectively suppress axis coupling.

Description

Technical Field

[0001] This invention belongs to the field of vibration table control technology, and more specifically, relates to an adaptive sinusoidal control method, device and medium. Background Technology

[0002] Using a multi-degree-of-freedom vibration table to conduct vibration simulation tests on the product under test can verify the structural characteristics and durability of the product. This plays a crucial role in the product design and actual use stages. Commonly used experiments include sinusoidal vibration tests; for example, the vibrations in equipment such as nuclear power plants, aerospace equipment, and automobiles are generally sinusoidal. Sinusoidal tests can be conducted by fixing the equipment onto the vibration table.

[0003] Adaptive sinusoidal control, as a control compensation technique, improves control fidelity by adding a variable gain controller to correct closed-loop amplitude and phase irregularities. It directly measures the dynamics of the control system and modifies the corresponding control compensation in real time to adapt to constantly changing system dynamics, achieving precise displacement or acceleration control at specified frequencies.

[0004] Methods for implementing sinusoidal control include: using a transfer matrix to achieve adaptive sinusoidal control; and using an adaptive dual-loop control system. Existing solutions sometimes require identifying the transfer function matrix before implementing sinusoidal control, resulting in low efficiency; other methods are only applicable to single-axis vibration tables and lack coupling compensation functionality for multi-degree-of-freedom control. Summary of the Invention

[0005] This invention addresses the aforementioned problems in the prior art. Therefore, there is a need for an adaptive sinusoidal control method, device, and medium to achieve sinusoidal control of a multi-degree-of-freedom vibration table, enabling a single axis to achieve the desired sinusoidal displacement or acceleration while suppressing coupled vibrations between other axes. This has significant theoretical and engineering value.

[0006] According to a first aspect of the present invention, an adaptive sinusoidal control method is provided, the method comprising: obtaining the real part γ of the original acceleration through a discrete Fourier transform. ω The imaginary part θ obtained from the original acceleration via discrete Fourier transform ω Reference sinusoidal gain coefficient k sin Reference cosine gain coefficient k cos The period count C is calculated. i Increment of sinusoidal coefficient I per control cycle sin Increment I of cosine coefficient per control cycle cos ;

[0007] Within each adaptive sinusoidal control coefficient update cycle, the sinusoidal coefficient increment I per control cycle sinand the increment of cosine coefficient I per control cycle cos The value remains unchanged, and the period count C i As it decreases continuously, the reference sinusoidal gain coefficient k sin and reference cosine gain coefficient k cos Update;

[0008] Based on the reference sinusoidal gain coefficient k sin and reference cosine gain coefficient k cos The adaptive sinusoidal control displacement excitation Cmd is calculated. z ;

[0009] Based on pose excitation Cmd z and response Pos z The control output is calculated.

[0010] Furthermore, the real part γ of the original acceleration obtained by the discrete Fourier transform is calculated using the following method. ω The imaginary part θ obtained from the original acceleration via discrete Fourier transform ω :

[0011] The Fourier series is defined as follows:

[0012]

[0013] Where f(t) is the Fourier series, C is a constant, n is the number of sampling points, and a n Here, f is the cosine coefficient, f0 is the frequency value, t is the time, and b is the frequency. n The coefficient is the sine coefficient.

[0014] The following can be derived using the orthogonality of trigonometric functions:

[0015]

[0016] Where T0 is the period of the sine wave;

[0017] Within the period of the sine wave, the number of sampling points in each period is N. T Then we have:

[0018]

[0019] Where F s The iteration frequency;

[0020] Therefore:

[0021]

[0022] Where A is the coefficient, b1 is the cosine coefficient, and a1 is the sine coefficient. N is the phase angle. i For discrete sampling points, NT This represents the total number of sampling points;

[0023] The previous formula can be simplified using the orthogonality of sine and cosine functions as follows:

[0024]

[0025] Real part γ ω and the imaginary part θ ω The calculation formula is as follows:

[0026]

[0027] Where a z ω is the amplitude, N is the angular frequency, and N is the discrete sampling point.

[0028] Furthermore, the real part γ obtained from the original acceleration via discrete Fourier transform... ω The imaginary part θ obtained from the original acceleration via discrete Fourier transform ω Reference sinusoidal gain coefficient k sin Reference cosine gain coefficient k cos The period count C is calculated. i Increment of sinusoidal coefficient I per control cycle sin Increment I of cosine coefficient per control cycle cos ,include:

[0029] Euler's formula for the complex frequency domain is:

[0030]

[0031] Where γ ω θ is the real part at a specific frequency. ω The imaginary part of the characteristic frequency. To express this complex number using an exponent, A ω Gain at a specific frequency, The phase angle is at a specific frequency, and j represents an imaginary number;

[0032] The gain at a specific frequency is determined as follows:

[0033]

[0034] Determine the amplitude iteration coefficients based on the gain at a specific frequency:

[0035]

[0036] Among them, A ref K represents the amplitude of the sinusoidal acceleration. pri The basic axis iteration coefficient;

[0037] The phase iteration coefficient is calculated using the following formula.

[0038]

[0039] in This represents the phase iteration coefficient from the previous iteration. This represents the updated phase iteration coefficients. Indicates the target phase of sinusoidal motion. Indicates the actual phase of the current axis. Indicates the phase difference coefficient;

[0040] The cycle count C is calculated using the following formula. i :

[0041]

[0042] Where F s F is the iteration frequency. ref The frequency of the sinusoidal motion;

[0043] The increment of the sine coefficient I per control cycle is calculated using the following formula. sin Increment I of cosine coefficient per control cycle cos :

[0044]

[0045] Among them, I sin (k) represents the current sinusoidal coefficient increment per control cycle, I sin (k-1) represents the increment of the sinusoidal coefficient per control cycle in the previous iteration, I cos (k) represents the current increment of the cosine coefficient per control cycle, I cos (k-1) represents the increment of the cosine coefficient for each control cycle in the previous iteration.

[0046] Furthermore, within each adaptive sinusoidal control coefficient update cycle, the sinusoidal coefficient increment I per control cycle sin and the increment of cosine coefficient I per control cycle cos The value remains unchanged, and the period count C i The value is continuously reduced, and the reference sinusoidal gain coefficient k is adjusted using the following formula. sin and reference cosine gain coefficient k cos Update;

[0047]

[0048] Where K sin (k) represents the updated reference sinusoidal gain coefficient, K sin (k-1) is the reference sinusoidal gain coefficient from the previous iteration, K cos(k) represents the updated reference cosine gain coefficient, K cos (k-1) is the reference cosine gain coefficient of the previous time.

[0049] Furthermore, based on the reference sinusoidal gain coefficient k sin and reference cosine gain coefficient k cos The adaptive sinusoidal control displacement excitation Cmd is calculated using the following formula. z :

[0050] Cmd z (k)=K sin (k)S sin +K cos (k)S cos

[0051] Among them, S sin For the desired sinusoidal displacement, S cos The desired cosine displacement.

[0052] Furthermore, based on the pose excitation Cmd z and response Pos z The control output is calculated using the following formula:

[0053] e(k)=Cmd z (k)-Pos z (k)

[0054]

[0055] Where e(k) is the difference between the expected and actual displacement values, Cmd z (k) represents the expected displacement at time k, Pos z (k) represents the actual displacement value at time k, u(k) is the control input, and K p K is the proportionality coefficient. I K is the integral coefficient. D Here are the differential coefficients, and e(k-1) is the difference between the expected and actual displacement values ​​at time k-1.

[0056] According to a second technical solution of the present invention, an adaptive sine wave control device is provided. The device includes:

[0057] The first calculation module is configured to calculate the real part γ obtained from the discrete Fourier transform of the original acceleration. ω The imaginary part θ obtained from the original acceleration via discrete Fourier transform ω Reference sinusoidal gain coefficient k sin Reference cosine gain coefficient k cos The period count C is calculated. i Increment of sinusoidal coefficient I per control cycle sinIncrement I of cosine coefficient per control cycle cos ;

[0058] The update module is configured to increment the sinusoidal coefficient by I per control cycle within each adaptive sinusoidal control coefficient update cycle. sin and the increment of cosine coefficient I per control cycle cos The value remains unchanged, and the period count C i As it decreases continuously, the reference sinusoidal gain coefficient k sin and reference cosine gain coefficient k cos Update;

[0059] The second calculation module is configured to calculate based on the reference sinusoidal gain coefficient k. sin and reference cosine gain coefficient k cos The adaptive sinusoidal control displacement excitation Cmd is calculated. z ;

[0060] The control output calculation module is configured to calculate based on the pose excitation Cmd. z and response Pos z The control output is calculated.

[0061] Furthermore, the first computing module is further configured as follows:

[0062] The real part γ of the original acceleration obtained by the discrete Fourier transform is calculated using the following method. ω The imaginary part θ obtained from the original acceleration via discrete Fourier transform ω :

[0063] The Fourier series is defined as follows:

[0064]

[0065] Where f(t) is the Fourier series, C is a constant, n is the number of sampling points, and a n Here, f is the cosine coefficient, f0 is the frequency value, t is the time, and b is the frequency. n The coefficient is the sine coefficient.

[0066] The following can be derived using the orthogonality of trigonometric functions:

[0067]

[0068] Where T0 is the period of the sine wave;

[0069] Within the period of the sine wave, the number of sampling points in each period is N. T Then we have:

[0070]

[0071] Where F sThe iteration frequency;

[0072] Therefore:

[0073]

[0074] Where A is the coefficient, b1 is the cosine coefficient, and a1 is the sine coefficient. N is the phase angle. i For discrete sampling points, N T This represents the total number of sampling points;

[0075] The previous formula can be simplified using the orthogonality of sine and cosine functions as follows:

[0076]

[0077] Real part γ ω and the imaginary part θ ω The calculation formula is as follows:

[0078]

[0079] Where a z ω is the amplitude, N is the angular frequency, and N is the discrete sampling point.

[0080] Furthermore, the first computing module is further configured as follows:

[0081] Euler's formula for the complex frequency domain is:

[0082]

[0083] Where γ ω θ is the real part at a specific frequency. ω The imaginary part of the characteristic frequency. To express this complex number using an exponent, A ω Gain at a specific frequency, The phase angle is at a specific frequency, and j represents an imaginary number;

[0084] The gain at a specific frequency is determined as follows:

[0085]

[0086] Determine the amplitude iteration coefficients based on the gain at a specific frequency:

[0087]

[0088] Among them, A ref K represents the amplitude of the sinusoidal acceleration. pri The basic axis iteration coefficient;

[0089] The phase iteration coefficient is calculated using the following formula.

[0090]

[0091] in This represents the phase iteration coefficient from the previous iteration. This represents the updated phase iteration coefficients. Indicates the target phase of sinusoidal motion. Indicates the actual phase of the current axis. Indicates the phase difference coefficient;

[0092] The cycle count C is calculated using the following formula. i :

[0093]

[0094] Where F s F is the iteration frequency. ref The frequency of the sinusoidal motion;

[0095] The increment of the sine coefficient I per control cycle is calculated using the following formula. sin Increment I of cosine coefficient per control cycle cos :

[0096]

[0097] Among them, I sin (k) represents the current sinusoidal coefficient increment per control cycle, I sin (k-1) represents the increment of the sinusoidal coefficient per control cycle in the previous iteration, I cos (k) represents the current increment of the cosine coefficient per control cycle, I cos (k-1) represents the increment of the cosine coefficient for each control cycle in the previous iteration.

[0098] According to a third technical solution of the present invention, a non-transitory computer-readable storage medium storing instructions is provided, which, when executed by a processor, performs the methods described in various embodiments of the present invention.

[0099] The adaptive sinusoidal control method, apparatus, and medium according to various embodiments of the present invention have at least the following beneficial effects:

[0100] (1) Users only need to set a few parameters to complete adaptive sinusoidal control, which is highly automated and convenient;

[0101] (2) The present invention can converge quickly, so that the acceleration of the corresponding axis can quickly reach the target value;

[0102] (3) This invention is applicable to multi-degree-of-freedom vibration tables and can effectively suppress axial coupling;

[0103] (4) The present invention has been tested and found to be highly reliable and effective in control. Attached Figure Description

[0104] In drawings that are not necessarily drawn to scale, the same reference numerals may describe similar parts in different views. The same reference numerals with or without letter suffixes may indicate different instances of similar parts. The drawings generally illustrate various embodiments by way of example rather than limitation and, together with the description and claims, serve to explain embodiments of the invention. Where appropriate, the same reference numerals are used in all drawings to refer to the same or similar parts. Such embodiments are illustrative and not intended to be exhaustive or exclusive embodiments of the apparatus or method.

[0105] Figure 1 A flowchart of an adaptive sinusoidal control method according to an embodiment of the present invention is shown.

[0106] Figure 2 A schematic diagram of the signal flow for adaptive sinusoidal control by a lower-level controller according to an embodiment of the present invention is shown.

[0107] Figure 3 This illustrates an embodiment of the present invention where the Z-axis is subjected to an acceleration at a frequency of 6 Hz and an acceleration amplitude of 10 m / s². 2 The sinusoidal control, the actual Z-axis acceleration curve.

[0108] Figure 4 A structural diagram of an adaptive sine wave control device according to an embodiment of the present invention is shown. Detailed Implementation

[0109] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and specific examples, but this is not intended to limit the present invention. If there is no necessary sequential relationship between the various steps described herein, the order in which they are described as examples should not be considered a limitation. Those skilled in the art should understand that the order can be adjusted, as long as it does not disrupt the logical consistency between them and render the entire process impossible.

[0110] Traditional sinusoidal control schemes for vibration tables suffer from drawbacks such as the need for prior identification before control, and the inability to perform multi-degree-of-freedom control coupling compensation. This invention provides an adaptive sinusoidal control method applicable to sinusoidal control of degree-of-freedom vibration tables. Taking a vibration test bench as an example, this method is primarily implemented through a host computer and a slave computer. Please refer to [link to relevant documentation]. Figure 1The diagram shows a flowchart of an adaptive sinusoidal control method, which includes the following steps:

[0111] Step 1: The user first sets the following parameters: the iteration frequency F of the vibration table control strategy. s For simplicity, this patent uses the Z-axis as an example for the axis used in the sine wave experiment; the amplitude A of the sinusoidal acceleration. ref The frequency F of the sinusoidal motion ref ; Target phase of sinusoidal motion Basic axis iteration coefficient k pri Cross-coupled axis iteration coefficient k cross Phase iteration coefficient k phase Simultaneously, the three key parameters of the adaptive control used in the lower-level controller are initialized: cycle count T. count Each control cycle T s Sine coefficient increment I sin The increment of the cosine coefficient I in each control cycle cos .

[0112] After the user sets the above parameters, they are transmitted to the host computer and simultaneously written to the lower controller.

[0113] Step 2: The lower-level controller obtains the real part γ of the original acceleration by performing a Discrete Fourier Transform (DFT). ω The imaginary part θ obtained from the original acceleration via discrete Fourier transform ω Z-direction reference sinusoidal gain coefficient k sin Z-direction reference cosine gain coefficient k cos The data is then transmitted to the host computer.

[0114] Step 3, the host computer will use the adaptive sine control algorithm to calculate C i I sin I cos The data is transmitted to the lower-level controller.

[0115] Step 4: The lower-level controller transmits the servo valve opening signal to the vibration table.

[0116] Step 5: Collect the expansion and contraction of the vibration table and the acceleration measured by the accelerometer on the vibration table and transmit them to the lower controller.

[0117] Figure 2 This diagram illustrates the signal flow of an adaptive sinusoidal control performed by a lower-level controller according to an embodiment of the present invention. Figure 2 As shown below, the specific details of the upper computer adaptive sinusoidal control method are given:

[0118] S1: Amplitude iteration coefficient ΔA calculate

[0119] Euler's formula for the complex frequency domain is:

[0120]

[0121] In the complex frequency domain, invH ω It can be expressed in complex form, where γ ω θ is the real part at a specific frequency. ω The imaginary part of the characteristic frequency. To express this complex number using an exponent, A ω Gain at a specific frequency, The phase angle is at a specific frequency, and j represents an imaginary number.

[0122] Therefore, the gain at a specific frequency is:

[0123] Amplitude iteration coefficients used:

[0124] S2: Phase iteration coefficient calculate

[0125]

[0126] in: This represents the phase iteration coefficient from the previous iteration. This represents the updated phase iteration coefficients. It is the target phase of sinusoidal motion. This indicates the actual phase of the current axis. This represents the phase difference coefficient.

[0127] S3: Adaptive sinusoidal control coefficient update cycle count C i calculate

[0128] Since the discrete Fourier transform module proposed in this invention only varies for a specific frequency, and the length of the window for performing the Fourier transform is specified as the period corresponding to the sine wave frequency, the C calculated by the host computer within the adaptive sine control coefficient update period... i I sin I cos The cycle length remains unchanged because discrete iterative calculations are performed in the lower-level controller, and the length of a cycle is determined by counting. The adaptive sinusoidal control coefficient updates the cycle count C. i The calculation formula is:

[0129]

[0130] S4: Calculation of reference sine and cosine gain coefficients

[0131]

[0132] Among them, I sin (k) represents the current sinusoidal coefficient increment per control cycle, I sin (k-1) represents the increment of the sinusoidal coefficient per control cycle in the previous iteration, I cos (k) represents the current increment of the cosine coefficient per control cycle, I cos (k-1) represents the increment of the cosine coefficient per control cycle in the previous iteration, K sin (k-1) is the reference sinusoidal gain coefficient from the previous iteration, K cos (k-1) is the reference cosine gain coefficient of the previous time.

[0133] The lower-level controller is a real-time controller, and the iteration frequency of the control strategy is F. s ,like Figure 2 As shown, the adaptive control module includes: a signal generator module, a zero-crossing detection module, a discrete Fourier transform module, an adaptive sinusoidal control displacement excitation calculation module, and a PID control module. Each module will be described separately below:

[0134] P1: Signal Generator Module

[0135] The signal generator module receives the sinusoidal frequency F from the host computer. ref The system outputs enable and stop signals, a reference sine wave signal, a reference cosine wave signal, and a square wave signal with a large value when crossing zero upwards in each cycle. The reference cosine wave signal is 90° ahead of the reference sine wave signal, has the same amplitude, and both have a frequency of F. ref .

[0136] P2: Zero-crossing detection module

[0137] The receiver receives the square wave signal output by the signal generator and detects the value of the square wave signal. If a larger value is detected, the output is 1; otherwise, the output is 0.

[0138] P3: Discrete Fourier Transform Module

[0139] This Discrete Fourier Transform (DFT) module differs from those in other books, papers, and patents. This patent's DFT module performs DFT only for specific frequencies. The DFT module utilizes the orthogonality of trigonometric functions, employing a method similar to Fourier series, using each complete cycle as a window for the DFT to avoid frequency leakage. It does not require integer frequencies or window sizes; the zero-crossing signal output by the signal generator is used as the criterion, but frequency equality is strictly required. The time-domain expression of a sine wave with unknown amplitude and initial phase is f(t) = Asin(2πft + φ0). Integrating this with reference signals of the same frequency, amplitude (1), and initial phase (0) – a sine wave sin(2πft) and a cosine wave cos(2πft) – over one cycle yields the real part and the imaginary part. The complex number formed by the real and imaginary parts gives the corresponding amplitude and phase angle.

[0140] The Fourier series is defined as follows:

[0141]

[0142] Where f(t) is the Fourier series, C is a constant, n is the number of sampling points, and a n Here, f is the cosine coefficient, f0 is the frequency value, t is the time, and b is the frequency. n The coefficient is the sine coefficient.

[0143] The following can be derived using the orthogonality of trigonometric functions:

[0144]

[0145] In the DFT module, since phase analysis is performed only on the single-frequency component signal f(t) = Asin(2πft + φ0), it is only necessary to obtain b1 (real part) and a1 (imaginary part) when n = 1. Because the lower-level controller is a discrete control system, taking the period T0 of the sine wave as an example, the number of sampling points per period is N. T :

[0146]

[0147] Therefore:

[0148]

[0149] Where A is the coefficient, b1 is the cosine coefficient, and a1 is the sine coefficient. N is the phase angle. i For discrete sampling points, N T This represents the total number of sampling points;

[0150] The above formula can be simplified using the orthogonality of sine and cosine functions as follows:

[0151]

[0152] Therefore, the real part γ of the original acceleration is calculated by the DFT module. ω and the imaginary part θ ω The calculation formula is:

[0153]

[0154] Where a z ω is the amplitude, N is the angular frequency, and N is the discrete sampling point.

[0155] P4: Adaptive Sinusoidal Control Displacement Excitation Calculation Module

[0156] This module receives C from the host computer. i I sin I cos In each adaptive sinusoidal control coefficient update period T ASC Inside, I sin and I cos The value remains unchanged, while C i The count decreases continuously until it reaches 0, thus referencing the sinusoidal gain coefficient k. sin and reference cosine gain coefficient k cos The update method is as follows:

[0157]

[0158]

[0159] Where K sin (k) represents the updated reference sinusoidal gain coefficient, K sin (k-1) is the reference sinusoidal gain coefficient from the previous iteration, K cos (k) represents the updated reference cosine gain coefficient, K cos (k-1) is the reference cosine gain coefficient of the previous time.

[0160] Adaptive sinusoidal control displacement excitation Cmd z The calculation formula is:

[0161] Cmd z (k)=K sin (k)S sin +K cos (k)S cos

[0162] Among them, S sin For the desired sinusoidal displacement, S cos The desired cosine displacement.

[0163] P4: PID control module

[0164] The PID module uses a traditional discrete PID module with pose excitation Cmd. z and response Pos z The control output u is calculated as follows:

[0165] e(k)=Cmd z (k)-Pos z (k)

[0166]

[0167] Where e(k) is the difference between the expected and actual displacement values, Cmd z (k) represents the expected displacement at time k, Pos z (k) represents the actual displacement value at time k, u(k) is the control input, and K p K is the proportionality coefficient. I K is the integral coefficient. D Here are the differential coefficients, and e(k-1) is the difference between the expected and actual displacement values ​​at time k-1.

[0168] To verify the effectiveness of the proposed adaptive sinusoidal control method, the Z-axis was subjected to a frequency of 6Hz and an acceleration amplitude of 10m / s². 2 The sinusoidal control, the actual Z-axis acceleration curve is as follows: Figure 3 As shown in the figure, the adaptive sinusoidal control method proposed in this invention has a very good effect.

[0169] It should be noted that the adaptive sinusoidal control method described in this paper is not only applicable to vibration tables, but also to other motion control products, devices, and systems. This embodiment is merely an example of the application scenario of the method of the present invention and is not intended to limit it.

[0170] This invention also provides an adaptive sine wave control device; please refer to [link to relevant documentation]. Figure 4 , Figure 4 A structural diagram of an adaptive sinusoidal control device according to an embodiment of the present invention is shown. The device includes:

[0171] The first calculation module 401 is configured to calculate the real part γ obtained from the original acceleration through the discrete Fourier transform. ω The imaginary part θ obtained from the original acceleration via discrete Fourier transform ω Reference sinusoidal gain coefficient k sin Reference cosine gain coefficient k cos The period count C is calculated. i Increment of sinusoidal coefficient I per control cycle sinIncrement I of cosine coefficient per control cycle cos ;

[0172] Update module 402 is configured to increment the sinusoidal coefficient by I per control cycle within each adaptive sinusoidal control coefficient update cycle. sin and the increment of cosine coefficient I per control cycle cos The value remains unchanged, and the period count C i As it decreases continuously, the reference sinusoidal gain coefficient k sin and reference cosine gain coefficient k cos Update;

[0173] The second calculation module 403 is configured to calculate based on the reference sinusoidal gain coefficient k. sin and reference cosine gain coefficient k cos The adaptive sinusoidal control displacement excitation Cmd is calculated. z ;

[0174] The control output calculation module 404 is configured to calculate the output based on the pose excitation Cmd. z and response Pos z The control output is calculated.

[0175] In some embodiments, the first computing module is further configured to:

[0176] The real part γ of the original acceleration obtained by the discrete Fourier transform is calculated using the following method. ω The imaginary part θ obtained from the original acceleration via discrete Fourier transform ω :

[0177] The Fourier series is defined as follows:

[0178]

[0179] Where f(t) is the Fourier series, C is a constant, n is the number of sampling points, and a n Here, f is the cosine coefficient, f0 is the frequency value, t is the time, and b is the frequency. n The coefficient is the sine coefficient.

[0180] The following can be derived using the orthogonality of trigonometric functions:

[0181]

[0182] Where T0 is the period of the sine wave;

[0183] Within the period of the sine wave, the number of sampling points in each period is N. T Then we have:

[0184]

[0185] Where Fs The iteration frequency;

[0186] Therefore:

[0187]

[0188] Where A is the coefficient, b1 is the cosine coefficient, and a1 is the sine coefficient. N is the phase angle. i For discrete sampling points, N T This represents the total number of sampling points;

[0189] The previous formula can be simplified using the orthogonality of sine and cosine functions as follows:

[0190]

[0191] Real part γ ω and the imaginary part θ ω The calculation formula is as follows:

[0192]

[0193] Where a z ω is the amplitude, N is the angular frequency, and N is the discrete sampling point.

[0194] In some embodiments, the first computing module is further configured to:

[0195] Euler's formula for the complex frequency domain is:

[0196]

[0197] Where γ ω θ is the real part at a specific frequency. ω The imaginary part of the characteristic frequency. To express this complex number using an exponent, A ω Gain at a specific frequency, The phase angle is at a specific frequency, and j represents an imaginary number;

[0198] The gain at a specific frequency is determined as follows:

[0199]

[0200] Determine the amplitude iteration coefficients based on the gain at a specific frequency:

[0201]

[0202] Among them, A ref K represents the amplitude of the sinusoidal acceleration. pri The basic axis iteration coefficient;

[0203] The phase iteration coefficient is calculated using the following formula.

[0204]

[0205] in This represents the phase iteration coefficient from the previous iteration. This represents the updated phase iteration coefficients. Indicates the target phase of sinusoidal motion. Indicates the actual phase of the current axis. Indicates the phase difference coefficient;

[0206] The cycle count C is calculated using the following formula. i :

[0207]

[0208] Where F s F is the iteration frequency. ref The frequency of the sinusoidal motion;

[0209] The increment of the sine coefficient I per control cycle is calculated using the following formula. sin Increment I of cosine coefficient per control cycle cos :

[0210]

[0211] Among them, I sin (k) represents the current sinusoidal coefficient increment per control cycle, I sin (k-1) represents the increment of the sinusoidal coefficient per control cycle in the previous iteration, I cos (k) represents the current increment of the cosine coefficient per control cycle, I cos (k-1) represents the increment of the cosine coefficient for each control cycle in the previous iteration.

[0212] In some embodiments, the update module is further configured to increment the sinusoidal coefficient by I per control cycle within each adaptive sinusoidal control coefficient update cycle. sin and the increment of cosine coefficient I per control cycle cos The value remains unchanged, and the period count C i The value is continuously reduced, and the reference sinusoidal gain coefficient k is adjusted using the following formula. sin and reference cosine gain coefficient k cos Update;

[0213]

[0214] Where K sin (k) represents the updated reference sinusoidal gain coefficient, K sin (k-1) is the reference sinusoidal gain coefficient from the previous iteration, Kcos (k) represents the updated reference cosine gain coefficient, K cos (k-1) is the reference cosine gain coefficient of the previous time.

[0215] In some embodiments, the second calculation module is further configured to calculate based on a reference sinusoidal gain coefficient k. sin and reference cosine gain coefficient k cos The adaptive sinusoidal control displacement excitation Cmd is calculated using the following formula. z :

[0216] Cmd z (k)=K sin (k)S sin +K cos (k)S cos

[0217] Among them, S sin For the desired sinusoidal displacement, S cos The desired cosine displacement.

[0218] In some embodiments, the control output calculation module is further configured to calculate based on the pose excitation Cmd z and response Pos z The control output is calculated using the following formula:

[0219] e(k)=Cmd z (k)-Pos z (k)

[0220]

[0221] Where e(k) is the difference between the expected and actual displacement values, Cmd z (k) represents the expected displacement at time k, Pos z (k) represents the actual displacement value at time k, u(k) is the control input, and K p K is the proportionality coefficient. I K is the integral coefficient. D Here are the differential coefficients, and e(k-1) is the difference between the expected and actual displacement values ​​at time k-1.

[0222] This invention also provides a non-transitory computer-readable medium storing instructions that, when executed by a processor, perform the method described according to any embodiment of the invention.

[0223] Furthermore, although exemplary embodiments have been described herein, their scope includes any and all embodiments based on the invention that have equivalent elements, modifications, omissions, combinations (e.g., schemes involving intersections of various embodiments), adaptations, or alterations. Elements in the claims will be interpreted broadly based on the language used in the claims and are not limited to the examples described in this specification or during the implementation of this application, and such examples will be interpreted as non-exclusive. Therefore, this specification and examples are intended to be considered illustrative only, and the true scope and spirit are indicated by the following claims and the full scope of their equivalents.

[0224] The above description is intended to be illustrative and not restrictive. For example, the above examples (or one or more of them) can be used in combination with each other. Other embodiments can be used by those skilled in the art when reading the above description. Furthermore, in the above detailed description, various features may be grouped together to simplify the invention. This should not be construed as an intention that a feature of an unclaimed invention is necessary for any claim. Rather, the subject matter of the invention may be less than all the features of a particular embodiment of the invention. Thus, the following claims are incorporated herein by reference as examples or embodiments, wherein each claim is an independent, separate embodiment, and these embodiments are contemplated to be combined with each other in various combinations or arrangements. The scope of the invention should be determined by reference to the appended claims and the full scope of their equivalents.

Claims

1. A method of adaptive sinusoidal control, characterized by, The method comprises: a real part γ of a discrete Fourier transform of the original acceleration ω , a real part γ of a discrete Fourier transform of the original acceleration ω , a reference sine gain coefficient k sin , a reference cosine gain coefficient k cos , a calculated sine coefficient increment I sin , a calculated cosine coefficient increment I cos , a calculated period count C i ; The value of the sine coefficient increment I sin and the cosine coefficient increment I cos is constant during each adaptive sine control coefficient update cycle, and the cycle count C i is continuously decreasing, the reference sine gain coefficient k sin and the reference cosine gain coefficient k cos are updated. According to the reference sine gain coefficient k sin and the reference cosine gain coefficient k cos The adaptive sine control displacement excitation Cmd z is calculated According to the pose excitation Cmd z and the response Pos z a control output is calculated.

2. The method of claim 1, wherein, The real part γ of the discrete Fourier transform of the raw acceleration is calculated by the following method ω The imaginary part θ of the discrete Fourier transform of the raw acceleration is calculated by the following method ω : The definition of Fourier series is: where f(t) is a Fourier series, C is a constant, n is a sampling point, a n is a cosine coefficient, f0is a frequency value, t is time, b n is a sine coefficient; The derivation is obtained by using the orthogonality of trigonometric functions: Where T0 is the period of the sine wave; The number of points collected in each cycle of the sine wave is N T Then, we have: where F s is the iteration frequency; Thus, there are: where A is a coefficient, b1 is a cosine coefficient, and a1 is a sine coefficient, is a phase angle, N i is a discrete sampling point, N T is a total number of sampling points; The last formula is simplified by using the orthogonality of sine and cosine functions: Real part γ ω and imaginary part θ ω The calculation formula is as follows: where a z is the amplitude, ω is the angular frequency, and N is the discrete sampling point.

3. The method of claim 1, wherein, the real part γ of the discrete Fourier transform of the original acceleration ω the imaginary part θ of the discrete Fourier transform of the original acceleration ω a reference sine gain coefficient k sin a reference cosine gain coefficient k cos a calculated sine coefficient increment I for each control period sin a calculated cosine coefficient increment I for each control period cos comprising: The Euler formula for complex frequency domain is: where γ ω is the real part of the specific frequency, θ ω is the imaginary part of the specific frequency, is the exponential representation of this complex number, A ω is the gain of the specific frequency, is the phase angle of the specific frequency, j represents the imaginary number; The gain of a specific frequency is determined as: The amplitude iteration coefficient is determined according to the gain of the specific frequency: wherein A ref is the amplitude of the sinusoidal acceleration, K pri is a preset base axis iteration coefficient; The phase iteration coefficient is calculated by the following equation wherein denotes the last phase iteration coefficient, denotes the updated current phase iteration coefficient, denotes the target phase of the sinusoidal motion, denotes the current shaft actual phase, denotes the phase difference value coefficient; The sine coefficient increment I for each control period is calculated by the following equation sin , the cosine coefficient increment I for each control period is calculated by the following equation cos : where I sin (k) is the current per control cycle sine coefficient increment, I sin (k-1) is the previous per control cycle sine coefficient increment, I cos (k) is the current per control cycle cosine coefficient increment, I cos (k-1) is the previous per control cycle cosine coefficient increment, K sin (k-1) is the previous reference sine gain coefficient, K cos (k-1) is the previous reference cosine gain coefficient; The cycle count C is calculated by the following equation i : where F s is the iteration frequency, F ref is the frequency of the sinusoidal motion.

4. The method of claim 1, wherein, The value of the sine coefficient increment I sin and the cosine coefficient increment I cos is constant for each adaptive sine control coefficient update cycle, the cycle count C i is constantly decreasing, and the reference sine gain coefficient k sin and the reference cosine gain coefficient k cos are updated by the following equations: where K sin (k) is the updated reference sine gain coefficient, K sin (k-1) is the previous reference sine gain coefficient, K cos (k) is the updated reference cosine gain coefficient, K cos (k-1) is the previous reference cosine gain coefficient.

5. The method of claim 4, wherein, According to the reference sine gain coefficient k sin and the reference cosine gain coefficient k cos , the adaptive sine control displacement excitation Cmd z is calculated by the following formula: Cmd z (k) = K sin (k) S sin + K cos (k) S cos where S sin is the desired sinusoidal displacement, S cos is the desired cosine displacement.

6. The method of claim 5, wherein, According to the pose excitation Cmd z and the response Pos z , the control output is calculated by the following formula: e(k) = Cmd z (k) - Pos z (k) where e(k) is the displacement desired value and actual value difference, Cmd z (k) is the displacement desired value at k time, Pos z (k) is the displacement actual value at k time, u(k) is the control input, K p is the proportional coefficient, K I is the integral coefficient, K D is the differential coefficient, e(k-1) is the displacement desired value and actual value difference at k-1 time.

7. An adaptive sinusoidal control device, characterized by, The device comprises: a first calculation module configured to calculate a real part γ of a discrete Fourier transform of the original acceleration ω a virtual part θ of the discrete Fourier transform of the original acceleration ω a reference sine gain coefficient k sin a reference cosine gain coefficient k cos a sine coefficient increment I calculated for each control period sin a cosine coefficient increment I calculated for each control period cos a period count C calculated according to an iteration frequency and a frequency of the sinusoidal motion i ; an update module configured to update the reference sine gain coefficient k sin and the reference cosine gain coefficient k cos with a constant value of the sine coefficient increment I i and the cosine coefficient increment I sin for each control period, with a constant value of the period count C i decreasing for each control period, and update the reference sine gain coefficient k sin and the reference cosine gain coefficient k cos a second calculation module configured to calculate an adaptive sinusoidal control displacement excitation Cmd according to a reference sinusoidal gain coefficient k sin and a reference cosine gain coefficient k cos z ;​ The control output calculation module is configured to calculate a control output according to the pose excitation Cmd z and the response Pos z .

8. The apparatus of claim 7, wherein, The first calculation module is further configured to: The real part γ of the discrete Fourier transform of the raw acceleration is calculated by the following method ω The imaginary part θ of the discrete Fourier transform of the raw acceleration is calculated by the following method ω : The definition of Fourier series is: where f(t) is a Fourier series, C is a constant, n is a sampling point, a n is a cosine coefficient, f0is a frequency value, t is time, b n is a sine coefficient; The derivation is obtained by using the orthogonality of trigonometric functions: Where T0 is the period of the sine wave; The number of points collected in each cycle of the sine wave is N T Then, there is: where F s is the iteration frequency; Thus, there are: where A is a coefficient, b1 is a cosine coefficient, and a1 is a sine coefficient, is a phase angle, N i is a discrete sampling point, N T is a total number of sampling points; The last formula is simplified by using the orthogonality of sine and cosine functions: Real part γ ω and imaginary part θ ω The calculation formula is as follows: where a z is the amplitude, ω is the angular frequency, and N is the discrete sampling point.

9. The apparatus of claim 8, wherein, The first calculation module is further configured to: The Euler formula for complex frequency domain is: where γ ω is the real part of the specific frequency, θ ω is the imaginary part of the specific frequency, is the exponential representation of this complex number, A ω is the gain of the specific frequency, is the phase angle of the specific frequency, j represents the imaginary number; The gain of a specific frequency is determined as: The amplitude iteration coefficient is determined according to the gain of the specific frequency: wherein A ref is the amplitude of the sinusoidal acceleration, K pri is a preset base axis iteration coefficient; The phase iteration coefficient is calculated by the following equation wherein denotes the last phase iteration coefficient, denotes the updated current phase iteration coefficient, denotes the target phase of the sinusoidal motion, denotes the current axis actual phase, denotes the phase difference value coefficient; The sine coefficient increment I for each control period is calculated by the following equation sin , the cosine coefficient increment I for each control period is calculated by the following equation cos : where I sin (k) is the current per control cycle sine coefficient increment, I sin (k-1) is the previous per control cycle sine coefficient increment, I cos (k) is the current per control cycle cosine coefficient increment, I cos (k-1) is the previous per control cycle cosine coefficient increment; The cycle count C is calculated by the following equation i : where F s is the iteration frequency, F ref is the frequency of the sinusoidal motion. 10.A non-transitory computer-readable storage medium storing instructions that, when executed by a processor, perform the method according to any one of claims 1 to 6.

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