High-gain stable time delay control method for realizing ultra-wideband active vibration isolation

Abstract

The invention discloses a high-gain stable time delay control method for realizing ultra-wideband active vibration isolation, which comprises the following steps of: constructing a dynamic model of an active vibration isolation system, and designing a proportional gain parameter, a time delay gain parameter and a time delay length parameter of a proportional-delay feedback controller; designing the order and cut-off frequency of a finite impulse response low-pass filter; replacing a pure time delay link in the proportional-delay feedback controller with a finite impulse response low-pass filter to obtain a high-gain stable time delay controller; an output signal of the high-gain stable time delay controller is input into an actuator of the active vibration isolation system to generate active control force, and the active control force is applied to an effective load or a vibration-isolated object of the active vibration isolation system, so that ultra-wideband vibration suppression is realized. According to the invention, in the field of vibration control, the low-frequency resonance of the active vibration isolation system can be significantly reduced and the high-frequency roll-off rate can be increased, so that the vibration isolation bandwidth is greatly improved.

Description

Technical Field

[0001] This invention relates to the field of vibration control technology, specifically a high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation, which can realize time-delay control for low-frequency, ultra-wideband vibration suppression. Background Technology

[0002] With the rapid development of precision manufacturing, measurement, and other fields, the requirements for vibration control performance are becoming increasingly stringent. Traditional passive vibration isolation systems, widely used due to their stability, reliability, and low cost, are no longer sufficient to meet the stringent demands of current ultra-low frequency and ultra-wideband vibration isolation. Therefore, researchers have gradually introduced active control strategies to construct active vibration isolation systems, further improving vibration isolation performance. Active vibration isolation systems achieve vibration suppression by applying controllable forces through actuators, offering advantages such as flexible design and strong adaptability. In recent years, various control algorithms have been applied in active vibration isolation systems, including PID control, robust control, adaptive control, sliding mode control, and intelligent control algorithms. However, regardless of the control strategy employed, time delay is an unavoidable phenomenon in control systems. From a control theory perspective, time delay typically causes system phase lag, thus affecting control performance and even threatening closed-loop stability. Nevertheless, recent research indicates that time delay is not always a negative factor; it can be actively designed and utilized in active vibration isolation systems, transforming into an effective control resource. Time delay feedback control structures are relatively simple and show good potential in suppressing nonlinear resonance, thus attracting widespread attention. This method effectively suppresses vibrations at specific frequencies by introducing a specific time delay to alter the system's equivalent dynamic characteristics. Existing active vibration isolation strategies based on time delay control are mostly limited to single-frequency or narrowband vibration suppression, while vibration environments in actual engineering often exhibit broadband random characteristics. Therefore, developing time delay control methods capable of covering a wide frequency band has significant theoretical and engineering value. Currently, extending time delay control to ultra-wideband vibration isolation still faces two key challenges: First, there is the issue of high-gain instability. To effectively suppress low-frequency resonance, a higher control gain is required. However, inherent time delays in actual control systems (such as delays introduced by sampling, calculation, and signal transmission) render the system a neutral time-delay system. Under high-gain conditions, the stability of such systems is severely limited, and traditional proportional-delay controllers struggle to simultaneously achieve high gain and stable operation, thus restricting their potential for low-frequency control.

[0003] Second, there is the problem of high-frequency local resonance. Time-delay feedback introduces a series of periodic high-frequency local resonance peaks in the high-frequency segment of the vibration transmissibility curve. These high-frequency local resonance peaks not only reduce the high-frequency vibration isolation effect, but may also excite high-frequency modes of the system, or even lead to system instability.

[0004] Therefore, there is an urgent need for a new method for ultra-wideband active vibration isolation control that can overcome high-gain instability and high-frequency local resonance peaks. Summary of the Invention

[0005] To address the shortcomings of the existing technologies, this invention provides a high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation. This method overcomes the technical problems of insufficient bandwidth, high-gain instability, and high-frequency local resonance peaks in traditional time-delay control. It can be used in different types of active vibration isolation systems and can effectively suppress ultra-wideband random vibrations. At the same time, the controller has a simple structure and is easy to implement.

[0006] To achieve the above objectives, the present invention provides a high-gain stable time-delay control method for realizing ultra-wideband active vibration isolation, comprising the following steps: Step 1: Obtain the effective load of the active vibration isolation system or the acceleration signal of the object being isolated as a feedback signal, and construct a dynamic model of the active vibration isolation system based on the feedback signal; Step 2: Based on the vibration suppression requirements of the low-frequency resonance region and the aforementioned dynamic model, design the proportional gain parameter, time delay gain parameter, and time delay parameter of the proportional-delay feedback controller; Step 3: Construct a finite impulse response low-pass filter, design the order of the finite impulse response low-pass filter based on the time delay parameter, and design the cutoff frequency of the finite impulse response low-pass filter based on the frequency partitioning strategy. Step 4: Replace the pure time delay element in the proportional-delay feedback controller with the finite impulse response low-pass filter to obtain a high-gain stable time delay controller; Step 5: Input the output signal of the high-gain stable time delay controller to the actuator of the active vibration isolation system to generate an active control force, which is applied to the effective load of the active vibration isolation system or the object being isolated, thereby achieving ultra-wideband vibration suppression.

[0007] Compared with the prior art, the present invention has the following beneficial technical effects: 1. Compared with the drawbacks of traditional time delay control, which is only effective for single-frequency and narrowband vibrations and has a low bandwidth, this invention can achieve comprehensive suppression of low-frequency and high-frequency vibrations, thus having a powerful ultra-wideband vibration isolation capability; 2. Compared with traditional time delay control, the present invention has a higher gain, thus making more effective use of the low-frequency vibration suppression effect of time delay control. In addition, the present invention effectively solves the high-frequency local resonance caused by time delay control, avoiding the impact of high-frequency local resonance on the high-frequency vibration isolation effect of the active vibration isolation system. 3. This invention requires only one accelerometer commonly used in vibration control for vibration signal detection, thus it is applicable to various types of vibration systems, has generality and versatility, and is easy to implement. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0009] Figure 1 This is a flowchart of a high-gain stable time-delay control method for implementing ultra-wideband active vibration isolation in an embodiment of the present invention; Figure 2 This is a schematic diagram of the active vibration isolation system in an embodiment of the present invention; Figure 3 C is used in the embodiments of the present invention. PR Different parameters of the controller g p A schematic diagram of the vibration transmissibility curve of the corresponding active vibration isolation system; Figure 4 C is used in the embodiments of the present invention. PR Different parameters of the controller g t A schematic diagram of the vibration transmissibility curve of the corresponding active vibration isolation system; Figure 5 The C obtained using the pole placement method in this embodiment of the invention PR A schematic diagram of the vibration transmissibility curve of the active vibration isolation system corresponding to the controller; Figure 6 This is a finite impulse response low-pass filter designed according to a frequency domain partitioning strategy in an embodiment of the present invention. tap coefficient h ( n ) Schematic diagram; Figure 7 C is used in the embodiments of the present invention. HGS Controller and C PR Bode diagram of the open-loop system of the controller's active vibration isolation system Figure 8 Based on the embodiments of the present invention Design C HGS A schematic diagram of the vibration transmissibility curve of the active vibration isolation system corresponding to the controller.

[0010] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0011] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0012] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0013] like Figure 1 The figure shown is a high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation disclosed in this embodiment, which includes the following steps: Step 1: Obtain the effective load of the active vibration isolation system or the acceleration signal of the object being isolated as a feedback signal, and construct a dynamic model of the active vibration isolation system based on the feedback signal; Step 2: Based on the vibration suppression requirements and dynamic model of the low-frequency resonance region, design the proportional gain parameter, time delay gain parameter, and time delay parameter of the proportional-delay feedback controller. Step 3: Construct a finite impulse response low-pass filter, design the order of the finite impulse response low-pass filter based on the time delay parameter, and design the cutoff frequency of the finite impulse response low-pass filter based on the frequency partitioning strategy. Step 4: Replace the pure time delay element in the proportional-delay feedback controller with a finite impulse response low-pass filter to obtain a high-gain stable time delay controller; Step 5: Input the output signal of the high-gain stable time delay controller to the actuator of the active vibration isolation system to generate an active control force, which is applied to the effective load of the active vibration isolation system or the object being isolated, thereby achieving ultra-wideband vibration suppression.

[0014] The control method in this embodiment uses a finite impulse response (FIR) low-pass filter to achieve an equivalent time delay effect, thus replacing the traditional pure time delay stage. The FIR filter has linear phase characteristics and can provide a frequency-independent constant group delay. This retains the advantage of time delay feedback in suppressing resonance peaks in the low-frequency band, while its low-pass characteristic causes time delay control to degrade in the high-frequency band, where proportional control dominates, effectively avoiding the excitation of high-frequency local resonance. Simultaneously, the control gain of the method in this embodiment can overcome the stability limitations of traditional pure time delay control, achieving controller stability at high gain. Furthermore, the control method in this embodiment can be conveniently designed using a frequency partitioning strategy, requiring only a single accelerometer. The system structure is simple and easy to implement in engineering, significantly reducing low-frequency resonance and increasing the high-frequency roll-off rate, thereby greatly improving the vibration isolation bandwidth. It is particularly suitable for low-frequency ultra-wideband vibration isolation in fields such as ultra-precision manufacturing and measurement.

[0015] refer to Figure 2 This is a schematic diagram of a single-degree-of-freedom active vibration isolation system. The active vibration isolation system includes a mass of... m The effective load and stiffness coefficient are k p A linear normal stiffness spring with a stiffness coefficient of k n This system comprises a nonlinear negative stiffness spring, actuator, accelerometer, drive, and control system. The nonlinear negative stiffness spring reduces the dynamic stiffness of the vibration isolation system, thereby lowering the system's natural frequency. The actuator is an electromagnetic actuator; the input current provides the control force required for active vibration isolation, and the actuator output constant is... K a The damping of the active vibration isolation system is generated by linear positive stiffness springs and nonlinear negative stiffness springs, with an equivalent damping coefficient of... c The drive and control system includes a general embedded control system and an industrial control computer, used to implement the high-gain stable delay controller in steps 4 and 5. The drive and control system has a relatively short but unavoidable inherent delay, the duration of which is... τ s The feedback signal of the active vibration isolation system is obtained by measuring the accelerometer mounted on the payload. To perform dynamic modeling of the active vibration isolation system, the stiffness coefficient of the nonlinear negative stiffness spring is first determined. k n Fit using a cubic polynomial: ,in, k n0 Let z be the linear stiffness coefficient component of the nonlinear negative stiffness spring, and z be the displacement of the effective load. k n3These are the coefficients of the cubic term in the polynomial used to fit the stiffness of the nonlinear negative stiffness spring. In practical applications, if higher accuracy is required, a higher-order polynomial can be used for fitting the nonlinear negative stiffness.

[0016] The parameters of the active vibration isolation system in this embodiment are as follows: m = 2 kg, c = 10 N s / m, k p = 39 kN / m, k n0 = -35.66 kN / m, k n3 = 1.5×10 8 N / m, τ s = 0.5 ms. For Figure 2 The dynamic model of the single-degree-of-freedom vibration system shown is as follows:

[0017] in, H ( t ) is a dynamic model, As a feedback signal, k = k n0 + k p The equivalent stiffness of the vibration isolation system, , These represent the relative velocity and displacement between the effective load and the base, respectively. f a ( t () represents the active control force output by the actuator. d This represents the unmodeled error.

[0018] In this embodiment, the specific implementation process for designing the proportional gain parameter, delay gain parameter, and delay parameter of the proportional-delay feedback controller is as follows: First, the basic form of the proportional-delay feedback controller is determined as follows:

[0019] in, C PR It is a proportional-delay feedback controller. g p , g t , τ These are the proportional gain parameter, the time delay gain parameter, and the time delay parameter, respectively. Then, based on the proportional-delay feedback controller CPR The active control force of the actuator is calculated, thus obtaining the dynamic model of the closed-loop system based on the proportional-delay controller. H PR ( t ),Right now:

[0020] Then, a low-order Pade (e.g., a first-order Pade) is used to approximate the dynamic model of the closed-loop system. H PR ( t After the time delay element in the model, the closed-loop system dynamics model will be... H PR ( t The Laplace transform is used to obtain the transfer function of the low-order closed-loop system. H PR ( s ); Finally, based on the requirement for suppressing low-frequency resonance peaks, the transfer function of the low-order closed-loop system is calculated using pole placement or other intelligent optimization algorithms. H PR ( s Thus, the proportional gain parameter is obtained. g p Delay gain parameters g t With time extension parameter τ .

[0021] In this embodiment, the dominant pole is configured as follows: The proportional gain parameter can be calculated. Delay gain parameter and duration parameter .

[0022] like Figure 3 The figures show the vibration transmissibility of the active vibration isolation system using pure proportional control, where each vibration transmissibility curve represents a different proportional gain parameter. g p It can be observed that, with | g p The increase of | reduces the high-frequency vibration transmissibility of the active vibration isolation system, which means an improvement in vibration isolation performance; however, the low-frequency resonance peaks gradually increase, which will lead to a stronger resonance phenomenon. Figure 4 This refers to the time extension parameter used in the active vibration isolation system. τ = 0.03s vibration transmissibility under pure time delay control, where each vibration transmissibility curve represents a different time delay gain parameter. g t It can be observed that, with | g tWith the increase of |, multiple high-frequency local resonance peaks appeared in the high-frequency band of the active vibration isolation system; however, the low-frequency resonance peaks gradually decreased, indicating that low-frequency vibrations were effectively suppressed; therefore, according to Figure 3 and Figure 4 Simulation results show that proportional control and time-delay control have complementary vibration control effects in both high and low frequency bands. For example... Figure 5 As shown, compared to passive vibration isolation systems, a proportional-delay controller is used. C PR The vibration transmissibility resonance peak of the corresponding active vibration isolation system was effectively suppressed, but the problem of high-frequency local resonance could not be avoided.

[0023] In this embodiment, the finite impulse response low-pass filter is specifically:

[0024] in, It is a finite impulse response low-pass filter. z -n Indicates based on n First delay, N Let the order of the finite impulse response low-pass filter be . h ( n ) is the first finite impulse response low-pass filter n There are 1 tap coefficient, which represents the filter parameters to be designed.

[0025] In practical implementation, the order of the finite impulse response low-pass filter can be designed using the time delay parameter, i.e.:

[0026] Therefore, a finite impulse response low-pass filter can be obtained. order N =181.

[0027] For the cutoff frequency of a finite impulse response low-pass filter f c Since time-delay feedback causes the vibration transmissibility of the active vibration isolation system to periodically exhibit high-frequency local resonance peaks, the basic principle of the frequency partitioning strategy in this embodiment is to select the cutoff frequency. f c The goal is to ensure that low-frequency delay feedback control remains unaffected while effectively attenuating the delay feedback effect in the high-frequency band. Therefore, the cutoff frequency in this embodiment... f c Select at the first high-frequency local resonant frequency f hr1 Transfer function of low-order closed-loop system H PR ( s The low-frequency principal resonant frequency Between, the low-frequency principal resonant frequency can be H PR ( s The poles are obtained. The first high-frequency local resonance peak is obtained. f hr1 Based on the dynamic model of the closed-loop system H PR ( t The frequency and duration parameters of the high-frequency local resonance peak are obtained through calculation. τ They are directly related, and the following relationship exists between them:

[0028] in, For the first j The frequency corresponding to each high-frequency local resonance peak. According to And take the first high-frequency local resonance peak, that is j = 1, then we get f hr1 = 11.1 Hz. Correspondingly, the cutoff frequency... f c It can be calculated using the following formula:

[0029] in, For adjusting the cutoff frequency f c The adjustment coefficient can be selected by weighing the specific vibration suppression requirements.

[0030] In the application process, cutoff frequency f c Dominant poles in Cocoa configuration The imaginary part is obtained, that is To ensure the combined effect of proportional and delay feedback is fully utilized in the low-frequency region, thereby reducing the natural frequency and resonance peak, a finite impulse response low-pass filter is used in the high-frequency region. The low-pass property weakens the effect of delay control, causing the control law to degenerate into proportional feedback. This embodiment selects... α = 0.5, thus obtaining f c = 7.2Hz.

[0031] In practical implementation, the tap coefficients of the finite impulse response low-pass filter are calculated using the window function method. The window type in the window function method can be a rectangular window, Hamming window, Hanning window, or Blackman window, etc. In this embodiment, a rectangular window is used for filter design, resulting in:

[0032] like Figure 6 As shown, this is a finite impulse response low-pass filter designed based on a rectangular window. The tap coefficient. Based on the calculated parameters: , , N = 181 and f c = 7.2 Hz, the high-gain stable delay controller can be obtained as follows:

[0033] in, G HGS It is a high-gain stable delay controller. This is a completed finite impulse response low-pass filter. C PR The pure time delay element in the middle is Ultimately, the active control force of the actuator in the active vibration isolation system is: .

[0034] In the specific implementation process, after the output signal of the high-gain stable time delay controller is input to the actuator of the active vibration isolation system to generate active control force, the stability of the active vibration isolation system is checked and analyzed. For example, the stability can be judged by methods such as Nyquist theorem, closed-loop pole distribution, and Lyapunov.

[0035] Furthermore, the phase margin and gain margin of the active vibration isolation system were analyzed based on the open-loop transfer function, thereby conducting a stability analysis. Figure 7 As shown, it is made using a proportional-delay controller. C PR The phase margin of the active vibration isolation system is -79.5°, which means that using a configuration with the dominant pole as Calculations yielded , and The use of a proportional-delay controller cannot be guaranteed. C PR The stability of the closed-loop active vibration isolation system. However, the high-gain stable time delay controller provided in this embodiment is used. C HGS The phase margin of the active vibration isolation system is 141.9°, which is sufficient to ensure the stability of the closed-loop system. Therefore, the high-gain stable time-delay control method for the ultra-wideband active vibration isolation system provided in this embodiment greatly improves the stability of the system.

[0036] The designed high-gain stable time delay controller C HGS For Figure 2The active vibration isolation system shown ultimately achieves ultra-wideband vibration isolation. For example... Figure 8 As shown, a high-gain stable delay controller is used. C HGS Active vibration isolation systems have proportional-delay controllers in the low-frequency range. C PR Nearly the same vibration isolation effect, low-frequency resonance peaks were effectively suppressed; in addition, a high-gain stable time-delay controller C HGS The proportional-delay controller was solved very well. C PR The problem of high-frequency local resonance.

[0037] The above description is only a preferred embodiment of the present invention and does not limit the scope of protection of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the scope of protection of the present invention.

Claims

1. A high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation, characterized in that, Includes the following steps: Step 1: Obtain the effective load of the active vibration isolation system or the acceleration signal of the object being isolated as a feedback signal, and construct a dynamic model of the active vibration isolation system based on the feedback signal; Step 2: Based on the vibration suppression requirements of the low-frequency resonance region and the aforementioned dynamic model, design the proportional gain parameter, time delay gain parameter, and time delay parameter of the proportional-delay feedback controller; Step 3: Construct a finite impulse response low-pass filter, design the order of the finite impulse response low-pass filter based on the time delay parameter, and design the cutoff frequency of the finite impulse response low-pass filter based on the frequency partitioning strategy. Step 4: Replace the pure time delay element in the proportional-delay feedback controller with the finite impulse response low-pass filter to obtain a high-gain stable time delay controller; Step 5: Input the output signal of the high-gain stable time delay controller to the actuator of the active vibration isolation system to generate an active control force, which is applied to the effective load of the active vibration isolation system or the object being isolated, thereby achieving ultra-wideband vibration suppression.

2. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to claim 1, characterized in that, In step 1, the dynamic model is specifically as follows: in, H ( t ) is a dynamic model, m For the mass of the payload, As a feedback signal, c For damping of the vibration isolation system, k The equivalent stiffness of the vibration isolation system, , These represent the relative velocity and displacement between the effective load and the base, respectively. f a ( t () represents the active control force output by the actuator. d This represents the unmodeled error.

3. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to claim 2, characterized in that, In step 2, the proportional gain parameter, delay gain parameter, and delay parameter of the designed proportional-delay feedback controller specifically include: The basic form of a proportional-delay feedback controller is: in, C PR It is a proportional-delay feedback controller. g p , g t , τ These are the proportional gain parameter, the time delay gain parameter, and the time delay parameter, respectively. τ s This is the inherent delay of the system; Based on proportional-delay feedback controller C PR The active control force of the actuator is calculated, thus obtaining the dynamic model of the closed-loop system based on the proportional-delay controller. H PR ( t ): in, K a The actuator output constant; The closed-loop system dynamic model is replaced by a low-order Pade approximation. H PR ( t After the time delay step in the closed-loop system dynamic model, H PR ( t The Laplace transform is used to obtain the transfer function of the low-order closed-loop system. H PR ( s ); Based on the requirement for suppressing low-frequency resonance peaks, the transfer function of the low-order closed-loop system is calculated using pole placement or other intelligent optimization algorithms. H PR ( s Thus, the proportional gain parameter is obtained. g p Delay gain parameters g t With time extension parameter τ .

4. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to claim 3, characterized in that, In step 3, the finite impulse response low-pass filter is specifically: in, It is a finite impulse response low-pass filter. h ( n ) is the first finite impulse response low-pass filter n Tap coefficient z -n Indicates based on n First delay, N Let be the order of the finite impulse response low-pass filter.

5. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to claim 4, characterized in that, In step 3, the order of the finite impulse response low-pass filter designed based on the time delay parameter is specifically as follows: .

6. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to claim 4, characterized in that, In step 3, the cutoff frequency of the finite impulse response low-pass filter designed based on the frequency partitioning strategy is specifically as follows: in, f c The cutoff frequency of the finite impulse response low-pass filter. The transfer function of the low-order closed-loop system H PR ( s The low-frequency principal resonant frequency of ) For adjusting the cutoff frequency f c Adjustment coefficient.

7. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to claim 4, characterized in that, The tap coefficients of the finite impulse response low-pass filter are calculated using the window function method, wherein the window type in the window function method is a rectangular window, a Hamming window, a Hanning window, or a Blackman window.

8. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to any one of claims 4 to 7, characterized in that, In step 4, the high-gain stable delay controller specifically refers to: in, G HGS It is a high-gain stable delay controller. It is a finite impulse response low-pass filter.

9. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to claim 8, characterized in that, In step 5, inputting the output signal of the high-gain stable delay controller to the active control force generated by the actuator specifically involves: .

10. The high-gain stable time-delay control method for achieving ultra-wideband active vibration isolation according to any one of claims 1 to 7, characterized in that, In step 5, after the output signal of the high-gain stable time delay controller is input to the actuator of the active vibration isolation system to generate active control force, the stability of the active vibration isolation system is checked and analyzed.

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