Quasi-zero stiffness vibration isolation system control method based on adaptive hyper-stable sliding mode control

Abstract

The application discloses a quasi-zero stiffness vibration isolation system control method based on adaptive super-hyper spiral sliding mode control and relates to the technical field of vibration isolation. The method comprises the following steps: 1) for the control target of a magnetic gas type quasi-zero stiffness vibration isolation system, a high control model under time-varying non-ideal load and a stiffness control model under time-varying non-ideal load are established; an adaptive super-hyper spiral sliding mode height controller based on a disturbance observer is designed; 3) a stiffness coarse-fine collaborative adjustment controller based on a super-hyper spiral sliding mode is designed; 4) the output of the adaptive super-hyper spiral sliding mode controller is obtained according to step 2) to realize height control; the output of the stiffness coarse-fine collaborative adjustment controller is obtained according to step 3) to realize stiffness control. The method has the significant advantages of low chattering, strong robustness and strong load adaptability.

Description

Technical Field

[0001] This invention relates to vibration isolation system control technology, and more particularly to a control method for a quasi-zero stiffness vibration isolation system based on adaptive superhelical sliding mode control. Background Technology

[0002] Quasi-zero stiffness vibration isolation systems are widely used in fields such as precision instruments, aerospace, and optical platforms where high-frequency vibration isolation is required. These systems achieve near-zero dynamic stiffness near the equilibrium position through a parallel combination of positive and negative stiffness elements, thus obtaining excellent vibration isolation performance in the low-frequency range. With the increasing demands for vibration control precision in high-end equipment, robust performance control of quasi-zero stiffness vibration isolation systems has become a research hotspot in the field of vibration control.

[0003] Magneto-Pneumatic Quasi-Zero Stiffness (QZS) is a high-performance vibration isolation system that combines a permanent magnet / electromagnetic negative stiffness mechanism with an air spring positive stiffness mechanism. Its core is to achieve high static stiffness and low dynamic stiffness, thus resolving the inherent contradiction between load-bearing capacity and low-frequency vibration isolation in traditional vibration isolators.

[0004] In the control technology of magnetic quasi-zero stiffness vibration isolation systems, existing solutions mainly employ PID control based on state feedback. This method measures the system's height deviation and calculates the control output using proportional, integral, and derivative components, adjusting the air spring pressure to maintain the system's equilibrium height. However, in quasi-zero stiffness vibration isolation systems, the positive stiffness of the air spring and the negative stiffness of the magnetic device exhibit very significant nonlinear characteristics. The stiffness of the air spring shows a complex nonlinear relationship with air pressure and volume, and the magnetic force, magnetic gap, and current of the negative stiffness device also exhibit strong nonlinearity. Traditional PID control, based on linearized model design, struggles to adapt to changes in the system's nonlinear characteristics, resulting in insufficient control accuracy.

[0005] Sliding mode control (SMD) is a robust nonlinear control strategy. Its core idea lies in designing a sliding mode surface (SMS surface) that allows the system state to converge to the SMD surface within a finite time and slide along it to the desired state. The main advantages of this method include robustness to system parameter variations and external disturbances; rapid convergence of the system state and maintenance of sliding motion; and a relatively intuitive design process that is easy to implement. SMD design utilizes a sliding surface and a sign function to construct a switching control law, allowing the system state to slide along the SMD surface to an equilibrium point, exhibiting strong robustness to parameter perturbations and external disturbances. However, traditional SMD uses a sign function as the switching function. When the system state approaches the SMD surface, the control input switches frequently between positive and negative values, causing severe chattering. Although saturation functions and boundary layer methods can mitigate chattering to some extent, they cannot fundamentally eliminate it. Furthermore, under complex operating conditions, SMD often requires high control gain to ensure system robustness, leading to severe oscillations in the controller output, which can even degrade system performance in severe cases.

[0006] In practical applications, quasi-zero stiffness vibration isolation systems also face the problem of time-varying load mass. When the load changes, the system's control gain changes with the load mass. Traditional control methods use fixed parameters, which cannot adapt to load changes in real time, leading to a decline in control performance.

[0007] Therefore, a control method is needed that can effectively reduce sliding mode chattering, improve control accuracy, and have the ability to adapt to time-varying loads and external disturbances, so as to meet the high-performance control requirements of quasi-zero stiffness vibration isolation systems in complex environments. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control, which addresses the deficiencies in the prior art.

[0009] The technical solution adopted by this invention to solve its technical problem is: a control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control, comprising the following steps: 1) To achieve the control objective of the magnetic quasi-zero stiffness vibration isolation system, a height control model and a stiffness control dynamic model under time-varying non-ideal loads are established. The height control model is established as follows: ; in, For system height, High rate of change; To control the gain, For time-varying load mass; This is the height control input, representing the height adjustment control quantity applied to the system. External disturbances The system is a nonlinear function; The stiffness control model is established as follows:

[0010] in, The total stiffness of the system; For permanent magnet magnetic gap Influence coefficient on stiffness; Electromagnetic coil current Influence coefficient on stiffness; Magnetic gap control input; For current control input; This represents the stiffness disturbance at time t during the stiffness adjustment process. 2) Design an adaptive superspiral sliding mode height controller based on a disturbance observer; the specific steps are as follows: 2.1) Design the sliding surface:

[0011] in, For high tracking error, The first derivative of the tracking error; To the desired height; These are the parameters of the sliding surface; To control the sliding surface at a certain height; 2.2) Design a disturbance observer; construct a nonlinear disturbance observer to dynamically compensate for external disturbances; 2.3) Design an adaptive law; design an adaptive law to estimate the time-varying load mass in real time; 2.4) Integrating adaptive and disturbance compensation principles, design an adaptive superspiral sliding mode controller: 3) Design a stiffness coarse-fine coordinated adjustment controller based on super-helical sliding mode; 3.1) Design a coarse adjustment controller to adjust the magnetic gap of the permanent magnet. Achieve rapid stiffness adjustment: 3.2) Design a fine-tuning controller to adjust the current of the electromagnetic coil. Achieve precise stiffness adjustment; Step 4) Execution Control Based on step 2), obtain the height control input from the adaptive superspiral sliding mode controller. To achieve height control; According to step 3), the magnetic gap control input output by the stiffness coarse adjustment controller is obtained. The electromagnetic coil current control input is the output of the stiffness fine-tuning controller. This enables stiffness control.

[0012] According to the above scheme, in step 1), The design is as follows:

[0013] Where c is the linear damping coefficient; According to the above scheme, in step 2.2), the disturbance observer is designed as follows:

[0014] in, , , These are estimates of altitude, speed, and disturbance, respectively. , This is the observer gain.

[0015] According to the above scheme, in step 2.3), an adaptive law is designed to estimate the time-varying load mass in real time, as follows: ; in, This is an estimate of the load mass. For adaptive gain, This is the acceleration due to gravity.

[0016] According to the above scheme, in step 2.4), an adaptive superspiral sliding mode controller is designed, as follows: ; in, ; This is an estimate of the system's nonlinear function; , , For control parameters; Let be the second derivative of the desired height.

[0017] According to the above scheme, step 3.1) is specifically as follows: 3.1.1) Design the coarse adjustment sliding surface : ; in, The total stiffness of the system; 3.1.2) Design a coarse-tuned disturbance observer to estimate external disturbances in real time:

[0018] in, , These are the estimated values ​​for stiffness and stiffness perturbation, respectively; , For observer gain; 3.1.3) Design a coarse adjustment controller:

[0019] in, , , , For control parameters; It controls the input.

[0020] According to the above scheme, step 3.2) is specifically as follows: 3.2.1) Design and fine-tune the sliding surface: ; 3.2.2) Design a fine-tuned perturbation observer: ; in, , For observer gain; 3.2.3) Design auxiliary system to compensate for input saturation: ; in, For ideal control input Compared with actual input Deviation; For auxiliary system gain; As an auxiliary variable; 3.2.4) Design a fine-tuning controller: ; in, , , , These are control parameters.

[0021] According to the above scheme, in step 3.2.4), the current in the fine-tuning stage is subject to input saturation constraints as follows:

[0022] in, This is the upper limit of the current.

[0023] The beneficial effects of this invention are: 1. This invention constructs a system dynamics model under time-varying non-ideal loads, and establishes a system height control model and stiffness adjustment model that include time-varying mass, parameter perturbation and external environmental disturbances, respectively, laying the foundation for the design of subsequent high-precision controllers.

[0024] 2. An adaptive superspiral sliding mode height control strategy based on a disturbance observer is proposed. To address the chattering problem inherent in traditional sliding mode control, a superspiral algorithm is introduced, utilizing integral terms to construct a continuous control law to mitigate chattering. Based on this, an adaptive law is designed to estimate the unknown time-varying load mass in real time, achieving adaptive adjustment to load changes. 3. A nonlinear disturbance observer was constructed to dynamically compensate for external disturbances, which significantly improved the system's ability to suppress disturbances. Attached Figure Description

[0025] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a flowchart of a method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the quasi-zero stiffness vibration isolation system according to an embodiment of the present invention; Figure 3 These are simulation results of the static balance working height control of the quasi-zero stiffness vibration isolation system according to an embodiment of the present invention; Figure 4 These are the simulation results of coarse and fine stiffness control of the quasi-zero stiffness vibration isolation system according to an embodiment of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0027] like Figure 1 As shown, a control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control includes the following steps: 1) To achieve the control objective of the quasi-zero stiffness vibration isolation system, a height control model and a stiffness control dynamic model under time-varying non-ideal loads are established. like Figure 2 As shown, the quasi-zero stiffness vibration isolation system includes: an air spring for providing positive stiffness; and a permanent magnet negative stiffness device, comprising a fixed permanent magnet and an adjustable permanent magnet, which adjusts the magnetic gap. Achieving coarse adjustment of negative stiffness; the electromagnetic coil negative stiffness device adjusts the excitation current. Achieve fine-tuning of negative stiffness; vibration isolation platform for bearing loads; The height model describes the dynamic characteristics of the system's static equilibrium position under time-varying loads and external disturbances, achieving constant height control. The stiffness model describes the dynamic characteristics of the system's stiffness adjustment, achieving a near-zero stiffness target. Together, the two models constitute the dynamic description of the time-varying non-ideal load system.

[0028] The height control model is established as follows:

[0029] in, For system height, High rate of change; To control the gain, For time-varying load mass; This is the height control input, representing the height adjustment control quantity applied to the system. External disturbances The system is a nonlinear function; The expression is as follows:

[0030] The stiffness control model is established as follows:

[0031] in, The total stiffness of the system; For permanent magnet magnetic gap Influence coefficient on stiffness; Electromagnetic coil current Influence coefficient on stiffness; Magnetic gap control input; For current control input; This represents the stiffness disturbance at time t during the stiffness adjustment process. By establishing a dynamic model that includes time-varying load mass and external disturbances, a foundation is provided for subsequent controller design.

[0032] 2) Design an adaptive superspiral sliding mode height controller based on a disturbance observer; the specific steps are as follows: 2.1) Design the sliding surface:

[0033] in, For high tracking error, The first derivative of the tracking error; To the desired height; These are the parameters of the sliding surface; To control the sliding surface at a certain height; 2.2) Design a disturbance observer; construct a nonlinear disturbance observer to dynamically compensate for external disturbances;

[0034] in, , , These are estimates of altitude, speed, and disturbance, respectively. , For observer gain; 2.3) Design an adaptive law; design an adaptive law to estimate the time-varying load mass in real time; ; in, This is an estimate of the load mass. For adaptive gain, It is the acceleration due to gravity; 2.4) Integrating adaptive and disturbance compensation principles, design an adaptive superspiral sliding mode controller: ; in, ; This is an estimate of the system's nonlinear function; , , For control parameters; The second derivative of the desired height; 3) Design a stiffness coarse-fine coordinated adjustment controller based on super-helical sliding mode; 3.1) Coarse adjustment controller, used to adjust the magnetic gap of the permanent magnet. Achieve rapid stiffness adjustment: 3.1.1) Design the coarse adjustment sliding surface : ; in, The total stiffness of the system; 3.1.2) Design a coarse-tuned disturbance observer to estimate external disturbances in real time:

[0035] in, , These are the estimated values ​​for stiffness and stiffness perturbation, respectively; , For observer gain; 3.1.3) Design a coarse adjustment controller:

[0036] in, , , , For control parameters; It is a control input; 3.2) Fine-tuning controller, used to adjust the current of the electromagnetic coil. Achieve precise stiffness adjustment; eliminate residual errors from the coarse adjustment stage; 3.2.1) Design and fine-tune the sliding surface: ; 3.2.2) Design a fine-tuned perturbation observer: ; in, , For observer gain; 3.2.3) Design auxiliary system to compensate for input saturation: ; in, For ideal control input Compared with actual input Deviation; For auxiliary system gain; As an auxiliary variable; 3.2.4) Design a fine-tuning controller: ; in, , , , For control parameters; The current during the fine-tuning stage is subject to input saturation constraints as follows:

[0037] in, This is the upper limit of the current. Setting the current control input during the coarse adjustment stage During the fine-tuning stage, the magnetic gap control input is set. This achieves decoupled control between coarse and fine adjustments.

[0038] This step proposes a hierarchical control strategy combining "coarse adjustment of permanent magnet displacement" and "fine adjustment of electromagnetic coil current" to address the quasi-zero stiffness characteristics. The coarse adjustment controller is responsible for offsetting positive stiffness over a large range, while the fine adjustment controller quickly compensates for residual stiffness errors. An auxiliary system is introduced to solve the input saturation problem, ensuring that the system stiffness can quickly and stably approach zero.

[0039] Step 4) Implement quasi-zero stiffness vibration isolation system control; Calculate the height control input according to step 2). Altitude control is achieved by adjusting the air pressure of the air spring; Calculate the stiffness control input according to step 3). and Stiffness control is achieved by adjusting the magnetic gap of the permanent magnet and the current of the electromagnetic coil.

[0040] The quasi-zero stiffness vibration isolation system and its adaptive super-helical sliding mode control method provided by this invention achieve high-precision height tracking control and stiffness adjustment under complex working conditions of time-varying loads and external disturbances. It has significant advantages such as low chattering, strong robustness and strong load adaptability, and provides effective technical support for the application of quasi-zero stiffness vibration isolation systems in the field of high-end equipment.

[0041] Simulation comparison experiment: Based on the control model established according to the present invention, the static balance working height of the load-bearing mass is used as the evaluation index. The system is simulated using Matlab / Simulink. The simulation model parameters are shown in Table 1.

[0042] Table 1. Parameters of the Simulink Simulation Model for Static Balancing Working Height Control

[0043] 2. Simulation of coarse and fine control of system stiffness Based on the established control model, the system stiffness was used as the evaluation index, and the system was simulated using Matlab / Simulink. The simulation model parameters are shown in Table 2.

[0044] Table 2. Parameters of the Simulink Simulation Model for Coarse and Fine Stiffness Control of the System

[0045] 3. Simulation Results Analysis Based on the two Simulink simulation models (static balance working height control simulation model and stiffness coarse and fine control simulation model) and the set parameters, the simulation was started and the data was exported and processed. Finally, the relevant data curves reflecting the key performance of the system for each model were obtained, as shown in the following figures. Figure 3 and Figure 4 As shown.

[0046] Figure 3This paper visually demonstrates the control effect of an adaptive superspiral sliding mode controller based on a disturbance observer on the static equilibrium height of a system under the combined effects of time-varying mass load and external disturbance. Firstly, regarding height tracking control and error convergence, as shown in subfigures (a) and (d), despite the system facing drastic load changes and external disturbances, the height displacement can still converge rapidly and lock stably at the zero equilibrium position. The tracking error curve further quantifies this performance, showing that the initial transient error is eliminated in a very short time, and the steady-state error remains within a micrometer range or even lower, establishing the controller's high-precision characteristics. Secondly, regarding state response and smooth control, as shown in subfigures (b) and (c), the rapid approach to zero of the load-bearing mass velocity indicates that system vibration is effectively suppressed. More notably, thanks to the unique construction of the superspiral algorithm, which places discontinuous sign functions in the integral term, the control input curve not only responds quickly but also exhibits continuous smoothness, significantly suppressing the inherent "chattering" phenomenon of traditional sliding mode control, which is crucial for extending the life of the actuator. Meanwhile, this is confirmed in the sliding surface dynamics, as shown in subfigure (e), where the sliding variable... The control strategy converges and remains in the zero neighborhood within a finite time. Its core advantages lie in parameter identification and disturbance rejection, as shown in subgraphs (f) and (g). The disturbance observer's estimation curve for external disturbances closely matches the actual changing trend, verifying the effectiveness of the observer design. The mass adaptive law exhibits excellent dynamic performance, accurately capturing the time-varying trajectory of the actual load in real time, indicating that the controller successfully decouples and adaptively compensates for non-ideal loads and model uncertainties. Finally, at the air pressure regulation control level, as shown in subgraph (h), the air spring pressure can be dynamically and precisely adjusted according to load fluctuations, ensuring a constant static balance height.

[0047] Figure 4 This paper demonstrates the dynamic response process of the magnetic negative stiffness mechanism driven by a coarse-fine coordinated adjustment strategy. First, considering the core characteristic of the system, namely the zero-stiffness characteristic, as shown in sub-figure (a), the total stiffness of the system rapidly decays from an initial positive value and asymptotically approaches zero, successfully constructing an ideal "quasi-zero stiffness" state. This signifies that the magnetic negative stiffness effectively cancels out the positive stiffness of the air spring, establishing the physical basis for the system to achieve low-frequency vibration isolation. This characteristic is achieved thanks to the hierarchical coordinated control architecture of the negative stiffness. In the coarse adjustment stage, as shown in sub-figures (d) and (e), the super-spiral controller drives the permanent magnet adjustment mechanism to overcome significant mechanical inertia and frictional resistance, smoothly adjusting the magnetic gap to the target range, primarily responsible for large-scale stiffness cancellation. In the fine adjustment stage, as shown in sub-figure (f), the electromagnet excitation current... The system primarily employs rapid, small-amplitude dynamic compensation to address residual stiffness errors during the coarse-tuning process. The stability of the control system was verified in the sliding surface dynamics, as shown in sub-figure (c). The sliding surfaces of both the coarse-tuning and fine-tuning subsystems converged synchronously to zero, demonstrating the effectiveness and convergence of the dual-loop collaborative working mechanism. Finally, regarding the physical limitations of the actuator (anti-saturation and robustness), although the electromagnet faces current input saturation constraints, thanks to the introduction of the anti-saturation auxiliary system, the final stiffness response did not exhibit divergence or severe oscillations caused by integral saturation, confirming the strong robustness of the control strategy under nonlinear constraints.

[0048] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control, characterized in that, Includes the following steps: 1) To achieve the control objectives of the magnetic quasi-zero stiffness vibration isolation system, a height control model and a stiffness control model under time-varying non-ideal loads are established. 2) Design an adaptive superspiral sliding mode height controller based on a disturbance observer; the specific steps are as follows: 2.1) Design the sliding surface: 2.2) Design a disturbance observer; construct a nonlinear disturbance observer to dynamically compensate for external disturbances; 2.3) Design an adaptive law; design an adaptive law to estimate the time-varying load mass in real time; 2.4) Integrating adaptive and disturbance compensation principles, design an adaptive superspiral sliding mode controller: 3) Design a stiffness coarse-fine coordinated adjustment controller based on super-helical sliding mode; 3.1) Design a coarse adjustment controller to adjust the magnetic gap of the permanent magnet. Achieve rapid stiffness adjustment: 3.2) Design a fine-tuning controller to adjust the current of the electromagnetic coil. Achieve precise stiffness adjustment; 4) Obtain the output of the adaptive superspiral sliding mode controller according to step 2) to achieve height control; obtain the output of the stiffness coarse and fine coordinated adjustment controller according to step 3) to achieve stiffness control.

2. The control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control according to claim 1, characterized in that, In step 1), The height control model is established as follows: ； in, For system height, High rate of change; To control the gain, For time-varying load mass; This is the height control input, representing the height adjustment control quantity applied to the system. External disturbances The system is a nonlinear function; The stiffness control model is established as follows: in, The total stiffness of the system; For permanent magnet magnetic gap Influence coefficient on stiffness; Electromagnetic coil current Influence coefficient on stiffness; Magnetic gap control input; For current control input; Let t be the stiffness disturbance at time t during the stiffness adjustment process.

3. The control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control according to claim 2, characterized in that, In step 1), The design is as follows: Where c is the linear damping coefficient; For the linear term coefficient of the negative stiffness of permanent magnets; For the cubic term coefficient of the negative stiffness of the permanent magnet; For the fifth-order coefficient of the negative stiffness of the permanent magnet; The coefficients of the linear term for electromagnetic negative stiffness; For the cubic term coefficient of electromagnetic negative stiffness; is the fifth-order coefficient of the electromagnetic negative stiffness; g is the gravitational acceleration.

4. The control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control according to claim 2, characterized in that, In step 2.2), the disturbance observer is designed as follows: in, , , These are estimates of altitude, speed, and disturbance, respectively. , This is the observer gain.

5. The control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control according to claim 1, characterized in that, In step 2.3), an adaptive law is designed to estimate the time-varying load mass in real time, as follows: ； in, This is an estimate of the load mass. For adaptive gain, It is the acceleration due to gravity. To control the sliding surface at a certain height.

6. The control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control according to claim 4, characterized in that, In step 2.4), an adaptive superspiral sliding mode controller is designed, as follows: ； in, , , For control parameters; The second derivative of the desired height; To control the sliding surface at a certain height.

7. The control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control according to claim 1, characterized in that, In step 3.1), the specific details are as follows: 3.1.1) Design the coarse adjustment sliding surface : ； in, The total stiffness of the system; 3.1.2) Design a coarse-tuned disturbance observer to estimate external disturbances in real time: in, , For observer gain; 3.1.3) Design a coarse adjustment controller: in, , , , For control parameters; It controls the input.

8. The control method for a quasi-zero stiffness vibration isolation system based on adaptive superspiral sliding mode control according to claim 1, characterized in that, In step 3.2), the specific details are as follows: 3.2.1) Design and fine-tune the sliding surface: ； 3.2.2) Design a fine-tuned perturbation observer: ； in, , For observer gain; 3.2.3) Design auxiliary system to compensate for input saturation: ； in, For ideal control input Compared with actual input Deviation; For auxiliary system gain; As an auxiliary variable; 3.2.4) Design a fine-tuning controller: in, , , , These are control parameters.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 8.

Images