Upgrade sliding mode robust control method for active-passive vibration isolation system

Abstract

The invention discloses an order-lifting sliding mode robust control method for an active-passive vibration isolation system, and belongs to the technical field of vibration isolation system control, and the method comprises the steps: introducing a feed-forward control path, predicting the vibration frequency and amplitude at a future moment based on the historical state information of a controlled system, building an overall vibration isolation target model based on the prediction, and carrying out the control of the overall vibration isolation target model. Resolving a target transfer function of an active execution mechanism through kinetic analysis of the active-passive vibration isolation system, so as to calculate a feedforward control signal; the method comprises the following steps: modeling an active-passive vibration isolation system, constructing a nonsingular terminal sliding mode surface, collecting system state error information, and generating a feedback control signal of an actual controlled system through integral controller design; a feedforward control signal and a feedback control signal are reasonably coupled and superposed to serve as control input of a controlled system. According to the order-lifting sliding mode robust control method for the active-passive vibration isolation system provided by the invention, the anti-interference capability and the stability of the active-passive vibration isolation system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of vibration isolation system control, and in particular to an elevated-order synovial robust control method for an active-passive vibration isolation system. Background Art

[0002] Vibration isolation systems are widely used in deep space exploration, maritime vessels, and ground inspections. They are crucial for improving sensor detection accuracy, protecting cargo safety, ensuring rugged terrain maneuverability, and ensuring passenger comfort. Vibration isolation systems are primarily implemented through passive, active, and a combination of the two: active-passive isolation. Passive isolation systems primarily utilize mechanical components such as springs, dampers, and inertia vessels for configuration design and parameter optimization. The forced motion of these components converts the system's mechanical energy into heat, thereby reducing kinetic energy and, consequently, the platform's vibration amplitude and velocity. While they offer the advantage of fast response, they are limited by their mechanical configuration and component characteristics, resulting in fixed performance and limited effectiveness in specific application scenarios. Active isolation systems primarily rely on controllable actuators such as electric, hydraulic, and pneumatic actuators for structural construction and algorithm design. They operate by applying a counteracting force to offset the system's kinetic energy with input energy. While they offer high adaptability, they are limited by the control bandwidth and drive capabilities of the controllable actuators, making them suitable only for low- and medium-frequency applications and less effective for high-frequency applications. Active-passive vibration isolation systems consist of passive mechanical elements and active actuators. Their interplay allows them to balance the rapid response of passive isolation systems with the robust adaptability of active isolation systems. Consequently, numerous researchers have conducted research on control algorithms for active-passive vibration isolation systems. Active actuators are used to simulate spring-damper-mass passive systems, forming parameter-adjustable isolation elements. However, due to the lack of posture and position information, complete vibration isolation cannot be achieved. For a robot with articulated legs connected to a series passive mechanism, the target angles of the leg joints are calculated based on the difference between the body's posture measured by sensors and the target posture. Joint position control allows the legs to adapt to ground undulations, while a spring-damper mechanism improves the compliance of the foot's contact with the ground. This allows for posture adjustment during robot movement and achieves effective vibration isolation. For active-passive vibration isolation systems composed of multiple controllable actuators and passive mechanisms, the control algorithm should ensure that the system quickly stabilizes under external vibration excitation while avoiding chattering of the control variable under severe disturbances, thereby improving the robustness of the algorithm. Summary of the Invention

[0003] The object of the present invention is to provide a raised-order sliding film robust control method for an active-passive vibration isolation system to solve the problems existing in the background technology.

[0004] To achieve the above object, the present invention provides a method for robust control of an active-passive vibration isolation system using a raised-order synovial membrane, comprising the following steps:

[0005] S1. Introducing a feedforward control path, a vibration prediction model is established based on the historical state information of the controlled system to predict the vibration frequency and amplitude at future moments. Based on this, an overall vibration isolation target model is established as the target transfer function. The transfer function of the active actuator is obtained, and the state space equation is derived and upgraded to obtain the designed integral control rate.

[0006] S2. Model the active-passive vibration isolation system, collect system state error information, and construct a non-singular terminal sliding mode surface. Based on the system Jacobian matrix, the output driving force of each active actuator is generated.

[0007] S3. Select a neuron activation function to perform nonlinear superposition fitting on the feedforward control signal and the feedback control signal.

[0008] Preferably, in the active-passive vibration isolation control system, several active-passive vibration isolation channels are numbered as W. i (i=1...n), n represents the total number of channels. According to the working principle of each mechanism and component, the channel W is derived. i The force F i , satisfying the following equation:

[0009]

[0010] Where, Indicates the output force of the active actuator. Through the optimized design of the drive circuit and algorithm, the control input and Functional relationship of Represents the force of the passive element and the spring stiffness Damping coefficient Distributed load mass Displacement change S i Related; Represents the friction force generated by the relative motion surface of the active actuator and the passive element; π i A vector composition function representing the forces.

[0011] Preferably, S1 includes high-frequency vibration isolation working conditions and low-frequency vibration isolation requirements, and a vibration prediction model is established for high-frequency vibration isolation working conditions, and the system posture state observation results are converted to As the model input, the vibration frequency ω and amplitude A at the future time are predicted. According to the actual system configuration, the spring-damper-mass second-order model is selected. With the excitation signal as input and the vibration displacement as output, the following vibration isolation target model G(s) is established as the target transfer function of the active-passive vibration isolation system:

[0012]

[0013] Through calculation, we know that the cutoff frequency of the target transfer function is ω, which means that when the vibration isolation target model G(s) is excited by the frequency ω, the transfer amplitude is 0, that is, the vibration of this frequency can be completely isolated; according to the channels W of the active-passive vibration isolation system i The mechanical connection structure is based on the passive element transfer function G p (s) and topological decoupling calculation, the target transfer function G of the active actuator a (s) meet the following requirements:

[0014]

[0015] Among them, the operators Π and Π i Related, its inverse process Π -1 The vector decomposition process of solving the internal forces by the system's resultant force is described;

[0016] Through frequency domain-time domain transformation, the system posture is obtained For the system state x = [x1(t)x2(t)] T , the state space equation of the active-passive vibration isolation control system can be obtained as:

[0017]

[0018] Among them, f vi (t,x) is the system function, and its time-varying characteristics mainly come from the target transfer function G a (s), in order to ensure the continuity of the designed control rate, the above model is upgraded to obtain:

[0019]

[0020] For this raised-order system function Find a positive definite boundary function ψ vi (t,x,x) satisfies:

[0021]

[0022] Then design the integral control rate u vi Satisfy the following form:

[0023]

[0024] Where x represents the system state vector, x1 represents the first component of the system state vector, which is defined as the system pose q.

[0025] Since G(s) is a feedforward model based on vibration prediction, the above feedforward-feedback fusion control law u vi It will give the control system excellent frequency response characteristics and certain predictive capabilities.

[0026] Preferably, in order to meet the requirements of low-frequency vibration isolation, a spatial multi-degree-of-freedom rigid body posture tracking model is established, which conforms to the following Cartesian space rigid body posture dynamics equation:

[0027]

[0028] Where, represents the rigid body inertia matrix, is the gravity acting on the rigid body, and The product of describes the centripetal force and Coriolis force on the rigid body during motion, τ is the generalized virtual force that drives the rigid body model to reach the position q; C and G represent matrices.

[0029] Preferably, in the controlled system, each active actuator of the active-passive vibration isolation platform outputs a driving force u pa Satisfy τ=Ju pa , where J is the Jacobian matrix of the active-passive vibration isolation system. Define q and target given q r The error between them is e=[e1 e2], and the error state equation is derived as:

[0030]

[0031] q r Indicates the target’s given pose;

[0032] Thus, a non-singular terminal sliding surface is constructed, which satisfies:

[0033]

[0034] In the formula, a and b are odd numbers and 2a>b>a>0, c s =diag{c1…c n} is a positive element c1…c n The constant coefficient matrix formed by .

[0035] Preferably, each active actuator is designed to output a driving force u pa for:

[0036]

[0037] Preferably, for the active-passive vibration isolation platform in S3, the control signal u generated by the controller running the algorithm includes u vi , which also contains u paIn order to ensure the continuity of the control signal and environmental applicability, the neuron activation function is selected for nonlinear fitting as follows:

[0038]

[0039] Among them, e is the natural base, and the positive real numbers ω0 and α are the adjustment parameters of the fitting function. When the predicted vibration frequency satisfies ω<<ω0, the system performs low-frequency vibration isolation, that is, u→u pa ; When the predicted vibration frequency satisfies ω>>ω0, high-frequency vibration isolation control is required, i.e. u→u vi .

[0040] Preferably, the active-passive vibration isolation control system includes a controller, a driver, an active actuator, a vibration isolation platform, a passive element, a posture sensor and a signal conditioning module. The controller receives system status information and feedback signals, generates a control signal and sends it to the driver. The driver drives the active actuator to follow the vibration excitation working condition according to the received control signal, and transmits the system status information to the controller. The active actuator and the passive element are mechanically connected in series, parallel or multi-stage hybrid mode. The posture sensor is used to measure the system vibration information and generate a feedback signal, which is amplified, filtered and transmitted to the controller through the signal conditioning module.

[0041] Therefore, the present invention adopts the above-mentioned raised-order synovial robust control method for active-passive vibration isolation system, which has the following beneficial effects:

[0042] (1) It is realized by combining the feedforward control channel with the feedback closed loop;

[0043] (2) In the design of the feedforward control channel, a vibration prediction model is established to obtain the transfer function of the active actuator, the state space equation is derived and the order is increased, and an integral link is introduced to generate control instructions;

[0044] (3) In the feedback closed-loop design, the target model and virtual force are introduced, and a non-singular terminal sliding surface is constructed to generate the output driving force of each active actuator according to the system Jacobian matrix;

[0045] (4) The control signals generated by the feedforward channel and feedback control work together, and the neuron activation function is selected for nonlinear superposition fitting.

[0046] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a schematic diagram of the feedforward-feedback control principle for an active-passive vibration isolation system according to an embodiment of the present invention;

[0048] Figure 2 This is a block diagram of the active-passive vibration isolation control system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0049] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort shall fall within the scope of protection of the present invention.

[0050] See also Figure 1 , a raised-order sliding film robust control method for an active-passive vibration isolation system, comprising the following steps:

[0051] In the active-passive vibration isolation control system, several active-passive vibration isolation channels are numbered as W. i (i=1...n), n represents the total number of channels. According to the working principle of each mechanism and component, the channel W is derived. i The force F i , satisfying the following equation:

[0052]

[0053] Where, Indicates the output force of the active actuator. Through the optimized design of the drive circuit and algorithm, the control input and Functional relationship of Represents the force of the passive element and the spring stiffness Damping coefficient Distributed load mass Displacement change S i Related; Represents the friction force generated by the relative motion surface of the active actuator and the passive element; π i The vector synthesis operation function represents the force. Influenced by the material properties and the state of motion, viscous friction, Coulomb friction, static friction and Stribeck friction effects are generated. In order to fully describe the above coupling mechanism, the LuGre friction model is established. Although the differentiability of the model equation can be guaranteed through approximate simplification, the mathematical model has strong nonlinearity and high order. The operator π i With channel W i It is related to the topological structure of the active-passive vibration isolation system and describes the vector coupling process of obtaining the overall resultant force through the internal components of the active-passive vibration isolation system.

[0054] S1. Introduce a feedforward control path and establish a vibration prediction model based on the historical state information of the controlled system to predict the vibration frequency and amplitude at future moments. Based on this, establish an overall vibration isolation target model as the target transfer function, obtain the transfer function of the active actuator, derive the state space equation and perform order-raising processing to obtain the designed integral control rate.

[0055] Including high-frequency vibration isolation conditions and low-frequency vibration isolation requirements, the good control effect of the active-passive vibration isolation system requires the control algorithm to have prediction capabilities and fast response characteristics. Therefore, a vibration prediction model is established for high-frequency vibration isolation conditions, and the system posture state observation results are used to As the model input, the vibration frequency ω and amplitude A at the future time are predicted. According to the actual system configuration, the spring-damper-mass second-order model is selected. With the excitation signal as input and the vibration displacement as output, the following vibration isolation target model G(s) is established as the target transfer function of the active-passive vibration isolation system:

[0056]

[0057] Through calculation, we know that the cutoff frequency of the target transfer function is ω, which means that when the vibration isolation target model G(s) is excited by the frequency ω, the transfer amplitude is 0, that is, the vibration of this frequency can be completely isolated; according to the channels W of the active-passive vibration isolation system i The mechanical connection structure is based on the passive element transfer function G p (s) and topological decoupling calculation, the target transfer function G of the active actuator a (s) meet the following requirements:

[0058]

[0059] Among them, the operators Π and Π i Related, its inverse process Π -1 The vector decomposition process of solving the internal forces by the system's resultant force is described;

[0060] Through frequency domain-time domain transformation, the system posture is obtained For the system state x = [x1(t)x2(t)] T , the state space equation of the active-passive vibration isolation control system can be obtained as:

[0061]

[0062] Among them, f vi (t,x) is the system function, and its time-varying characteristics mainly come from the target transfer function G a (s), in order to ensure the continuity of the designed control rate, the above model is upgraded to obtain:

[0063]

[0064] For this raised-order system function Find a positive definite boundary function satisfy:

[0065]

[0066] Then design the integral control rate u vi Satisfy the following form:

[0067]

[0068] Where x represents the system state vector, x1 represents the first component of the system state vector, which is defined as the system pose q.

[0069] Since G(s) is a feedforward model based on vibration prediction, the above feedforward-feedback fusion control law u vi It will give the control system excellent frequency response characteristics and certain predictive capabilities.

[0070] In response to the need for low-frequency vibration isolation, a spatial multi-degree-of-freedom rigid body posture tracking model is established, which conforms to the following Cartesian space rigid body posture dynamics equation:

[0071]

[0072] Where, represents the rigid body inertia matrix, is the gravity acting on the rigid body, and The product of describes the centripetal force and Coriolis force on the rigid body during motion, τ is the generalized virtual force that drives the rigid body model to reach the position q; C and G represent matrices.

[0073] S2. Model the active-passive vibration isolation system, collect system state error information, and construct a non-singular terminal sliding surface. Generate the output driving force of each active actuator based on the system Jacobian matrix.

[0074] In the controlled system, each active actuator of the active-passive vibration isolation platform outputs a driving force u pa Satisfy τ=Ju pa , where J is the Jacobian matrix of the active-passive vibration isolation system. Define q and target given q r The error between them is e=[e1 e2], and the error state equation is derived as:

[0075]

[0076] q r Indicates the target’s given pose;

[0077] Thus, a non-singular terminal sliding surface is constructed, which satisfies:

[0078]

[0079] In the formula, a and b are odd numbers and 2a>b>a>0, c s =diag{c1…c n} is a positive element c1…c n The constant coefficient matrix formed by .

[0080] Design the output driving force u of each active actuator pa for:

[0081]

[0082] S3. Select a neuron activation function to perform nonlinear superposition fitting on the feedforward control signal and the feedback control signal.

[0083] For different working conditions, the control signal u generated by the controller running the algorithm of the active-passive vibration isolation platform includes u vi , which also contains u pa In order to ensure the continuity of the control signal and environmental applicability, the neuron activation function is selected for nonlinear fitting as follows:

[0084]

[0085] Among them, e is the natural base, and the positive real numbers ω0 and α are the adjustment parameters of the fitting function. When the predicted vibration frequency satisfies ω<<ω0, the system performs low-frequency vibration isolation, that is, u→u pa ; When the predicted vibration frequency satisfies ω>>ω0, high-frequency vibration isolation control is required, i.e. u→u vi .

[0086] The block diagram of the active-passive vibration isolation control system is as follows: Figure 2 As shown, the system is equipped with a controller, driver, active actuators, passive components, attitude sensors, and a signal conditioning module. The controller receives system status information and feedback signals, generates control signals, and transmits them to the driver. Based on the received control signals, the driver drives the active actuators to follow the vibration excitation and transmits system status information to the controller. The active actuators and passive components are mechanically connected in series, parallel, or multi-stage series-parallel configurations. The attitude sensor measures system vibration and generates feedback signals, which are amplified, filtered, and transmitted to the controller by the signal conditioning module.

[0087] In active-passive vibration isolation control systems, passive elements often include mechanical components such as springs, dampers, and tube containers, while active actuators include electric, hydraulic, pneumatic and other servo drive elements.

[0088] Therefore, the present invention adopts the above-mentioned raised-order synovial robust control method for the active-passive vibration isolation system, and proposes a raised-order synovial robust control method combining feedforward and feedback for the active-passive vibration isolation system. The state of the control system can ensure the stability of finite-time convergence when subjected to external vibration excitation, and the control law designed by model raising can ensure that the actual system generates continuous control quantity when applying this method, avoiding the system oscillation phenomenon caused by the step of the control quantity, and improving the anti-interference ability and stability of the active-passive vibration isolation system.

[0089] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for robust control of active-passive vibration isolation systems using a raised-order synovial membrane, characterized in that: The following steps are involved: S1. Introducing a feedforward control path, a vibration prediction model is established based on the historical state information of the controlled system to predict the vibration frequency and amplitude at future moments. Based on this, an overall vibration isolation target model is established as the target transfer function. The transfer function of the active actuator is obtained, and the state space equation is derived and upgraded to obtain the designed integral control rate. S2. Model the active-passive vibration isolation system, collect system state error information, and construct a non-singular terminal sliding mode surface. Based on the system Jacobian matrix, the output driving force of each active actuator is generated. S3. Select a neuron activation function to perform nonlinear superposition fitting on the feedforward control signal and the feedback control signal.

2. The method for robust control of an active-passive vibration isolation system according to claim 1, characterized in that: In the active-passive vibration isolation control system, several active-passive vibration isolation channels are numbered as W. i (i=1...n), n represents the total number of channels. According to the working principle of each mechanism and component, the channel W is derived. i The force F i , satisfying the following equation: F i (t)=Π i (F i e (t),F i a (t),F i f (t)) (1) Where, F i e (t) represents the output force of the active actuator; F i a (t) represents the force of the passive element and the spring stiffness Damping coefficient Distributed load mass Displacement change S i Related; F i f (t) represents the friction force generated by the relative motion surfaces of the active actuator and the passive element; i A vector composition function representing the forces.

3. The method for robust control of active-passive vibration isolation system according to claim 2, characterized in that: S1 includes high-frequency vibration isolation conditions and low-frequency vibration isolation requirements. A vibration prediction model is established for high-frequency vibration isolation conditions. The system posture state observation results are converted into As the model input, the vibration frequency ω and amplitude A at the future time are predicted. According to the actual system configuration, the spring-damper-mass second-order model is selected. With the excitation signal as input and the vibration displacement as output, the following vibration isolation target model G(s) is established as the target transfer function of the active-passive vibration isolation system: Through calculation, we know that the cutoff frequency of the target transfer function is ω, which means that when the vibration isolation target model G(s) is excited by the frequency ω, the transfer amplitude is 0, and the vibration of this frequency can be completely isolated; according to the channels W of the active-passive vibration isolation system i The mechanical connection structure is based on the passive element transfer function G p (s) and topological decoupling calculation, the target transfer function G of the active actuator a (s) meet the following requirements: G a (s)=Π -1 (G(s),G p (s)) (3) Among them, the operators Π and Π i Related, its inverse process Π -1 The vector decomposition process of solving the internal forces by the system's resultant force is described; Through frequency domain-time domain transformation, the system posture is obtained For the system state x = [x1(t)x2(t)] T , the state space equation of the active-passive vibration isolation control system is obtained as: Among them, f vi (t,x) is the system function, and its time-varying characteristics come from the target transfer function G a (s) is updated, and the order of formula (4) is upgraded to obtain: For this raised-order system function Find a positive definite boundary function satisfy: Then design the integral control rate u vi Satisfy the following form: Where x represents the system state vector, x1 represents the first component of the system state vector, which is defined as the system pose q.

4. The method for robust control of an active-passive vibration isolation system according to claim 3, characterized in that: In response to the need for low-frequency vibration isolation, a spatial multi-degree-of-freedom rigid body posture tracking model is established, which conforms to the following Cartesian space rigid body posture dynamics equation: Where, represents the rigid body inertia matrix, is the gravity acting on the rigid body, and The product of describes the centripetal force and Coriolis force on the rigid body during motion, τ is the generalized virtual force that drives the rigid body model to reach the position q; C and G represent matrices.

5. The method for controlling active-passive vibration isolation system with a raised-order synovial robust control system according to claim 4, characterized in that: In the controlled system, each active actuator of the active-passive vibration isolation platform outputs a driving force u pa Satisfy τ=Ju pa , where J is the Jacobian matrix of the active-passive vibration isolation system, and q is defined as the target given q r The error between them is e=[e1 e2], and the error state equation is derived as: q r Indicates the target’s given pose; Thus, a non-singular terminal sliding surface is constructed, which satisfies: In the formula, a and b are odd numbers and 2a>b>a>0, c s =diag{c1…c n } is a positive element c1…c n The constant coefficient matrix formed by .

6. The method for robust control of an active-passive vibration isolation system according to claim 5, characterized in that: Design the output driving force u of each active actuator pa for:

7. The method for robust control of an active-passive vibration isolation system according to claim 6, characterized in that: In the active-passive vibration isolation platform of S3, for different working conditions, the control signal u generated by the controller running the algorithm includes u vi and u pa , the neuron activation function is selected for the following nonlinear fitting: Among them, e is the natural base, and the positive real numbers ω0 and α are the adjustment parameters of the fitting function. When the predicted vibration frequency satisfies ω<<ω0, the system performs low-frequency vibration isolation, u→u pa ; When the predicted vibration frequency satisfies ω>>ω0, high-frequency vibration isolation control is required, u→u vi .

8. The method for robust control of an active-passive vibration isolation system according to claim 2, characterized in that: The active-passive vibration isolation control system includes a controller, a driver, an active actuator, a vibration isolation platform, a passive element, a posture sensor and a signal conditioning module. The controller receives system status information and feedback signals, generates a control signal and sends it to the driver. The driver drives the active actuator to follow the vibration excitation working condition according to the received control signal, and transmits the system status information to the controller. The active actuator and the passive element are mechanically connected in series, parallel or multi-stage hybrid mode. The posture sensor is used to measure the system vibration information and generate a feedback signal, which is amplified, filtered and transmitted to the controller through the signal conditioning module.

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