Magnetorheological semi-active suspension system feedback control method based on Koopman operator

Abstract

The invention belongs to the technical field of automobile nonlinear control, and discloses a magneto-rheological semi-active suspension system feedback control method based on a Koopman operator, and the method comprises the steps: obtaining a damping characteristic curve of a magneto-rheological damper through collecting the input and output data of a magneto-rheological damper characteristic experiment; constructing a nonlinear model of the magnetorheological damper according to the damping characteristic curve; raising the dimension of the nonlinear model of the magnetorheological damper to a high-dimensional space by utilizing a Koopman operator theory and an extended dynamic mode decomposition algorithm, realizing global linearization of the nonlinear model of the magnetorheological damper, and obtaining a Koopman high-dimensional linear model; road excitation is considered, and an integrated linear model for dynamic coupling of the magnetorheological damper and the hub driving suspension system is constructed based on a Koopman high-dimensional linear model; and a feedback controller acting on the magneto-rheological semi-active suspension system is designed based on the integrated linear model by taking vehicle body vertical acceleration limitation, suspension stroke limitation, tire load limitation and actuator physical limitation as constraint conditions.

Description

Technical Field

[0001] The invention belongs to the technical field of automobile nonlinear control, and in particular relates to a magnetorheological semi-active suspension system feedback control method based on a Koopman operator. Background Art

[0002] Conventional magnetorheological semi-active suspension control systems mostly employ a hierarchical structure, first calculating the desired damping force through upper-level optimization, and then solving the driving current using the lower-level damper inverse model. However, existing control systems lack coordination, making it difficult to achieve global optimal control. Especially in the context of significant dynamic coupling between the magnetorheological damper and the suspension system, hierarchical control strategies fail to fully exploit the coupling characteristics between the control input (current) and the system response. For example, a complex magnetorheological nonlinear relationship exists between current and damping force, while the damping force bidirectionally affects multiple dynamic indicators of the suspension system, such as acceleration, vehicle body posture, and tire contact force. Furthermore, vehicle suspension control must simultaneously meet the objectives of ride comfort and driving safety, subject to constraints such as dynamic travel limits and actuator saturation. This essentially transforms the control problem into a nonlinear, strongly coupled, multi-objective optimal control problem. Summary of the Invention

[0003] In view of this, in order to solve the problems raised in the above background technology, the purpose of the present invention is to provide a feedback control method for a magnetorheological semi-active suspension system based on the Koopman operator. Specifically, by constructing an integrated model of the dynamic coupling between the magnetorheological damper and the wheel hub driven suspension system and introducing the Koopman operator theory, the nonlinear system is mapped into a high-dimensional linear system, simplifying the controller design process. Using output feedback Broad sense This method directly uses current as the optimization variable to minimize vehicle vertical acceleration and improve ride comfort while satisfying the dissipative and saturation properties of the magnetorheological damper, as well as the suspension travel and driving safety constraints. This method improves control accuracy, robustness, and real-time performance, and is suitable for wheel-drive vehicle suspension systems equipped with magnetorheological dampers.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A feedback control method for a magnetorheological semi-active suspension system based on a Koopman operator, comprising:

[0006] S1. Obtaining the damping characteristic curve of the magnetorheological damper by collecting input and output data of the magnetorheological damper characteristic experiment, and constructing a nonlinear model of the magnetorheological damper according to the damping characteristic curve;

[0007] S2. Using the Koopman operator theory and the extended dynamic mode decomposition algorithm, the nonlinear model of the magnetorheological damper is upgraded to a high-dimensional space, achieving global linearization of the nonlinear model of the magnetorheological damper and obtaining the Koopman high-dimensional linear model.

[0008] S3. Considering road excitation, an integrated linear model of the dynamic coupling between the magnetorheological damper and the wheel-driven suspension system is constructed based on the Koopman high-dimensional linear model.

[0009] S4. Taking the vehicle body vertical acceleration limit, suspension travel limit, tire load limit, and actuator physical limit as constraints, a feedback controller is designed based on an integrated linear model, and the control variable output by the feedback controller is applied to the magnetorheological semi-active suspension system.

[0010] Preferably, in step S1, the input data of the magnetorheological damper are the control current I, the relative displacement s of the piston and the piston movement speed v, and the output data is the damping force F.

[0011] Preferably, in step S2, the Koopman high-dimensional linear model is expressed as:

[0012] ;

[0013] Where: is the state quantity after dimensionality increase, is the state improvement function; is the input of the magnetorheological damper; is the predicted output damping force; is the matrix to be solved.

[0014] Preferably, in step S3, the integrated linear model is expressed as:

[0015] ;

[0016] Where: is the reference input of the wheel-driven suspension system, and pass Denormalization is performed to obtain; is the state vector of the wheel-driven suspension system, is the suspension system state matrix; Motivation for the road.

[0017] Preferably, in step S4, the disturbance constraint is designed with the vehicle body vertical acceleration limit as a constraint condition: .

[0018] Preferably, based on The perturbation constraint described in the norm design is:

[0019] ;

[0020] ;

[0021] Where: Indicates motivation from the road To the perturbation constraint output The closed-loop transfer function.

[0022] Preferably, in step S4, the time domain hard constraints are designed with the suspension travel limit, tire load limit, and actuator physical limit as constraint conditions. .

[0023] Preferably, based on a broad The time domain hard constraints described in the norm design are:

[0024] ;

[0025] ;

[0026] Where: Indicates motivation from the road To the time domain hard constraint output The closed-loop transfer function is Indicates the time domain hard constraint output The infinite norm of .

[0027] Preferably, in step S4: by defining an augmentation function Transform the integrated linear model into .

[0028] Preferably, in step S4, the feedback control law of the feedback controller is defined as Where: is the actual output of the magnetorheological semi-active suspension system.

[0029] Preferably, in step S4, the gain function of the feedback controller is defined as Where: , initial value , is the identity matrix, is a positive definite symmetric matrix, is the dimension-raising matrix obtained by solving the following inequality;

[0030] ;

[0031] ;

[0032] .

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] The present invention breaks the limitation of traditional hierarchical control structure by building an integrated model, and achieves the consistency and coupling coordination of modeling. The Koopman operator is used to perform global linearization on the nonlinear system, which significantly improves the feasibility of control design. Broad sense The control method not only achieves suspension system stability but also takes into account vehicle comfort and safety, and comprehensively optimizes suspension performance indicators. At the same time, the designed controller has a concise and clear structure, which is easy to implement in engineering, and has good practicality and platform adaptability, making it suitable for a variety of vehicle application scenarios equipped with magnetorheological dampers. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is the damping characteristic curve of the magnetorheological damper;

[0036] Figure 2 Output the tracking curve of damping force and actual damping force for Koopman high-dimensional linear model;

[0037] Figure 3 is a control block diagram of the control method of the present invention;

[0038] Figure 4 The graph is a relationship between the piston movement speed and the output damping force under the control of the control method of the present invention. DETAILED DESCRIPTION

[0039] To further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. The structures, proportions, sizes, etc. illustrated in the drawings of this specification are only used to match the content disclosed in the specification, so that people familiar with the technology can understand and read them. They are not used to limit the limitations of the implementation of the present invention and therefore have no technical significance. Any structural modifications, changes in proportional relationships, or adjustments in size should still fall within the scope of the technical content disclosed in the present invention without affecting the efficacy and objectives that can be achieved by the present invention. At the same time, terms such as "upper", "lower", "left", "right", and "middle" used in this specification are only for ease of description and are not used to limit the scope of implementation. Changes or adjustments in their relative relationships should also be considered as the scope of implementation of the present invention without substantially changing the technical content. It should be noted that the terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way are interchangeable where appropriate for the embodiments of the present application described herein.

[0040] Example

[0041] This embodiment provides a magnetorheological semi-active suspension system feedback control method based on the Koopman operator, comprising the following steps:

[0042] S1. Obtaining the damping characteristic curve of the magnetorheological damper by collecting input and output data of the magnetorheological damper characteristic experiment, and constructing a nonlinear model of the magnetorheological damper according to the damping characteristic curve;

[0043] Complete the experimental test of the magnetorheological damper characteristics and collect a large amount of input and output data of the magnetorheological damper. Specifically, the input data of the magnetorheological damper is the control current I, the relative displacement s of the piston and the piston movement speed v, and the output data is the damping force F. Figure 1 As shown, control currents of 0 A, 0.1 A, ..., 0.9 A, and 1 A are sequentially introduced, and input and output data of the magnetorheological damper are recorded to obtain a damping characteristic curve of the magnetorheological damper.

[0044] It is worth noting that there is an order of magnitude difference between the input and output data of the magnetorheological damper. In order to facilitate data processing, the input and output data need to be normalized. The normalization method is:

[0045] Where, is the normalized data; For the collected data; are the maximum and minimum values ​​in the collected data respectively.

[0046] S2. Using the Koopman operator theory and the extended dynamic mode decomposition algorithm, the nonlinear model of the magnetorheological damper is upgraded to a high-dimensional space, achieving global linearization of the nonlinear model of the magnetorheological damper and obtaining the Koopman high-dimensional linear model.

[0047] Specifically, the Koopman high-dimensional linear model is expressed as:

[0048] ;

[0049] Where: is the state quantity after dimensionality increase, is the state improvement function; is the input of the magnetorheological damper (including the normalized values ​​of the control current I, the relative displacement s of the piston, and the piston velocity v); is the predicted output damping force; is the matrix to be solved.

[0050] In addition, the output damping force of the magnetorheological damper was simulated and tested using the Koopman high-dimensional linear model. Figure 2 The tracking curve shown in FIG. 1 shows that the Koopman high-dimensional linear model constructed in the present invention has a good prediction effect on the output damping force of the magnetorheological damper.

[0051] S3. Considering road excitation, an integrated linear model of the dynamic coupling between the magnetorheological damper and the wheel-driven suspension system is constructed based on the Koopman high-dimensional linear model.

[0052] Specifically, the integrated linear model is expressed as:

[0053] ;

[0054] Where: is the reference input of the wheel-driven suspension system, and pass Denormalization is performed to obtain; is the state vector of the wheel-driven suspension system, is the suspension system state matrix; Motivation for the road.

[0055] S4. Design a feedback controller based on an integrated linear model, taking the vehicle body vertical acceleration limit, suspension travel limit, tire load limit, and actuator physical limit as constraints.

[0056] Specifically, the feedback controller adopts feedback Broad sense Control mechanism, the design process of the feedback controller is:

[0057] (1) By defining the augmentation function Transform the integrated linear model into ;

[0058] (2) Taking the vertical acceleration limit of the vehicle body as the constraint condition, the vehicle ride comfort is improved by minimizing the vertical acceleration of the vehicle body. Therefore, based on The perturbation constraint is designed by the norm and output as: Specifically, it is used to constrain the disturbance suppression capability of the magnetorheological semi-active suspension system to control the maximum response of the vehicle body's vertical acceleration and ensure that the system has good robustness.

[0059] (3) Suspension travel limit, tire load limit, and actuator physical limit are used as constraints, and based on the generalized Norm design of time domain hard constraints Specifically, the dynamic load on the tire should not exceed its static load to ensure vehicle driving safety. Due to the limitations of the vehicle's mechanical structure, the suspension system's operating stroke must be controlled within the specified maximum allowable range. The control current is limited to the interval [0, 1] to meet the physical limitations of the actual actuator.

[0060] (4) Based on the above constraints, the constraint objective is described as:

[0061] ;

[0062] ;

[0063] Where: Indicates motivation from the road To the perturbation constraint output The closed-loop transfer function.

[0064] ;

[0065] ;

[0066] Where: Indicates motivation from the road To the time domain hard constraint output The closed-loop transfer function is Indicates the time domain hard constraint output The infinite norm of .

[0067] (5) The feedback control law of the feedback controller is defined as Where: is the actual output of the magnetorheological semi-active suspension system;

[0068] (6) The gain function of the feedback controller is defined as Where: , initial value , is the identity matrix, is a positive definite symmetric matrix, is the dimension-raising matrix obtained by solving the following inequality:

[0069] ;

[0070] ;

[0071] .

[0072] S5. Applying the control variable output by the feedback controller to the magnetorheological semi-active suspension system.

[0073] Finally, the effectiveness of the magnetorheological semi-active suspension system control method based on Koopman operator proposed in this invention is verified by simulation: given a sinusoidal road excitation of 4 Hz, and using the controller designed above to simulate the control of the hub-driven magnetorheological semi-active suspension system, the following is obtained: Figure 4 As shown, Figure 4 The graph is a relationship between the piston movement speed and the output damping force of the magnetorheological damper, which shows that the output damping force meets the energy dissipation characteristics of the magnetorheological damper.

[0074] The present invention further discloses a magnetorheological semi-active suspension system feedback control system based on a Koopman operator provided by an exemplary embodiment, the system comprising:

[0075] Data acquisition module, used to collect input and output data of magnetorheological damper characteristic experiment;

[0076] a data processing module, configured to process input and output data and obtain a damping characteristic curve of the magnetorheological damper;

[0077] A model building module is used to build a nonlinear model of the magnetorheological damper according to the damping characteristic curve;

[0078] The model processing module is used to upgrade the nonlinear model of the magnetorheological damper to a high-dimensional space based on the Koopman operator theory and the extended dynamic mode decomposition algorithm, thereby realizing the global linearization of the nonlinear model of the magnetorheological damper and obtaining the Koopman high-dimensional linear model.

[0079] The model coupling module is used to construct an integrated linear model of the dynamic coupling between the magnetorheological damper and the hub-driven suspension system based on the Koopman high-dimensional linear model and the road excitation mechanism.

[0080] A controller building module is used to design and build a feedback controller based on an integrated linear model using vehicle body vertical acceleration limits, suspension travel limits, tire load limits, and actuator physical limits as constraints.

[0081] The output module is used to apply the control quantity output by the feedback controller to the magnetorheological semi-active suspension system.

[0082] Regarding the device in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0083] In summary, the magnetorheological semi-active suspension system control method and control system based on the Koopman operator provided in the embodiment of the present invention specifically constructs an integrated model of the dynamic coupling between the magnetorheological damper and the wheel hub driven suspension system, and introduces the Koopman operator theory to map the nonlinear system into a high-dimensional linear system, thereby simplifying the controller design process. Broad sense This method directly uses current as the optimization variable to minimize vehicle vertical acceleration and improve ride comfort while satisfying the dissipative and saturation properties of the magnetorheological damper, as well as the suspension travel and driving safety constraints. This method improves control accuracy, robustness, and real-time performance, and is suitable for wheel-drive vehicle suspension systems equipped with magnetorheological dampers.

[0084] In another exemplary embodiment, an electronic device is provided. The electronic device includes a memory and a processor, and a program stored in the memory. When the processor executes the program, one or more steps of the above method are implemented.

[0085] In another exemplary embodiment, a computer-readable storage medium including program instructions is provided. When executed by a processor, the program instructions implement the steps of the aforementioned method for controlling a magnetorheological semi-active suspension system based on a Koopman operator. For example, the computer-readable storage medium may be a first memory including the program instructions. The program instructions may be executed by a first processor of an electronic device to implement the aforementioned method for controlling a magnetorheological semi-active suspension system based on a Koopman operator.

[0086] In another exemplary embodiment, a computer program product is also provided, which includes a computer program that can be executed by a programmable device, and the computer program has a code portion for executing the above-mentioned magnetorheological semi-active suspension system control method based on the Koopman operator when executed by the programmable device. In some embodiments, part or all of the computer program can be loaded and / or installed on the device via a ROM and / or a communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of the aforementioned method can be performed. Alternatively, in other embodiments, the CPU can be configured to execute one or more steps of the aforementioned method by any other appropriate means (for example, by means of firmware).

[0087] Note that the above are only preferred embodiments of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments, and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments and may include many other equivalent embodiments without departing from the concept of the present invention. The scope of the present invention is determined by the scope of the appended claims.

Claims

1. A feedback control method for a magnetorheological semi-active suspension system based on Koopman operator, characterized in that: The steps include: S1. Obtaining the damping characteristic curve of the magnetorheological damper by collecting input and output data of the magnetorheological damper characteristic experiment, and constructing a nonlinear model of the magnetorheological damper according to the damping characteristic curve; S2. Using the Koopman operator theory and the extended dynamic mode decomposition algorithm, the nonlinear model of the magnetorheological damper is upgraded to a high-dimensional space, achieving global linearization of the nonlinear model of the magnetorheological damper and obtaining the Koopman high-dimensional linear model. S3. Considering road excitation, an integrated linear model of the dynamic coupling between the magnetorheological damper and the wheel-driven suspension system is constructed based on the Koopman high-dimensional linear model. S4. Taking the vehicle body vertical acceleration limit, suspension travel limit, tire load limit, and actuator physical limit as constraints, a feedback controller is designed based on an integrated linear model, and the control variable output by the feedback controller is applied to the magnetorheological semi-active suspension system.

2. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 1, characterized in that: In step S1 , the input data of the magnetorheological damper are the control current I, the relative displacement s of the piston and the piston movement speed v, and the output data is the damping force F.

3. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 2, characterized in that: In step S2, the Koopman high-dimensional linear model is expressed as: ； Where: is the state quantity after dimensionality increase, is the state improvement function; is the input of the magnetorheological damper; is the predicted output damping force; is the matrix to be solved.

4. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 3 is characterized in that: In step S3, the integrated linear model is expressed as: ； Where: is the reference input of the wheel-driven suspension system, and pass Denormalization is performed to obtain; is the state vector of the wheel-driven suspension system, is the suspension system state matrix; Motivation for the road.

5. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 4 is characterized in that: In step S4, the disturbance constraint is designed with the vehicle body vertical acceleration limit as a constraint condition: .

6. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 5, characterized in that: In step S4, the time domain hard constraints are designed with the suspension travel limit, tire load limit, and actuator physical limit as constraints. .

7. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 6, characterized in that: based on The perturbation constraint described in the norm design is: and Where: Indicates motivation from the road To the perturbation constraint output The closed-loop transfer function of Based on the broad The time domain hard constraints described in the norm design are: and Where: Indicates motivation from the road To the time domain hard constraint output The closed-loop transfer function is Indicates the time domain hard constraint output The infinite norm of .

8. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 7, characterized in that: In step S4: by defining the augmentation function Transform the integrated linear model into .

9. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 8, characterized in that: In step S4, the feedback control law of the feedback controller is defined as Where: is the actual output of the magnetorheological semi-active suspension system.

10. The magnetorheological semi-active suspension system feedback control method based on Koopman operator according to claim 9, characterized in that: In step S4, the gain function of the feedback controller is defined as Where: , initial value , is the identity matrix, is a positive definite symmetric matrix, is the dimension-raising matrix obtained by solving the following inequality; ； ； 。

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