A semi-active vehicle ISD suspension system and fractional order skyhook control method

Abstract

The application discloses a kind of semi-active vehicle ISD suspension systems and fractional order ground shelf control method, comprising the following working steps: step one: build the vehicle ISD suspension structure model based on fractional order ground shelf semi-active control;Step two: fractional order ground shelf semi-active control method analytical expression;Step three: the variable value and objective function are solved using optimization algorithm;Step four: dynamic performance simulation analysis.The beneficial effects of the present application are that the dynamic characteristics of complex systems can be more accurately described;Improve the road friendliness of vehicle.

Description

Technical Field

[0001] This invention relates to the field of vehicle suspension vibration isolation technology, and in particular to a semi-active vehicle ISD suspension system and a fractional-step floor control method. Background Technology

[0002] With the rapid development of my country's highway transportation and road transport industry, heavy vehicles, as the main equipment for highway passenger and freight transport, are seeing increasing production, sales, and ownership. However, with the trend of heavy-duty freight transport, the damage to roads caused by the large tire dynamic load of heavy vehicles during operation is becoming increasingly prominent. Therefore, comprehensively coordinating the driving smoothness and road friendliness of heavy vehicles has important theoretical significance and engineering application value. The fixed spring stiffness and damping coefficient of traditional passive suspension systems limit further improvements in the overall performance of the suspension system, leading to the development of semi-active and active suspension systems. Compared to active suspensions, semi-active suspensions consume less energy, have a simpler structure, lower cost, and higher reliability, while maintaining performance similar to active suspensions, making them the main development direction for intelligent suspensions in the near future. The technical challenge of semi-active suspension systems has always focused on the design of control strategies, the quality of which directly affects the vehicle's dynamic characteristics. The floor control algorithm is one of the earliest proposed semi-active suspension control methods. Due to its simplicity and ability to effectively improve road friendliness, it is currently the most researched and widely used control method. Furthermore, existing control algorithms, including ceiling, floor, mixed-floor control, and fuzzy PID control, are mostly based on integer orders, which cannot meet our current application needs.

[0003] In view of the above, it is necessary to improve the existing semi-active suspension control method so that it can meet the current needs of semi-active suspension control. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the above-mentioned control methods and provide a semi-active vehicle ISD suspension system and a fractional-step floor control method, which can more accurately describe the dynamic characteristics of complex systems and further improve the road friendliness of vehicles.

[0005] The technical solution of the present invention to achieve the above objectives is a semi-active vehicle ISD suspension system and a fractional-step floor control method, comprising the following steps:

[0006] Step 1: Construct a vehicle ISD suspension structure model based on fractional-step canopy semi-active control;

[0007] Step 2: Analytical expression of the fractional-order semi-active control method for greenhouses;

[0008] Step 3: Solve for the variable values ​​and objective function using optimization algorithms;

[0009] Step 4: Dynamic performance simulation analysis.

[0010] As a further supplement to this technical solution, step one utilizes parallel active actuators to achieve the purpose of semi-active control of the fractional-step ground shed.

[0011] As a further supplement to this technical solution, the dynamic equations of the quarter-suspension system in step one, which involves constructing the suspension structure model, are as follows:

[0012]

[0013] A further supplement to this technical solution is the semi-active control force F in the suspension. d Controlled by different floor covering components, where F d The expression can be written as:

[0014]

[0015] In the formula, F d It is a semi-active suspension control force, F c It is the fractional-step semi-active suspension damping force, F b It is the fractional-order semi-active suspension inertial force.

[0016] As a further supplement to this technical solution, the fractional calculus in step two is defined as any one of the definitions by Caputo, Riemann-Liouville, or Grünwald Letnikov, and a unified fractional calculus operator D is introduced from among them. α The damping force F applied to the semi-active suspension of the vehicle's ISD suspension system. c and the semi-active suspension inertial force F b List its parsing expression.

[0017] Fractional calculus, also known as non-integer calculus, has been defined differently by various mathematicians from their own perspectives. The rationality and scientific validity of these definitions have been tested in practice.

[0018]

[0019] In the formula, This is a fractional-order calculus operator, where t is the independent variable, t0 is the lower bound of the operator, and α is the calculus order, which is limited to real numbers. If α ≥ 0 and t0 = 0, the notation t0 can be omitted. If the independent variable is t and there are no other variables, t can also be omitted. If α > 0, A fractional-order differential operator represents the α-order derivative of a function with respect to the independent variable t. α = 0 represents the original signal, and if α < 0, it represents the -α-order integral.

[0020] In practical engineering applications, the most commonly used definitions of fractional calculus are the Riemann-Liouville (RL) definition, the Grünwald-Letnikov (GL) definition, and the Caputo fractional calculus definition.

[0021] The RL definition is:

[0022]

[0023] where: m - 1 < α < m, and Γ is the well-known Euler-Gamma function.

[0024] The GL definition is:

[0025]

[0026] The Caputo definition is:

[0027]

[0028] By introducing the fractional-order operation operator Differentiation and integration are formally unified. It can be seen that the RL definition is more suitable for mathematical derivation, the GL definition is more suitable for numerical calculation, and the Caputo definition is applicable to the study of non-zero initial values. Therefore, the GL definition is selected in this scheme.

[0029] According to the Grünwald-Letnikov (GL) definition, the analytical expression of the fractional-order ground-hitch semi-active control method is as follows.

[0030] The fractional-order ground-hitch semi-active suspension damping force F c Control expression:

[0031]

[0032] where D α is the fractional-order calculus operator, c min is the minimum damping coefficient that the semi-active damper can provide, c max is the maximum damping coefficient that the semi-active damper can provide

[0033] The fractional-order ground-hitch semi-active suspension inertial force F b Control expression:

[0034]

[0035] where D β is the fractional-order calculus operator, b min is the minimum inertia coefficient that the semi-active inertance can provide, b maxIt is the maximum inertial mass coefficient that a semi-active inertial container can provide.

[0036] The optimization variables are selected as follows: minimum damping coefficient c min Maximum damping coefficient c max Minimum inertia coefficient b min Maximum inertia coefficient b max Fractional order α, β, and basic damping c; during the optimization process, the range of variables is set as follows:

[0037]

[0038] As a further supplement to this technical solution, step three uses road friendliness in vehicle driving performance as an evaluation index. By studying the root mean square value of tire dynamic load under random road input conditions and using an improved ant colony algorithm, the optimal fractional-order semi-active suspension parameters can be obtained.

[0039] To further supplement this technical solution, the root mean square value of tire dynamic load under random road input conditions was studied, and the objective function of the optimization algorithm in step three is:

[0040]

[0041] The mathematical expression for J is as follows:

[0042]

[0043] In the formula, DTL is the tire dynamic load, and N is the number of samples.

[0044] To further supplement this technical solution, an improved ant colony optimization algorithm is used to solve for the optimization parameters. The initial population is generated randomly using real-valued encoding. In the ant colony algorithm, each ant independently selects a route based on pheromones and heuristic factors. The path node selection rules are as follows:

[0045]

[0046] Where q is a random number uniformly distributed in [0,1], argmax is a function that evaluates the parameters of the function, and τ ij (t), η ij (t) represents the pheromone and heuristic factor at node t, respectively, φ and κ are the weights of the pheromone and heuristic factor, the constant q0 is preset to 0.33, and S is a random node.

[0047] After each iteration of the algorithm, the node pheromones need to be updated to strengthen the path containing the optimal solution. The pheromone τ ij (t) The update rule is:

[0048] τij (t+1)=ρτ ij (t)+Δ

[0049] In the formula, ρ is the persistence coefficient and Δ is the node pheromone increment.

[0050] Let X b X represents the global optimal solution. b1 The optimal solution in this case is represented by the expression Δ:

[0051]

[0052] A heavy vehicle suspension model was built in Simulink, and a script was written in MATLAB for simulation. The number of ants was 32, the initial number of nodes was 50, the crossover probability was 0.7, the mutation probability was 0.02, the pheromone weight φ=4, the heuristic weight κ=6, the persistence coefficient ρ=0.5, and the number of iterations was 500.

[0053] During the optimization process, the constraints on the performance metrics are as follows:

[0054] J≤J pas

[0055] If the performance constraints are exceeded, the objective function will be penalized; the penalty rule adds a large number to the objective function, and the penalty value in this paper is set to 100.

[0056] As a further supplement to this technical solution, the specific implementation method of step four is as follows: determine the ISD suspension model and suspension parameters, and drive at a vehicle speed of 30 km / h over a road surface with an unevenness coefficient of 256 × 10⁻⁶. -6 m 3 ·cycle -1 The road surface was simulated for 10 seconds with a sampling interval of 0.02 seconds. A random road surface model determined by Gaussian white noise with a mean of zero was selected. The tire dynamic load suspension performance index of integer-order and fractional-order ground suspension elements under random road surface input conditions was calculated and compared with the corresponding index of passive suspension.

[0057] Its beneficial effects are as follows: 1. This invention combines fractional calculus theory and introduces a unified fractional calculus operator D. α The fractional calculus operator D was studied. α How to apply this to vehicle ISD suspension systems, the control methods of fractional-order semi-active elements are listed, which can more accurately describe the dynamic characteristics of complex systems;

[0058] 2. The vehicle ISD suspension optimization design method proposed in this invention utilizes the advantages of fast local convergence and high solution efficiency of the improved ant colony algorithm to obtain the optimal fractional-order semi-active suspension parameters. Simulation results show that, compared with integer-order floor elements (floor damping, floor inertia) and passive suspension, the vehicle ISD suspension based on fractional-order floor element semi-active control can further suppress tire dynamic load and improve vehicle road friendliness. Attached Figure Description

[0059] Figure 1 This is a flowchart of a semi-active vehicle ISD suspension system and a fractional-step floor control method.

[0060] Figure 2 This is a diagram of the ISD suspension dynamics model for a quarter-vehicle.

[0061] In the formula of this invention, m s It is the sprung mass, m u Here, k is the unsprung mass, k is the stiffness of the supporting spring, and c is the damping coefficient. t It is the equivalent spring stiffness of the tire, z r It is the vertical input displacement of the road surface roughness, z u It is the vertical displacement under the spring, z s It is the vertical displacement on the spring; Z s Z u and Z r They are z s z u and z r The Laplace transform of F; d It is a semi-active suspension control force, F c It is the fractional-step semi-active suspension damping force, F b It is the fractional-order semi-active suspension inertial force; D α It is a fractional calculus operator; α and β are fractional orders, c min It is the minimum damping coefficient that a semi-active damper can provide, c max b is the maximum damping coefficient that a semi-active damper can provide. min It is the minimum mass coefficient that a semi-active inertial container can provide, b max It is the maximum inertial mass coefficient that a semi-active inertial container can provide. Detailed Implementation

[0062] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0063] like Figure 1 As shown, a semi-active vehicle ISD suspension system and a fractional-step floor control method are characterized by the following main steps:

[0064] Step 1: Construct a vehicle ISD suspension structure model based on fractional-step canopy semi-active control;

[0065] Step 2: Analytical expression of the fractional-order semi-active control method for greenhouses;

[0066] Step 3: Solve for the variable values ​​and objective function using optimization algorithms;

[0067] Step 4: Dynamic performance simulation analysis;

[0068] Step one considers that even an ideal fractional-step ISD suspension is difficult to implement in actual vehicles. This paper equates it to something like... Figure 2 The model shown uses parallel active actuators to achieve the semi-active control of the fractional-step floor. The difference between the control strategy and the ideal fractional-step floor is that while the actuator generates floor damping force on the sprung mass, it also applies an additional force to the unsprung mass.

[0069] In step one, the fractional-step semi-active ISD suspension with attached Figure 2 Taking the example shown, the dynamic equations of the quarter suspension system are established as follows:

[0070]

[0071] In the formula F d The expression can be written as:

[0072]

[0073] In the formula, F d It is a semi-active suspension control force, F c It is the fractional-step semi-active suspension damping force, F b It is the fractional-order semi-active suspension inertial force.

[0074] Based on a mature vehicle model, the parameters of the quarter-vehicle ISD suspension system are shown in Table 1.

[0075] Table 1. Quarter-vehicle ISD suspension parameters

[0076]

[0077]

[0078] Semi-active control force F in suspension dIt is controlled by different floor elements, and there are corresponding control methods for floor damping and floor inertance. Fractional calculus has a wide range of definitions. In this paper, three main definitions are applied: Riemann-Liouville, Grünwald Letnikov, and Caputo, and a unified fractional calculus operator D is introduced α , based on the theory of fractional calculus, study the fractional calculus operator D α How to be applied to the semi-active suspension damping force F in the vehicle ISD suspension system c And the semi-active suspension inertial force F b , and list its analytical expression

[0079] Fractional calculus is non-integer order calculus. Different mathematicians have given different definitions of fractional calculus from their respective perspectives, and the rationality and scientificity of their definitions have been verified in practice:

[0080]

[0081] In the formula, is the fractional calculus operator, where t is the independent variable, t0 is the lower limit of the operation operator, α is the calculus order, which is limited to real numbers here. If α≥0 and t0 = 0, the notation t0 can be omitted. If the independent variable is t and there are no other variables, t can also be omitted. If α>0, The fractional differential operator represents the α-order derivative of the function with respect to the independent variable t. α = 0 represents the original signal. If α<0, it represents the -α-order integral

[0082] In practical engineering applications, the most commonly used fractional calculus definitions are the Riemann-Liouville (RL) definition, the Grünwald-Letnikov (GL) definition, and the Caputo fractional calculus definition

[0083] The RL definition is:

[0084]

[0085] In the formula: m - 1 < α < m, Γ is the famous Euler-Gamma function

[0086] The GL definition is:

[0087]

[0088] The Caputo definition is:

[0089]

[0090] By introducing the fractional operation operator Differentiation and integration are formally unified. It can be seen that the RL definition is more suitable for mathematical derivation, the GL definition is more suitable for numerical computation, and the Caputo definition is suitable for the study of non-zero initial values. Therefore, this paper chooses the GL definition.

[0091] According to Grünwald-Letnikov (GL) definition, the analytical expression of the fractional-order semi-active control method for ground cover is as follows.

[0092] Fractional-step semi-active suspension damping force F c Control Expression:

[0093]

[0094] In the formula, D α It is a fractional calculus operator, c min It is the minimum damping coefficient that a semi-active damper can provide, c max It is the maximum damping coefficient that a semi-active damper can provide;

[0095] Fractional-step semi-active suspension inertial force F b Control Expression:

[0096]

[0097] In the formula, D β It is a fractional calculus operator, b min It is the minimum mass coefficient that a semi-active inertial container can provide, b max It is the maximum inertial mass coefficient that a semi-active inertial container can provide.

[0098] In determining the ISD suspension parameters, on the one hand, the mechanical network based on the "inertia container-spring-damper" structure has a large number of components, making it a multi-parameter optimization problem; on the other hand, it is necessary to ensure that the road friendliness of the vehicle suspension is optimal. To solve these problems, road friendliness in vehicle driving performance is used as the evaluation index. By studying the root mean square value of tire dynamic load under random road input conditions, and utilizing the fast local convergence speed and high solution efficiency of the improved ant colony algorithm, the optimal fractional-order semi-active suspension parameters can be obtained. Step three studies the dynamic performance index, including the root mean square value of tire dynamic load under random road input conditions. The objective function of the optimization algorithm is:

[0099]

[0100] In the formula, J is the root mean square value of the tire dynamic load of the fractional-order semi-active ISD suspension to be optimized. pas It is the root mean square value of the dynamic load on the tires of the passive suspension, which is 580N.

[0101] Its mathematical expression is as follows:

[0102]

[0103] In the formula, DTL is the tire dynamic load, and N is the sample size. The optimization variables are selected as follows: minimum damping coefficient c min Maximum damping coefficient c max Minimum inertia coefficient b min Maximum inertia coefficient b max The fractional order α, β, and basic damping c are used. During optimization, the ranges of the variables are set as follows:

[0104]

[0105] This paper employs an improved ant colony algorithm to further supplement the existing technical solution. The improved algorithm is used to solve for the optimization parameters. The initial population is generated randomly using real-valued encoding. In the ant colony algorithm, each ant independently chooses its route based on pheromones and heuristic factors. The path node selection rules are as follows:

[0106]

[0107] Where q is a random number uniformly distributed in [0,1], argmax is a function that evaluates the parameters of the function, and τ ij (t), η ij (t) represents the pheromone and heuristic factor at node t, respectively, φ and κ are the weights of the pheromone and heuristic factor, the constant q0 is preset to 0.33, and S is a random node.

[0108] After each iteration of the algorithm, the node pheromones need to be updated to strengthen the path containing the optimal solution. The pheromone τ ij (t) The update rule is:

[0109] τ ij (t+1)=ρτ ij (t)+Δ

[0110] In the formula, ρ is the persistence coefficient and Δ is the node pheromone increment.

[0111] Let X b X represents the global optimal solution. b1 The optimal solution in this case is represented by the expression Δ:

[0112]

[0113] A heavy vehicle suspension model was built in Simulink, and a script was written in MATLAB for simulation. The number of ants was 32, the initial number of nodes was 50, the crossover probability was 0.7, the mutation probability was 0.02, the pheromone weight φ=4, the heuristic weight κ=6, the persistence coefficient ρ=0.5, and the number of iterations was 500.

[0114] During the optimization process, the constraints on the performance metrics are as follows:

[0115] J≤J pas

[0116] If performance constraints are exceeded, the objective function will be penalized. The penalty rule adds a large number to the objective function. In this paper, the penalty value is set to 100.

[0117] After repeated optimization, the final optimized variable values ​​are shown in Table 2.

[0118] Table 2 Vehicle ISD Suspension Parameters After Model Parameter Optimization

[0119]

[0120] Step four, dynamic performance simulation analysis, is implemented as follows:

[0121] according to Figure 2 The established ISD suspension model, using the suspension parameters in Table 1, travels at a speed of 30 km / h over a road surface with an unevenness coefficient of 256 × 10⁻⁶. -6 m 3 ·cycle -1 The road surface was simulated for 10 seconds with a sampling interval of 0.02 seconds. A random road surface model determined by Gaussian white noise with a mean of zero was selected. The tire dynamic load suspension performance index of integer-order and fractional-order ground suspension elements under random road surface input conditions was calculated and compared with the corresponding index of passive suspension. The results are shown in Table 3.

[0122] Table 3 Suspension performance indicators under random road surface input

[0123]

[0124]

[0125] Simulations on random road surfaces show that fractional-order floor elements, including fractional-order damping and inertia capacitance, are generally superior to integer-order floor elements and passive suspensions, further improving the wheel restraint performance of the vehicle's ISD suspension. This also demonstrates that the fractional-order floor control method can more accurately describe the dynamic characteristics of complex systems, further enhancing the vehicle's road friendliness and exhibiting superior performance.

[0126] The embodiments described are preferred embodiments of the present invention, but the present invention is not limited to these embodiments. Modifications, variations and substitutions made by those skilled in the art without departing from the essential content of the present invention are all within the protection scope of the present invention.

Claims

1. A semi-active vehicle ISD suspension system and a fractional-step floor control method, characterized in that, The work includes the following steps: Step 1: Construct a vehicle ISD suspension structure model based on fractional-step canopy semi-active control; Step 2: Analytical expression of the fractional-order semi-active control method for greenhouses; Step 3: Solve for the variable values ​​and objective function using optimization algorithms; Step 4: Dynamic performance simulation analysis; Step one utilizes parallel active actuators to achieve the purpose of semi-active control of the fractional-stage ground shed. The dynamic equations of the quarter-suspension system, constructed in step one, are as follows: ； In the formula: m s It is the sprung mass. m u It is the unsprung mass. k It is the stiffness of the supporting spring. c It is the damping coefficient. k t It is the equivalent spring stiffness of the tire. z r It is the vertical input displacement of the road surface roughness. z u It is the vertical displacement under the spring. z s It is the vertical displacement on the spring. F d It is a semi-active suspension control force; Semi-active control force in suspension F d Controlled by different floor covering components, in the formula F d The expression can be written as: ； In the formula, F d It is a semi-active suspension control force. F c It is the fractional-step semi-active suspension damping force. F b It is the fractional-order semi-active suspension inertial force; The fractional calculus in step two is defined as any one of the definitions by Caputo, Riemann-Liouville, or Grünwald-Letnikov, and a unified fractional calculus operator is introduced from among them. D α Semi-active suspension damping force applied in vehicle ISD suspension systems F c and the inertial force of the semi-active suspension F b List its parsing expression; The unified fractional differential and integral operator is: ； In the formula, It is a fractional calculus operator, where, t As the independent variable, t 0 It is the lower bound of the operator. α For the order of the calculus, here we are limited to real numbers; if α ≥ 0 and t 0 = 0, then the notation can be omitted. t 0 If the independent variable t And if there are no other variables, then t It can also be omitted; if α > 0, Fractional differential operators represent functions with respect to independent variables t of α First derivative, α = 0 represents the original signal, if α < 0 indicates - α Order integral; Using the definition by Grünwald Letnikov, according to which, when a function is given f(t) of α The first derivative is defined as: ； Based on the above definition, the analytical expression for the fractional-order semi-active control method for ground cover is as follows: Fractional-step semi-active suspension damping force F c Control Expression: ； In the formula, D α It is a fractional calculus operator. c min It is the minimum damping coefficient that a semi-active damper can provide. c max It is the maximum damping coefficient that a semi-active damper can provide; Fractional-step semi-active suspension inertial force F b Control Expression: ； In the formula, D β It is a fractional calculus operator. b min It is the minimum inertial mass coefficient that a semi-active inertial container can provide. b max It is the maximum inertial mass coefficient that a semi-active inertial container can provide; In the optimization process, the optimization variables are selected as follows: minimum damping coefficient. c min Maximum damping coefficient c max Minimum inertia coefficient b min Maximum inertia coefficient b max Fractional order α , β and base value damping coefficient c The range of variables is set as follows: ； Step three uses road friendliness in vehicle driving performance as an evaluation index. By studying the root mean square value of tire dynamic load under random road input conditions and using an improved ant colony algorithm, the optimal fractional-order semi-active suspension parameters can be obtained.

2. The semi-active vehicle ISD suspension system and fractional-step floor control method according to claim 1, characterized in that, The study investigated dynamic performance indicators, including the root mean square value of tire dynamic load under random road input conditions. The objective function of the optimization algorithm in step three is: ； In the formula, J It is based on the root mean square value of the tire dynamic load of the fractional-order semi-active ISD suspension to be optimized. J pas It is the root mean square value of the dynamic load on the tires of the passive suspension, which is 580 N; in J The mathematical expression is as follows: ； In the formula, DTL It is the tire dynamic load. N It refers to the number of samples.

3. The semi-active vehicle ISD suspension system and fractional-step floor control method according to claim 2, characterized in that, An improved ant colony optimization algorithm is used to solve for the optimization parameters. The initial population is generated by random numbers using real-valued encoding. In the ant colony optimization algorithm, each ant independently chooses a route based on pheromones and heuristic factors. The path node selection rules are as follows: ； in, q Let argmax be a random number uniformly distributed in the range [0,1], and let argmax be a function that evaluates the parameters of the function. τ ij ( t ), η ij ( t ) are respectively t Pheromones and heuristics at specific time points , The weights of pheromones and heuristic factors are pre-set by constants. q 0 is 0.

33. S For random nodes; After each iteration of the algorithm, the node pheromones need to be updated to enhance the path containing the optimal solution. τ ij ( t The update rules are as follows: ； In the formula, ρ This is the durability coefficient. For node pheromone increment; set up X b This represents the globally optimal solution. X b1 This represents the optimal solution in this case. The expression is: ； During the optimization process, the constraints on the performance metrics are as follows: ； If the performance constraints are exceeded, the objective function will be penalized; the penalty rule adds a large number to the objective function, and the penalty value in this paper is set to 100.

4. The semi-active vehicle ISD suspension system and fractional-step floor control method according to claim 1, characterized in that, The specific implementation method of step four is as follows: determine the ISD suspension model and suspension parameters, and drive at a speed of 30km / h over a road surface with an unevenness coefficient of 256×10. -6 m 3 ·cycle -1 The road surface was simulated for 10 seconds with a sampling interval of 0.02 seconds. A random road surface model determined by Gaussian white noise with a mean of zero was selected. The tire dynamic load suspension performance index of integer-order and fractional-order ground suspension elements under random road surface input conditions was calculated and compared with the corresponding index of passive suspension.

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