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

Abstract

The application discloses a semi-active vehicle ISD suspension system and a fractional order control method, and comprises the following working steps: step one, constructing a vehicle ISD suspension structure model based on fractional order semi-active control; step two, fractional order semi-active control method analytical expression; step three, solving variable values and objective functions by using an optimization algorithm; and step four, dynamic performance simulation analysis.The application has the beneficial effects that the dynamic characteristics of a complex system can be more accurately described, and the vehicle ride comfort is improved.

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 fractional-order control method. Background Technology

[0002] Semi-active suspensions, due to their simple structure and ease of control, achieve an optimal trade-off between manufacturing cost, equipment complexity, energy consumption, and suspension performance, and have been widely researched and applied in recent years. However, because semi-active suspensions are based on a fixed suspension structure, it is difficult to guarantee optimal performance under different road conditions and vehicle operating conditions. The technical challenges of semi-active suspension systems have always focused on the design of control strategies, the quality of which directly affects the vehicle's dynamic characteristics. The roof control algorithm is one of the earliest proposed semi-active suspension control methods. Due to its simplicity and ability to effectively improve vehicle ride comfort, it is currently the most researched and widely used control method. Whether it's damping or stiffness-adjustable semi-active suspension, like traditional passive suspensions, they are based on classical vibration isolation theory and built upon a "spring-damping" suspension structure system, which limits further improvements in suspension performance. Furthermore, the control algorithms studied, including roof, floor, mixed roof control, and fuzzy PID control, are mostly based on integer orders, which cannot meet our current usage 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 fractional-order control method, which can more accurately describe the dynamic characteristics of complex systems and further improve the ride comfort 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-order control method, comprising the following steps:

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

[0007] Step 2: Analytical representation of fractional semi-active control method;

[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 fractional-order semi-active ceiling control.

[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 ceiling 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-order semi-active suspension damping force, F b It is a 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 semi-active suspension damping force F applied in the vehicle 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 definition.

[0021] RL is defined as:

[0022]

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

[0024] GL is defined as:

[0025]

[0026] Caputo is defined as:

[0027]

[0028] By introducing fractional operators 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 studying non-zero initial values. Therefore, this scheme chooses the GL definition.

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

[0030] Fractional semi-active suspension damping force F c Control Expression:

[0031]

[0032] 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.

[0033] Fractional order semi-active suspension inertial force F b Control Expression:

[0034]

[0035] 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.

[0036] As a further supplement to this technical solution, step three uses ride comfort as an evaluation index in vehicle driving performance. By studying the root mean square value of vehicle acceleration under random road input conditions, the optimal fractional-order semi-active suspension parameters can be obtained using the particle swarm optimization algorithm.

[0037] To further supplement this technical solution, the root mean square value of vehicle acceleration under random road input conditions was studied as a dynamic performance index. The objective function of the optimization algorithm in step three is:

[0038]

[0039] The mathematical expression for J is as follows:

[0040]

[0041] In the formula, BA is the vehicle acceleration, 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 Fractional order α, β, and basic damping c; during the optimization process, the range of variables is set as follows:

[0042]

[0043] To further supplement this technical solution, a particle swarm optimization algorithm is used to solve for the optimization parameters. The relationship between particle position and velocity is shown below:

[0044]

[0045] In the formula, ω represents the inertia weight, which is generally taken as [0.8, 1.2]; c1 and c2 represent the learning factor or acceleration constant; r1 and r2 represent random numbers in [0, 1]; k represents the number of iterations; represents the individual extreme value; represents the population extreme value; V k V represents the particle velocity at iteration number k; k+1 X represents the particle's velocity at iteration number k+1; k Indicates the position of the particle when the number of iterations is k; x k+1 This represents the particle's position at iteration number k+1; the performance index constraints during optimization are as follows:

[0046] J≤J pas

[0047] 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.

[0048] 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 simulation duration was 10s, the sampling interval was 0.02s, and a random road surface model determined by Gaussian white noise with zero mean was selected. The vehicle acceleration suspension performance index of integer order ceiling element and fractional order ceiling element under random road surface input conditions was calculated and compared with the corresponding index of passive suspension.

[0049] 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 method of fractional-order ceiling semi-active elements is listed, which can more accurately describe the dynamic characteristics of complex systems;

[0050] 2. The vehicle ISD suspension optimization design method proposed in this invention utilizes the characteristics of fast local convergence speed and high solution efficiency of the particle swarm optimization algorithm to obtain the optimal fractional-order semi-active suspension parameters. Simulation results show that, compared with integer-order ceiling elements (ceiling damping, ceiling inertia) and passive suspension, the vehicle ISD suspension based on fractional-order ceiling element semi-active control can further suppress vehicle acceleration and improve vehicle ride comfort. Attached Figure Description

[0051] Figure 1 This is a flowchart of a semi-active vehicle ISD suspension system and a fractional-order control method.

[0052] Figure 2 This is a diagram of the ISD suspension dynamics model for a quarter-vehicle.

[0053] 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 rThe Laplace transform of F; d It is a semi-active suspension control force, F c It is the fractional-order 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, where 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

[0054] 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.

[0055] like Figure 1 As shown, a semi-active vehicle ISD suspension system and fractional-order control method are characterized by the following main steps:

[0056] Step 1: Construct a vehicle ISD suspension structure model based on fractional-order semi-active control;

[0057] Step 2: Analytical representation of fractional semi-active control method;

[0058] Step 3: Solve for the variable values ​​and objective function using optimization algorithms;

[0059] Step 4: Dynamic performance simulation analysis;

[0060] Step one of the above considers that even an ideal fractional-order roof 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-order ceiling. The difference between the control strategy and the ideal fractional-order ceiling is that while the actuator generates ceiling damping force on the sprung mass, it also applies an additional force to the unsprung mass.

[0061] In step one, the fractional-order ceiling semi-active control ISD suspension is attached... Figure 2 Taking the example shown, the dynamic equations of the quarter suspension system are established as follows:

[0062]

[0063] In the formula F d The expression can be written as:

[0064]

[0065] In the formula, F d It is a semi-active suspension control force, F c It is the fractional-order semi-active suspension damping force, F b It is a fractional-order semi-active suspension inertial force.

[0066] Based on a mature vehicle model, the parameters of the quarter-vehicle ISD suspension system are shown in Table 1.

[0067] Table 1. Quarter-vehicle ISD suspension parameters

[0068]

[0069]

[0070] Semi-active control force F in suspension d Controlled by different ceiling elements, ceiling damping and ceiling inertia each have their corresponding control methods. Fractional calculus has a wide range of definitions; this paper applies three main definitions: Riemann-Liouville, Grünwald Letnikov, and Caputo, and introduces a unified fractional calculus operator D. α Based on the theory of fractional calculus, this study investigates the fractional calculus operator D. α How is the semi-active suspension damping force F applied to the ISD suspension system of a vehicle? c and the semi-active suspension inertial force F b List its parsing expression.

[0071] 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.

[0072]

[0073] 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.

[0074] 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 definition.

[0075] RL is defined as:

[0076]

[0077] In the formula: m-1<α<m, Γ is the well-known Euler-Gamma function.

[0078] GL is defined as:

[0079]

[0080] Caputo is defined as:

[0081]

[0082] By introducing fractional operators 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.

[0083] According to the Grünwald-Letnikov (GL) definition, the analytical expression for the fractional-order semi-active control method is as follows.

[0084] Semi-active suspension damping force F c Control Expression:

[0085]

[0086] 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.

[0087] Fractional order semi-active suspension inertial force F b Control Expression:

[0088]

[0089] 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.

[0090] 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 vehicle suspension achieves optimal ride comfort. To solve these problems, ride comfort is used as the evaluation index for vehicle driving performance. By studying the root mean square value of vehicle acceleration under random road input conditions, and utilizing the fast local convergence speed and high solution efficiency of the particle swarm optimization 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 vehicle acceleration under random road input conditions. The objective function of the optimization algorithm is:

[0091]

[0092] In the formula, J is the root mean square value of the vehicle acceleration of the fractional-order semi-active ISD suspension to be optimized. pas It is the root mean square value of the vehicle acceleration of the passive suspension, which is 0.78 m / s². -2

[0093] Its mathematical expression is as follows:

[0094]

[0095] In the formula, BA is the vehicle acceleration, 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 the basic damping coefficient c are used. During optimization, the ranges of the variables are set as follows:

[0096]

[0097] This paper adopts the Particle Swarm Optimization (PSO) algorithm, which boasts advantages such as simple principle, ease of implementation, fast convergence speed, and strong versatility. Its significant advancements make it easier to find the global optimum and avoid getting trapped in local optima. Therefore, the PSO algorithm is used to solve for the optimization parameters. The update rules for particle position and velocity are as follows:

[0098]

[0099] In the formula, ω represents the inertia weight, which is generally taken as [0.8, 1.2]; c1 and c2 represent the learning factor or acceleration constant; r1 and r2 represent random numbers in [0, 1]; k represents the number of iterations; represents the individual extreme value; represents the population extreme value; V k V represents the particle velocity at iteration number k; k+1X represents the particle's velocity at iteration number k+1; k X represents the position of the particle at iteration number k; k+1 This represents the particle's position at iteration number k+1. During the optimization process, the performance metrics are constrained as follows:

[0100] J≤J pas

[0101] 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.

[0102] After repeated optimization, the final optimized variable values ​​are shown in Table 2.

[0103] Table 2 Vehicle ISD Suspension Parameters After Model Parameter Optimization

[0104]

[0105]

[0106] Step four, dynamic performance simulation analysis, is implemented as follows:

[0107] 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 vehicle acceleration suspension performance index of integer-order and fractional-order ceiling 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.

[0108] Table 3 Suspension performance indicators under random road surface input

[0109]

[0110] Simulations on random road surfaces demonstrate that fractional-order ceiling elements, including fractional-order damping and inertia capacitance, outperform integer-order ceiling elements and passive suspensions overall, further improving the vehicle's ISD suspension's body vibration suppression performance. This also proves that fractional-order control methods can more accurately describe the dynamic characteristics of complex systems, further enhancing vehicle ride comfort and exhibiting superior performance.

[0111] 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 fractional-order control method, characterized in that, The work includes the following steps: Step 1: Construct a vehicle ISD suspension structure model based on fractional-order semi-active control; Step 2: Analytical representation of fractional semi-active control method; 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 fractional-order semi-active control of the ceiling. 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 suspension control force F d Controlled by different ceiling components, in the formula F d The expression can be written as: ； 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 calculus 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 calculus, here 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 semi-active control method is as follows: Fractional 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 order 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; During the optimization process, the range of variables is set as follows: ； In the formula, α , β For fractional order, c The base value damping coefficient; Step three uses ride comfort as an evaluation index in vehicle driving performance. By studying the root mean square value of vehicle acceleration under random road input conditions, and using the particle swarm optimization algorithm, the optimal fractional-order semi-active suspension parameters can be obtained.

2. The semi-active vehicle ISD suspension system and fractional-order control method according to claim 1, characterized in that, The dynamic performance index, including the root mean square value of vehicle acceleration under random road input conditions, was studied. 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 vehicle acceleration of the fractional-order semi-active ISD suspension to be optimized. J pas It is the root mean square value of the vehicle body acceleration of the passive suspension, which is 0.78 m·s⁻¹. -2 ; in J The mathematical expression is as follows: ； In the formula, BA It's the vehicle's acceleration. N It refers to the number of samples.

3. The semi-active vehicle ISD suspension system and fractional-order control method according to claim 2, characterized in that, The optimization parameters are solved using the particle swarm optimization algorithm. The relationship between particle position and velocity is shown below: ； In the formula, ω This represents the inertia weight, typically set to [0.8, 1.2]. c 1 and c 2 represents the learning factor or acceleration constant; r 1 and r 2 represents a random number within the range [0, 1]. k Indicates the number of iterations; P id Indicates an individual extreme value; P gd Indicates the extreme value of the group; V k Indicates the number of iterations. k The velocity of the particle at that time; V k+1 Indicates the number of iterations. k The particle's velocity at +1; X k Indicates the number of iterations. k The position of the particle at that time; X k+1 Indicates the number of iterations. k The position of the particle at +1 is determined by the following constraints on the performance metrics during the optimization process: ； 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-order 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, drive at a speed of 30km / h, and drive over a road surface with an unevenness coefficient of 256×10. -6 m 3 ·cycle -1 The simulation duration was 10s, the sampling interval was 0.02s, and a random road surface model determined by Gaussian white noise with zero mean was selected. The vehicle acceleration suspension performance index of integer order ceiling element and fractional order ceiling element under random road surface input conditions was calculated and compared with the corresponding index of passive suspension.

Images