An active suspension low-computing-power preview control method considering actuator time delay and vehicle speed change

Abstract

The application belongs to the technical field of automatic driving test, and in particular to a low-computing-power preview control method for active suspension considering actuator time delay and vehicle speed change. The method comprises the following steps: step one, establishing a quarter vehicle active suspension model considering time delay and an active suspension continuous time state space equation and performing discretization; step two, establishing a road model capable of changing with vehicle speed and obtaining spatial domain road elevation information within a preview range by using a perception sensor, and then converting the spatial domain road elevation information into time domain road elevation information through time domain conversion; step three, designing an active suspension preview control method based on the discretized state space equation of the active suspension and the time domain road elevation information. The application can effectively reduce the computing power of the control method while ensuring the control performance of the active suspension.

Description

Technical Field

[0001] The present invention belongs to the technical field of autonomous driving testing, and specifically provides a low-computing-power preview control method for an active suspension that takes actuator time lag and vehicle speed changes into consideration. Background Art

[0002] The suspension system is a crucial component of the vehicle chassis and a key element in ensuring both ride comfort and road-holding performance. For vehicles equipped with traditional passive and semi-active suspensions, it's often difficult to simultaneously meet the demands for ride comfort and road-holding performance. Therefore, effectively balancing these two performance requirements on roads with varying degrees of bumpiness has become a hot topic of research. Compared to passive and semi-active suspensions, which lack an external power source, active suspensions offer actuators with fast response and high actuation force, and are considered an ideal solution to this performance trade-off in suspension systems.

[0003] At the same time, high-performance perception sensors such as lidar, millimeter-wave radar, and binocular cameras have improved the accuracy of road profile recognition. Active suspensions can use the elevation information of the road ahead, detected in advance by perception sensors, to perform preview control, ensuring optimal ride comfort and road-holding performance as the vehicle traverses the road ahead. Therefore, active suspension preview control has garnered extensive attention from numerous researchers. Model predictive control, due to its excellent control performance and ability to handle multiple constraints, is considered one of the optimal solutions for active suspension preview control. However, current research still faces several limitations. First, current control methods often ignore the nonlinearity caused by actuator lag in the active suspension when building the suspension model, resulting in an inability to guarantee the vehicle's vertical performance during actual control. Second, current preview control uses road elevation information within a fixed timeframe. As vehicle speed changes, the distance of the road elevation information required for control also changes. However, in practice, perception sensors use a fixed preview distance, meaning that current preview methods are only applicable to active suspension control at a constant vehicle speed and cannot adapt to the speed fluctuations experienced during actual driving. Finally, although traditional model predictive control methods can greatly improve the performance of active suspension, the use of quadratic programming to solve the optimal control sequence will significantly increase computing power, resulting in longer calculation time and difficulty in actual application on vehicles. Summary of the Invention

[0004] To solve the above problems, the present invention provides a low-computing-power preview control method for active suspension that takes into account actuator lag and vehicle speed changes, which can effectively reduce the computing power of the control method while ensuring the control performance of the active suspension.

[0005] The technical solution of the present invention is described as follows in conjunction with the accompanying drawings:

[0006] A low-computation preview control method for an active suspension that considers actuator time lag and vehicle speed variation includes the following steps:

[0007] Step 1: Establish a quarter-vehicle active suspension model and active suspension continuous-time state space equations considering time delay and discretize them;

[0008] Step 2: Establish a road surface model that can change with vehicle speed and use perception sensors to obtain spatial domain road elevation information within the preview range, and then convert the spatial domain road elevation information into temporal domain road elevation information through time domain conversion;

[0009] Step 3: Based on the discretized state space equation of the active suspension and the time domain road elevation information, the active suspension preview control method is designed.

[0010] Furthermore, the specific method of step one is as follows:

[0011] 11) A quarter-vehicle active suspension model with time lag is established, which includes the sprung mass, active suspension, unsprung mass, and wheels. The controller for the active suspension outputs an ideal control force that, after a time lag, becomes the actual control force output to the suspension system.

[0012] 12) Based on the quarter-car active suspension model considering time lag and the principles of vehicle dynamics, the dynamic equations of the quarter-car active suspension considering time lag are obtained as follows:

[0013]

[0014] Where m s is the sprung mass; m u is the unsprung mass; k s is the spring stiffness; c s is the suspension damping coefficient; F r is the actual force of the active suspension; F is the ideal force of the active suspension; c t is the vertical equivalent damping of the tire; k t is the vertical equivalent stiffness of the tire; z s is the vertical displacement of the sprung mass; z u is the vertical displacement of the unsprung mass; z r is the road height; τ is the time constant of the actuator's time lag characteristic;

[0015] 13) Select the sprung mass displacement z s (t), unsprung mass displacement z u (t), sprung mass displacement velocity Unsprung mass displacement velocity and the actual force F r(t) is the state variable; the sprung mass acceleration is selected Suspension travel z u (t)-z s (t) and tire dynamic deflection z r (t)-z u (t) is the output variable of the system; then the ideal force F(t) and the road height z are selected respectively. r are the input variables and disturbances of the system; the quarter-vehicle active suspension dynamics equation (1) is rewritten as the system state space equation under continuous time, as shown below:

[0016]

[0017] in,

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] Where x(t) is the state variable; is the derivative of the state variable; y(t) is the output variable; u(t) is the input variable; ω(t) is the disturbance variable; A is the suspension system matrix; B is the suspension input matrix; C is the suspension output matrix; D is the direct transfer matrix; E is the state disturbance matrix; L is the output disturbance matrix; z s (t) is the displacement of the sprung mass; z u (t) is the unsprung mass displacement; is the sprung mass displacement velocity; is the displacement velocity of the unsprung mass; F r (t) Actual power; r is the road surface height; m s is the sprung mass; m u is the unsprung mass; k s is the spring stiffness; c s is the suspension damping coefficient; c t is the vertical equivalent damping of the tire; k t is the vertical equivalent stiffness of the tire;

[0024] 14) Discretize the system state space equation under continuous time. Use the zero-order hold discretization method to discretize the continuous time matrix in formula (2) and obtain the discretized system state space equation as shown below:

[0025]

[0026]

[0027] Where A is the suspension system matrix; B is the suspension input matrix; E is the state interference matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; T s is the sampling period of the active suspension control system; is the discrete suspension system matrix; Input matrix for discrete suspension; is the discrete state interference matrix; x(k) is the state variable of the kth period; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; ω(k) is the interference variable of the kth period.

[0028] Furthermore, the specific method of step 2 is as follows:

[0029] 21) The road surface in the preview area is evenly divided into multiple grids of length Δl by the perception sensor, so the number of grids in the preview range in the spatial domain is obtained as:

[0030]

[0031] Where N is the number of grids in the preview range in the spatial domain; L p is the length of the preview area; Δl is the grid length;

[0032] 22) The spatial domain road elevation information is stored in the road elevation information set Ψ(t), which is expressed as:

[0033] Ψ(t)={h1(t),h2(t),...,h N (t)} (6)

[0034] Where Ψ(t) is the spatial domain road elevation information set; h i (t) is the height corresponding to the i-th grid point at time t;

[0035] 23) Set the sampling period of active suspension to T s , then the distance traveled by the vehicle in each sampling period and the number of grids passed in p sampling periods are:

[0036] l s =v×T s (7)

[0037]

[0038] Where v is the vehicle speed; T s is the sampling period of the active suspension; n(k,v) is the number of grids that the vehicle passes through at speed v within p sampling periods; l s is the distance traveled by the vehicle in each sampling period; Δl is the grid length;

[0039] 24) If the vehicle is in kT s The road surface height at h i (kT s ), then when the time is (k+1)T s When the vehicle is on the road, the height is h i+n(1,v) (kT s ); Get the vehicle in kT s The road elevation information set Γ(k,v) in the time domain when the speed is v is:

[0040]

[0041] in,

[0042] H i (k,v)=h n(i-1,v) (kT s ),i=1,2,...,N tp (v) (10)

[0043]

[0044] Where v is the vehicle speed; T s is the sampling period of the active suspension control system; Γ(k,v) is the road elevation information set in the time domain when the vehicle travels at a speed of v for k sampling periods; H i (k,v) is kT s The height of the i-th sampling point at time; N tp (v) is the number of sampling points in the time domain when the vehicle speed is v; n(p,v) is the number of grids that the vehicle passes through at speed v within p sampling times; h i (kT s ) is the vehicle in kT s The road surface height at the i-th grid point obtained by the sensing sensor; L p is the length of the preview area.

[0045] Furthermore, the specific method of step three is as follows:

[0046] 31) Design the cost function for the active suspension system optimization problem:

[0047]

[0048] Where J is the cost function; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; Q is N tp ×N tp The positive definite output weight matrix of N tp ×N tp The positive definite input weight matrix N tp is the number of sampling points;

[0049] The constraints are expressed as follows:

[0050]

[0051] Where u(k) is the input variable of the kth cycle; x1(k) is the displacement of the sprung mass of the kth cycle; x2(k) is the displacement of the unsprung mass of the kth cycle; f max is the maximum force that the active suspension can generate; max is the maximum compression of the active suspension;

[0052] 32) The Laguerre function is used to fit the optimal actuating force, and combined with the time domain road elevation information, a discrete model predictive control method that adapts to speed is designed, as follows:

[0053] 321) Read the vehicle state x(k) and speed v in the kth cycle;

[0054] 322) Calculate the number of sampling points N tp and disturbance variables ω(k);

[0055] 323) Using Laguerre function to fit the optimal input sequence of active suspension;

[0056] 324) Input the fitted system into the sequence u(k) with the previous control step length N c The value is used as the optimal control value of the actual suspension U opt Output;

[0057] 325) Repeat the whole process in the k+1th cycle.

[0058] Furthermore, the specific method of step 323) is as follows:

[0059] 3231) The active suspension input sequence is expressed using a discrete Laguerre function. The discrete form of the Laguerre function is shown in the following formula:

[0060]

[0061] Where, ξ i(z) is a discrete Laguerre polynomial; 0 < a < 1 is a pole of the discrete polynomial; N is the number of terms of the discrete Laguerre function;

[0062] For simplifying the analysis of the active suspension discrete system, ξ i (z) is expressed in the following form by z-transforming the discrete Laguerre function:

[0063] L(k) = [l1(k), l2(k),..., l N (k)] T (15)

[0064] In the formula, l i (k) is the z-transform of the discrete Laguerre polynomial ξ i (z); L(k) is the designed active suspension Laguerre function;

[0065] In combination with formula (14) and formula (15), the active suspension Laguerre function is recursively expressed as follows:

[0066] L(k+1) = A l L(k) (16)

[0067]

[0068]

[0069] In the formula, L(k) is the active suspension Laguerre function; A l is the recursive matrix; a is the pole of the discrete polynomial;

[0070] The input quantity u(k+i) of the active suspension at the k+i time is described by the discrete Laguerre function:

[0071]

[0072] In the formula, u(k) is the input variable of the kth period; η = [c1, c2,..., c N ] T is the Laguerre fitting coefficient; l j (i) is the discrete Laguerre polynomial; L(i) is the active suspension Laguerre function; N is the number of grids in the preview range in the spatial domain;

[0073] 3232) The active suspension discrete state space equation and the cost function are rewritten by using the input quantity u(k) described by the discrete Laguerre function; the active suspension system input quantity u(k) is brought into the active suspension discrete state space equation, i.e. formula (3), and the following iterative derivation is performed in combination with formula (16) to obtain the system state quantity and the output quantity represented by the Laguerre function:

[0074]

[0075]

[0076] Where, is the discrete suspension system matrix; Input matrix for discrete suspension; is the discrete state interference matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; x(k) is the state variable of the kth period; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; ω(k) is the interference variable of the kth period; L(k) is the active suspension Laguerre function of the kth period; η is the Laguerre fitting coefficient;

[0077] The cost function (12) is rewritten as the Laguerre function:

[0078]

[0079]

[0080] Where, is the discrete suspension system matrix; is the discrete suspension input matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; x(k) is the state variable of the kth period; ω(k) is the interference variable of the kth period; L(k) is the active suspension Laguerre function of the kth period; η is the Laguerre fitting coefficient; Q is N tp ×N tp The positive definite output weight matrix of N tp ×N tp The positive definite input weight matrix N tp is the number of sampling points in the time domain;

[0081] 3233) The optimal input sequence of the active suspension is obtained by differentiating the Laguerre fitting coefficient η; the goal of active suspension control is to find a suitable input sequence to minimize the value of the established cost function; through the above conversion, the cost function has been described as a function of the Laguerre fitting coefficient η, so by differentiating the cost function with respect to η to zero, the corresponding optimal Laguerre fitting coefficient η can be obtained. opt :

[0082]

[0083] η opt =-Ω -1 ×G (25)

[0084]

[0085] In the formula, J is a cost function; η is a Laguerre fitting coefficient; is a discrete suspension system matrix; C is a suspension output matrix; D is a direct transfer matrix; L is an output disturbance matrix; x(k) is a state variable of the kth period; ω(k) is a disturbance variable of the kth period; Q is an N tp ×N tp positive definite output weight matrix; R is an N tp ×N tp positive definite input weight matrix; L(k) is an active suspension Laguerre function of the kth period; η opt is an optimal Laguerre fitting coefficient of the active suspension system; Ω and G are N×N and N×1 matrices respectively; N is the number of grids in the preview range in the spatial domain; N tp is the number of sampling points in the time domain;

[0086] The fitted input sequence u(k) is obtained through the above derivation calculation and combined with formula (19), and the first control step N c numerical value is selected, that is, the optimal input sequence U opt of the active suspension system.

[0087] The beneficial effects of the present application are:

[0088] 1) The present application establishes a quarter vehicle active suspension model considering actuator time delay, can consider the time delay of actual actuator actuation, improves the robustness of the active suspension system, and improves the vertical performance of the vehicle;

[0089] 2) The present application designs a road elevation information collection mechanism in the time domain, which can adapt the collected road elevation information to the change of vehicle speed under a fixed preview distance, and match the actual demand of the road information for the active suspension preview control method;

[0090] 3) The present application designs an active suspension model predictive control method based on Laguerre function, which uses Laguerre function fitting to replace the link of solving the optimal control sequence by quadratic programming in the traditional model predictive control method, and can significantly reduce the computing power demand of the control method. BRIEF DESCRIPTION OF DRAWINGS

[0091] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced below, and it should be understood that the following drawings only show some embodiments of the present application, and should not be regarded as a limitation on the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0092] Figure 1This is a simplified architecture diagram of a low-computation preview control method for an active suspension that takes into account actuator time lag and vehicle speed changes, as described in the present invention;

[0093] Figure 2 Schematic diagram of a quarter vehicle active suspension model considering time delay;

[0094] Figure 3 This is a schematic diagram of road elevation information in the spatial domain;

[0095] Figure 4 Schematic diagram of road elevation information in the time domain that changes with vehicle speed;

[0096] Figure 5 This is a schematic diagram of the distribution of discrete road elevation information;

[0097] Figure 6 Schematic diagram for comparison of sprung mass acceleration;

[0098] Figure 7 A schematic diagram showing the comparison of algorithm running time. DETAILED DESCRIPTION

[0099] The present invention will be further described in detail below with reference to the accompanying drawings and examples. It will be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. It should also be noted that, for ease of description, the accompanying drawings only illustrate portions relevant to the present invention, not all structures.

[0100] Example 1

[0101] See Figure 1 The present invention provides a low-computation preview control method for an active suspension that takes into account actuator time lag and vehicle speed changes, comprising the following steps:

[0102] Step 1: Establish a quarter-vehicle active suspension model and the active suspension continuous-time state-space equations taking into account time delay and discretize them as follows:

[0103] 11) Establish Figure 2 The quarter-car active suspension model with time lag shown in the figure includes four components: sprung mass, active suspension, unsprung mass, and wheels. The controller for the active suspension outputs an ideal control force that, after a time lag, becomes the actual control force output to the suspension system.

[0104] 12) Based on the quarter-car active suspension model considering time lag and the principles of vehicle dynamics, the dynamic equations of the quarter-car active suspension considering time lag are obtained as follows:

[0105]

[0106] Where ms is the sprung mass; m u is the unsprung mass; k s is the spring stiffness; c s is the suspension damping coefficient; F r is the actual force of the active suspension; F is the ideal force of the active suspension; c t is the vertical equivalent damping of the tire; k t is the vertical equivalent stiffness of the tire; z s is the vertical displacement of the sprung mass; z u is the vertical displacement of the unsprung mass; z r is the road surface height; τ is the time constant that characterizes the time lag characteristics of the actuator;

[0107] 13) Select the sprung mass displacement z s (t), unsprung mass displacement z u (t), sprung mass displacement velocity Unsprung mass displacement velocity and the actual force F r (t) is the state variable; the sprung mass acceleration is selected Suspension travel z u (t)-z s (t) and tire dynamic deflection z r (t)-z u (t) is the output variable of the system; then the ideal force F(t) and the road height z are selected respectively. r are the input variables and disturbances of the system; the quarter-vehicle active suspension dynamics equation (1) is rewritten as the system state space equation under continuous time, as shown below:

[0108]

[0109] in,

[0110]

[0111]

[0112]

[0113]

[0114]

[0115] Where x(t) is the state variable; is the derivative of the state variable; y(t) is the output variable; u(t) is the input variable; ω(t) is the disturbance variable; A is the suspension system matrix; B is the suspension input matrix; C is the suspension output matrix; D is the direct transfer matrix; E is the state disturbance matrix; L is the output disturbance matrix; z s (t) is the displacement of the sprung mass; z u (t) is the unsprung mass displacement; is the sprung mass displacement velocity; is the displacement velocity of the unsprung mass; F r (t) Actual power; r is the road surface height; m s is the sprung mass; m u is the unsprung mass; k s is the spring stiffness; c s is the suspension damping coefficient; c t is the vertical equivalent damping of the tire; k t is the vertical equivalent stiffness of the tire;

[0116] 14) Model predictive control uses a discrete model to predict the future state of the controlled object and obtains the optimal control quantity through rolling optimization. The system state space equation under continuous time is discretized. The continuous time matrix in formula (2) is discretized using the zero-order hold discretization method, and the discretized system state space equation is obtained as follows:

[0117]

[0118]

[0119] Where A is the suspension system matrix; B is the suspension input matrix; E is the state interference matrix; D is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; T s is the sampling period of the active suspension control system; is the discrete suspension system matrix; Input matrix for discrete suspension; is the discrete state interference matrix; x(k) is the state variable of the kth period; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; ω(k) is the interference variable of the kth period.

[0120] Step 2: Establish a road surface model that can change with vehicle speed and use perception sensors to obtain spatial domain road elevation information within the preview range, and then convert the spatial domain road elevation information into temporal domain road elevation information through time domain conversion;

[0121] Previous active suspension preview control methods always used road elevation information within a fixed timeframe. As vehicle speed changes, the distance of road elevation information required for preview control also changes. However, in practice, the preview distance of the sensing sensor remains fixed, meaning that previous methods are only applicable to active suspension preview control at a constant speed and are unable to adapt to the speed fluctuations experienced during actual driving. Therefore, a road surface model within a fixed preview distance that can change with vehicle speed should be established for active suspension preview control at variable speeds. The specific approach is as follows:

[0122] 21) The road elevation information in the spatial domain obtained by the sensor is as follows: Figure 3 As shown in the figure, the road surface in the preview area is evenly divided into multiple grids of length Δl by the perception sensor, so the number of grids in the preview range in the spatial domain is:

[0123]

[0124] Where N is the number of grids in the preview range in the spatial domain; L p is the length of the preview area; Δl is the grid length;

[0125] 22) The spatial domain road elevation information is stored in the road elevation information set Ψ(t), which is expressed as:

[0126] Ψ(t)={h1(t),h2(t),...,h N (t)} (6)

[0127] Where Ψ(t) is the spatial domain road elevation information set; h i (t) is the height corresponding to the i-th grid point at time t;

[0128] 23) Set the sampling period of active suspension to T s , then the distance traveled by the vehicle in each sampling period and the number of grids passed in p sampling periods are:

[0129] l s =v×T s (7)

[0130]

[0131] Where v is the vehicle speed; T s is the sampling period of the active suspension; n(k,v) is the number of grids that the vehicle passes through at speed v within p sampling periods; l s is the distance traveled by the vehicle in each sampling period; Δl is the grid length;

[0132] 24) If the vehicle is in kT s The road surface height at hi (kT s ), then when the time is (k+1)T s When the vehicle is on the road, the height is h i+n(1,v) (kT s ); Get the vehicle in kT s The road elevation information set Γ(k,v) in the time domain when the speed is v is:

[0133]

[0134] in,

[0135] H i (k,v)=h n(i-1,v) (kT s ),i=1,2,...,N tp (v) (10)

[0136]

[0137] Where v is the vehicle speed; T s is the sampling period of the active suspension control system; Γ(k,v) is the road elevation information set in the time domain when the vehicle travels at a speed of v for k sampling periods; H i (k,v) is kT s The height of the i-th sampling point at time; N tp (v) is the number of sampling points in the time domain when the vehicle speed is v; n(p,v) is the number of grids that the vehicle passes through at speed v within p sampling times; h i (kT s ) is the vehicle in kT s The road surface height at the i-th grid point obtained by the sensing sensor; L p is the length of the preview area.

[0138] According to the above road model establishment method, the time domain road elevation information at different speeds can be obtained, such as Figure 4 As shown in the figure, blue and red represent time-domain road elevation information at low and high speeds, respectively. It can be seen that when the preview distance remains constant, the higher the vehicle speed, the fewer the number of system sampling points, and the sparser the distribution of sampling points in the spatial domain, which is consistent with the actual sampling behavior of the perception sensor as vehicle speed changes.

[0139] Step 3: Based on the discretized state space equation of the active suspension and the time-domain road elevation information, the active suspension preview control method is designed;

[0140] Due to the vehicle's energy consumption and performance requirements, the active suspension needs to minimize actuator output while maximizing the vehicle's vertical performance. Therefore, the control objectives of the active suspension can be summarized as follows:

[0141] 1) The vehicle should ensure driving comfort, safety and grounding during driving, which correspond to the three output variables of the system respectively z u (t)-z s (t), z r (t)-z u (t); therefore, the values ​​of the three output variables should be minimized.

[0142] 2) The active actuators in the active suspension require external energy. Each movement consumes energy, and the greater the force generated, the more energy is consumed. Therefore, to reduce energy consumption, the force F(t) output at each moment needs to be reduced, as follows:

[0143] 31) Based on the above control objectives, design the cost function for the active suspension system optimization problem:

[0144]

[0145] Where J is the cost function; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; Q is N tp ×N tp The positive definite output weight matrix of N tp ×N tp The positive definite input weight matrix N tp is the number of sampling points;

[0146] 32) Because the actuators in active suspensions generate limited actuating forces, and the range of these forces significantly impacts the damping performance of the active suspension, the limitations of these forces should be considered when designing active suspension control methods. Furthermore, to prevent suspension damage and ensure vehicle safety, requirements should also be placed on the maximum compression of the active suspension. The specific constraints can be expressed as follows:

[0147]

[0148] Where u(k) is the input variable of the kth cycle; x1(k) is the displacement of the sprung mass of the kth cycle; x2(k) is the displacement of the unsprung mass of the kth cycle; f max is the maximum force that the active suspension can generate; max is the maximum compression of the active suspension;

[0149] 32)For the traditional model predictive control method, the optimal actuator sequence is solved by using quadratic programming; but the quadratic programming method requires high computing power and cannot meet the real-time requirements of vehicle driving. Therefore, the Laguerre function is used to fit the optimal actuator to replace the quadratic programming link in the model predictive control, reduce the computing power of the control method, and combine the time domain road elevation information, the application designs a discrete model predictive control method suitable for speed, as follows:

[0150] 321)Read the vehicle state x(k) and speed v in the kth period;

[0151] 322)Calculate the sampling point number N tp and the disturbance variable ω(k);

[0152] 323)Use the Laguerre function to fit the optimal input sequence of the active suspension, as follows:

[0153] 3231)Use the discrete Laguerre function to express the active suspension input sequence, and the discrete form of the Laguerre function is as follows:

[0154]

[0155] In the formula, ξ i (z) is a discrete Laguerre polynomial; 0≤α≤1 is the pole of the discrete polynomial; N is the term number of the discrete Laguerre function;

[0156] To simplify the analysis of the discrete system of the active suspension, the z transform of ξ i (z) is performed to express the discrete Laguerre function as follows:

[0157] L(k)=[l1(k),l2(k),...,l N (k)] T (15)

[0158] In the formula, l i (k) is the z transform of the discrete Laguerre polynomial ξ i (z); L(k) is the designed active suspension Laguerre function;

[0159] Combined with formula (14) and formula (15), the active suspension Laguerre function is recursively expressed as follows:

[0160] L(k+1)=A l L(k) (16)

[0161]

[0162]

[0163] where L(k) is the active suspension Laguerre function; A l is the recurrence matrix; and a is the pole of the discrete polynomial;

[0164] The input quantity u(k+i) of the active suspension at the k+i moment is described by the discrete Laguerre function:

[0165]

[0166] where u(k) is the input variable of the kth period; η = [c1, c2, …, c N ] T is the Laguerre fitting coefficient; l j (i) is the discrete Laguerre polynomial; L(i) is the active suspension Laguerre function; and N is the number of grids in the preview range in the spatial domain.

[0167] 3232) The active suspension discrete state space equation and the cost function are rewritten by using the input quantity u(k) described by the discrete Laguerre function; the active suspension system input quantity u(k) is brought into the active suspension discrete state space equation, i.e., equation (3), and combined with equation (16) to perform the following iterative derivation to obtain the system state quantity and the output quantity expressed by the Laguerre function:

[0168]

[0169]

[0170] where, is the discrete suspension system matrix; is the discrete suspension input matrix; is the discrete state disturbance matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output disturbance matrix; x(k) is the state variable of the kth period; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; ω(k) is the disturbance variable of the kth period; L(k) is the active suspension Laguerre function of the kth period; and η is the Laguerre fitting coefficient;

[0171] The cost function equation (12) is rewritten in the form of using the Laguerre function expression:

[0172]

[0173]

[0174] where, is the discrete suspension system matrix; is the discrete suspension input matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; x(k) is the state variable of the kth period; ω(k) is the interference variable of the kth period; L(k) is the active suspension Laguerre function of the kth period; η is the Laguerre fitting coefficient; Q is N tp ×N tp The positive definite output weight matrix of N tp ×N tp The positive definite input weight matrix N tp is the number of sampling points in the time domain;

[0175] 3233) The optimal input sequence of the active suspension is obtained by differentiating the Laguerre fitting coefficient η; the goal of active suspension control is to find a suitable input sequence to minimize the value of the established cost function; through the above conversion, the cost function has been described as a function of the Laguerre fitting coefficient η, so by differentiating the cost function with respect to η to zero, the corresponding optimal Laguerre fitting coefficient η can be obtained. opt :

[0176]

[0177] η opt =-Ω -1 ×G (25)

[0178]

[0179] Where J is the cost function; η is the Laguerre fitting coefficient; is the discrete suspension system matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; x(k) is the state variable of the kth period; ω(k) is the interference variable of the kth period; Q is N tp ×N tp The positive definite output weight matrix of N tp ×N tp The positive definite input weight matrix; L(k) is the active suspension Laguerre function of the k-th period; η opt is the optimal Laguerre fitting coefficient of the active suspension system; Ω and G are N×N and N×1 matrices respectively; N is the number of grids in the preview range in the spatial domain; N tp is the number of sampling points in the time domain;

[0180] Through the above derivation and calculation combined with formula (19), the fitted input sequence u(k) is obtained. The front control step length N is selected. c The value is the optimal input sequence U of the active suspension system. opt ;

[0181] 324) Input the fitted system into the sequence u(k) with the previous control step length Nc The value is used as the optimal control value of the actual suspension U opt Output;

[0182] 325) Repeat the whole process in the k+1th cycle.

[0183] In summary, the present invention first constructs a quarter-vehicle active suspension model that accounts for time lag and discretizes the state-space equations to enable its use in model predictive control. Second, a road surface model is constructed using road elevation information obtained by sensory sensors. This spatial-domain road elevation information is converted into temporal-domain information, enabling it to adapt to changes in vehicle speed at a fixed preview distance, meeting the practical road surface information requirements of active suspension preview control. Finally, an active suspension preview control method is constructed, replacing the quadratic programming step in solving the optimal control sequence in traditional model predictive control with Laguerre function fitting, significantly reducing the computational power required by the control method.

[0184] Example 2

[0185] In order to verify the effectiveness and superiority of the method proposed in the invention, the following Figure 5 The discrete road surface shown in the figure is simulated and verified, with the vehicle speed set to 5m / s and the simulation time to 6s. The comparison of the sprung mass acceleration and the algorithm running time is shown in Figure 2. Figure 6 and Figure 7 shown.

[0186] As shown in the figure, the proposed velocity-adaptive discrete model predictive control method closely approximates traditional model predictive control methods in terms of control effectiveness, significantly reducing sprung mass acceleration. Furthermore, the proposed control method significantly reduces the runtime of traditional model predictive control methods, meeting the computing power and real-time requirements of active suspension control.

[0187] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A low-computation preview control method for active suspension considering actuator time lag and vehicle speed variation, characterized in that: The following steps are involved: Step 1: Establish a quarter-vehicle active suspension model and active suspension continuous-time state space equations considering time delay and discretize them; Step 2: Establish a road surface model that can change with vehicle speed and use perception sensors to obtain spatial domain road elevation information within the preview range, and then convert the spatial domain road elevation information into temporal domain road elevation information through time domain conversion; Step 3: Using the time-domain road elevation information, design an active suspension preview control method based on the discrete system state space equation; The specific method of step one is as follows: 11) A quarter-vehicle active suspension model with time lag is established, which includes the sprung mass, active suspension, unsprung mass, and wheels. The controller for the active suspension outputs an ideal control force that, after a time lag, becomes the actual control force output to the suspension system. 12) Based on the quarter-car active suspension model considering time lag and the principles of vehicle dynamics, the dynamic equations of the quarter-car active suspension considering time lag are obtained as follows: Where m s is the sprung mass; m u is the unsprung mass; k s is the spring stiffness; c s is the suspension damping coefficient; F r is the actual force of the active suspension; F is the ideal force of the active suspension; c t is the vertical equivalent damping of the tire; k t is the vertical equivalent stiffness of the tire; z s is the vertical displacement of the sprung mass; z u is the vertical displacement of the unsprung mass; z r is the road surface height; τ is the time constant that characterizes the time lag characteristics of the actuator; 13) Select the sprung mass displacement z s (t), unsprung mass displacement z u (t), sprung mass displacement velocity Unsprung mass displacement velocity and the actual force F r (t) is the state variable; the sprung mass acceleration is selected Suspension travel z u (t)-z s (t) and tire dynamic deflection z r (t)-z u (t) is the output variable of the system; then the ideal force F(t) and the road height z are selected respectively. r are the input variables and disturbances of the system; the quarter-vehicle active suspension dynamics equation (1) is rewritten as the system state space equation under continuous time, as shown below: in, Where x(t) is the state variable; is the derivative of the state variable; y(t) is the output variable; u(t) is the input variable; ω(t) is the disturbance variable; A is the suspension system matrix; B is the suspension input matrix; C is the suspension output matrix; D is the direct transfer matrix; E is the state disturbance matrix; L is the output disturbance matrix; z s (t) is the displacement of the sprung mass; z u (t) is the unsprung mass displacement; is the sprung mass displacement velocity; is the displacement velocity of the unsprung mass; F r (t) Actual power; r is the road surface height; m s is the sprung mass; m u is the unsprung mass; k s is the spring stiffness; c s is the suspension damping coefficient; c t is the vertical equivalent damping of the tire; k t is the vertical equivalent stiffness of the tire; 14) Discretize the system state space equation under continuous time. Use the zero-order hold discretization method to discretize the continuous time matrix in formula (2) and obtain the discretized system state space equation as shown below: Where A is the suspension system matrix; B is the suspension input matrix; E is the state interference matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; T d is the discrete time step of the system; is the discrete suspension system matrix; Input matrix for discrete suspension; is the discrete state interference matrix; x(k) is the state variable of the kth period; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; ω(k) is the interference variable of the kth period; The specific method of step three is as follows: 31) Design the cost function for the active suspension system optimization problem: Where J is the cost function; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; Q is N tp ×N tp The positive definite output weight matrix of N tp ×N tp The positive definite input weight matrix N tp is the number of sampling points; The constraints are expressed as follows: Where u(k) is the input variable of the kth cycle; x1(k) is the displacement of the sprung mass of the kth cycle; x2(k) is the displacement of the unsprung mass of the kth cycle; f max is the maximum force that the active suspension can generate; max is the maximum compression of the active suspension; 32) The Laguerre function is used to fit the optimal actuating force, and combined with the time domain road elevation information, a discrete model predictive control method that adapts to speed is designed, as follows: 321) Read the state variable x(k) and velocity v of the kth cycle; 322) Calculate the number of sampling points N tp and disturbance variables ω(k); 323) Using Laguerre function to fit the optimal input sequence of active suspension; 324) Input the fitted system into the sequence u(k) with the previous control step length N c The value is used as the optimal control value of the actual suspension U opt Output; 325) Repeat the whole process in the k+1th cycle.

2. The low-computation preview control method for active suspension considering actuator time lag and vehicle speed change according to claim 1, characterized in that: The specific method of step 2 is as follows: 21) The road surface in the preview area is evenly divided into multiple grids of length Δl by the perception sensor, so the number of grids in the preview range in the spatial domain is obtained as: Where N is the number of grids in the preview range in the spatial domain; L p is the length of the preview area; Δl is the grid length; 22) The spatial domain road elevation information is stored in the road elevation information set Ψ(t), which is expressed as: Ψ(t)={h1(t),h2(t),...,h N (t)} (6) Where Ψ(t) is the spatial domain road elevation information set; h1(t),h2(t),…,h N (t) are the heights corresponding to the 1st, 2nd, …, Nth grid points at time t; 23) Set the sampling period of the active suspension control system to T s , then the distance traveled by the vehicle in each sampling period and the number of grids passed in p sampling periods are: l s =v×T s (7) Where v is the vehicle speed; T s is the sampling period of the active suspension control system; n(p,v) is the number of grids that the vehicle passes through at speed v within p sampling periods; l s is the distance traveled by the vehicle in each sampling period; Δl is the grid length; 24) If the vehicle is at kT s The road surface height at h i (kT s ), then when the time is (k+1)T s When the vehicle is on the road, the height is h i+n(1,v) (kT s ); Get the vehicle in kT s The road elevation information set Γ(k,v) in the time domain when the speed is v is: in, Where v is the vehicle speed; T s is the sampling period of the active suspension control system; Γ(k,v) is the road elevation information set in the time domain when the vehicle travels at a speed of v for k sampling periods; H i (k,v) is kT s The height of the i-th sampling point at time; N tp (v) is the number of sampling points in the time domain when the vehicle speed is v; h i (kT s ) is the vehicle in kT s The road surface height at the i-th grid point obtained by the sensing sensor; L p is the length of the preview area.

3. The low-computation preview control method for active suspension considering actuator time lag and vehicle speed change according to claim 1, characterized in that: The specific method of step 323) is as follows: 3231) The active suspension input sequence is expressed using a discrete Laguerre function. The discrete form of the Laguerre function is shown in the following formula: Where, ξ i (z) is the discrete Laguerre polynomial; 0≤α≤1 is the pole of the discrete polynomial; N is the number of terms in the discrete Laguerre function; In order to simplify the analysis of the active suspension discrete system, ξ i (z) Perform z-transformation to express the discrete Laguerre function as follows: L(k)=[l1(k),l2(k),...,l N (k)] T (15) Where, l i (k) is the discrete Laguerre polynomial ξ i (z) is the z-transform; L(k) is the Laguerre function of the designed active suspension; Combining Equations (14) and (15), the active suspension Laguerre function is recursively expressed as follows: L(k+1)=A l L(k) (16) Where L(k) is the Laguerre function of the designed active suspension; A l is the recursive matrix; α is the pole of the discrete polynomial; The input u(k+i) of the active suspension at time k+i is described by the discrete Laguerre function: Where u(k) is the input variable of the kth period; η=[c1,c2,…,c N ] T is the Laguerre fitting coefficient; l j (i) is the discrete Laguerre polynomial; L(i) is the active suspension Laguerre function; N is the number of grids in the preview range in the spatial domain; 3232) The active suspension discrete state space equation and cost function are rewritten using the input u(k) described by the discrete Laguerre function. The active suspension system input u(k) is substituted into the active suspension discrete state space equation, i.e., Equation (3). Combined with Equation (16), the following iterative derivation is performed to obtain the system state and output expressed by the Laguerre function: Where, is the discrete suspension system matrix; Input matrix for discrete suspension; is the discrete state interference matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; x(k) is the state variable of the kth period; y(k) is the output variable of the kth period; u(k) is the input variable of the kth period; ω(k) is the interference variable of the kth period; L(k) is the designed active suspension Laguerre function; η is the Laguerre fitting coefficient; The cost function (12) is rewritten as the Laguerre function: Where, is the discrete suspension system matrix; is the discrete suspension input matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; x(k) is the state variable of the kth period; ω(k) is the interference variable of the kth period; L(k) is the designed active suspension Laguerre function; η is the Laguerre fitting coefficient; Q is N tp ×N tp The positive definite output weight matrix of N tp ×N tp The positive definite input weight matrix N tp is the number of sampling points in the time domain; 3233) The optimal input sequence of the active suspension is obtained by differentiating the Laguerre fitting coefficient η; the goal of active suspension control is to find a suitable input sequence to minimize the value of the established cost function; through the above conversion, the cost function has been described as a function of the Laguerre fitting coefficient η, so by differentiating the cost function with respect to η to zero, the corresponding optimal Laguerre fitting coefficient η can be obtained. opt : Where J is the cost function; η is the Laguerre fitting coefficient; is the discrete suspension system matrix; C is the suspension output matrix; D is the direct transfer matrix; L is the output interference matrix; x(k) is the state variable of the kth period; ω(k) is the interference variable of the kth period; Q is N tp ×N tp The positive definite output weight matrix of N tp ×N tp The positive definite input weight matrix of ; L(k) is the designed active suspension Laguerre function; η opt is the optimal Laguerre fitting coefficient of the active suspension system; Ω and G are N×N and N×1 matrices respectively; N is the number of grids in the preview range in the spatial domain; N tp is the number of sampling points in the time domain; Through the above derivation and calculation combined with formula (19), the fitted input sequence u(k) is obtained. The front control step length N is selected. c The value is the optimal input sequence U of the active suspension system. opt .

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