Design method of secondary expansion sliding mode controller based on three-mass two-stage active suspension

Abstract

The invention discloses a secondary expansion sliding mode controller design method based on a three-mass two-stage active suspension in the field of automotive suspensions, which comprises the following steps of: manufacturing a motor, a hydraulic pump / motor and a shock absorber hydraulic cylinder of an active shock absorption structure into a whole to serve as a suspension third-mass design secondary expansion sliding mode controller, and establishing a motion differential equation of the suspension; the unsprung mass acceleration, the third mass acceleration and the sprung mass acceleration serve as state quantities respectively and are expanded into state vectors, a state matrix and a control matrix are expanded, comprehensive performance evaluation indexes are rewritten and substituted into a Riccati equation, a unique solution and a feedback vector are solved, and the sprung mass acceleration and the sprung mass acceleration are obtained. And finally, solving an extended optimal sliding mode control vector and an active control force. The method only depends on one acceleration sensor, the vehicle state vector containing the nonlinear force is reconstructed through the acceleration signal easy to measure, more accurate suspension structure information is provided for a controller, high-frequency vibration transmitted to a vehicle body from the ground is effectively absorbed, and the control precision is improved.

Description

Technical Field

[0001] The invention belongs to the field of automobile suspension, in particular to a design method of an active suspension structure and a suspension system controller. Background Art

[0002] Suspension is a general term for all force transmission and connection devices between the vehicle body and the wheels, and plays a vital role in the vehicle's handling, stability and ride comfort. According to its working principle, the suspension can be divided into active suspension, semi-active suspension and passive suspension. Among them, the active suspension has excellent vibration reduction performance, which can keep the vehicle running smoothly even under harsh road conditions. During long-distance driving of the car, it is necessary to effectively suppress the high-frequency vibration transmitted to the vehicle body, but few existing active suspension structures are specifically optimized for high-frequency vibration reduction. In addition, the nonlinearity of the active suspension is a problem that must be considered when designing the suspension controller. If it is not processed, the control accuracy of the active suspension will decrease, reducing the ride comfort of the vehicle. At present, the more mature solution to the nonlinear problem of active suspension is to use the existing optimal sliding mode controller. The optimal sliding mode controller has the advantage of processing uncertain information and has a certain robustness, but it relies on various high-precision sensors to collect the vehicle state information required to control the vehicle, which increases the cost, and some vehicle state information is not easy to obtain.

[0003] The Chinese patent publication number CN112549892B, entitled "Secondary Vibration Damping Hydraulic-Electric Active Suspension with Adjustable Additional Stiffness and Damping and Working Method", proposes a secondary active suspension with an additional vibration isolation structure on the basis of the active vibration reduction structure of the general active suspension, which can isolate part of the vibration transmitted by the wheel in advance and reduce the required control force of the active vibration reduction structure, but it cannot effectively suppress the high-frequency vibration input from the road surface. The Chinese patent publication number CN114571940A, entitled "A Nonlinear Suspension Control System under Uncertain Conditions", discloses a sliding mode control strategy based on the inverse control law, which has the problem that various high-precision sensors including road excitation, vehicle body force conditions and vehicle motion state are required to collect external information to provide the required information for the sliding mode controller to calculate the active control force, but over-reliance on high-precision sensors will lead to excessively high costs for the entire system, and signals including the speed of the suspension and wheels are also difficult to accurately measure through sensors. Summary of the invention

[0004] In view of the problem that most existing active suspension controllers rely on various high-precision sensors to collect external and vehicle state information and are difficult to effectively control a three-mass two-stage active suspension with large nonlinearity, the present invention proposes a design method of a quadratic extended sliding mode controller based on a three-mass two-stage active suspension. The quadratic extended sliding mode controller designed for the three-mass two-stage active suspension can accurately observe the nonlinear force caused by changes in the working states of the accumulator and the hydraulic pump / motor, thereby improving the control effect.

[0005] The technical solution adopted by the three-mass two-stage active suspension of the present invention comprises the following steps:

[0006] 1) The hydraulic pump / motor and the motor are fixed on the outer cylinder wall of the two hydraulic cylinders of the three-mass two-stage active suspension, respectively, near the bottom of the cylinder and located on the same side, and the dynamic model of the three-mass two-stage active suspension is established, including the sprung mass m2 composed of the vehicle body mass, the first elastic force F generated by the first accumulator, and the a , the active control force F generated by the active vibration reduction structure e , the equivalent inertial force F generated by the active vibration reduction structure m , the third mass m formed by the first hydraulic cylinder, the second hydraulic cylinder, the motor and the hydraulic pump / motor c , the second elastic force F generated by the second accumulator i , the damping force F generated by the vibration isolation structure cp , unsprung mass m1 and tire stiffness k1;

[0007] 2) Establish the differential equation of motion of the suspension and select the state vector X = (x1, x2, x3, x4, x5, x6, x7) Τ , rewrite the differential equation into a nonlinear elastic force △F of the suspension vibration isolation structure composed of state matrix A, state vector X, control matrix B, control vector U, interference matrix G, and interference vector W i , nonlinear elastic force of active vibration reduction structure of suspension △F a , nonlinear active control force △F e , nonlinear inertial force △F m The state equation of the three-mass two-stage active suspension Where x1 = z1-q, x2 = z c -z1,x3=z2-z c , z1 is the displacement of the unsprung mass m1, q is the road roughness input, z c is the third mass m c is the displacement of the sprung mass m2, z2 is the displacement of the sprung mass m2, is the first-order differential of z1, For z cThe first-order differential of is the first-order differential of z2, m e is the equivalent inertial mass, T is the matrix transpose;

[0008] 3) Unsprung mass acceleration The third mass acceleration and sprung mass acceleration The corresponding acceleration observation values ​​fed back at the previous moment Subtract to get the corresponding error vector The error vector e y As the input of the sliding mode switching function, the switching term is obtained ρ is the sliding mode switching gain, which is a positive number less than 200; δ is the low-pass filter parameter, which is a positive number less than 1;

[0009] 4) Unsprung mass acceleration The third mass acceleration and sprung mass acceleration As state variables Expand to the state vector X to obtain the expanded state vector And expand the state matrix A and control matrix B to obtain the expanded state matrix A a and control matrix B a ;

[0010] 5) According to the state vector X and control vector U, the comprehensive performance evaluation index In δ2(z1-q) 2 ,δ3(z2-z1) 2 Rewrite it into quadratic form to get the quadratic standard form of the index function Q is the state vector weight matrix, R is the control vector weight matrix; N is the cross vector weight matrix of Q and R, is the total running time, δ1, δ2, and δ3 are Weighting coefficients of (z1-q) and (z2-z1);

[0011] 6) The quadratic form is in standard form Substitute the matrices Q, N, and R in the Riccati equation to find the unique solution P a , based on the unique solution P a Solve for the feedback vector K;

[0012] 7) According to the control vector Solve for the extended optimal sliding mode control vector U a =-[KB a1 ] -1 [KAa1 X a1 +λ a KX a1 +KG a1 W], yes The first 7 rows of λ a is the sliding mode approach coefficient;

[0013] 8) Expand the optimal sliding mode control vector U a Substitution Find the control vector U required to control the three-mass two-stage active suspension, that is, the active control force F e .

[0014] Furthermore, the state matrix Control Matrix Control vector U = (F e ), interference matrix G = [G0 G1 G2], G0 = [-1 0 0 0 0 0 0] T , T0=[0 -1 1] T ,G1=[0 0 0 0 1 / (m c +m e ) 0 0] T ,G2=[0 0 0 0 m e / (m c +m e ) 0 1] T , interference vector Damping Matrix Mass Matrix Stiffness Matrix is the disturbance caused by the nonlinearity of the three-mass two-stage active suspension, λ is 0.001, is the first-order differential of the road roughness input q, F e is the active control force, c p is the damping of the vibration isolation structure; k i is the stiffness of the second accumulator, k a is the stiffness of the first accumulator.

[0015] Furthermore, the expanded state matrix Expanded control matrix A f1 represents the low-pass filter gain parameter, and B(4:6,:) is the submatrix consisting of the 4th to 6th rows of the control matrix B.

[0016] The outstanding technical effects of the present invention after adopting the above technical solution are:

[0017] In view of the fact that existing controllers are unable to effectively control the nonlinearity generated by the three-mass two-level active suspension, the present invention integrates the motor, hydraulic pump / motor and shock absorber hydraulic cylinder of the active vibration reduction structure into one body on the basis of the existing two-level vibration reduction structure and uses them as the third mass of the suspension. A secondary extended sliding mode controller is designed, which only relies on one acceleration sensor and reconstructs the vehicle state vector including the nonlinear force not considered by the existing controller through an acceleration signal that is easy to measure. It can provide the controller with more accurate suspension structure information, effectively absorb high-frequency vibrations transmitted from the ground to the vehicle body, and improve control accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of the structure of a three-mass two-stage active suspension;

[0019] Figure 2 It is a schematic diagram of the dynamic model of the three-mass two-stage active suspension;

[0020] Figure 3 It is a block diagram of the design method of the quadratic extended sliding mode controller of the present invention;

[0021] Figure 4 It is a simulation diagram comparing the power spectrum density of vehicle body acceleration between the existing two-stage active suspension based on LQG control and the suspension of the present invention;

[0022] Figure 5 It is a simulation diagram comparing the power spectrum density of vehicle body acceleration of the suspension of the present invention based on the existing sliding mode controller and the suspension of the present invention based on the secondary extended sliding mode controller 6. DETAILED DESCRIPTION

[0023] like Figure 1The three-mass two-stage active suspension structure shown in the figure is located between the vehicle body 1 and the wheel 10 in the vertical direction. The three-mass two-stage active suspension is composed of a first hydraulic cylinder 17, a first piston rod 3, a first piston 4, a hydraulic pump / motor 7, an electric motor 8, a first accumulator 5 constituting an active vibration reduction structure and a second piston rod 12, a second piston 13, a second hydraulic cylinder 14, an adjustable flow valve 15, a second accumulator 16 constituting a vibration isolation structure, as well as a vehicle body acceleration sensor 2, a suspension hydraulic cylinder acceleration sensor 9 and a wheel acceleration sensor 11. The secondary extended sliding mode controller 6 is respectively connected to three acceleration sensors, namely the vehicle body acceleration sensor 2, the suspension hydraulic cylinder acceleration sensor 9 and the wheel acceleration sensor 11. The acceleration signal is input into the secondary extended sliding mode controller 6. The secondary extended sliding mode controller 6 measures the sprung mass acceleration signal, the third mass acceleration signal and the unsprung mass acceleration signal through the three acceleration sensors and transmits the signals to the secondary extended sliding mode controller 6. The secondary extended sliding mode controller 6 then controls the motor 8 to generate a torque of corresponding magnitude, which is converted into hydraulic pressure through the hydraulic pump / motor 7 for vibration attenuation.

[0024] In the vertical direction, the first hydraulic cylinder 17 is fixed to the bottom of the second hydraulic cylinder 14. One end of the first piston rod 3 outside the cylinder body is connected to the vehicle body 1, and one end inside the cylinder body is connected to the first piston 4. The first piston 4 contacts the inner cylinder wall of the first hydraulic cylinder 17 and can move up and down along the inner cylinder wall. The hydraulic pump / motor 7 is fixed to the outer wall of the cylinder bottom of the first hydraulic cylinder 17. One end of the oil inlet and outlet is connected to the oil inlet and outlet at the bottom of the first hydraulic cylinder 17 through the oil circuit, and the other end of the oil inlet and outlet is connected to the first accumulator 5 through the oil circuit. The motor 8 is fixed to the outer cylinder wall of the second hydraulic cylinder 14, and the hydraulic pump / motor 7 and the motor 8 are connected through a coupling to transmit power. One end of the second piston rod 12 outside the cylinder body is connected to the wheel, and one end inside the cylinder body is connected to the second piston 13. The second piston 13 contacts the inner cylinder wall of the second hydraulic cylinder 14 and can move up and down along the inner cylinder wall. The second accumulator 16 is connected to the oil inlet and outlet at the bottom of the second hydraulic cylinder 14 through the oil pipe and is equipped with an adjustable flow valve 15. The vibration isolation structure can initially attenuate the vibration transmitted from the wheel 7 to the vehicle body 1. At the same time, the hydraulic pump / motor 7, the motor 8, the first hydraulic cylinder 17, and the second hydraulic cylinder 14 are made into an integral structure as the third mass of the suspension to absorb the high-frequency vibration transmitted from the wheel 10 to the vehicle body 1.

[0025] Establish Figure 1 The dynamic model of the three-mass two-stage active suspension is shown in FIG. Figure 2 As shown, the three-mass two-stage active suspension dynamics model includes the sprung mass m2 composed of the vehicle body mass, the first elastic force F generated by the first accumulator 5, and the first elastic force F generated by the first accumulator 5. a , active control force F generated by the active vibration reduction structuree , the equivalent inertial force F generated by the active vibration reduction structure m , a third mass m formed by the first hydraulic cylinder 17, the second hydraulic cylinder 14, the motor 8 and the hydraulic pump / motor 7 c , the second elastic force F generated by the second accumulator 16 i , the damping force F generated by the vibration isolation structure cp , unsprung mass m1 and tire stiffness k1, body acceleration sensor 2 for measuring sprung mass acceleration, suspension hydraulic cylinder sensor 9 for measuring third mass acceleration, wheel acceleration sensor 11 for measuring unsprung mass acceleration, and control active control force F e The size of the quadratic extended sliding mode controller 6 etc. In the vertical direction, Figure 1 The wheel 10 in the figure is composed of an unsprung mass m1 and a tire stiffness k1 equivalent to a spring. The wheel is located below the sprung mass m2. An active vibration reduction structure and a vibration isolation structure are connected in series from top to bottom between the sprung mass m2 and the unsprung mass m1. During operation, the vibration caused by the unevenness of the road surface is transmitted to the vehicle body through the wheel, firstly through the second elastic force F i and the damping force F cp The vibration is initially isolated and attenuated, and then the third mass m c Effectively absorb high-frequency vibrations, and finally the first elastic force F a , equivalent inertia force F m and active control force F e The vibration that has been partially isolated and absorbed is actively controlled accurately to minimize the impact of the vibration generated by road excitation on the vehicle body. The nonlinear elastic force of the active vibration reduction structure generated by the nonlinear change in the relationship between the gas and pressure inside the first accumulator 5 is △F a The nonlinear elastic force of the vibration isolation structure generated by the nonlinear change of the relationship between the gas and pressure inside the second accumulator 16 is △F i The nonlinear active control force and nonlinear inertia force generated by the active vibration reduction structure due to the change of the transmission ratio of the hydraulic pump / motor in the working state are △F e and ∆F m .

[0026] Improve the arrangement of the hydraulic pump / motor 7 and the motor 8, and fix the hydraulic pump / motor 7 and the motor 8 on the outer cylinder wall of the first hydraulic cylinder 17 and the second hydraulic cylinder 14 on the same side near the cylinder bottom, so that the hydraulic pump / motor 7, the motor 8, the first hydraulic cylinder 17, and the second hydraulic cylinder 14 together serve as the third mass m of the three-mass two-stage active suspension c That is, on the basis of the existing two-stage damping active suspension structure, the third mass m is increased by improving the arrangement of the hydraulic pump / motor 7 and the motor 8. c quality.

[0027] like Figure 3 As shown, the secondary extended sliding mode controller 6 includes an extended sliding mode observation module, a sliding mode switching function and an extended control module. a , Nonlinear elastic force of the vibration isolation structure △F i , nonlinear active control force △F e , nonlinear inertial force △F m The quadratic extended sliding mode controller designed in the present invention can control the unsprung mass acceleration which is easily measured by the sensor. The third mass acceleration sprung mass acceleration The vehicle state vector including nonlinear forces not considered by the existing controller is reconstructed through the extended sliding mode observation module, providing more accurate suspension structure information for the extended control module and improving control accuracy. The specific design method of the secondary extended sliding mode controller 6 also includes the following steps:

[0028] Step 1: Establish the state equation of three-mass two-stage active suspension.

[0029] according to Figure 2 , a detailed dynamic analysis of the three-mass two-stage active suspension motion is conducted in the vertical direction, and the following nonlinear elastic force △F of the active vibration reduction structure that is not considered in the existing two-stage active suspension is established: a , Nonlinear elastic force of the vibration isolation structure △F i , nonlinear active control force △F e , nonlinear inertial force △F m The differential equation of motion of the three-mass two-stage active suspension is:

[0030]

[0031] Where: k i k is the stiffness of the second accumulator 16; a is the stiffness of the first accumulator 5; c p is the damping of the vibration isolation structure; m e is the equivalent inertial mass; z1 is the displacement of m1; z c The third mass m of the three-mass two-stage active suspension c The displacement of the sprung mass m2 is z2; represents the first-order differential of z1; Indicates z c The first order differential of represents the first-order differential of z2; represents the second-order differential of z1; Indicates z c The second order differential of represents the second-order differential of z2; k a (z2-z c ) is the first elastic force F a , that is, F a =k a (z2-z c );k i (z c -z1) is the second elastic force F i , that is, F i =k i (z c -z1); is the equivalent inertia force F m ,Right now is the damping force F cp ,Right now q represents the road roughness input; is the first-order differential of q; n0 is the spatial reference frequency, take 0.1m -1 ; w represents a road white noise signal with a mean of 0 and a power spectrum density of 1; G q (n0) is the road roughness coefficient; u represents the vehicle running speed; f0 represents the lower cutoff frequency of the road input, which is equal to 0.011u; then the nonlinear elastic force of the active vibration reduction structure Where P a01 is the internal gas pressure of the first accumulator 5 at the equilibrium position, P ai1 is the charging pressure of the first accumulator 5, S c1 is the working area of ​​the rodless end of the first piston 4, V ai1 is the initial gas volume of the first accumulator 5, n1 is the gas adiabatic index; the nonlinear elastic force of the vibration isolation structure Where P a02 is the internal gas pressure of the second accumulator 16 at the equilibrium position, P ai2 is the charging pressure of the second accumulator 16, S c2 is the working area of ​​the rodless end of the second piston 13, V ai2 is the initial gas volume of the second accumulator 16; nonlinear inertial force Where I is the moment of inertia of the hydraulic pump / motor 7 and the motor 8, is the working state transmission ratio of the hydraulic pump / motor 7, q b,0 is the theoretical displacement of the hydraulic pump / motor for one revolution, φ0 is the ideal transmission ratio of the hydraulic pump / motor 7; Where T L is the motor torque, η is the mechanical efficiency of the hydraulic pump / motor 7, and sgn() is the sign function.

[0032] Select state vector X = (x1, x2, x3, x4, x5, x6, x7) Τ , where: x1 = z1-q, x2 = z c -z1,x3=z2-z c , T is the matrix transpose,

[0033] Based on modern control theory, the three-mass second-order active differential equation shown in equation (1) is rewritten as the nonlinear elastic force △F containing the vibration isolation structure, which is composed of the state matrix A, state vector X, control matrix B, control vector U, interference matrix G, and interference vector W. i and the nonlinear elastic force △F of the active vibration reduction structure a , nonlinear active control force △F e , nonlinear inertial force △F m The state equation of the three-mass two-stage active suspension is:

[0034]

[0035] Where: state matrix Control Matrix Control vector U = (F e ); Interference matrix G = [G0 G1 G2], G0 = [-1000000] T , T0=[0-11] T , G1=[00001 / (m c +m e )00] T ,G2=[0000m e / (m c +m e )01] T ; Interference vector Damping Matrix Mass Matrix Stiffness Matrix λ is a positive scalar, usually 0.001; The disturbance generated by the nonlinearity of the three-mass two-stage active suspension.

[0036] Step 2: Construct the sliding mode switching function. The third mass acceleration sprung mass acceleration The observed value of the corresponding acceleration at the previous moment corresponding to the feedback Subtract the error vector The error vector e y As the input of the sliding mode switching function of formula (4), we can obtain the error vector e y Switch v so that it is close to the 0 vector.

[0037]

[0038] Where: ρ is the sliding mode switching gain, affecting e y Convergence speed, take a positive number less than 200; δ is the low-pass filter parameter, take a positive number less than 1.

[0039] Step 3: Unsprung mass acceleration The third mass acceleration and sprung mass acceleration As state variables Expand the state vector X in equation (3) to obtain the expanded state vector The corresponding state matrix A, control matrix B and interference matrix G are expanded to obtain the expanded state matrix A a , control matrix B a and the interference matrix G a : 0 7×1 is the control matrix B a A zero matrix with 7 rows and 1 column.

[0040] The error vector e y With the switch term v as input, the expanded state vector As the output, the extended sliding mode observation module is designed, and the canonical state equation of the extended sliding mode observation module is obtained as follows:

[0041]

[0042] Where: are the corresponding observation values ​​of the feedback of x1, x2, x3, x4, x5, x6, and x7 at the previous moment, is the unsprung mass acceleration Observed value is the third mass acceleration Observed value is the sprung mass acceleration Observed value for The first derivative of ; A f1 Represents the low-pass filter gain parameter. B(4:6,:) is the submatrix composed of the 4th to 6th rows of the control matrix B; C a =I 10 ;I 10 is the 10th-order identity matrix; I7 and I3 are 7th-order and 3rd-order identity matrices, respectively; L is any one such that A a (1:7,1:7)+L*A a The spectrum of (8:10,1:7) falls in the left half of the complex plane. The 7×3 matrix; H is an arbitrary 3×3 stable matrix; 0 m×n is a zero matrix with m rows and n columns.

[0043] Step 4: Construct the comprehensive performance evaluation index J of the three-mass two-stage active suspension:

[0044]

[0045] Where: is the total running time, is the sprung mass acceleration; (z1-q) is the tire dynamic deformation; (z2-z1) is the suspension dynamic deformation; T is the vehicle driving time; δ1, δ2, δ3 are The weighted coefficients of (z1-q) and (z2-z1) are obtained by the method provided in the literature [A method for determining the weighted coefficients of LQG control of vehicle suspension. Chen Shian, Qiu Feng, He Ren, Lu Senlin. Vibration and Shock. 2008(02): 65-68+176] to obtain δ1, δ2 and δ3.

[0046] Step 5: According to the state vector X and control vector U obtained in step 1, the comprehensive performance evaluation index J in formula (6) is δ2(z1-q) 2 ,δ3(z2-z1) 2 Rewrite it into quadratic form to get the quadratic standard form of the comprehensive performance evaluation index function J of the three-mass two-stage active suspension:

[0047]

[0048] State vector weight matrix Control vector weight matrix The cross vector weight matrix of Q and R Weighting coefficient matrix A(6,:) and B(6,:) are the 6th rows of matrix A and matrix B in step 1 respectively.

[0049] Step 6: Suspension comprehensive performance evaluation index function The quadratic standard form of Eq. (7) is converted into the comprehensive performance evaluation index function Substitute the matrices Q, N, and R in the quadratic form into the following Riccati equation and solve for the unique solution P a :

[0050]

[0051] Where: A M (1:7,1:7) represents the matrix A M A submatrix consisting of rows 1 to 7 and columns 1 to 7; M (1:7,8) is the matrix A M The submatrix formed by rows 1 to 7 and columns 8; Q M (1:7,1:7) is the matrix Q M The submatrix consisting of the intersection of rows 1 to 7 and columns 1 to 7; Q M (1:7,8) is the matrix Q M The submatrix formed by the intersection of rows 1 to 7 and column 8; Q M (8,8) is the matrix Q M The submatrix formed by the intersection of the 8th row and the 8th column; a and b are two small positive scalars, each of which is 0.001.

[0052] Step 7: Substitute the P obtained in step 6 a Multiply A on the left M (1:7,8) T And with Q M (1:7,8) T Add and insert 1 on the right, and multiply the resulting row vector by Q on the left M (8,8) -1 , right multiply Finally, the feedback vector K required for the quadratic extended optimal sliding mode controller to control the three-mass two-level active suspension is solved:

[0053]

[0054] Step 8: Based on the state matrix A, control matrix B, interference matrix G given in step 1, and the expanded state vector obtained in step 3 The feedback vector K obtained in step 7 is used to construct an extended control module as shown in formula (10), and then the feedback vector K obtained in step 3 is used to construct an extended control module as shown in formula (10). The first 7 lines The control vector U of the previous moment fed back is e ) to obtain the control vector The control vector X a As the input of the extended control module, the extended optimal sliding mode control vector U is solved a :

[0055] U a =-[KB a1 ] -1 [KA a1 X a1 +λ a KXa1 +KG a1 W] (10)

[0056] Where: λ a is the sliding mode approach coefficient, satisfying in max(w) represents the maximum absolute value of the interference input W that can be estimated in advance.

[0057] Step 9: Based on the extended optimal sliding mode control vector U a And a and b given in step 6 construct the extended equation shown in formula (11), and the extended optimal sliding mode control vector U a As the input of the extended equation, the output is the control vector U = (F e ):

[0058]

[0059] Where: is the control vector U=(F e ), so the control vector U required to control the three-mass two-stage active suspension is (F e ), that is, the active control force F e .

[0060] Taking a certain vehicle model as an example, the relevant parameters of the vehicle and controller design are shown in Table 1. The simulation program is written by MATLAB, and the existing two-stage active suspension and the suspension of the present invention are used to perform a comparative simulation verification of the acceleration power spectrum density of the vehicle body. During the verification, the commonly used LQG algorithm is used for active control. The simulation results are shown in Figure 4 As shown in Table 2. Then, a simulation model was built through MATLAB / Simulink, and the three-mass two-stage active suspension using the existing sliding mode controller and the three-mass two-stage active suspension using the secondary extended sliding mode controller 6 were simulated and verified on a D-level road at 50 km / h for 120 seconds. The simulation results are shown in Figure 5 As shown in Table 3, RMS is the abbreviation of root mean square value.

[0061] Table 1

[0062]

[0063] Table 2

[0064]

[0065] Table 3

[0066]

[0067] According to the data in Table 2, it can be seen that the suspension of the present invention with vibration absorption function has a root mean square value of the acceleration power spectrum density of the vehicle body reduced by 42.17% compared with the existing two-stage active suspension. Figure 5 As shown in FIG. 1 , the RMS value of the vehicle acceleration of the suspension of the present invention in the high frequency region is significantly lower than that of the existing two-stage active suspension, which verifies the third mass m having a vibration absorption function. c The suspension of the present invention has superior performance in absorbing high frequency vibration. Figure 5 It can be seen that the body acceleration power spectrum density of the suspension of the present invention using the quadratic extended sliding mode controller is significantly lower than that of the suspension of the present invention using the existing sliding mode controller. According to the data in Table 3, the root mean square value of the body acceleration power spectrum density of the former is reduced by 3.91% compared with the latter, and the comprehensive performance index J of the suspension is improved by 15%, which verifies that the controller of the present invention has superior control performance for the three-mass two-level active suspension with more nonlinearity.

[0068] When the secondary extended sliding mode controller 6 constructed by the present invention is working, the wheel acceleration sensor 11 measures Suspension hydraulic cylinder acceleration sensor 9 measured The body acceleration sensor 2 measures Output of the extended sliding mode observation module Subtract to get the error vector e y , the error vector e y Input into the sliding mode switching function to get the switching vector v. From the error vector e y , the switch vector v output by the sliding mode switching function, and the control vector U output by the extended equation are used as the input of the extended sliding mode observation module, and the observation is obtained and will The first 7 lines Combined with the control vector U fed back by the expansion vector, we get X a As the input of the extended control module, the extended optimal sliding mode control vector U is solved a , and at the same time a Substituting into the expanded equation To find the control vector U = (F e ). The obtained control vector U=(F e ) input to the active vibration reduction structure to control the entire three-mass two-level active suspension.

Claims

1. A design method for a quadratic extended sliding mode controller based on a three-mass two-stage active suspension, characterized in that The following steps are involved: 1) The hydraulic pump / motor and the motor are fixed on the outer cylinder wall of the two hydraulic cylinders of the three-mass two-stage active suspension, respectively, near the bottom of the cylinder and located on the same side, and the dynamic model of the three-mass two-stage active suspension is established, including the sprung mass m2 composed of the vehicle body mass, the first elastic force F generated by the first accumulator, and the a , the active control force F generated by the active vibration reduction structure e , the equivalent inertial force F generated by the active vibration reduction structure m , the third mass m formed by the first hydraulic cylinder, the second hydraulic cylinder, the motor and the hydraulic pump / motor c , the second elastic force F generated by the second accumulator i , the damping force F generated by the vibration isolation structure cp , unsprung mass m1 and tire stiffness k1; 2) Establish the differential equation of motion of the suspension and select the state vector X = (x1, x2, x3, x4, x5, x6, x7) Τ , rewrite the differential equation into a nonlinear elastic force △F of the suspension vibration isolation structure composed of state matrix A, state vector X, control matrix B, control vector U, interference matrix G, and interference vector W i , nonlinear elastic force of active vibration reduction structure of suspension △F a , nonlinear active control force △F e , nonlinear inertial force △F m The state equation of the three-mass two-stage active suspension Where x1 = z1-q, x2 = z c -z1,x3=z2-z c , z1 is the displacement of the unsprung mass m1, q is the road roughness input, z c is the third mass m c is the displacement of the sprung mass m2, z2 is the displacement of the sprung mass m2, is the first-order differential of z1, For z c The first-order differential of is the first-order differential of z2, m e is the equivalent inertial mass, T is the matrix transpose; 3) Unsprung mass acceleration The third mass acceleration and sprung mass acceleration The corresponding acceleration observation values ​​fed back at the previous moment Subtract to get the corresponding error vector The error vector e y As the input of the sliding mode switching function, the switching term is obtained ρ is the sliding mode switching gain, which is a positive number less than 200; δ is the low-pass filter parameter, which is a positive number less than 1; 4) Unsprung mass acceleration The third mass acceleration and sprung mass acceleration As state variables Expand to the state vector X to obtain the expanded state vector And expand the state matrix A and control matrix B to obtain the expanded state matrix A a and control matrix B a ; 5) According to the state vector X and control vector U, the comprehensive performance evaluation index In δ2(z1-q) 2 ,δ3(z2-z1) 2 Rewrite it into quadratic form to get the quadratic standard form of the index function Q is the state vector weight matrix, R is the control vector weight matrix; N is the cross vector weight matrix of Q and R, is the total running time, δ1, δ2, and δ3 are Weighting coefficients of (z1-q) and (z2-z1); 6) The quadratic form is in standard form Substitute the matrices Q, N, and R in the Riccati equation to find the unique solution P a , based on the unique solution P a Solve for the feedback vector K; 7) According to the control vector Solve for the extended optimal sliding mode control vector U a =-[KB a1 ] -1 [KA a1 X a1 +λ a KX a1 +KG a1 W], yes The first 7 rows of λ a is the sliding mode approach coefficient; 8) Expand the optimal sliding mode control vector U a Substitution Find the control vector U required to control the three-mass two-stage active suspension, that is, the active control force F e .

2. The method for designing a quadratic extended sliding mode controller based on a three-mass two-stage active suspension according to claim 1 is characterized in that: The state matrix Control Matrix Control vector U = (F e ), interference matrix G = [G0 G1 G2], G0 = [-1 0 0 0 0 0 0] T , T0=[0 -1 1] T , G1=[0 0 0 01 / (m c +m e ) 0 0] T ,G2=[0 0 0 0 m e / (m c +m e ) 0 1] T , interference vector Damping Matrix Mass Matrix Stiffness Matrix is the disturbance caused by the nonlinearity of the three-mass two-stage active suspension, λ is 0.001, is the first-order differential of the road roughness input q, F e is the active control force, c p is the damping of the vibration isolation structure; k i is the stiffness of the second accumulator, k a is the stiffness of the first accumulator.

3. The method for designing a quadratic extended sliding mode controller based on a three-mass two-stage active suspension according to claim 2 is characterized in that: Expanded state matrix Expanded control matrix A f1 represents the low-pass filter gain parameter, and B(4:6,:) is the submatrix consisting of the 4th to 6th rows of the control matrix B.

4. The method for designing a quadratic extended sliding mode controller based on a three-mass two-stage active suspension according to claim 3 is characterized by: The error vector e y With the switch term v as input, the expanded state vector As the output, the extended sliding mode observation module is designed, and the canonical state equation of the extended sliding mode observation module is obtained as follows: are the corresponding observation values ​​fed back at the previous moment of x1, x2, x3, x4, x5, x6, and x7, respectively. is the unsprung mass acceleration Observed value is the third mass acceleration Observed value is the sprung mass acceleration Observed value for The first derivative of a =I 10 , I 10 is the 10th-order identity matrix, I7 and I3 are 7th-order and 3rd-order identity matrices respectively, L is any one such that A a (1:7,1:7)+L*A a The spectrum of (8:10,1:7) falls on the 7×3 matrix in the left half of the complex plane. H is an arbitrary 3×3 stable matrix, 0 m×n is a zero matrix with m rows and n columns.

5. The method for designing a quadratic extended sliding mode controller based on a three-mass two-stage active suspension according to claim 4 is characterized in that: Vector weight matrix Control vector weight matrix Cross-vector weight matrix Weighting coefficient matrix A(6,:) and B(6,:) are the 6th rows of the state matrix A and the control matrix B respectively.

6. The method for designing a quadratic extended sliding mode controller based on a three-mass two-stage active suspension according to claim 5 is characterized by: The Riccati equation is: A M (1:7,1:7) represents the matrix A M A is a submatrix consisting of rows 1 to 7 and columns 1 to 7. M (1:7,8) is the matrix A M The submatrix consisting of rows 1 to 7 and columns 8, Q M (1:7,1:7) is the matrix Q M The submatrix consisting of the intersection of rows 1 to 7 and columns 1 to 7, Q M (1:7,8) is the matrix Q M The submatrix formed by the intersection of rows 1 to 7 and column 8, Q M (8,8) is the matrix Q M In the submatrix formed by the intersection of the 8th row and the 8th column, a and b are 0.

001.

7. The method for designing a quadratic extended sliding mode controller based on a three-mass two-stage active suspension according to claim 6 is characterized by: Feedback Vector 8. The method for designing a quadratic extended sliding mode controller based on a three-mass two-stage active suspension according to claim 1 is characterized by: The sliding mode approach coefficient in max(w) represents the maximum absolute value of the interference input W that can be estimated in advance.

9. The method for designing a quadratic extended sliding mode controller based on a three-mass two-stage active suspension according to claim 1 is characterized by: Nonlinear elastic force P a01 is the internal gas pressure of the first accumulator at the equilibrium position, P ai1 is the charging pressure of the first accumulator, S c1 is the working area of ​​the first piston rodless end, V ai1 is the initial gas volume of the first accumulator, n1 is the gas adiabatic index; Nonlinear elastic force P a02 is the internal gas pressure of the second accumulator at the equilibrium position, P ai2 is the second accumulator charging pressure, S c2 is the working area of ​​the second piston rod end, V ai2 is the initial gas volume of the second accumulator; Nonlinear inertial force I is the moment of inertia of the hydraulic pump / motor and the electric motor, is the working state transmission ratio of the hydraulic pump / motor, q b,0 is the theoretical displacement of the hydraulic pump / motor for one revolution, φ0 is the ideal transmission ratio of the hydraulic pump / motor 7; Nonlinear active control force T L is the motor torque, η is the mechanical efficiency of the hydraulic pump / motor, and sgn() is the sign function.

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