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

Abstract

The application discloses a secondary expansion sliding mode controller design method based on a three-mass secondary active suspension in the field of automobile suspension, a motor, a hydraulic pump / motor and a shock absorber hydraulic cylinder of an active damping structure are integrated as a third mass of the suspension to design a secondary expansion sliding mode controller, a motion differential equation of the suspension is established, a non-sprung mass acceleration, a third mass acceleration and a sprung mass acceleration are respectively expanded into a state vector as state quantities, a state matrix and a control matrix are expanded, a comprehensive performance evaluation index is rewritten, a unique solution and a feedback vector are solved out by substituting into Riccati equation, and finally an expansion optimal sliding mode control vector and an active control force are solved out; the application only relies on an acceleration sensor, a vehicle state vector containing a nonlinear force is reconstructed through an easily measured acceleration signal, more accurate suspension structure information is provided for the controller, high-frequency vibration transmitted from the ground to the vehicle body is effectively absorbed, and the control precision is improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of automobile suspension, and particularly relates to a design method of an active suspension structure and a suspension system controller. BACKGROUND

[0002] Suspension is a general term for all force transmission and connecting devices between the vehicle body and the wheels, and plays a crucial role in the controllability, stability and smoothness of the vehicle. 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 damping performance, and can keep the vehicle running smoothly even in harsh road conditions. In long-distance driving of the automobile, it is necessary to effectively suppress the high-frequency vibration transmitted to the vehicle body, but the existing active suspension structure has few corresponding optimizations for high-frequency damping. Moreover, the nonlinearity of the active suspension is a problem that must be considered when designing the suspension controller. If not handled, it will lead to a decrease in the control accuracy of the active suspension and reduce the ride comfort of the vehicle. At present, the mature solution to the problem of nonlinearity of the active suspension is to use the existing optimal sliding mode controller. The optimal sliding mode controller has the advantage of handling uncertain information and has a certain robustness, but it relies on various high-precision sensors to collect the vehicle state information required for controlling the vehicle, which increases the cost, and some vehicle state information is difficult to obtain.

[0003] The document with the Chinese patent publication number CN112549892B and the name "Two-stage damping liquid-electric active suspension with adjustable additional stiffness and damping and working method" proposes a two-stage active suspension with an additional vibration isolation structure based on the general active suspension active damping structure, which can isolate part of the vibration transmitted by the wheels in advance and reduce the demand control force of the active damping structure, but it cannot effectively suppress the high-frequency vibration input by the road. The document with the Chinese patent publication number CN114571940A and the name "Nonlinear suspension control system under uncertain conditions" discloses a sliding mode control strategy based on backstepping control law, which has the problem that various high-precision sensors including road excitation, vehicle body stress and vehicle motion state are used to collect external information to provide demand information for the active control force calculated by the sliding mode controller, but excessive dependence on high-precision sensors will lead to high cost of the entire system, and signals such as the speed of the suspension and the wheel are also difficult to accurately measure by sensors. SUMMARY

[0004] The present application aims at the problem that existing active suspension controllers mostly rely on various high-precision sensors to collect external and vehicle state information and are difficult to effectively control three-mass two-stage active suspension with large nonlinearity, and proposes a design method of a quadratic extended sliding mode controller based on three-mass two-stage active suspension; the quadratic extended sliding mode controller for three-mass two-stage active suspension can accurately observe the nonlinear force caused by the working state change of the accumulator and the hydraulic pump / motor, and improve the control effect.

[0005] The technical scheme of the three-mass two-stage active suspension comprises the following steps:

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

[0007] 2) Establish the motion differential equation of the suspension, select the state vector X=(x1, x2, x3, x4, x5, x6, x7) Τ , and rewrite the differential equation into the state equation of the three-mass two-stage active suspension composed of the state matrix A, the state vector X, the control matrix B, the control vector U, the disturbance matrix G and the disturbance vector W, which contains the nonlinear elastic force △F i of the suspension vibration isolation structure, the nonlinear elastic force △F a of the suspension active damping structure, the nonlinear active control force △F e , and the nonlinear inertial force △F m Wherein, 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 displacement of the third mass m c , z2 is the displacement of the sprung mass m2, is the first-order differential of z1, is the first-order differential of z c ​the first derivative of z2, the first derivative of z2, m e is the equivalent inertia mass, T is the matrix transpose;

[0008] 3) subtract the corresponding acceleration observation value the third mass acceleration and the sprung mass acceleration from the previous time feedback respectively to obtain the corresponding error vector the error vector e y is taken as the input of the sliding mode switching function to obtain the switching term ρ is the sliding mode switching term 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) take the non-sprung mass acceleration the third mass acceleration and the sprung mass acceleration as the state variable extended to the state vector X to obtain the extended state vector and extend the state matrix A and the control matrix B to obtain the extended state matrix A a and the control matrix B a ;

[0010] 5) rewrite the comprehensive performance evaluation index in the quadratic form to obtain the quadratic standard form of the index function δ2(z1-q) 2 , δ3(z2-z1) 2 according to the state vector X and the control vector U Q is the state vector weighting matrix, R is the control vector weighting matrix; N is the cross vector weighting matrix of Q and R, is the total running time, δ1, δ2, δ3 are the weighting coefficients of (z1-q), (z2-z1) respectively;

[0011] 6) substitute the matrices Q, N, R in the quadratic standard form into the Riccati equation to solve the unique solution P a , based on the unique solution P a solving the feedback vector K;

[0012] 7) according to the control vector solving the extended optimal sliding mode control vector U a = -[KB a1 ] -1 [KA​a1 X a1 +λ a KX a1 +KG a1 W], is the first 7 lines, λ a is the sliding mode approach coefficient;

[0013] 8) the extended optimal sliding mode control vector U a is substituted into the formula to obtain the control vector U required for controlling the three-mass secondary active suspension, i.e., the active control force F e .

[0014] Further, the state matrix the control matrix the control vector U=(F e ), the disturbance 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 , the disturbance vector the damping matrix the mass matrix the stiffness matrix is the nonlinear disturbance generated by the three-mass secondary 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] Further, the extended state matrix the extended control matrix A f1 represents the low-pass filter gain parameter, and B(4:6,:) is a submatrix composed of the 4th to 6th rows of the control matrix B.

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

[0017] The present application aims at the fact that the existing controller cannot effectively control the nonlinearity generated by the three-mass two-stage active suspension, and on the basis of the existing two-stage damping structure, the motor, hydraulic pump / motor and damper hydraulic cylinder of the active damping structure are integrated and used as the third mass of the suspension, a twice extended sliding mode controller is designed, only relying on an acceleration sensor, the vehicle state vector containing the nonlinear force not considered by the existing controller is reconstructed through the easily measured acceleration signal, the controller can be provided with more accurate suspension structure information, the high frequency vibration transmitted from the ground to the vehicle body can be effectively absorbed, and the control precision is improved. BRIEF DESCRIPTION OF DRAWINGS

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

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

[0020] Figure 3 Fig. 3 is a block diagram of the design method of the twice extended sliding mode controller of the present application;

[0021] Figure 4 Fig. 4 is a comparison simulation diagram of the body acceleration power spectral density of the existing two-stage active suspension based on LQG control and the suspension of the present application;

[0022] Figure 5 Fig. 5 is a comparison simulation diagram of the body acceleration power spectral density of the suspension of the present application based on the existing sliding mode controller and the suspension of the present application based on the twice extended sliding mode controller 6. DETAILED DESCRIPTION

[0023] As Figure 1The three-mass two-stage active suspension structure shown is located between the vehicle body 1 and the wheels 10 in the vertical direction. The three-mass two-stage active suspension consists of a first hydraulic cylinder 17, a first piston rod 3, a first piston 4, a hydraulic pump / motor 7, a motor 8, and a first accumulator 5, which constitute the active damping 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, a vehicle body acceleration sensor 2, a suspension hydraulic cylinder acceleration sensor 9, and a wheel acceleration sensor 11, which constitute the vibration isolation structure. The secondary extended sliding mode controller 6 is connected to three acceleration sensors, namely the body acceleration sensor 2, the suspension hydraulic cylinder acceleration sensor 9, and the wheel acceleration sensor 11. The acceleration signal is input to 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 corresponding torque, which is converted into hydraulic pressure by the hydraulic pump / motor 7 for vibration damping.

[0024] Vertically, the bottoms of the first hydraulic cylinder 17 and the second hydraulic cylinder 14 are fixed together. One end of the first piston rod 3 outside the cylinder body is connected to the vehicle body 1, and the other 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 on the outer wall of the bottom of the first hydraulic cylinder 17. One end of the oil inlet / outlet is connected to the bottom oil inlet / outlet of the first hydraulic cylinder 17 through an oil passage, and the other end of the oil inlet / outlet is connected to the first accumulator 5 through an oil passage. The motor 8 is fixed on the outer cylinder wall of the second hydraulic cylinder 14, and the hydraulic pump / motor 7 and the motor 8 are connected by a coupling for power transmission. One end of the second piston rod 12 outside the cylinder body is connected to the wheel, and the other 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 bottom oil inlet / outlet of the second hydraulic cylinder 14 through an oil pipe and is equipped with an adjustable flow valve 15. The vibration isolation structure can initially attenuate the vibrations transmitted from the wheel 7 to the body 1. At the same time, by integrating the hydraulic pump / motor 7, the motor 8, the first hydraulic cylinder 17, and the second hydraulic cylinder 14 into an integral structure as the third mass of the suspension, high-frequency vibrations transmitted from the wheel 10 to the body 1 are absorbed.

[0025] Establish Figure 1 The dynamic model of the three-mass two-stage active suspension shown is as follows: Figure 2 As shown, the three-mass two-stage active suspension dynamics model includes the sprung mass m2 composed of the vehicle body mass and the first elastic force F generated by the first accumulator 5. a The active control force F generated by the active vibration reduction structuree The equivalent inertial force F generated by the active vibration reduction structure m The third mass m is composed of 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 Damping force F generated by the vibration isolation structure cp 1. Unsprung mass m1 and tire stiffness k1, and a vehicle body acceleration sensor 2 for measuring sprung mass acceleration; 2. Suspension hydraulic cylinder sensor 9 for measuring third mass acceleration; 3. Wheel acceleration sensor 11 for measuring unsprung mass acceleration; and 4. Control active force F. e Size-dependent secondary expansion sliding mode controller 6, etc. In the vertical direction, Figure 1 The wheel 10 consists 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 damping 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, vibrations caused by road surface unevenness are transmitted to the vehicle body through the wheel, first via the second elastic force F. i With damping force F cp The vibration is initially isolated and attenuated, and then passed through a third mass m. c Effective absorption of high-frequency vibrations, ultimately due to the first elastic force F a Equivalent inertial force F m and active control force F e Precise active control is performed on vibrations that have already been partially isolated and absorbed, minimizing the impact of road-excited vibrations on the vehicle body. The nonlinear elastic force of the active damping structure generated by the nonlinear change in the relationship between the gas and pressure inside the first accumulator 5 is ΔF. a The nonlinear elastic force of the vibration isolation structure generated by the nonlinear change in the relationship between the gas and pressure inside the second accumulator 16 is ΔF. i The nonlinear active control force and nonlinear inertial force generated by the active vibration damping structure due to the change in the transmission ratio of the hydraulic pump / motor under varying operating conditions are respectively ΔF e and △F m .

[0026] The arrangement of the hydraulic pump / motor 7 and the motor 8 is improved by fixing the hydraulic pump / motor 7 and the motor 8 to the outer cylinder wall on the same side near the bottom of the first hydraulic cylinder 17 and the second hydraulic cylinder 14, respectively. This makes 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 In other words, based on the existing two-stage active suspension structure, a third mass m was added by improving the arrangement of the hydraulic pump / motor 7 and the motor 8. c The quality.

[0027] As Figure 3 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. For the existing two-stage suspension controller, it is unable to control the nonlinear elastic force △F a of the three-mass two-stage active suspension active damping structure, the nonlinear elastic force △F i of the isolation structure, the nonlinear active control force △F e , and the nonlinear inertial force △F m . The secondary extended sliding mode controller designed in the application can reconstruct the vehicle state vector containing the nonlinear force not considered by the existing controller through the non-sprung mass acceleration easily measured by the sensor , the third mass acceleration , and the sprung mass acceleration , and provide more accurate suspension structure information for the extended control module to improve the control accuracy. The specific design method of the secondary extended sliding mode controller 6 further includes the following steps:

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

[0029] According to Figure 2 , a detailed dynamic analysis is performed on the vertical motion of the three-mass two-stage active suspension, and the following differential equation of the three-mass two-stage active suspension motion containing the nonlinear elastic force △F a of the active damping structure, the nonlinear elastic force △F i of the isolation structure, the nonlinear active control force △F e , and the nonlinear inertial force △F m not considered by the existing two-stage active suspension is established:

[0030]

[0031] In the formula: k i is the stiffness of the second accumulator 16; k a is the stiffness of the first accumulator 5; c p is the damping of the isolation structure; m e is the equivalent inertial mass; z1 is the displacement of m1; z c is the displacement of the third mass m c of the three-mass two-stage active suspension; z2 represents the displacement of the sprung mass m2; represents the first derivative of z1; represents the first derivative of z c ; represents the first derivative of z2; represents the second derivative of z1; represents the second derivative of z c ; second order differential of z2; k a (z2-z c ) is the first elastic force F a , i.e. F a = k a (z2-z c ); k i (z c -z1) is the second elastic force F i , i.e. F i = k i (z c -z1); is the equivalent inertia force F m , i.e. is the damping force F cp , i.e. q represents the road roughness input; is the first order differential of q; n0 is the spatial reference frequency, taken as 0.1 m -1 ; w represents the road white noise signal with mean value 0 and power spectral density 1; G q (n0) is the road roughness coefficient; u represents the vehicle running speed; f0 represents the lower cut-off frequency of the road input, equal to 0.011u; then the active vibration reduction structure nonlinear elastic force 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 side of the first piston 4, V ai1 is the initial gas volume of the first accumulator 5, and n1 is the gas adiabatic index; the vibration isolation structure nonlinear elastic force 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 side of the second piston 13, V ai2 is the initial gas volume of the second accumulator 16; the nonlinear inertia force where I is the rotational 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 rotation, and 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] Choose the 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 a nonlinear elastic force ΔF, which includes the vibration isolation structure, and consists of state matrix A, state vector X, control matrix B, control vector U, disturbance matrix G, and disturbance vector W. i and the nonlinear elastic force ΔF of the active vibration reduction structure a Nonlinear active control force △F e Nonlinear inertial force ΔF m The three-mass two-stage active suspension state equation:

[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 taken as 0.001; This is the interference caused by the nonlinearity of the three-mass two-stage active suspension.

[0036] Step 2, construct the sliding mode switching function. The unsprung mass acceleration... Third mass acceleration Spring mass acceleration The corresponding observed acceleration value from the previous moment, as fed back. Subtraction yields the error vector The error vector e y As input to the sliding mode switching function in equation (4), the error vector e that can be suppressed is obtained. y The switching term v that makes it close to the vector 0.

[0037]

[0038] In the formula: ρ is the gain of the sliding mode switching term, which affects 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, accelerate the unsprung mass. Third mass acceleration and the acceleration of the sprung mass They are respectively used as state variables The extended state vector is obtained from the state vector X in equation (3). The corresponding state matrix A, control matrix B, and disturbance matrix G are then extended to obtain the extended state matrix A. a Control Matrix B a and interference matrix G a : 0 7×1 For control matrix B a A 7x1 matrix of zeros.

[0040] The error vector e y The expanded state vector is obtained by taking the switch term v as input. Using the output as the basis for designing the extended sliding mode observation module, the canonical state equations of the extended sliding mode observation module are obtained as follows:

[0041]

[0042] In the formula: These are the corresponding observations of the feedback at the previous time step, representing x1, x2, x3, x4, x5, x6, and x7, respectively. Unsprung mass acceleration Observations For the third mass acceleration Observations For the acceleration of the sprung mass Observations for The first derivative; A f1 This represents the gain parameter of the low-pass filter. B(4:6,:) is the submatrix formed by rows 4 to 6 of the control matrix B; C a =I 10 ;I 10 It is a 10th-order identity matrix; I7 and I3 are 7th and 3rd order identity matrix respectively; L is any matrix that makes A a (1:7, 1:7) + L*A a (8:10, 1:7) whose spectrum falls in the left half of the complex plane; H is any 3rd order stable matrix; 0 m×n is a zero matrix of 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] In the formula: 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 weighting coefficients of (z1-q), (z2-z1) respectively, and δ1, δ2 and δ3 are obtained according to the method provided in the literature [A method for determining the weighting coefficients of vehicle suspension LQG control. Chen Shian, Qiu Feng, He Ren, Lu Senlin. Vibration and Shock. 2008 (02): 65-68+176].

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

[0047]

[0048] State vector weighting matrix Control vector weighting matrix Cross vector weighting 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, based on the quadratic standard form of the suspension comprehensive performance evaluation index function , substitute the matrices Q, N, R in the quadratic standard form of the comprehensive performance evaluation index function of formula (7) into the Riccati equation as follows to solve the unique solution P a :

[0050]

[0051] In the formula: A M (1:7, 1:7) represents matrix A. M A submatrix consisting of rows 1 to 7 and columns 1 to 7; A M (1:7,8) is matrix A M The submatrix formed by rows 1 to 7 and column 8; Q M (1:7, 1:7) is the matrix Q. M The submatrix formed by the intersection of rows 1 to 7 and columns 1 to 7; Q M (1:7,8) is 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 taking the value 0.001.

[0052] Step 7, take the P obtained in step 6 a Left multiply A M (1:7,8) T and Q M (1:7,8) T Add them together and insert 1s on the right, then multiply the resulting row vector by Q on the left. M (8,8) -1 right multiplication Finally, the feedback vector K required for the quadratic extended optimal sliding mode controller to control the three-mass two-stage active suspension is calculated:

[0053]

[0054] Step 8: Based on the state matrix A, control matrix B, disturbance matrix G given in Step 1, and the extended state vector obtained in Step 3... The extended control module shown in equation (10) is constructed using the feedback vector K obtained in step 7, and then based on the result obtained in step 3... The first 7 lines The control vector U = (F) from the previous moment is fed back. e The control vector is obtained by merging. control vector X a The extended optimal sliding mode control vector U is obtained by using it as input to the extended control module. a :

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

[0056] wherein: λ a is a sliding mode approaching coefficient, satisfying wherein max(w) represents the maximum value of the absolute value of the disturbance input W which can be predicted in advance.

[0057] Step 9, constructing an extended equation as shown in formula (11) based on the extended optimal sliding mode control vector U a and a and b given in step 6, the extended optimal sliding mode control vector U a is taken as the input of the extended equation, and the output is obtained as the control vector U=(F e ) required for controlling the three-mass secondary active suspension:

[0058]

[0059] wherein: is the first derivative of the control vector U=(F e ), so as to obtain the control vector U=(F e ) required for controlling the three-mass secondary active suspension, that is, the active control force F e .

[0060] Taking a certain vehicle model as an example, the vehicle and controller design related parameters are shown in Table 1. Through MATLAB, a simulation program is written, and a comparative simulation verification of the body acceleration power spectral density is carried out between the existing secondary active suspension and the suspension of the present application. In the verification, the commonly used LQG algorithm is used for active control, and the simulation results are shown in Figure 4 and Table 2. Then, through MATLAB / Simulink, a simulation model is built, and a three-mass secondary active suspension with an existing sliding mode controller and a three-mass secondary active suspension with a quadratic extended sliding mode controller 6 are simulated and verified on a D-level road at a speed of 50 km / h for 120 seconds, and the simulation results are shown in Figure 5 and Table 3, wherein RMS is the abbreviation of root mean square value.

[0061] Table 1

[0062]

[0063] Table 2

[0064]

[0065] Table 3

[0066]

[0067] As shown in Table 2, the suspension system of this invention with vibration absorption function, compared with existing two-stage active suspensions, reduces the root mean square value of the vehicle body acceleration power spectral density by 42.17%. Figure 5 As shown, the root mean square value of the vehicle body acceleration in the high-frequency region of the suspension of the present invention is significantly reduced compared with the existing two-stage active suspension, verifying the third mass m with vibration absorption function. c The suspension system of this invention exhibits superior performance in absorbing high-frequency vibrations. Figure 5 It can be seen that the suspension of the present invention using a secondary extended sliding mode controller has a significantly lower vehicle body acceleration power spectral density compared to the suspension of the present invention using an existing sliding mode controller. According to the data in Table 3, the root mean square value of the vehicle body acceleration power spectral density of the former is 3.91% lower than that of the latter, and the overall performance index J of the suspension is improved by 15%. This verifies that the controller of the present invention has superior control performance for a three-mass two-stage active suspension with a lot of nonlinearity.

[0068] When the secondary extended sliding mode controller 6 constructed according to the present invention is working, the acceleration measured by the wheel acceleration sensor 11 will be... Acceleration sensor 9 of the suspension hydraulic cylinder measured The acceleration measured by vehicle body acceleration sensor 2 With the output of the extended sliding mode observation module Subtraction yields the error vector e y , the error vector e y The switching vector v is obtained by inputting the sliding mode switching function. The error vector e is then used to determine the switching vector. y The switching vector v output by the sliding mode switching function and the control vector U output by the extended equation are used as inputs to the extended sliding mode observation module to observe... And The first 7 lines Combined with the control vector U fed back from the extended vector, we obtain X a The extended optimal sliding mode control vector U is obtained by using it as input to the extended control module. a At the same time, U a Substitute into the extension equation To find the control vector U = (F e The obtained control vector U = (F) e The input is given to the active damping structure to control the entire three-mass two-stage active suspension.

Claims

1. A design method for a secondary extended sliding mode controller based on a three-mass two-stage active suspension, characterized by: Includes the following steps: 1) Fix the hydraulic pump / motor and the electric motor to the outer cylinder wall on the same side near the bottom of the two hydraulic cylinders of the three-mass two-stage active suspension, and establish a dynamic model of the three-mass two-stage active suspension, including the sprung mass m2 composed of the vehicle body mass and the first elastic force F generated by the first accumulator. a Active control force F generated by active vibration damping structure e The equivalent inertial force F generated by the active vibration reduction structure m The third mass m consists of a first hydraulic cylinder, a second hydraulic cylinder, an electric motor, and a hydraulic pump / motor. c The second elastic force F generated by the second accumulator i Damping force F generated by the vibration isolation structure cp Unsprung mass m1 and tire stiffness k1; 2) Establish the differential equation of motion for the suspension and select the state vector X = (x1, x2, x3, x4, x5, x6, x7). Τ The differential equation is rewritten as a system consisting of state matrix A, state vector X, control matrix B, control vector U, disturbance matrix G, and disturbance vector W, which includes the nonlinear elastic force ΔF of the suspension vibration isolation structure. i Nonlinear elastic force ΔF of active damping structure of suspension a Nonlinear active control force △F e Nonlinear inertial force ΔF m The state equation of a 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 surface roughness input, z c For the third mass m c The displacement of z1 is given by z2, where z2 is the displacement of the spring-loaded mass m2. For the first differential of z1, For z c The first-order differential, For the first differential of z2, m e The equivalent inertial mass is T, where T is the matrix transpose. 3) Acceleration of unsprung mass Third mass acceleration and the acceleration of the sprung mass Compare the corresponding acceleration observations fed back from the previous moment. Subtraction yields the corresponding error vector The error vector e y As input to the sliding mode switching function, the switching term is obtained. ρ is the gain of the sliding mode switching term, which is a positive number less than 200; δ is the low-pass filter parameter, which is a positive number less than 1. 4) Acceleration of unsprung mass Third mass acceleration and the acceleration of the sprung mass They are respectively used as state variables Extending to the aforementioned state vector X yields the extended state vector. Then, the state matrix A and control matrix B are extended to obtain the extended state matrix A. a and control matrix B a ; 5) Based on the aforementioned state vector X and control vector U, the comprehensive performance evaluation index is... In δ2(z1-q) 2 δ3(z2-z1) 2 Rewriting it in quadratic form yields the standard quadratic form of the index function. Q is the state vector weighting matrix, R is the control vector weighting matrix, and N is the cross-vector weighting matrix between Q and R. This is the total running time, where δ1, δ2, and δ3 are respectively... The weighting coefficients of (z1-q) and (z2-z1); 6) The aforementioned quadratic standard form Substituting the matrices Q, N, and R into the Riccati equation, we can find the unique solution P. a Based on the unique solution P a Solve for the feedback vector K; 7) Based on 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 lines, λ a This is the sliding mode convergence coefficient; 8) Extend the optimal sliding mode control vector U a Substitution Find the control vector U required to control the three-mass two-stage active suspension, i.e., the active control force F. e .

2. The design method for a secondary extended sliding mode controller based on a three-mass two-stage active suspension according to claim 1, characterized in that: The state matrix Control Matrix Control vector U = (F e The interference matrix is ​​G = [G0 G1 G2], where 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 The disturbance caused by the nonlinearity of the three-mass two-stage active suspension is represented by λ, which is set to 0.

001. F is the first derivative of the road surface roughness input q. e For active control, c p For damping of the vibration isolation structure; k i k is the stiffness of the second accumulator. a The stiffness of the first accumulator.

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

4. The design method for a secondary extended sliding mode controller based on a three-mass two-stage active suspension according to claim 3, characterized in that: The error vector e y The expanded state vector is obtained by taking the switch term v as input. Using this as the output, we design an extended sliding mode observation module, resulting in the following canonical state equation: These are the corresponding observations fed back at the previous time step, representing x1, x2, x3, x4, x5, x6, and x7, respectively. Unsprung mass acceleration Observations For the third mass acceleration Observations For the acceleration of the sprung mass Observations for The first derivative; C a =I 10 I 10 It is a 10th order identity matrix. I7 and I3 are the 7th and 3rd order identity matrices, respectively. Let L be any one such that A a (1:7,1:7)+L*A a The spectrum of (8:10, 1:7) lies in a 7×3 matrix in the left half of the complex plane, where H is any 3×3 stable matrix, 0 m×n It is a zero matrix with m rows and n columns.

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

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

001.

7. The design method for a secondary extended sliding mode controller based on a three-mass two-stage active suspension according to claim 6, characterized in that: Feedback vector 8. The design method for a secondary extended sliding mode controller based on a three-mass two-stage active suspension according to claim 1, characterized in that: The sliding mode approach coefficient in max(w) represents the maximum absolute value of the disturbance input W that can be predicted in advance.

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

Images