Active suspension neural network adaptive control method and system

Abstract

The invention discloses an active suspension neural network adaptive control method and system, and the method comprises the steps: constructing a multi-layer bionic reference model of an active suspension, and carrying out the calculation based on the bionic reference model, and obtaining an expected path of the stroke of the active suspension; tracking errors of the suspension stroke are introduced, system uncertainty factors are approximated through a radial basis function neural network, an active suspension controller is designed, and the controller is used for controlling the stroke of the active suspension to accurately track the stroke expected track output by the bionic reference model. The control method does not depend on any linearization operation, an original nonlinear model is not limited, a nonlinear closed-loop system is converted into an all-wheel-drive system, and asymptotic convergence of the system state is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of active suspension control, and in particular to an active suspension neural network adaptive control method and system. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Due to the inevitable uncertainty factors in practical applications, it is very difficult to establish an accurate active suspension system model. In order to solve the problem of uncertainty factors, researchers have designed many robust control methods for active suspension systems, such as adaptive control, H ∞ Control, sliding mode control, output feedback control, observer-based control, etc. However, these control methods require a full understanding of the upper and lower bounds of uncertainty factors. In response to the situation where uncertainty information is unknown, researchers have proposed many intelligent control methods, such as fuzzy logic systems and neural networks.

[0004] Although the control methods of the above-mentioned active suspension systems are all very meaningful, some methods still require special forms or conditions and there is no general theoretical method. It is well known that in most cases, it is extremely difficult to construct a suitable Lyapunov candidate function, which makes most control methods unusable in practice and lacks theoretical guarantees. In order to solve this problem, the prior art proposes all-wheel drive system methods. These methods can transform the original nonlinear model into an equivalent all-wheel drive system model, promote the construction of the required closed-loop dynamic model, and deal with unknown system parameters, external interference and other problems. However, the control of the active suspension system still faces the following technical problems:

[0005] (1) For active suspension systems with system uncertainty and input dead zone, it is urgent to ensure that the system state converges to zero in theory, adapt to various requirements, and simplify the derivation as much as possible. However, there is currently no comprehensive control framework that can simultaneously guarantee the requirements of adaptability, tracking accuracy, and versatility.

[0006] (2) Most existing active suspension system control methods rely on accurate model parameters. However, for most cases, system parameters, such as sprung mass, may vary greatly in different control tasks and are difficult to measure accurately. Therefore, the control performance of these control methods may be degraded to a large extent.

[0007] (3) In order to simplify the controller design process, most existing control methods directly ignore the input dead zone problem. However, this simplification may greatly reduce the control performance and may cause system instability problems.

[0008] (4) In order to achieve satisfactory driving comfort and road handling, active suspension systems need to consume a lot of control energy. However, in practice, this energy may be limited and lead to increased exhaust emissions. Researchers generally believe that nonlinear factors in active suspension systems are inevitable. However, most existing control methods aim to eliminate nonlinear dynamic responses in order to achieve satisfactory vibration suppression effects. These methods may cause unnecessary energy consumption in the control process. Summary of the invention

[0009] In order to solve the above problems, the present invention proposes an active suspension neural network adaptive control method and system, which combines a bionic reference model and an all-wheel drive system method, solves the problems of system uncertainty and input dead zone constraints, and can ensure that all states of the active suspension system converge to zero.

[0010] In some embodiments, the following technical solutions are adopted:

[0011] An active suspension neural network adaptive control method, comprising:

[0012] Constructing a multi-layer bionic reference model of an active suspension, and calculating a desired trajectory of the active suspension travel based on the bionic reference model;

[0013] The tracking error of the suspension stroke is introduced, and the uncertainty factor of the system is approximated by a radial basis function neural network, and an active suspension controller is designed. The active suspension stroke is controlled by the controller to accurately track the desired trajectory of the stroke output by the bionic reference model.

[0014] The active suspension multi-layer bionic reference model is an X-shaped structure, which is composed of springs, rotational joints and connecting rods.

[0015] As a further solution, the expected trajectory of the active suspension travel is calculated based on the bionic reference model, specifically:

[0016]

[0017] Among them, M a is the mass of the isolated object, z pd is the expected trajectory of the suspension travel, are the first-order derivative and second-order derivative of the desired trajectory of the suspension travel, c1, c2 and Υ are auxiliary functions, s v 、s h are the vertical and horizontal stiffness of the spring, n is the number of layers of the bionic reference model, α1 and α2 are the air resistance coefficient and the rotational friction coefficient, respectively, n x is the number of joints of the bionic reference model, is the second-order derivative of the unsprung displacement; L a , L b are the lengths of the two connecting rods in each layer, θ a ,θ b are the initial angles of the connecting rod with the horizontal direction.

[0018] As a further solution, the tracking error of the suspension travel is specifically:

[0019] e=z p -z pd ;

[0020]

[0021] Among them, z p is the suspension travel, z pd is the expected trajectory of the suspension travel, is the third-order derivative of the desired trajectory of the suspension travel, and e is the suspension travel error; are the first, second and third derivatives of the suspension travel error, respectively, m u0 、m s0 are the sprung and unsprung masses of the active suspension, is the first-order derivative of the uncertainty factor, is the first-order derivative of the active suspension control input, k s0 , k d0 are the stiffness coefficient and the damping coefficient respectively.

[0022] As a further solution, the uncertainty factors of the system are approximated by radial basis neural network, specifically:

[0023]

[0024] in, are the first, second and third derivatives of the suspension travel error, is the first-order derivative of the system uncertainty factor, ω represents the bounded output weight vector, Φ(·) is the activation function, satisfying ||Φ(·)||≤1, and ε represents the approximation error; z pd , are the expected trajectory of suspension travel, the first-order derivative and the second-order derivative of the expected trajectory of suspension travel respectively; is the first derivative of the active suspension control input.

[0025] As a further solution, an active suspension controller is designed, specifically:

[0026]

[0027] Among them, m u0 、m s0 are the sprung and unsprung masses of the active suspension, Respectively represent the estimates of ω and ε, A 0-2 =[a0 a1 a2], a0, a1, a2 are the control gains to be adjusted, k s0 , k d0 are the stiffness coefficient and the damping coefficient respectively.

[0028] As a further solution, the active suspension controller can make the suspension travel, suspension travel speed and suspension travel acceleration of the active suspension converge to zero asymptotically.

[0029] In other embodiments, the following technical solutions are adopted:

[0030] An active suspension neural network adaptive control system, comprising:

[0031] A bionic reference model building module, used to build a multi-layer bionic reference model of an active suspension, and calculate the expected trajectory of the active suspension travel based on the bionic reference model;

[0032] The suspension travel control module is used to introduce the tracking error of the suspension travel, and approximate the system uncertainty factors through the radial basis neural network, and design an active suspension controller. The controller controls the travel of the active suspension to accurately track the expected trajectory of the travel output by the bionic reference model.

[0033] In other embodiments, the following technical solutions are adopted:

[0034] A terminal device includes a processor and a memory, wherein the processor is used to implement instructions; the memory is used to store multiple instructions, and the instructions are suitable for being loaded by the processor and executing the above-mentioned active suspension neural network adaptive control method.

[0035] In other embodiments, the following technical solutions are adopted:

[0036] A computer-readable storage medium stores a plurality of instructions, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the above-mentioned active suspension neural network adaptive control method.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] (1) The control method of the present invention does not rely on any linearization operation, does not impose any restrictions on the original nonlinear model, and transforms the nonlinear closed-loop system into an all-wheel drive system, thereby ensuring the asymptotic convergence of the system state.

[0039] (2) The control method of the present invention introduces a bionic reference model, utilizes the beneficial response of nonlinearity, selectively suppresses the harmful dynamic response of nonlinearity, effectively suppresses vibration, and saves control energy.

[0040] (3) The present invention introduces a radial basis neural network to approximate system uncertainty factors, handles problems such as system uncertainty and input dead zone, and effectively reduces tracking errors.

[0041] (4) The method of the present invention can ensure that all states of the active suspension system (suspension travel, suspension travel speed and suspension travel acceleration) converge asymptotically to zero rather than a small region.

[0042] Other features and additional advantages of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a flow chart of the active suspension neural network adaptive control method in an embodiment of the present invention;

[0044] Figure 2 A schematic diagram of a quarter active suspension system in an embodiment of the present invention;

[0045] Figure 3 Schematic diagram of the X-shaped structure of the multi-layer bionic reference model of the active suspension in an embodiment of the present invention;

[0046] Figure 4 A mechanical diagram of a multi-layer bionic reference model of an active suspension in an embodiment of the present invention;

[0047] Figure 5 Schematic diagram of deformation analysis of a multi-layer bionic reference model of an active suspension in an embodiment of the present invention. DETAILED DESCRIPTION

[0048] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0049] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0050] Embodiment 1

[0051] In one or more embodiments, a neural network adaptive control method for active suspension is disclosed, combining Figure 1 , specifically including:

[0052] S101: constructing a multi-layer bionic reference model of an active suspension, and calculating a desired trajectory of the active suspension travel based on the bionic reference model.

[0053] Bionic approaches can always provide effective solutions to engineering problems. Biologically inspired or behavioral-based approaches have been widely adopted in the design of robotic systems, including mechanical structure design, robotic motion and control algorithms. A large number of biological structures have excellent directional isolation vibration characteristics for physical safety and motion control (e.g., mechanical, vibration). The research inspiration of this embodiment comes from the motion isolation system of limb biological structures, and a bionic limb-rod type structure is used to study the application of beneficial nonlinear characteristics in active control. Biological structures can maintain excellent stability through freely moving legs. Obviously, there is a nonlinear relationship between the displacement and force provided by the legs. In order to describe this nonlinear characteristic, the body, joints and leg bones are considered to be mass, joints and rods, respectively. Muscles and tendons can be imitated by springs with different stiffness coefficients. Therefore, the bionic structure consists of links of asymmetric lengths, horizontal and vertical springs (see Figure 3-Figure 5 ).

[0054] Specifically, the active suspension multi-layer bionic reference model of this embodiment is composed of springs, revolute joints and connecting rods, such as Figure 3-Figure 5 As shown in the figure, the structure is biomimetic and the mass of the isolated object is represented by M a Each layer has four connecting rods, which are composed of two lengths of connecting rods La and Lb. The two lengths of connecting rods are composed of L a ,L b , and the initial angle relative to the horizon is θ a ,θ b Indicates. Note that L b Not less than L a , you can choose And the corresponding initial angle θ a ≥θ b . With a stiffness of s h The lateral linear spring has a stiffness of s v The vertical linear spring is used to simulate the passive muscle. The mass of the isolated object M a The absolute motion displacement is expressed as z pd where upward is chosen as the positive direction and the excitation of the substrate is given by z u express.

[0055] All motion variables are defined by geometric deflection relations, such as Figure 4 and 5 Therefore, the rotational motion of each connecting rod is determined by β a ,β b Indicates that the horizontal motion of the left and right joints at the bottom is represented by x a ,x b Indicates. Figure 4 and 5 It can be seen that this bionic reference model is a one-degree-of-freedom structure, because the rotational motion and horizontal motion can be achieved through the relative motion z pd express.

[0056] The specific parameters of the bionic reference model are as follows: a is the mass of the isolated object, L a ,L b are the lengths of connecting rod A and connecting rod B respectively, θ a ,θ b are the initial angles of link A and link B with the horizontal direction, x a ,x b are the horizontal displacements of connecting rod A and connecting rod B, β a ,β b are the rotation angles of connecting rod A and connecting rod B, n, n x are the number of layers and joints of the bionic reference model, α1 and α2 are the air resistance coefficient and rotational friction coefficient, s v ,s h are the vertical and horizontal stiffness of the spring respectively.

[0057] After calculation, the output of the bionic reference model, that is, the expected trajectory of the suspension travel, is as follows:

[0058]

[0059] Among them, c1 and c2 represent the following auxiliary functions:

[0060]

[0061] Among them, Υ represents the following auxiliary function:

[0062]

[0063] S102: Introduce the tracking error of the suspension travel, and approximate the system uncertainty factors through the radial basis neural network to design an active suspension controller;

[0064] As a specific implementation, this embodiment considers a quarter active suspension system, such as Figure 2 As shown, its dynamic model can be described as follows:

[0065]

[0066]

[0067] Among them, z s ,z u are the sprung displacement and the unsprung displacement respectively; z r is the road excitation, m s ,m u are the sprung mass and unsprung mass, F s (z s ,z u ), are the spring force and damping force, F t (z u ,z r ), are the tire elastic force and damping force respectively, Z(u(t)) is the final control input, and u(t) is the original control input calculated by the control method.

[0068] The expressions for spring force and damping force are as follows:

[0069] F s (z s ,z u ) = k s (z s -z u ) (6)

[0070]

[0071] Among them, k s and k d denote the stiffness and damping coefficient respectively, represent the sprung mass velocity and the unsprung mass velocity respectively.

[0072] In practical applications, there is always an input dead zone for servo motors. The actual control input Z(u(t)) can be described as:

[0073]

[0074] Where b1 and b2 represent the lower and upper bounds of the dead zone, respectively, and a1 and a2 represent unknown functions related to the dead zone characteristics, respectively. To simplify the controller design, the control input is divided into two parts:

[0075] Z(u(t))=u(t)+Δu(t) (9)

[0076] Where Δu(t) represents the control input associated with the deadband.

[0077] From equation (4) and equation (5), we can get:

[0078]

[0079] Then, the suspension travel z is introduced p for:

[0080] z p =z s -z u (11)

[0081] Substituting formula (11) into formula (10), we can get:

[0082]

[0083] To facilitate the subsequent controller design, the tracking error e of the suspension travel is introduced as:

[0084] e=z p -z pd (13)

[0085] Among them, z pd Indicates the suspension travel z p The expected trajectory can be output by the active suspension multi-layer bionic reference model, which will be described in detail later.

[0086] From equations (12) and (13), we can get:

[0087]

[0088] Among them, m u0 , m s0 , k s0 , k d0 Respectively represent m u , m s , k s , k d The nominal value (i.e. given value) of Ω represents the following parameter uncertainty factors:

[0089]

[0090] Obviously, or ∞, so the error system (11) is an all-wheel drive system.

[0091] Taking the derivative of both ends of equation (14) with respect to time, we can obtain:

[0092]

[0093] Among them, m u0 、m s0are the sprung and unsprung masses of the active suspension, is the first-order derivative of the uncertainty factor, is the first-order derivative of the active suspension control input (i.e., controller), k s0 , k d0 are the stiffness coefficient and the damping coefficient respectively.

[0094] To facilitate the subsequent controller design, the following lemma is introduced:

[0095] Lemma 1: For any τ>0, there exists a positive definite symmetric matrix So that:

[0096] φ T (A 0～n-1 ) Β +P Β φ(A 0～n-1 )≤-τP Β (16)

[0097] in,

[0098]

[0099] Where I is the identity matrix, A0, A1, A n-1 is the matrix to be adjusted, A 0～n-1 Need to meet:

[0100]

[0101] Among them, δ>0, λ max (·) indicates the largest eigenvalue.

[0102] The system uncertainty factor Ω can be approximated by the following radial basis neural network:

[0103]

[0104] in, ω represents the bounded output weight vector, Φ(·) is the activation function, satisfying ||Φ(·)||≤1, and ε represents the approximation error.

[0105] Inspired by the all-wheel drive system approach, the controller is designed to:

[0106]

[0107] Among them, A 0-2 =[a0 a1 a2], a0, a1, a2 are the control gains to be adjusted, They represent the estimates of ω and ε respectively, which can be obtained by the following update rate:

[0108]

[0109] Wherein, Γ represents a positive definite diagonal parameter matrix, σ is a positive control gain, and P3 represents the third column of the matrix P, which will be given as follows.

[0110] Substituting formula (19) into formula (15), we can get:

[0111]

[0112] in, They represent ω, The estimation error.

[0113] The closed-loop system (21) can be written as a state-space equation in the following form:

[0114]

[0115] From Lemma 1, we can see that there exists a positive definite symmetric matrix satisfy:

[0116] φ T (A 0～2 )P+Pφ(A 0～2 )≤-τ1P(23)

[0117] where τ1>0 and

[0118]

[0119] The convergence of the system is analyzed below:

[0120] The Lyapunov candidate function is selected as follows:

[0121]

[0122] By taking the derivative of equation (24) with respect to time and substituting the results of equations (19)-(23) into it, we can obtain:

[0123]

[0124] This shows that the closed-loop system is Lyapunov stable and

[0125]

[0126] It can be seen that the suspension travel and its first-order and second-order derivatives (i.e., suspension travel velocity and suspension travel acceleration) all converge asymptotically to 0.

[0127] S103: Controlling the stroke of the active suspension by the controller to accurately track the desired trajectory of the stroke output by the bionic reference model.

[0128] The main purpose of this embodiment is to construct a neural network adaptive control method for an active suspension system so that the suspension travel z p Accurately track the bionic reference model z pd , which is mathematically described as:

[0129]

[0130] In order to better evaluate the control performance of the designed control method, the vehicle body acceleration is introduced The root mean square of energy consumption E is used as evaluation indicators, among which the body acceleration directly corresponds to the ride comfort, and the energy consumption evaluates the energy consumption.

[0131] Vehicle acceleration The root mean square evaluation indicators of energy consumption E are expressed as follows:

[0132]

[0133] Where T represents the experimental time, and the expression of E is:

[0134]

[0135] By controlling the travel of the active suspension through the controller of this embodiment, the desired travel trajectory output by the bionic reference model can be accurately tracked; the vehicle body acceleration obtained under the control method of this embodiment The root mean square evaluation index of energy consumption E is smaller than the corresponding evaluation index obtained by the existing control method, which proves that the vehicle comfort and energy consumption under the control method of this embodiment are better, and the control performance is better.

[0136] Embodiment 2

[0137] In one or more embodiments, an active suspension neural network adaptive control system is disclosed, comprising:

[0138] A bionic reference model building module, used to build a multi-layer bionic reference model of an active suspension, and calculate the expected trajectory of the active suspension travel based on the bionic reference model;

[0139] The suspension travel control module is used to introduce the tracking error of the suspension travel, and approximate the system uncertainty factors through the radial basis neural network, and design an active suspension controller. The controller controls the travel of the active suspension to accurately track the expected trajectory of the travel output by the bionic reference model.

[0140] The specific implementation of the above modules is the same as that in Example 1 and will not be described in detail.

[0141] Embodiment 3

[0142] In one or more embodiments, a terminal device is disclosed, including a server, the server including a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the active suspension neural network adaptive control method in Example 1 when executing the program. For the sake of brevity, the specific process is not repeated.

[0143] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0144] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0145] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software.

[0146] Embodiment 4

[0147] In one or more embodiments, a computer-readable storage medium is disclosed, in which a plurality of instructions are stored, wherein the instructions are suitable for being loaded by a processor of a terminal device and executing the active suspension neural network adaptive control method described in Example 1.

[0148] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. An active suspension neural network adaptive control method, characterized in that: include: Constructing a multi-layer bionic reference model of an active suspension, and calculating a desired trajectory of the active suspension travel based on the bionic reference model; The tracking error of the suspension stroke is introduced, and the uncertainty factor of the system is approximated by a radial basis function neural network, and an active suspension controller is designed. The active suspension stroke is controlled by the controller to accurately track the desired trajectory of the stroke output by the bionic reference model.

2. The active suspension neural network adaptive control method according to claim 1, characterized in that: The active suspension multi-layer bionic reference model is an X-shaped structure, which is composed of a spring, a rotation joint and a connecting rod.

3. The active suspension neural network adaptive control method according to claim 1, characterized in that: The expected trajectory of the active suspension travel is calculated based on the bionic reference model, specifically: Among them, M a is the mass of the isolated object, z pd is the expected trajectory of the suspension travel, are the first-order derivative and second-order derivative of the desired trajectory of the suspension travel, c1, c2 and Υ are auxiliary functions, s v 、s h are the vertical and horizontal stiffness of the spring, n is the number of layers of the bionic reference model, α1 and α2 are the air resistance coefficient and the rotational friction coefficient, respectively, n x is the number of joints of the bionic reference model, is the second-order derivative of the unsprung displacement; L a , L b are the lengths of the two connecting rods in each layer, θ a ,θ b are the initial angles of the connecting rod with the horizontal direction.

4. The active suspension neural network adaptive control method according to claim 1, characterized in that: The tracking error of the suspension travel is specifically: e=z p -with pd ; Among them, z p is the suspension travel, z pd is the expected trajectory of the suspension travel, is the third-order derivative of the desired trajectory of the suspension travel, and e is the suspension travel error; are the first, second and third derivatives of the suspension travel error, respectively, m u0 、m s0 are the sprung and unsprung masses of the active suspension, is the first-order derivative of the uncertainty factor, is the first-order derivative of the active suspension control input, k s0 , k d0 are the stiffness coefficient and the damping coefficient respectively.

5. The active suspension neural network adaptive control method according to claim 1, characterized in that: The uncertainty factors of the system are approximated by radial basis neural network, specifically: in, are the first, second and third derivatives of the suspension travel error, is the first-order derivative of the system uncertainty factor, ω represents the bounded output weight vector, Φ(·) is the activation function, satisfying ||Φ(·)||≤1, and ε represents the approximation error; z pd , are the expected trajectory of suspension travel, the first-order derivative and the second-order derivative of the expected trajectory of suspension travel respectively; is the first derivative of the active suspension control input.

6. The active suspension neural network adaptive control method according to claim 5, characterized in that: Design an active suspension controller by: Among them, m u0 、m s0 are the sprung and unsprung masses of the active suspension, Respectively represent the estimates of ω and ε, A 0-2 =[a0 a1 a2], a0, a1, a2 are the control gains to be adjusted, k s0 , k d0 are the stiffness coefficient and the damping coefficient respectively.

7. The active suspension neural network adaptive control method according to claim 6, characterized in that: The active suspension controller can make the suspension travel, suspension travel speed and suspension travel acceleration of the active suspension converge to zero asymptotically.

8. An active suspension neural network adaptive control system, characterized in that: include: A bionic reference model building module, used to build a multi-layer bionic reference model of an active suspension, and calculate the expected trajectory of the active suspension travel based on the bionic reference model; The suspension travel control module is used to introduce the tracking error of the suspension travel, and approximate the system uncertainty factors through the radial basis neural network, and design an active suspension controller. The controller controls the travel of the active suspension to accurately track the expected trajectory of the travel output by the bionic reference model.

9. A terminal device, comprising a processor and a memory, wherein the processor is used to implement instructions; and the memory is used to store multiple instructions, characterized in that: The instructions are suitable for being loaded by a processor and executing the active suspension neural network adaptive control method described in any one of claims 1-7.

10. A computer-readable storage medium storing a plurality of instructions, characterized in that: The instructions are suitable for being loaded by a processor of a terminal device and executing the active suspension neural network adaptive control method described in any one of claims 1-7.

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