Active disturbance rejection control method and system based on error compensation type extended state observer

Abstract

The application discloses a self-disturbance rejection control method and system based on an error compensation type extended state observer, and the method comprises the following steps: a linear self-disturbance rejection controller acquires input signals and each output state of an extended state observer, and outputs a first control signal; the linear self-disturbance rejection controller acquires input signals and each output state of the extended state observer, and outputs the first control signal; an estimation error model of the extended state observer for output displacement is constructed, a controlled object is converted into an integrator series type form, and an output displacement signal is obtained based on the controlled object; the output displacement signal and a control input signal are input into the extended state observer, and each output state is obtained; and then the linear self-disturbance rejection controller and the output displacement model are fed back. The estimation capability of the observer is greatly improved without increasing the bandwidth of the observer; the error compensation type disturbance observer is combined with the self-disturbance rejection control, and the tracking performance of the self-disturbance rejection control is further improved.

Description

Technical Field

[0001] This invention relates to the field of control technology, and in particular to an active disturbance rejection control method and system based on an error-compensated extended state observer. Background Technology

[0002] Piezoelectric actuator-driven nanostages are core components in precision engineering, widely used in atomic force microscopy, micro / nano fabrication, and precision servo systems. With the rapid development of nanotechnology, practical demands for the accuracy and response speed of nanostages are constantly increasing. However, the inherent hysteresis and creep nonlinearity of piezoelectric materials severely affect the accuracy of nanostages. Furthermore, the low damping characteristics of the platform itself make it easy for input signals to excite low-order resonant modes of the nanostage, leading to oscillations in the output displacement. Hysteresis and mechanical resonance couple at high frequencies, further reducing positioning accuracy. Although piezoelectric actuator-driven nanostages offer advantages such as fast response speed, frictionless operation, and high positioning resolution, the aforementioned problems severely hinder further performance improvements.

[0003] The main problem with the widely used linear extended state observer is that when the total disturbance of the system is completely unknown, the observer's ability to estimate the system state and disturbance heavily depends on the observer bandwidth. However, increasing the observer bandwidth leads to a decrease in the system noise level and reduces the system's stability margin. Therefore, how to improve its estimation performance under limited observer bandwidth is an urgent problem to be solved. Solving these problems from the perspective of control systems is of great significance for the practical application of nanostations. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides an active disturbance rejection control method and system based on an error-compensated extended state observer.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0006] An active disturbance rejection control method based on an error-compensated extended state observer includes the following steps:

[0007] The linear active disturbance rejection controller acquires the input signal and the various output states of the extended state observer, and outputs the first control signal;

[0008] An estimation error model of the output displacement by the extended state observer is constructed. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type, and the output displacement signal is obtained based on the controlled object.

[0009] The output displacement signal and control input signal are input to the extended state observer, and the various output states of the extended state observer are output.

[0010] The output states are fed back to the linear active disturbance rejection controller and the output displacement model.

[0011] As one possible implementation, the displacement estimation error model of the extended state observer is constructed by the following steps:

[0012] Acquire the first control signal and total disturbance information to determine the output displacement of the nano-positioning stage;

[0013] Based on the output displacement, system order, and third control signal, a corresponding extended state observer is constructed, and the relevant parameters and bandwidth of the extended state observer are obtained.

[0014] The output displacement of the nanostage is combined with the first estimated state of the extended state observer to obtain the estimation error of the extended state observer with respect to the first state.

[0015] The estimation error of the first state is combined with the first control signal to obtain the second control signal;

[0016] The second control signal is combined with the full disturbance signal to obtain the third control signal;

[0017] By performing a Laplace transform on the error equations for all states of the extended state observer, a frequency domain expression for the first state estimation error of the extended state observer can be obtained.

[0018] As one possible implementation, the output displacement model is represented as: y (n) =f+bu

[0019] Where y represents the output displacement, u represents the first control signal, f represents the total disturbance information, and b is the gain of the first control signal.

[0020] As one possible implementation, the actual state of the linear active disturbance rejection controller is defined as the output displacement and its derivatives, expressed as x1 = y,...,x n =y (n-1) ,x n+1 =f

[0021] The corresponding extended state observer is represented as:

[0022]

[0023] Among them, z i (i = 1...n+1) represent the output states of the extended state observer. ω represents the parameters of the extended state observer. o This represents the bandwidth of the extended state observer, where u represents the first control signal, and when ω o When the output states of the extended state observer approach the preset threshold, they approximate the actual states of the linear active disturbance rejection controller, i.e., z i →x i (i = 1...n).

[0024] As one possible implementation, assume the first control signal is represented as:

[0025]

[0026] The first output displacement is obtained by combining the output displacement model, and the first output displacement is expressed as:

[0027]

[0028] The error of the first extended state observer corresponding to the output displacement is expressed as:

[0029]

[0030] Applying a Laplace transform to the first-state estimation error of the extended state observer yields the observation error of the extended state observer:

[0031] Where E1(s) and D1(s) are the Laplace transforms of e1 and d1, respectively, l n e1 is a low-frequency approximation of the residual perturbation d1.

[0032] As one possible implementation, the linear active disturbance rejection controller is represented as follows:

[0033] u1 = k1(r-z1)-k2z2-...-k n z n

[0034] Where, k i (i=1...n) are the control parameters of the linear active disturbance rejection controller.

[0035] As one possible implementation, assume the second output displacement is expressed as:

[0036] The linear active disturbance rejection controller is then expressed as: u = (k p (r-z1)-k d z2) / b

[0037] in, k d =2ω c ω cThe control bandwidth is represented by d, the disturbance d is a square wave signal, and b represents the gain of the first control signal.

[0038] An active disturbance rejection control system based on an error-compensated extended state observer includes a first module, a second module, a third module, and a fourth module;

[0039] The first module is configured to: acquire the input signal and the various output states of the extended state observer, and output a first control signal;

[0040] The second module is used to construct an estimation error model of the extended state observer for the output displacement. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type, and the output displacement signal is obtained based on the controlled object.

[0041] The third module is used to input the output displacement signal and the control input signal to the extended state observer and output the various output states of the extended state observer.

[0042] The fourth module is used to feed back the various output states to the linear active disturbance rejection controller and the output displacement model.

[0043] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described above.

[0044] An active disturbance rejection control device based on an error-compensated extended state observer includes a memory, a processor, and a computer program stored in the memory and running on the processor. When the processor executes the computer program, it implements the method described above.

[0045] This invention, by adopting the above technical solutions, has significant technical effects:

[0046] This invention significantly improves the estimation capability of the observer without increasing the observer bandwidth; by combining the error-compensated disturbance observer with active disturbance rejection control, the tracking performance of active disturbance rejection control is further improved. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1This is a flowchart of the overall method of the present invention;

[0049] Figure 2 This is a schematic diagram illustrating the construction process of the extended state observer;

[0050] Figure 3 This is a schematic diagram of the extended state observer;

[0051] Figure 4 This is a schematic diagram of active disturbance rejection control based on an extended state observer;

[0052] Figure 5 This is a schematic diagram comparing the control performance based on the extended state observer;

[0053] Figure 6 This is a schematic diagram of the triangular wave tracking results of the nano-positioning stage;

[0054] Figure 7 This is a structural block diagram provided in this application;

[0055] Figure 8 This is a schematic diagram of an electronic device structure provided in this application;

[0056] Figure 9 This is a schematic diagram of the overall system of this application. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the embodiments. The following embodiments are explanations of the present invention, but the present invention is not limited to the following embodiments.

[0058] Example 1:

[0059] An active disturbance rejection control method based on an error-compensated extended state observer, the structure of which can be referred to in the appendix. Figure 7 As shown, the method is as follows Figure 1 As shown, it includes the following steps:

[0060] S100: The linear active disturbance rejection controller acquires the input signal and the various output states of the extended state observer, and outputs the first control signal;

[0061] S200. Construct an estimation error model of the output displacement for the extended state observer. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type, and the output displacement signal is obtained based on the controlled object.

[0062] S300: Input the output displacement signal and control input signal to the expansion state observer, and output the various output states of the expansion state observer;

[0063] S400, Feed back each output state to the linear active disturbance rejection controller and the output displacement model.

[0064] In one embodiment: such as Figure 2 As shown, the process of constructing the displacement estimation error model for the extended state observer is as follows:

[0065] S110. Obtain the first control signal and full disturbance information, and determine the output displacement of the nano-positioning stage;

[0066] S120. Based on the output displacement, system order, and third control signal, construct the corresponding extended state observer and obtain the relevant parameters and bandwidth of the extended state observer.

[0067] S130. Combine the output displacement of the nano-positioning stage with the estimated value of the first state by the extended state observer to obtain the estimation error of the first state by the extended state observer. Combine this error with the first control signal to obtain the second control signal. Based on this, combine the second control signal with the total disturbance estimate to obtain the third control signal.

[0068] S140. Perform a Laplace transform on the error of the extended state observer to obtain the observation error of the extended state observer.

[0069] The output displacement model constructed using the first control signal and the total disturbance information is expressed as: y (n) =f+bu

[0070] Where y represents the output displacement, u represents the first control signal, f represents the total disturbance information, and b is the gain of the first control signal.

[0071] In one embodiment, the actual state of the linear active disturbance rejection controller is assumed to be defined as the output displacement and its derivatives, denoted as x1 = y,...,x n =y (n-1) ,x n+1 If f = , then the corresponding extended state observer is expressed as:

[0072]

[0073] Among them, z i (i = 1...n+1) represent the output states of the extended state observer. ω represents the parameters of the extended state observer. o This represents the bandwidth of the extended state observer, where u represents the first control signal, and when ω o When the output states of the extended state observer approach the preset threshold, they approximate the actual states of the linear active disturbance rejection controller, i.e., z i →x i(i = 1...n).

[0074] In one embodiment, the observation error of the extended state observer is obtained through the following process:

[0075] Assume the first control signal is represented as:

[0076]

[0077] The first output displacement is obtained by combining the output displacement model, and the first output displacement is expressed as:

[0078]

[0079] The estimation error of the extended state observer for each state is expressed as:

[0080]

[0081] This can be further converted to:

[0082] By performing a Laplace transform on the estimation error of the extended state observer for the first state, we obtain the transfer function of this error, i.e.:

[0083] Where E1(s) and D1(s) are the Laplace transforms of e1 and d1, respectively, l n e1 is a low-frequency approximation of the residual perturbation d1.

[0084] In one embodiment, the linear active disturbance rejection controller can be expressed as: u1 = k1(r-z1)-k2z2-...-k n z n

[0085] Where, k i (i=1...n) are the control parameters of the linear active disturbance rejection controller.

[0086] To further illustrate the superiority of the error-compensated extended state observer, the following comparative analysis is conducted, assuming the second output displacement is expressed as:

[0087] The linear active disturbance rejection controller is then expressed as: u = (k p (r-z1)-k d z2) / b

[0088] in, k d =2ω c ω cLet represent the control bandwidth, d be a square wave signal, and b represent the gain of the first control signal. Compare the system's disturbance immunity in the following three scenarios when using this as the control signal and applying square wave disturbances (disturbance amplitude of 20) at t=4 seconds and t=6 seconds:

[0089] Option 1: The total disturbance f is known, and a traditional extended state observer is used.

[0090] Option 2: The total disturbance f is unknown, so a traditional extended state observer is used.

[0091] Option 3: The total disturbance f is unknown, so an error-compensated state observer is used.

[0092] The comparison results are as follows Figure 5 As shown.

[0093] Therefore, it can be seen that the error-compensated extended state observer can still achieve a control effect similar to that when the disturbance is known, even when the disturbance is completely unknown.

[0094] Figure 6 The image shows a comparison of the results of triangular wave tracking using a nanostation under different control methods. The resonant frequency of the nanostation is 100Hz, the damping ratio is 0.02, the ESO bandwidth is 200Hz, and the control bandwidth is 100Hz. It can be seen that the hysteresis and resonant characteristics of the nanostation can be effectively compensated when using closed-loop control. Furthermore, the error curves of active disturbance rejection control based on traditional ESO and error-improved ESO are compared. It can be seen that the method proposed in this invention can reduce the tracking error by more than 50% under the condition that the control parameters are exactly the same, thus verifying the innovation and effectiveness of this invention.

[0095] Example 2:

[0096] An active disturbance rejection control system based on an error-compensated extended state observer, such as Figure 9 As shown, it includes a first module 100, a second module 200, a third module 300, and a fourth module 400;

[0097] The first module 100 is configured to: acquire the input signal and the various output states of the extended state observer, and output the first control signal;

[0098] The second module 200 is used to construct an estimation error model of the output displacement by the extended state observer. Based on the first control signal, the full disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type, and the output displacement signal is obtained based on the controlled object.

[0099] The third module 300 is used to input the output displacement signal and the control input signal to the expansion state observer and output the various output states of the expansion state observer.

[0100] The fourth module 400 is used to feed back each output state to the linear active disturbance rejection controller and the output displacement model.

[0101] Based on the same inventive concept, this application also provides an electronic device that can realize the aforementioned active disturbance rejection control function based on an error-compensated extended state observer. The electronic device includes:

[0102] At least one processor and a memory 82 connected to at least one processor 81. In this embodiment, the specific connection medium between the processor 81 and the memory 82 is not limited. Figure 8 The example shown is the connection between processor 81 and memory 82 via bus 80. Bus 80 is... Figure 8 The connections between other components are indicated by thick lines and are for illustrative purposes only, not as limiting information. Bus 80 can be divided into address bus, data bus, control bus, etc., for ease of representation. Figure 8 The term is represented by a single thick line, but this does not imply that there is only one bus or one type of bus. Alternatively, the processor 81 can also be called a controller; there is no restriction on the name.

[0103] In this embodiment, memory 82 stores instructions executable by at least one processor 81. By executing the instructions stored in memory 82, at least one processor 81 can perform the EGR control method described above. Processor 81 can implement... Figure 7 The functions of each module in the device shown.

[0104] The processor 81 is the control center of the device. It can connect to various parts of the control device through various interfaces and lines. By running or executing instructions stored in memory 82 and calling data stored in memory 82, the processor can perform various functions and process data, thereby monitoring the device as a whole.

[0105] In one possible design, processor 81 may include one or more processing units. Processor 81 may integrate an application processor and a modem processor, wherein the application processor mainly handles the operating system, user interface, and applications, and the modem processor mainly handles wireless communication. It is understood that the modem processor may also not be integrated into processor 81. In some embodiments, processor 81 and memory 82 may be implemented on the same chip; in some embodiments, they may also be implemented on separate chips.

[0106] Processor 81 can be a general-purpose processor, such as a central processing unit (CPU), digital signal processor, application-specific integrated circuit, field-programmable gate array or other programmable logic device, discrete gate or transistor logic device, or discrete hardware component, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the EGR control method disclosed in the embodiments of this application can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules within the processor.

[0107] Memory 82, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs, non-volatile computer-executable programs, and modules. Memory 82 may include at least one type of storage medium, such as flash memory, hard disk, multimedia card, card-type memory, random access memory (RAM), static random access memory (SRAM), programmable read-only memory (PROM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), magnetic storage, magnetic disk, optical disk, etc. Memory 82 can be any other medium capable of carrying or storing desired program code in the form of instructions or data structures that can be accessed by a computer, but is not limited thereto. In the embodiments of this application, memory 82 may also be a circuit or any other device capable of implementing storage functions for storing program instructions and / or data.

[0108] By designing and programming the processor 81, the code corresponding to the EGR control method described in the foregoing embodiments can be embedded into the chip, enabling the chip to execute the code during operation. Figure 4 The steps of the EGR control method in the illustrated embodiment are as follows. How to design and program the processor 81 is a technique well-known to those skilled in the art and will not be described further here.

[0109] Based on the same inventive concept, embodiments of this application also provide a storage medium storing computer instructions that, when executed on a computer, cause the computer to perform the EGR control method described above.

[0110] In some possible implementations, various aspects of the EGR control method provided in this application may also be implemented as a program product comprising program code that, when the program product is run on a device, causes the control device to perform the steps of the EGR control method according to the various exemplary embodiments of this application described above.

[0111] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0112] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0113] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0114] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0115] Furthermore, it should be noted that the shapes and names of the parts and components described in the specific embodiments described in this specification may differ. All equivalent or simple variations made to the structure, features, and principles described in this patent concept are included within the protection scope of this patent. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to replace them, as long as they do not depart from the structure of this invention or exceed the scope defined in these claims, they should all fall within the protection scope of this invention.

Claims

1. A method for active disturbance rejection control based on an error-compensated extended state observer, characterized in that, Includes the following steps: The linear active disturbance rejection controller acquires the input signal and the various output states of the extended state observer, and outputs the first control signal; An estimation error model of the output displacement by the extended state observer is constructed. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type, and the output displacement signal is obtained based on the controlled object. The output displacement signal and control input signal are input to the extended state observer, and the various output states of the extended state observer are output. The output states are fed back to the linear active disturbance rejection controller and the output displacement model; Specifically, an estimation error model for the output displacement by the extended state observer is constructed. Based on the first control signal, the total disturbance signal, and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type. The output displacement signal is then obtained based on the controlled object. Acquire the first control signal and total disturbance information to determine the output displacement of the nano-positioning stage; Based on the output displacement, system order, and third control signal, a corresponding extended state observer is constructed, and the relevant parameters and bandwidth of the extended state observer are obtained. The output displacement of the nanostage is combined with the first estimated state of the extended state observer to obtain the estimation error of the extended state observer with respect to the first state. The estimation error of the first state is combined with the first control signal to obtain the second control signal; The second control signal is combined with the full disturbance signal to obtain the third control signal; By performing a Laplace transform on the error equations for all states of the extended state observer, a frequency domain expression for the first state estimation error of the extended state observer is obtained. The output displacement model is represented as: in, express n First-order output displacement, u Indicates the first control signal. f This represents the full perturbation information. b The gain of the first control signal; The first control signal is represented as: The first output displacement is obtained by combining the output displacement model, and the first output displacement is expressed as: The error of the first extended state observer corresponding to the output displacement is expressed as: Applying a Laplace transform to the first-state estimation error of the extended state observer yields the observation error of the extended state observer: in, and They are and Laplace transform, It is a residual disturbance The low-frequency approximation, Indicates residual disturbance; The linear active disturbance rejection controller is represented as: in, These are the control parameters for the linear active disturbance rejection controller.

2. The active disturbance rejection control method based on an error-compensated extended state observer according to claim 1, characterized in that, The actual state of a linear active disturbance rejection controller is defined as the output displacement and its derivatives, expressed as: The corresponding extended state observer is represented as: in, The first line represents the linear active disturbance rejection controller. A real state, Indicates the output displacement. express First-order output displacement, For each output state of the extended state observer, The parameters represent the extended state observer. This represents the bandwidth of the extended state observer. u Indicates the first control signal, when When the output states of the extended state observer approach the preset threshold, they closely approximate the actual states of the linear active disturbance rejection controller. .

3. The active disturbance rejection control method based on an error-compensated extended state observer according to claim 1, characterized in that, Assume the second output displacement is expressed as: ; The linear active disturbance rejection controller is then expressed as: in, , Indicates control bandwidth, disturbance d A square wave signal is used, and b represents the gain of the first control signal.

4. A self-disturbance rejection control system based on an error-compensated extended state observer, characterized in that, It includes Module 1, Module 2, Module 3, and Module 4; The first module is configured to: acquire the input signal and the various output states of the extended state observer, and output a first control signal; The second module is used to construct an estimation error model of the extended state observer for the output displacement. Based on the first control signal, the total disturbance signal and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type, and the output displacement signal is obtained based on the controlled object. The third module is used to input the output displacement signal and the control input signal to the extended state observer and output the various output states of the extended state observer. The fourth module is used to feed back the various output states to the linear active disturbance rejection controller and the output displacement model; Specifically, an estimation error model for the output displacement by the extended state observer is constructed. Based on the first control signal, the total disturbance signal, and the estimation error of the extended state observer, the controlled object is transformed into a series integrator type. The output displacement signal is then obtained based on the controlled object. Acquire the first control signal and total disturbance information to determine the output displacement of the nano-positioning stage; Based on the output displacement, system order, and third control signal, a corresponding extended state observer is constructed, and the relevant parameters and bandwidth of the extended state observer are obtained. The output displacement of the nanostage is combined with the first estimated state of the extended state observer to obtain the estimation error of the extended state observer with respect to the first state. The estimation error of the first state is combined with the first control signal to obtain the second control signal; The second control signal is combined with the full disturbance signal to obtain the third control signal; By performing a Laplace transform on the error equations for all states of the extended state observer, a frequency domain expression for the first state estimation error of the extended state observer is obtained. The output displacement model is represented as: in, express n First-order output displacement, u Indicates the first control signal. f This represents the full perturbation information. b The gain of the first control signal; The first control signal is represented as: The first output displacement is obtained by combining the output displacement model, and the first output displacement is expressed as: The error of the first extended state observer corresponding to the output displacement is expressed as: Applying a Laplace transform to the first-state estimation error of the extended state observer yields the observation error of the extended state observer: in, and They are and Laplace transform, It is a residual disturbance The low-frequency approximation, Indicates residual disturbance; The linear active disturbance rejection controller is represented as: in, These are the control parameters for the linear active disturbance rejection controller.

5. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 3.

6. An active disturbance rejection control device based on an error-compensated extended state observer, comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 3.

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