A stability evaluation method suitable for a multiple-input multiple-output system

Abstract

The application discloses a stability evaluation method suitable for a multiple-input multiple-output system and belongs to the technical field of stability control, which obtains the amplitude margin and the phase margin of the multiple-input multiple-output system by calculating the gain solution of the system at different frequencies when the system is critically stable. The application comprises the following steps: calculating the maximum range of the amplitude margin corresponding frequency according to the spectral radius of the transfer function of the multiple-input multiple-output system; calculating whether the amplitude gain solution exists at different frequencies within the frequency range, and if the amplitude gain solution exists, calculating the corresponding amplitude margin; drawing all the amplitude gains and solving the intersection points with the gain curve to obtain the amplitude margin; calculating the maximum range of the phase margin corresponding frequency according to the spectral radius of the transfer function of the multiple-input multiple-output system; calculating whether the phase gain solution exists at different frequencies within the frequency range, and if the phase gain solution exists, calculating the corresponding phase margin; and drawing all the phase gains and solving the intersection points with the phase gain curve to obtain the phase margin.

Description

Technical Field

[0001] This invention relates to a stability evaluation method applicable to multiple input multiple output systems, belonging to the field of aircraft stability control technology. Background Technology

[0002] The flight envelope of new-generation aircraft is constantly expanding, and the demand for maneuverability is increasing. Their symmetrical configuration results in strong three-channel multi-input multi-output (MIMO) control of pitch, yaw, and roll. Such controlled objects are essentially transformed into MIMO systems, and traditional lateral and longitudinal separation modeling and single-input single-output stability domain evaluation methods can no longer meet the requirements of high-precision control.

[0003] In current technologies, stability margin assessment for multi-input multi-output (MIMO) systems typically involves disconnecting other loops in the MIMO system and using single-input single-output (SSO) system analysis methods to approximate the system's stability margin. This approach assumes other channels are stationary and calculates the stability margin independently for each loop. However, the resulting stability margin is inaccurate and cannot accurately characterize the robustness of the stability control system. Furthermore, common MIMO stability margin assessment methods, such as structural singular value analysis, [further details needed]. The stability margin obtained by analytical methods is relatively small compared to the actual perturbation range of the control system, exhibiting strong conservatism and limiting the dynamic performance in the design process of stable control systems. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a stability evaluation method suitable for multi-input multi-output systems, so as to achieve accurate and fast calculation of stability margin and enhance the system robustness evaluation capability.

[0005] The technical solution of the present invention is: Firstly, a stability evaluation method suitable for multi-input multi-output systems, comprising: A multi-input multi-output model is established based on the kinematic and dynamic characteristics of the aircraft system; Based on the transfer function and maximum amplitude estimation of the multiple input multiple output model, determine the frequency range corresponding to the amplitude margin; Calculate the amplitude gain solution at different frequency ranges within the frequency range corresponding to the amplitude margin; Based on the gain solutions for different frequency ranges, the gain margin is obtained using a graphical method. Based on the transfer function and maximum phase estimate of the multiple-input multiple-output model, determine the frequency range corresponding to the phase margin; Calculate the phase gain solution for different frequency ranges within the frequency range corresponding to the phase margin; Based on the phase gain solutions at different frequency ranges, the phase margin is obtained using a graphical method, enabling stability assessment of the aircraft's multi-input multi-output system.

[0006] Further, determining the frequency range corresponding to the gain margin includes: determining the maximum frequency corresponding to the gain margin based on the spectral radius of the transfer function of the multi-input multi-output system, wherein the maximum frequency corresponding to the gain margin is...

[0007] in , The frequency of maximum amplitude gain. The virtual part, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. Let be the transfer function for input two and output two. To estimate the maximum gain.

[0008] Furthermore, the calculation of the amplitude gain solution in different frequency ranges includes: S21, Calculate frequency At time zero, the main channel gain and secondary channel gain Functional relationship:

[0009] in, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. The transfer function for input two and output two; S22, the calculated frequency is In the complex plane domain, the solution to the generalized closed-loop transfer function is obtained if and only if there exists a non-zero unit vector. satisfy:

[0010] The generalized closed-loop transfer function has a solution; construct an algebraic intermediate variable. ,along with change, It will form a straight line on the complex plane, as change, This will form a circle on the complex plane, if the complex plane; Solve The corresponding circle radius R, and the intersection criterion M of the complex plane circle and the line.

[0011]

[0012] in, Represents the transfer function In frequency The virtual part of the space, Represents the transfer function In frequency The real part of the location; S23, when If a gain solution exists, calculate the gain solution:

[0013] in:

[0014] Obtain the gain solution:

[0015] when At that frequency point, there is no critical stable gain; S24, let Repeat steps S22 and S23 until the frequency reaches its maximum range. ,in For the current calculated frequency point, For the next frequency calculation point, To ensure the accuracy of frequency calculations within the frequency range, This refers to the frequency point index in the iterative operation.

[0016] Furthermore, the gain margin obtained based on the graphical method includes: plotting all gain values, and solving for the intersection of the line y=x and the gain curve to obtain the gain margin: The x-axis is... Plot all of them on the y-axis All gain solutions divide the complex plane into multiple regions, and the region containing the origin is the parameter stable region of the system. The intersection of the region with the line y=x is determined to obtain the gain margin.

[0017] Further, determining the frequency range corresponding to the phase margin includes determining the maximum frequency corresponding to the phase margin based on the spectral radius of the transfer function of the multi-input multi-output system; the maximum frequency corresponding to the phase margin is...

[0018] in , The frequency of maximum phase delay The virtual part, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. Let be the transfer function for input two and output two. To estimate the maximum gain.

[0019] Furthermore, the calculation of the phase gain solution in different frequency ranges includes: S61, when calculating the frequency w, solve for the generalized closed-loop transfer function in the complex plane domain if and only if a non-zero unit vector exists. satisfy:

[0020] The generalized closed-loop transfer function has a solution; construct an algebraic intermediate variable. ,along with , change, , Each of these will form a circle on the complex plane; corresponding Corresponding circle radius , Corresponding circle radius The straight-line distance between the centers of the two circles

[0021]

[0022]

[0023]

[0024] in, For phase delay frequency, The virtual part, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. Let be the transfer function for input two and output two. Represents the transfer function In frequency The virtual part of the space, Represents the transfer function In frequency The real part of the place; S62, if satisfy:

[0025] There are two intersection points:

[0026] in:

[0027]

[0028] in, , for , The corresponding center of the circle, for , The angle between the corresponding circle and the X-axis; Obtaining the phase solution and :

[0029] like Not satisfied There is no critical stable gain at this frequency point; S63, order Repeat steps S61 and S62 until the frequency reaches its maximum range. ,in For the current calculated frequency point, For the next frequency calculation point, To ensure the accuracy of frequency calculations within the frequency range, This refers to the frequency point index in the iterative operation.

[0030] Furthermore, the phase margin obtained based on the graphical method includes: plotting all gain values, and solving for the intersection of the line y=x and the gain curve to obtain the gain margin: The x-axis is... Plot all of them on the y-axis All gain solutions divide the complex plane into multiple regions, and the region containing the origin is the parameter stable region of the system. The intersection of the region with the line y=x is determined to obtain the phase margin.

[0031] In a second aspect, a computer-readable storage medium storing a computer program, characterized in that, when executed by a processor, the computer program implements the steps of the stability evaluation method applicable to a multiple-input multiple-output system.

[0032] Thirdly, a stability evaluation device suitable for multiple-input multiple-output systems includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: when the processor executes the computer program, it implements the steps of the stability evaluation method suitable for multiple-input multiple-output systems.

[0033] The advantages of this invention compared to the prior art are: (1) Based on the estimation of the spectral radius and maximum amplitude / phase of the transfer function, this invention introduces a frequency range estimation method, which effectively reduces the calculation of invalid frequency points and shortens the solution time; (2) This invention introduces a method based on the closed-loop characteristic equation to solve for the gain margin and phase margin at different frequency points, thereby achieving accurate calculation of the critical stable gain and phase. (3) The present invention introduces a plotting method, with the main channel gain as the abscissa and the secondary channel gain as the ordinate, to plot the critical stable solution at all frequency points. The critical stable point divides the plane into several regions, and the region containing the nominal state is the stable region. By selecting an appropriate range, the accurate gain margin and phase margin values ​​can be obtained. Attached Figure Description

[0034] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings: Figure 1 This is a block diagram of a multi-input multi-output model provided in an embodiment of the present invention. Detailed Implementation

[0035] To better understand the above technical solutions, the technical solutions of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solutions of the present invention, rather than limitations on the technical solutions of the present invention. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0036] The following description, in conjunction with the accompanying drawings, provides a more detailed explanation of a stability evaluation method for multi-input multi-output systems provided by embodiments of the present invention. Figure 1 Specific implementation methods may include: establishing a multi-input multi-output (MIMO) model based on the system's kinematics and dynamics; obtaining the frequency range corresponding to the gain margin based on the MIMO model's transfer function and maximum amplitude estimation; obtaining the gain gain solution at different frequencies within the range based on the gain margin's frequency range; obtaining the gain margin based on the gain gain solution at different frequency ranges using a graphical method; obtaining the frequency range corresponding to the phase margin based on the MIMO model's transfer function and maximum phase estimation; obtaining the phase gain solution at different frequencies within the range based on the phase margin's frequency range; and obtaining the phase margin based on the phase gain solution at different frequency ranges using a graphical method.

[0037] In the solution provided in the embodiments of the present invention, in the above-mentioned stability evaluation method applicable to multi-input multi-output systems, the frequency range corresponding to the gain margin is obtained by the following formula based on the multi-input multi-output model transfer function and maximum amplitude estimation:

[0038] in , The frequency of maximum amplitude gain. The virtual part, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. Let be the transfer function for input two and output two. To estimate the maximum gain.

[0039] In the stability evaluation method for multiple-input multiple-output systems described above, the gain solution at different frequencies within the gain margin range is obtained using the following formula: Step 1: Calculate the frequency At time zero, the main channel gain and secondary channel gain Functional relationship:

[0040] Step 2: Calculate R and M corresponding to frequency w.

[0041]

[0042] in, Represents the transfer function In frequency The virtual part of the space, Represents the transfer function In frequency The real part of the place; The third step, This indicates the existence of a gain solution. Calculate the gain solution:

[0043] in:

[0044] Further obtain the gain solution:

[0045] like There is no critical stable gain at this frequency point. Let Repeat step two until the frequency reaches its maximum range. ,in For the current calculated frequency point, For the next frequency calculation point, The accuracy of frequency calculations is determined for traversing the frequency range.

[0046] In the stability evaluation method for multiple-input multiple-output systems described above, the gain margin is obtained based on the gain solutions at different frequency ranges using a graphical method. Plot all gain values ​​using MATLAB, and obtain the gain margin by finding the intersection points of the line y=x and the gain curve. The x-axis is... Plot all of them on the y-axis All gain solutions divide the complex plane into multiple regions, and the region containing the origin is the parameter stable region of the system. By determining the intersection of the region with the line y=x, the gain margin of the system can be obtained.

[0047] In the stability evaluation method for multi-input multi-output systems described above, the frequency range corresponding to the phase margin is obtained from the multi-input multi-output model transfer function and maximum phase estimation using the following formula:

[0048] in , The frequency of maximum phase delay The virtual part, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. Let be the transfer function for input two and output two. To estimate the maximum gain.

[0049] In the stability evaluation method for multi-input multi-output systems described above, the phase gain solution at different frequencies within the phase margin range is obtained using the following formula: Step 1: Calculate the corresponding frequency w. , ,

[0050]

[0051]

[0052]

[0053] like satisfy:

[0054] There are two intersection points:

[0055] in:

[0056]

[0057] Further obtain phase solution and :

[0058] like Not satisfied There is no critical stable gain at this frequency point. Let Repeat step two until the frequency reaches its maximum range. ,in For the current calculated frequency point, For the next frequency calculation point, The accuracy of frequency calculations is determined for traversing the frequency range.

[0059] In the stability evaluation method for multi-input multi-output systems described above, the phase margin is obtained based on the phase gain solutions at different frequency ranges using a graphical method. Plot all gain values ​​using MATLAB, and obtain the gain margin by finding the intersection points of the line y=x and the gain curve. The x-axis is... Plot all of them on the y-axis All gain solutions divide the complex plane into multiple regions, and the region containing the origin is the parameter stable region of the system. By determining the intersection of the region with the line y=x, the phase margin of the system can be obtained.

[0060] Based on and Figure 1Following the same inventive concept, this invention also provides a stability margin evaluation system based on a multiple-input multiple-output (MIMO) system, comprising: a first module for obtaining the frequency range corresponding to the gain margin based on the MIMO model transfer function and maximum amplitude estimation; a second module for obtaining the gain gain solution at different frequencies within the gain margin range; a third module for obtaining the gain margin based on the gain gain solution at different frequency ranges using a graphical method; a fourth module for obtaining the frequency range corresponding to the phase margin based on the MIMO model transfer function and maximum phase estimation; a fifth module for obtaining the phase gain solution at different frequencies within the phase margin range; and a sixth module for obtaining the phase margin based on the phase gain solution at different frequency ranges using a graphical method.

[0061] This invention provides a computer-readable storage medium storing computer instructions that, when executed on a computer, cause the computer to perform... Figure 1 The method described.

[0062] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention 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 and optical storage) containing computer-usable program code.

[0063] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. 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 illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0064] 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.

[0065] 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.

[0066] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

[0067] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A stability evaluation method applicable to multiple-input multiple-output systems, characterized in that, include: A multi-input multi-output model is established based on the kinematic and dynamic characteristics of the aircraft system; Based on the transfer function and maximum amplitude estimation of the multiple input multiple output model, determine the frequency range corresponding to the amplitude margin; Calculate the amplitude gain solution at different frequency ranges within the frequency range corresponding to the amplitude margin; Based on the gain solutions for different frequency ranges, the gain margin is obtained using a graphical method. Based on the transfer function and maximum phase estimate of the multiple-input multiple-output model, determine the frequency range corresponding to the phase margin; Calculate the phase gain solution for different frequency ranges within the frequency range corresponding to the phase margin; Based on the phase gain solutions at different frequency ranges, the phase margin is obtained using a graphical method, enabling stability assessment of the aircraft's multi-input multi-output system.

2. The stability evaluation method for a multi-input multi-output system according to claim 1, characterized in that, The determination of the frequency range corresponding to the gain margin includes: determining the maximum frequency corresponding to the gain margin based on the spectral radius of the transfer function of the multi-input multi-output system, wherein the maximum frequency corresponding to the gain margin is... in , The frequency of maximum amplitude gain. The virtual part, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. Let be the transfer function for input two and output two. To estimate the maximum gain.

3. The stability evaluation method for a multi-input multi-output system according to claim 1, characterized in that, The calculation of the amplitude gain solution in different frequency ranges includes: S21, Calculate frequency At time zero, the main channel gain and secondary channel gain Functional relationship: in, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. The transfer function for input two and output two; S22, the calculated frequency is In the complex plane domain, the solution to the generalized closed-loop transfer function is obtained if and only if there exists a non-zero unit vector. satisfy: The generalized closed-loop transfer function has a solution; construct an algebraic intermediate variable. ,along with change, It will form a straight line on the complex plane, as change, This will form a circle on the complex plane, if the complex plane; Solve The corresponding circle radius R, and the intersection criterion M of the complex plane circle and the line. in, Represents the transfer function In frequency The virtual part of the space, Represents the transfer function In frequency The real part of the location; S23, when If a gain solution exists, calculate the gain solution: in: Obtain the gain solution: when At that frequency point, there is no critical stable gain; S24, let Repeat steps S22 and S23 until the frequency reaches its maximum range. ,in For the current calculated frequency point, For the next frequency calculation point, To calculate the accuracy of frequencies traversed within the frequency range, This refers to the frequency point index in the iterative operation.

4. The stability evaluation method for a multi-input multi-output system according to claim 3, characterized in that, The gain margin obtained based on the graphical method includes: plotting all gain values, and solving for the intersection of the line y=x and the gain curve to obtain the gain margin. The x-axis is... Plot all of them on the y-axis All gain solutions divide the complex plane into multiple regions, and the region containing the origin is the parameter stable region of the system. The intersection of the region with the line y=x is determined to obtain the gain margin.

5. The stability evaluation method for a multi-input multi-output system according to claim 1, characterized in that, Determining the frequency range corresponding to the phase margin includes determining the maximum frequency corresponding to the phase margin based on the spectral radius of the transfer function of the multi-input multi-output system; the maximum frequency corresponding to the phase margin is... in , The frequency of maximum phase delay The virtual part, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. Let be the transfer function for input two and output two. To estimate the maximum gain.

6. The stability evaluation method for a multi-input multi-output system according to claim 1, characterized in that, The calculation of the phase gain solution at different frequency ranges includes: S61, when calculating the frequency w, solve for the generalized closed-loop transfer function in the complex plane domain if and only if a non-zero unit vector exists. satisfy: The generalized closed-loop transfer function has a solution; construct an algebraic intermediate variable. ,along with , change, , Each of these will form a circle on the complex plane; corresponding Corresponding circle radius , Corresponding circle radius The straight-line distance between the centers of the two circles in, For phase delay frequency, The virtual part, A transfer function that corresponds to one input and one output. This is the transfer function for input one to output two. Let be the transfer function for input 2 corresponding to output 1. Let be the transfer function for input two and output two. Represents the transfer function In frequency The virtual part of the space, Represents the transfer function In frequency The real part of the place; S62, if satisfy: There are two intersection points: in: in, , for , The corresponding center of the circle, for , The angle between the corresponding circle and the X-axis; Obtaining the phase solution and : like Not satisfied There is no critical stable gain at this frequency point; S63, order Repeat steps S61 and S62 until the frequency reaches its maximum range. ,in For the current calculated frequency point, For the next frequency calculation point, To calculate the accuracy of frequencies traversed within the frequency range, This refers to the frequency point index in the iterative operation.

7. The stability evaluation method for a multi-input multi-output system according to claim 1, characterized in that, The phase margin obtained based on the graphical method includes: plotting all gain values, solving for the intersection of the line y=x and the gain curve to obtain the gain margin; and using... The x-axis is... Plot all of them on the y-axis All gain solutions divide the complex plane into multiple regions, and the region containing the origin is the parameter stable region of the system. The intersection of the region with the line y=x is determined to obtain the phase margin.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 7.

9. A stability evaluation device for a multiple-input multiple-output system, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

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