A Gain-Scheduled Autopilot Design Method Based on Radial Basis Function

Abstract

The present invention discloses a gain-scheduled autopilot design method based on radial basis functions, belonging to the field of aircraft control technology. The method comprises the following steps: obtaining a gain-scheduled vector and a value range, an LPV model of a nonlinear system, a selected controller structure, and a control system design index; selecting sample points uniformly distributed in the value space of the gain-scheduled vector as characteristic points for gain adjustment of a multi-objective non-smooth optimization algorithm; determining constraints in the form of H∞ norms of closed-loop transfer functions according to the control system design indexes, and using them to establish an optimization problem for gain adjustment at the characteristic points; solving the optimization problem established at each characteristic point, and using them to adjust the controller gain; using a radial basis function model to fit the gain surface of each structural controller respectively, and obtain an RBF surface of all gains; and adjusting the controller gain change according to the RBF curve of all gains, and obtaining a gain-scheduled controller based on the radial basis function.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft control, and in particular relates to a gain-scheduled autopilot design method based on radial basis functions. Background Art

[0002] In existing gain-scheduled autopilots, the classic gain-scheduling design involves selecting characteristic points and designing the corresponding LTI controller. The controller gain surface is typically obtained using linear interpolation. However, due to the first-order discontinuity of linear interpolation, this can cause sudden changes in controller gain, which can impact controller performance. To address this, global adjustments and verification of controller gains are often performed in engineering to ensure smooth transitions.

[0003] To globally adjust and verify controller gains, existing methods for parameterizing controller gain surfaces parameterize the surface of controller gain variation with the dispatch amount using basis functions such as polynomials. Then, using a non-smooth optimization algorithm, with performance and stability indicators at characteristic points as the objective function, the entire controller gain surface is adjusted by adjusting the gain surface parameters. This results in a smooth controller gain surface, eliminating post-processing. However, because the characteristics of the controller gain variation with the gain dispatch amount are difficult to determine in advance, the selection of basis functions is quite challenging. For example, if the polynomial order is too low, the gain surface's nonlinear expressiveness will be limited, resulting in performance loss. If the order is too high, the gain surface will have too many parameters to adjust, introducing a high-dimensional optimization problem and causing the non-smooth optimization algorithm to take too long to find the optimal solution. Furthermore, the "curse of dimensionality" caused by too many adjustment parameters increases the problem complexity, making optimization difficult.

[0004] Therefore, the present invention proposes a design method for a gain-scheduled autopilot based on radial basis functions, which adopts radial basis functions to fit the gain surface. With the help of the strong nonlinear expression ability of radial basis functions, the controller gain surface can be expressed or fitted with higher accuracy through fewer feature points, avoiding the difficulty in selecting basis functions. At the same time, the smooth characteristics of the radial function itself can better avoid the problem of gain mutation, further improving the reliability and practicality of the gain-scheduled autopilot. Summary of the Invention

[0005] In view of this, an object of the present invention is to provide a gain-scheduled autopilot design method based on radial basis functions to solve the above problems.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention provides a gain-scheduled autopilot design method based on radial basis functions, comprising:

[0008] Step 1: Obtain the gain scheduling vector and its value range, the LPV model of the nonlinear system, the selected controller structure and the control system design indicators;

[0009] Step 2: Select sample points evenly distributed in the value space of the gain scheduling vector as feature points for gain adjustment of the multi-objective non-smooth optimization algorithm;

[0010] Step 3: Determine the constraints of the closed-loop transfer function in the form of H∞ norm according to the control system design indicators, and use them to establish the optimization problem of gain adjustment at the characteristic points;

[0011] Step 4: Solve the optimization problem established at each characteristic point to adjust the controller gain;

[0012] Step 5: Use the radial basis function model to fit the gain surface of each structural controller to obtain the RBF surface of all gains;

[0013] Step 6: Adjust the controller gain change according to the RBF curve of all gains to obtain a gain scheduling controller based on radial basis function.

[0014] Furthermore, step 1 includes:

[0015] Acquire the height h, Mach number Mach, speed V, and dynamic pressure q as gain scheduling variables, and determine the value range of the gain scheduling vector according to preset value data;

[0016] Obtain the linear steady-state model of the attitude dynamics of the target device pre-installed in the autopilot, obtain the linear steady-state model of multiple feature points, fit the parameters in the state space expression, and obtain the LPV model of the nonlinear system of the target device motion;

[0017] Obtain the selected controller structure, including: using the classic two-loop autopilot as the basic structure, adding a feedforward link, and using a proportional-integral method to track the pitch angle command;

[0018] Obtain control system design indicators, including the first-order link equivalent time constant and overshoot of the closed-loop system to evaluate the tracking performance of the target device's autopilot, and the relative margin and amplitude margin to evaluate the steady-state performance of the target device's autopilot.

[0019] Furthermore, a linear steady-state model of the attitude dynamics of the target device pre-installed in the autopilot is obtained, including:

[0020]

[0021] in, is the angle of attack, is the pitch angle, is the pitch angular velocity, is the elevator deflection angle; is the dynamic coefficient, which characterizes the dynamic characteristics of the target equipment.

[0022] Furthermore, the parameters in the state space expression are fitted according to the linear steady-state model of multiple characteristic points to obtain the LPV model of the nonlinear system of the target device motion, including:

[0023]

[0024] in, is the angle of attack, is the pitch angle, is the pitch angular velocity, is the elevator deflection angle, h is the altitude of the glider; Ma is the flight Mach number of the glider; 、 、 It represents the value obtained by interpolation after parameter fitting when the glider altitude is h and the Mach number is Ma; 、 It represents the value obtained by interpolation after parameter fitting when the glider altitude is h and the Mach number is Ma.

[0025] Furthermore, the first-order link equivalent time constant and overshoot of the closed-loop system are used to evaluate the tracking performance of the target device's autopilot, while the relative margin and amplitude margin are used to evaluate the steady-state performance of the target device's autopilot, including:

[0026] The equivalent time constant of the first-order link of the overload circuit is 0.5s, and the overshoot of the unit step response is no more than 20%;

[0027] The equivalent time constant of the first-order link of the pitch angle tracking loop is 2s, and the overshoot of the unit step response is no more than 20%;

[0028] The amplitude margin of the closed-loop system shall not be less than 3dB, and the phase margin shall not be less than 30°.

[0029] Furthermore, step 2 includes:

[0030] Based on the Latin hypercube sampling method, the sample points in the gain scheduling variable value space are uniformly sampled, and a preset number of sample points are selected as the feature points of gain adjustment of the multi-objective non-smooth optimization algorithm.

[0031] Furthermore, the constraints for determining the H∞ norm form of the closed-loop transfer function based on the control system design indicators include:

[0032] The tracking performance of the overload loop and pitch angle tracking loop in the control system design index is obtained as the objective function, and the constraints of its closed-loop transfer function in the form of H∞ norm can be expressed as:

[0033] pass represents the tracking performance requirement of the overload instruction; where, Indicates that the instruction is overloaded Tracking Error The transfer function, is the first weight coefficient of the bandpass filter form related to the equivalent time constant and overshoot of the first-order link;

[0034] pass represents the tracking performance requirement of the pitch angle command; where, Indicates the pitch angle command Tracking Error The transfer function, is the second weight coefficient of the bandpass filter form related to the equivalent time constant and overshoot of the first-order link;

[0035] With the stability margin index as the constraint, represents the stability margin requirement; where, Indicates the interference signal To rudder angle command The transfer function, Used to characterize amplitude margin and phase margin, for norm.

[0036] Furthermore, the optimization problem established at each feature point is solved, including:

[0037] A non-smooth algorithm compatible with multiple design criteria is used to solve the optimization problem established at each feature point.

[0038] Furthermore, step 5 includes:

[0039] The basic form of the radial basis function is:

[0040]

[0041] in, is the number of sample points; Representative sample points; represents a constant or polynomial model; is the radial function weight coefficient solved by the linear equation system; represents the radial function;

[0042]

[0043] in, is the shape parameter, and its value is or ,when When it is a constant, the value is zero or calculated by the following formula:

[0044]

[0045] in, is the response value of the sample point, when When the polynomial model is taken as:

[0046]

[0047] in, represents the number of terms in the polynomial function, represents the weight coefficient of the response;

[0048] When the number of polynomials reaches a preset threshold, the orthogonality condition is obtained: , combining the orthogonality condition and radial basis function, we get:

[0049]

[0050] in, , represents the value of the sample point at each radial function; , represents the value of the sample point at each polynomial; , is the weight coefficient of the radial function term; is the weight coefficient of the polynomial term; Represents the transposed matrix of matrix P.

[0051] The beneficial effects of the present invention are:

[0052] Compared with the gain scheduling design method based on parameterized gain surface, the technical solution of the present invention does not require function form selection, avoids the trade-off between nonlinear expression ability and optimization problem dimension, simplifies the design steps, reduces the design difficulty, and is conducive to the automation of aircraft autopilot design.

[0053] Other advantages, objectives, and features of the present invention will be described in the following description and will be apparent to those skilled in the art to some extent, or may be taught by those skilled in the art from the practice of the present invention. The purposes and other advantages of the present invention may be realized and obtained through the structures particularly pointed out in the written description and the accompanying drawings.

[0054] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0056] Figure 1 Flowchart of a method for designing a gain-scheduled autopilot based on radial basis functions in an embodiment of the present invention;

[0057] Figure 2 Schematic diagram of the structure of a pitch channel autopilot for a gliding aircraft in a gain-scheduling autopilot design method based on radial basis functions in an embodiment of the present invention;

[0058] Figure 3 Schematic diagram of characteristic points of an autopilot design in a gain-scheduled autopilot design method based on radial basis functions in an embodiment of the present invention;

[0059] Figure 4 Schematic diagram of a gain-scheduling controller with a fixed structure in a gain-scheduling autopilot design method based on radial basis functions in an embodiment of the present invention;

[0060] Figure 5 Schematic diagram of an overload unit step response curve at a characteristic point in a gain-scheduled autopilot design method based on radial basis functions in an embodiment of the present invention;

[0061] Figure 6 This is a unit step response curve of the pitch angle at a characteristic point in a gain-scheduled autopilot design method based on radial basis functions in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0063] See also Figure 1 , a gain-scheduled autopilot design method based on radial basis function, comprising:

[0064] Step 1: Obtain the gain scheduling vector and its value range, the LPV model of the nonlinear system, the selected controller structure and the control system design indicators;

[0065] Step 2: Select sample points evenly distributed in the value space of the gain scheduling vector as feature points for gain adjustment of the multi-objective non-smooth optimization algorithm;

[0066] Step 3: Determine the constraints of the closed-loop transfer function in the form of H∞ norm according to the control system design indicators, and use them to establish the optimization problem of gain adjustment at the characteristic points;

[0067] Step 4: Solve the optimization problem established at each characteristic point to adjust the controller gain;

[0068] Step 5: Use the radial basis function model to fit the gain surface of each structural controller to obtain the RBF surface of all gains;

[0069] Step 6: Adjust the controller gain change according to the RBF curve of all gains to obtain a gain scheduling controller based on radial basis function;

[0070] The working principle of the above technical solution is as follows: the present invention adopts the optimal Latin hypersquare algorithm to select some uniformly distributed feature points in the entire flight airspace and speed domain, expresses the control system design index in the form of H∞ norm, and establishes the optimization problem of autopilot parameter adjustment at the feature point by imposing constraints on the amplitude of the closed-loop transfer function. The non-smooth optimization algorithm is used to adjust the autopilot gain at the feature point, and finally the radial basis function is used to construct a nonlinear interpolation model of the smooth gain surface to form a gain-scheduled autopilot based on the radial basis function; specifically, the following steps are included: first, a gain scheduling vector and its value range, an LPV model of the nonlinear system, a selected controller structure and a control system design index are given, and uniformly distributed sample points are selected in the value space of the gain scheduling vector as feature points for gain adjustment of the multi-objective non-smooth optimization algorithm. It is recommended to use the improved translation propagation algorithm for processing; then, the control system design index is described as a constraint in the form of the closed-loop transfer function H∞ norm, and the optimization problem of gain adjustment at the feature point is established. Then, at each feature point, the controller gain is adjusted by solving the above-established optimization problem. In this solution, a nonsmooth optimization algorithm compatible with multiple design criteria is preferably used (Nonsmooth optimization algorithm algorithms) to solve the optimization problem; finally, a radial basis function model is used to fit the gain surface of each structural controller to obtain the RBF surface of all gains. The controller gains are adjusted according to the obtained gain RBF surface to obtain a radial basis function-based gain scheduling controller. Finally, the autopilot design is completed based on this gain scheduling controller.

[0071] The beneficial effects of the above technical solution are as follows: the present invention adopts radial basis functions to fit the gain surface. With the help of the strong nonlinear expression ability of the radial basis function, the controller gain surface can be expressed or fitted with higher precision through fewer feature points, avoiding the difficulty in selecting the basis function. At the same time, the smooth characteristics of the radial function itself can better avoid the problem of gain mutation, further improving the reliability and practicality of the gain-scheduled autopilot.

[0072] In one embodiment, step 1 includes:

[0073] Acquire the height h, Mach number Mach, speed V, and dynamic pressure q as gain scheduling variables, and determine the value range of the gain scheduling vector according to preset value data;

[0074] Obtain the linear steady-state model of the attitude dynamics of the target device pre-installed in the autopilot, obtain the linear steady-state model of multiple feature points, fit the parameters in the state space expression, and obtain the LPV model of the nonlinear system of the target device motion;

[0075] Obtain the selected controller structure, including: using the classic two-loop autopilot as the basic structure, adding a feedforward link, and using a proportional-integral method to track the pitch angle command;

[0076] Obtain control system design indicators, including the first-order link equivalent time constant and overshoot of the closed-loop system to evaluate the tracking performance of the target equipment autopilot, and the relative margin and amplitude margin to evaluate the steady-state performance of the target equipment autopilot;

[0077] The working principle and beneficial effects of the above technical solution are as follows: To better describe the technical solution of the present invention, the following uses a gliding aircraft as a specific target device and the autopilot design of a gliding aircraft to illustrate the specific implementation of the radial basis function-based gain scheduling design in the present technical solution. By comparing the radial basis function-based gain scheduling design method (RBFT method) and the parameterized gain surface-based gain scheduling design method (GST method) for gliding aircraft autopilot design, the advantages of the RBFT method of the present invention are obtained;

[0078] Among them, for a gliding aircraft, the nonlinear dynamic equation in the plumb plane is:

[0079]

[0080] in, is the mass of the glider; Indicates the speed of the glider; It represents the drag of the glider in the velocity coordinate system; is the acceleration due to gravity; is the ballistic inclination angle; is the lift of the glider in the velocity coordinate system; It represents the moment of inertia of the glider along the Oz1 axis of the missile body coordinate system; Indicates the angular velocity of the gliding flight along the Oz1 axis; Indicates the moment acting on the Oz1 axis; Indicates the position of the glider along the Ox axis in the ground coordinate system; Indicates the position of the glider along the Oy axis in the ground coordinate system;

[0081] Since the angle of attack of a glider cannot be measured and its range of use is generally within the linear region, long-period variables such as altitude (h), Mach number (Mach), speed (V), and dynamic pressure (q) are used as gain scheduling variables.

[0082] In this specific embodiment, altitude and Mach number are selected as gain scheduling variables. After the values of the gain scheduling variables are given, that is, after the characteristic points are selected, only the attitude motion and dynamics of the glider are of interest. Considering that the glider in this embodiment has no power, the equilibrium point is obtained when the rate of change of the trajectory inclination angle and the rate of change of the pitch angular velocity are zero, that is:

[0083]

[0084] in, is the ballistic inclination angle; Indicates the angular velocity of the gliding flight along the Oz1 axis;

[0085] The values of other variables are given directly, and the differential equations describing the plumb bob plane motion of the glider are Jacobi linearized at the equilibrium point;

[0086] After linearization and replacing the ballistic inclination angle with the angle of attack, the state equation describing the long-period perturbation motion of the glider can be obtained:

[0087]

[0088] in, , For speed, is the angle of attack, is the pitch angle, is the pitch angular velocity, is the elevator deflection angle; is the power coefficient, which characterizes the dynamic characteristics of the aircraft;

[0089] Since the design of the glider control system only focuses on short-cycle motion, the change in speed is ignored and the incremental sign is removed. , ignoring the effect of the rate of change of angle of attack on the pitch angle acceleration, the linear steady-state model that can be used to describe the attitude dynamics of the glider aircraft is further organized as follows:

[0090]

[0091] After obtaining the linear steady-state model at multiple characteristic points, the parameters in the state space expression are fitted to obtain the LPV model of the glider motion:

[0092]

[0093] Wherein, h represents the altitude of the glider; Ma represents the flight Mach number of the glider; 、 、 It represents the value obtained by interpolation after parameter fitting when the glider altitude is h and the Mach number is Ma; 、 It represents the value obtained by interpolation after parameter fitting when the glider altitude is h and the Mach number is Ma;

[0094] At the same time, the first-order link equivalent time constant and overshoot of the closed-loop system are used to evaluate the tracking performance of the glider autopilot, and the phase margin and amplitude margin are used to evaluate the steady-state performance of the glider autopilot. The specific description is as follows:

[0095] (1) The equivalent time constant of the first-order link of the overload circuit is about 0.5s, and the unit step response overshoot should not be greater than 20%;

[0096] (2) The equivalent time constant of the first-order link of the pitch angle tracking loop is about 2s, and the overshoot of the unit step response should not exceed 20%;

[0097] (3) The amplitude margin of the closed-loop system should be no less than 3dB, and the phase margin should be no less than 30°;

[0098] Under the above control system design indicators, the designed autopilot structure is as follows Figure 2 As shown;

[0099] The classic two-loop autopilot is used as the basic structure, with an additional feedforward link to reduce the burden on the feedback loop and further improve the dynamic characteristics of the overload response. Since the steady-state overload response has little impact on the performance of the guidance system, the autopilot structure does not directly consider the control of the steady-state value of the overload response.

[0100] On this basis, in response to the pitch angle control requirements of the mid-range guidance phase, the proportional integral (PI) method is adopted to increase the tracking control of the pitch angle command;

[0101] The altitude and Mach number of the glider are taken as gain scheduling variables, and its servo is described by a second-order oscillation link;

[0102] Since the possible flight altitude and Mach number of a glider aircraft vary greatly, resulting in significant changes in the dynamic characteristics of the glider aircraft, it is difficult to find a satisfactory design result using the traditional GST method. Therefore, the altitude value range of this embodiment is [2000, 12000], and the Mach number value range is [0.45, 0.85].

[0103] In one embodiment, step 2 includes:

[0104] Based on the Latin hypercube sampling method, the sample points in the gain scheduling variable value space are uniformly sampled, and a preset number of sample points are selected as the feature points of the gain adjustment of the multi-objective non-smooth optimization algorithm;

[0105] The working principle and beneficial effects of the above technical solution are as follows: In order to better describe the technical solution, taking the above-mentioned glider as an example, the Latin hypercube sampling method is used to uniformly sample in the gain scheduling variable value space, and 30 feature points are selected for autopilot parameter adjustment. The distribution of feature points is as follows Figure 3 The number of feature points here should be consistent with that of the GST method to facilitate the performance comparison of the autopilot.

[0106] In one embodiment, the constraints of the closed-loop transfer function H∞ norm form are determined according to the control system design index, including:

[0107] The tracking performance of the overload loop and pitch angle tracking loop in the control system design index is obtained as the objective function, and the constraints of its closed-loop transfer function in the form of H∞ norm can be expressed as:

[0108] pass represents the tracking performance requirement of the overload instruction; where, Indicates that the instruction is overloaded Tracking Error The transfer function, is the first weight coefficient of the bandpass filter form related to the equivalent time constant and overshoot of the first-order link;

[0109] pass represents the tracking performance requirement of the pitch angle command; where, Indicates the pitch angle command Tracking Error The transfer function, is the second weight coefficient of the bandpass filter form related to the equivalent time constant and overshoot of the first-order link;

[0110] With the stability margin index as the constraint, represents the stability margin requirement; where, Indicates the interference signal To rudder angle command The transfer function, Used to characterize amplitude margin and phase margin, for norm;

[0111] The working principle and beneficial effects of the above technical solution are as follows: In order to better describe the present technical solution, taking the aforementioned glider as an example, with the tracking performance index of the overload loop and the pitch angle tracking loop as the objective function, its closed-loop transfer function H∞ is expressed as: represents the tracking performance requirement of the overload instruction; where, Indicates that the instruction is overloaded Tracking Error The transfer function, is the first weight coefficient of the bandpass filter in the form of a first-order link equivalent time constant and overshoot. In this specific embodiment, the first weight coefficient is preferably ;pass represents the tracking performance requirement of the pitch angle command; where, Indicates the pitch angle command Tracking Error The transfer function, is a second weight coefficient in the form of a bandpass filter related to the first-order link equivalent time constant and overshoot. In this specific embodiment, the second weight coefficient is preferably = ; With the stability margin index as the constraint, through represents the stability margin requirement; where, Indicates the interference signal To rudder angle command The transfer function, Used to characterize amplitude margin and phase margin, for norm; in this specific embodiment, =0.27 can be guaranteed dB amplitude margin and 30.2° phase margin.

[0112] In one embodiment, solving the optimization problem established at each feature point includes:

[0113] A non-smooth algorithm compatible with multiple design criteria is used to solve the optimization problem established at each feature point;

[0114] The working principle and beneficial effects of the above technical solution are as follows: In order to better describe this technical solution, taking the above-mentioned gliding aircraft as an example, according to the above-established optimization problem:

[0115]

[0116] Where x represents all adjustable gains in the structured controller, and the function and All represent control system evaluation indicators, among which, It is called soft requirements, and as the objective function, It is called hard requirements and is treated as a constraint. and Can be converted into the form shown in the following formula:

[0117]

[0118] in, express norm, is the weight function in the frequency domain, Represents the input and output channel selection function, express Figure 4 The fixed-structure gain-scheduled controller shown in the figure is arrive The closed-loop transfer function of

[0119] exist Figure 4 middle, represents the gain scheduling vector; represents the pending scheduling vector Changing controller gains; and The signals required to represent the control system design indicators; The LPV model representing the nonlinear system consists of all parts except the controller gain;

[0120] For the above optimization problem, due to its one-way infinity, non-convex and non-smooth characteristics, this solution preferably adopts a non-smooth algorithm compatible with multiple design criteria to solve the optimization problem established for each feature point.

[0121] It is worth mentioning that for Figure 2 The pitch channel autopilot structure of the glider shown is shown, Figure 4 The form shown can be transformed by a similar linear fractional method to take the input signal , performance-related output signals , and highlight the gain item to be adjusted.

[0122] In one embodiment, step 5 includes:

[0123] The basic form of the radial basis function is:

[0124]

[0125] in, is the number of sample points; Representative sample points; represents a constant or polynomial model; is the radial function weight coefficient solved by the linear equation system; represents a radial function; in this specific embodiment, this solution preferably adopts a multi-quadratic function as the radial function, and its basic form is:

[0126]

[0127] in, is the shape parameter, and its value is or ,when When it is a constant, the value is zero or calculated by the following formula:

[0128]

[0129] in, is the response value of the sample point, when When the polynomial model is taken as:

[0130]

[0131] in, represents the number of terms in the polynomial function, represents the weight coefficient of the response;

[0132] After adding the polynomial, in order to avoid underdetermination of the radial function, the orthogonality condition is further added: , combined with the orthogonality condition ( ) and the basic form of the radial basis function ( ) can be obtained:

[0133]

[0134] in, , represents the value of the sample point at each radial function; , represents the value of the sample point at each polynomial; , is the weight coefficient of the radial function term; is the weight coefficient of the polynomial term; represents the transposed matrix of matrix P;

[0135] Furthermore, in the radial basis function construction, the global approximation term Take a constant value, the radial function uses the default multi-quadratic function, and the shape parameter Take a constant value, which is the inverse of the sample point size.

[0136] After some debugging, the configuration of the GST method for comparison with RBFT is as follows: each variable takes a standard quadratic polynomial, and uses their product to construct a preset gain surface. Its basic form is:

[0137]

[0138] in, Indicates the adjustable parameters of the preset gain surface, a total of 9; Indicates the height of the preset i-th point; represents the Mach number of the preset j-th point;

[0139] Figure 5 and Figure 6 The unit step response curves of normal overload and pitch angle at characteristic points of the gain-scheduled autopilot designed using the RBFT method and the GST method are compared.

[0140] Analysis of the controller response curves shows that the controller designed using the RBFT method can better meet the tracking performance requirements for normal g-load and pitch angle. In contrast, although the GST method can produce a stable autopilot, the transient responses to normal g-load and pitch angle at different feature points vary greatly, making it unable to meet the tracking performance requirements for normal g-load.

[0141] Based on the above technical solution, the present invention does not require the selection of function form, avoids the trade-off between nonlinear expression ability and optimization problem dimension, simplifies the design steps, reduces the difficulty and conservatism of the design, and is conducive to the automated realization of gliding aircraft autopilot design. At the same time, in a large airspace and speed range, the controller designed using the RBFT method can better meet the tracking performance requirements of normal overload and pitch angle; even in areas where control instructions change rapidly, such as initial release conditions, near the mid-terminal intersection, and at the ballistic terminal, the attitude angle response still has appropriate damping, and the rudder deflection angle remains within a reasonable range.

[0142] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A gain-scheduled autopilot design method based on radial basis function, characterized in that: include: Step 1: Obtain the gain scheduling vector and its value range, the LPV model of the nonlinear system, the selected controller structure and the control system design indicators; Step 2: Select sample points evenly distributed in the value space of the gain scheduling vector as feature points for gain adjustment of the multi-objective non-smooth optimization algorithm; Step 3: Determine the constraints of the closed-loop transfer function in the form of H∞ norm according to the control system design indicators, and use them to establish the optimization problem of gain adjustment at the characteristic points; Step 4: Solve the optimization problem established at each characteristic point to adjust the controller gain; Step 5: Use the radial basis function model to fit the gain surface of each structural controller to obtain the RBF surface of all gains; Step 6: Adjust the controller gain change according to the RBF curve of all gains to obtain a gain scheduling controller based on radial basis function; Wherein, step 5 includes: The basic form of the radial basis function is: in, is the number of sample points; represents the sample point; Indicates the input point; Represents a constant or polynomial model; is the radial function weight coefficient solved by the linear equation system; represents a radial function; in, is the shape parameter, and its value is or ,when When it is a constant, the value is zero or calculated by the following formula: in, is the response value of the sample point, when When the polynomial model is taken as: in, represents the number of terms in the polynomial function, represents the weight coefficient of the response, For about No. polynomials; When the number of polynomials reaches a preset threshold, the orthogonality condition is obtained: , combining the orthogonality condition and radial basis function, we get: in, , represents the value of the sample point at each radial function, express The first Rank List items; , represents the value of the sample point at each polynomial, express The first Rank List items; , is the weight coefficient of the radial function term; is the weight coefficient of the polynomial term; Represents the transposed matrix of matrix P.

2. The design method of a gain-scheduled autopilot based on radial basis function according to claim 1, characterized in that: Step 1 includes: Acquire the height h, Mach number Mach, speed V, and dynamic pressure q as gain scheduling variables, and determine the value range of the gain scheduling vector according to preset value data; Obtain the linear steady-state model of the attitude dynamics of the target device pre-installed in the autopilot, fit the parameters in the state space expression based on the linear steady-state model of multiple feature points, and obtain the LPV model of the nonlinear system of the target device motion; Obtain the selected controller structure, including: using the classic two-loop autopilot as the basic structure, adding a feedforward link, and using a proportional-integral method to track the pitch angle command; Obtain control system design indicators, including the first-order link equivalent time constant and overshoot of the closed-loop system to evaluate the tracking performance of the target device's autopilot, and the relative margin and amplitude margin to evaluate the steady-state performance of the target device's autopilot.

3. The design method of a gain-scheduled autopilot based on radial basis function according to claim 2, characterized in that: Obtain the linear steady-state model of the target device's attitude dynamics pre-installed in the autopilot, including: in, is the angle of attack, is the pitch angle, is the pitch angular velocity, is the elevator deflection angle; is the dynamic coefficient, which characterizes the dynamic characteristics of the target equipment.

4. The method for designing a gain-scheduled autopilot based on radial basis functions according to claim 2, wherein: The parameters in the state space expression are fitted based on the linear steady-state model of multiple characteristic points to obtain the LPV model of the nonlinear system of the target device motion, including: in, is the angle of attack, is the pitch angle, is the pitch angular velocity, is the elevator deflection angle, h is the altitude of the glider; Ma is the flight Mach number of the glider; 、 、 It represents the value obtained by interpolation after parameter fitting when the glider altitude is h and the Mach number is Ma; 、 It represents the value obtained by interpolation after parameter fitting when the glider altitude is h and the Mach number is Ma.

5. The design method of a gain-scheduled autopilot based on radial basis function according to claim 2, characterized in that: The first-order link equivalent time constant and overshoot of the closed-loop system are used to evaluate the tracking performance of the target device's autopilot. The relative margin and amplitude margin are used to evaluate the steady-state performance of the target device's autopilot, including: The equivalent time constant of the first-order link of the overload circuit is 0.5s, and the overshoot of the unit step response is no more than 20%; The equivalent time constant of the first-order link of the pitch angle tracking loop is 2s, and the overshoot of the unit step response is no more than 20%; The amplitude margin of the closed-loop system shall not be less than 3dB, and the phase margin shall not be less than 30°.

6. The design method of a gain-scheduled autopilot based on radial basis function according to claim 1, characterized in that: Step 2 includes: Based on the Latin hypercube sampling method, the sample points in the gain scheduling variable value space are uniformly sampled, and a preset number of sample points are selected as the feature points of gain adjustment of the multi-objective non-smooth optimization algorithm.

7. The design method of a gain-scheduled autopilot based on radial basis function according to claim 1, characterized in that: The constraints for determining the H∞ norm form of the closed-loop transfer function based on the control system design indicators include: The tracking performance of the overload loop and pitch angle tracking loop in the control system design index is obtained as the objective function, and the constraints of its closed-loop transfer function in the form of H∞ norm can be expressed as: pass represents the tracking performance requirement of the overload instruction; where, Indicates that the instruction is overloaded Tracking Error The transfer function, is the first weight coefficient of the bandpass filter form related to the equivalent time constant and overshoot of the first-order link; pass represents the tracking performance requirement of the pitch angle command; where, Indicates the pitch angle command Tracking Error The transfer function, is the second weight coefficient of the bandpass filter form related to the equivalent time constant and overshoot of the first-order link; With the stability margin index as the constraint, represents the stability margin requirement; where, Indicates the interference signal To rudder angle command The transfer function, Used to characterize amplitude margin and phase margin, for norm, is the identity matrix.

8. The method for designing a gain-scheduled autopilot based on radial basis functions according to claim 1, wherein: Solve the optimization problem established at each feature point, including: A non-smooth algorithm compatible with multiple design criteria is used to solve the optimization problem established at each feature point.

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