An optimization method for the rotor cross-tilt angle of a multi-rotor aircraft

Abstract

The present invention discloses a method for optimizing the cross-tilt angle of the rotors of a multi-rotor aircraft, including a method for cross-tilt configuration of the rotors and a specific analysis and optimization method for the cross-tilt angle of the rotors. The method of the present invention can comprehensively consider the influence of the cross-tilt angle of the rotors on the throttle of each channel of the aircraft, as well as the influence of the installation error of the tilted rotors on the yaw control throttle. The cross-tilt angle of the rotors optimized by the present invention can not only improve the maneuvering efficiency of the yaw motion of the multi-rotor aircraft, reduce the yaw control throttle amount, but also minimize its coupling with the attitude and lift control channels, and further reduce the requirements for the installation accuracy of the rotor power system.

Description

Technical Field

[0001] The present invention belongs to the field of aircraft design, and particularly relates to a method for optimizing the cross-tilt angle of the rotors of a multi-rotor aircraft. Background Art

[0002] Urban air transportation and various special flight missions (such as aerial sightseeing, logistics transportation, anti-terrorism and riot prevention, post-disaster rescue, etc.) have put forward higher requirements for the yaw (steering) control performance of multi-rotor aircraft. During the actual flight process, the installation error of the tilted rotors has a great influence on the yaw control, and the installation accuracy problem is inevitable. Especially in the case of large loads, as the tangential component of the rotor thrust increases, the yaw control throttle needs to be further increased, making it more difficult to maintain and control the body's turning, and even shortening the endurance time. Therefore, it is necessary to study a method to improve the yaw control operation efficiency of multi-rotor aircraft without affecting other control channels as much as possible.

[0003] Adopting the scheme of cross-tilted rotors can well improve the yaw control operation efficiency of multi-rotor aircraft. However, too small a cross-tilt angle of the rotors cannot effectively improve the yaw operation efficiency and reduce the yaw throttle; too large a cross-tilt angle of the rotors will greatly reduce the vertical component of the rotor thrust, thereby increasing the hover throttle and increasing the coupling effect between each control channel, which will instead shorten the endurance time and even lead to control difficulties. In addition, when determining the cross-tilt angle of the rotors, the influence of the installation error of the tilted rotors on the yaw control throttle also needs to be considered. Therefore, it is necessary to propose an optimization method for the cross-tilt angle of the rotors of a multi-rotor aircraft that can improve the yaw operation efficiency of the multi-rotor aircraft, does not affect other control channels as much as possible, and can reduce the installation accuracy requirements of the rotor power system. Summary of the Invention

[0004] The purpose of the present invention is to provide an optimization method for the cross-tilt angle of the rotors of a multi-rotor aircraft in view of the deficiencies of the prior art.

[0005] The purpose of the present invention is achieved through the following technical solutions: An optimization method for the cross-tilt angle of the rotors of a multi-rotor aircraft, comprising:

[0006] (1) Establish a flight dynamics model of a multi-rotor aircraft with the cross-tilt angle i n parameter.

[0007] (2) Add the installation error or tolerance range of the tilted rotors to the above model.

[0008] (3) Design a numerical optimization method with double iteration properties, taking the minimum sum of the squares of the total throttle of each channel of the aircraft as the objective function, and optimize to obtain the cross-tilt angle of the rotors under the current load, flight speed, and the installation error or tolerance range of the tilted rotors.

[0009] Further, step (3) includes:

[0010] The design variable for the main iteration optimization is the rotor cross-tilt angle i n , the constraint of the design variable is the available range of the rotor cross-tilt angle, and the initial iteration value of the design variable i n is 0 degrees, and the objective function is to minimize the sum of squares of the total throttle commands of the aircraft, where the sum of squares of the total throttle commands of the aircraft is obtained by sub-iteration. The main iteration uses a numerical optimization method to determine whether the objective function converges. If it converges, the current rotor cross-tilt angle i n is output, otherwise, according to the objective function and the current design variable, the rotor cross-tilt angle i n is continuously updated until convergence.

[0011] The design variables for the sub-iteration optimization are the state variables and control variables in the flight dynamics model, and the initial iteration values are defaulted to 0, where the initial values of the body-axis system velocities can be given according to the flight mission or defaulted to 0; the end values are the earth-axis system flight velocities required by the flight mission, and the objective function is to trim the right-hand side of the flight dynamics model to make the aircraft reach a steady-level flight state. The sub-iteration uses a numerical optimization method to determine whether the objective function converges. If it converges, the sum of squares of the total throttle commands of the aircraft is output and the main iteration is entered, otherwise the state variables and control variables are continuously updated until convergence.

[0012] Further, the rotor tilts around the direction of the arm, where the tilt angle directions between adjacent rotors are opposite and the magnitudes are the same. After tilting, the rotor generates a tangential tension component, thereby generating a yaw moment on the center of gravity of the fuselage.

[0013] If it has been ensured that the yaw moment is in the same direction as the negative torque generated by the rotor on the fuselage, the constraint equation for the main iteration design variable is:

[0014] 0° ≤ i n ≤ 30°

[0015] If it is not certain whether the yaw moment is in the same direction as the negative torque generated by the rotor on the fuselage, the constraint equation for the main iteration design variable is:

[0016] -30° ≤ i n ≤ 30°

[0017] Further, step (3) includes the following steps:

[0018] (3.1) Give the initial value of the main iteration design variable i n , and the initial iteration value is defaulted to 0.

[0019] (3.2) Enter the main iteration calculation process: Use the current main iteration design variable i nUpdate the flight dynamics model of the multi-rotor aircraft, and add the rotor tilt installation error or tolerance range to the model.

[0020] (3.3) Enter the sub-iteration calculation process: Give the initial value and end value of the sub-iteration design variables. The initial value of the design variable iteration is defaulted to 0, and the initial value of the body-axis system speed can be given according to the flight mission or defaulted to 0; the end value is the earth-axis system flight speed required by the flight mission. Use the numerical optimization method for iterative calculation until the right-hand side term of the trimmed flight dynamics mathematical model is balanced, and then output the sum of squares of the total throttle commands of the aircraft to the main iteration;

[0021] (3.4) Then enter the main iteration calculation process: Use the numerical optimization method to determine whether the sum of squares of the current total throttle commands of the aircraft converges. If so, output i n ; if not, update the main iteration design variable i n and return to step (3.2).

[0022] Further, the numerical optimization method is the sequential quadratic programming algorithm.

[0023] Further, the iteration accuracy of the main iteration objective function is 10 -5 .

[0024] Further, the iteration accuracy of the sub-iteration objective function is 10 -5 .

[0025] Further, the multi-rotor aircraft is an aircraft with four or more even rotors.

[0026] Further, the cross-tilt means that the rotor tilts around the direction of the arm, and the tilt angles between adjacent rotors are opposite.

[0027] Further, analyze the rotor cross-tilt angles under different loads, different absolute values of the total rotor tilt installation errors, and different flight speeds, and finally select a reasonable rotor cross-tilt angle with the flight mission as the goal.

[0028] The beneficial effects of the present invention are as follows: The present invention comprehensively considers the influence of the rotor cross-tilt angle on the throttle of each channel of the aircraft, and the influence of the rotor tilt installation error on the yaw control throttle. The rotor cross-tilt angle optimized by the present invention can not only improve the maneuvering efficiency of the yaw motion of the multi-rotor aircraft, reduce the yaw control throttle amount, but also minimize its coupling with the attitude and lift control channels, and further reduce the requirements for the installation accuracy of the rotor power system. Description of the Drawings

[0029] Figure 1 Flowchart of the rotor cross-tilt angle optimization method;

[0030] Figure 2 It is a schematic diagram of the rotor cross-tilt scheme;

[0031] Figure 3 It is a schematic diagram of a numerical optimization method with double iterative properties. Specific implementation manners

[0032] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0033] As Figure 1 shown, an optimization method for the rotor cross-tilt angle of a multi-rotor aircraft according to the present invention, wherein the multi-rotor aircraft specifically refers to a vertical take-off and landing aircraft with four or more even rotors, and the cross-tilt specifically refers to the rotor tilting at a small angle with the arm direction as the axis, and the tilting angles between adjacent rotors are opposite; specifically including:

[0034] 1) A rotor cross-tilt configuration method, including the following steps:

[0035] 1.1) As Figure 2 shown, the rotor tilts at a small angle with the arm direction as the axis, and the tilting angle directions between adjacent rotors are opposite and the magnitudes are the same.

[0036] 1.2) After tilting, the rotor generates a small tangential tension component, which will generate a yaw moment on the center of gravity of the fuselage.

[0037] 1.3) Ensure that the yaw moment is in the same direction as the negative torque generated by the rotor on the fuselage.

[0038] 2) A specific analysis and optimization method for the rotor cross-tilt angle, which is realized through the following steps:

[0039] 2.1) Establish a flight dynamics model of a multi-rotor aircraft with a rotor cross-tilt angle i n parameter.

[0040] 2.2) In the flight dynamics model of the multi-rotor aircraft established in step 2.1), add the rotor tilting installation error or tolerance range.

[0041] 2.3) Design a numerical optimization method with double iterative properties, with the minimum sum of the squares of the total throttle of each channel of the aircraft as the objective function, and optimize to obtain the rotor cross-tilt angle under the current load, flight speed and rotor tilting installation error (or tolerance range).

[0042] The design variable of the main iterative optimization is the rotor cross-tilt angle i n, the design variable constraint is the available range of the rotor cross-tilt angle (0 to 30 degrees), the initial iteration value is 0 degrees, the objective function is to minimize the sum of the squares of the total throttle of each channel of the aircraft, and the sum of the squares of the total throttle commands of the aircraft is obtained by sub-iteration. The main iteration uses a numerical optimization method to judge whether the objective function converges (for example, the iteration accuracy is 10 -5 ), if it converges, output the current rotor cross-tilt angle i n , otherwise, continue to update the rotor cross-tilt angle i according to the objective function and the design variable n until it converges.

[0043] The design variables for sub-iteration optimization are the state variables and control variables in the flight dynamics model. The initial values of the sub-iteration design variables are defaulted to 0. Among them, the initial value of the body-axis system speed in the state variables can be given according to the flight mission or defaulted to 0; the end value is the earth-axis system flight speed required by the flight mission; the objective function is to trim the right-hand side of the flight dynamics mathematical model, that is, the aircraft reaches a steady-state level flight state. The sub-iteration uses a numerical optimization method to judge whether the objective function converges (for example, the iteration accuracy is 10 -5 ), if it converges, output the sum of the squares of the total throttle commands of the aircraft and enter the main iteration, otherwise continue to update the state variables and control variables until it converges.

[0044] 4) Analyze the rotor cross-tilt angles under different loads, different absolute values of the total rotor tilt installation error, and different flight speeds, and finally select a reasonable rotor cross-tilt angle with the flight mission as the goal.

[0045] Taking an eight-axis and sixteen-propeller multi-rotor aircraft of a certain model as an example, an embodiment of the rotor cross-tilt angle optimization method for a multi-rotor aircraft of the present invention is as follows:

[0046] Basic parameters of the whole machine: the unloaded mass is 374 kg, 47-inch propellers and U15L model Tmotor power system, the distance from the rotor motor mount to the center is 1.7 m, and the upper and lower propeller blades rotate at the same speed and in the same direction.

[0047] First, establish a flight dynamics model of a multi-rotor aircraft with the rotor cross-tilt angle i n parameter:

[0048]

[0049] Among them, t represents time. The state variable x includes the body-axis system speed (u, v, w), angular velocity (p, q, r), attitude angles (phi, theta, psi), and earth-axis system speed (Vx, Vy, Vz); u, v, and w respectively represent the forward, lateral, and vertical speeds in the body-axis system; p, q, and r respectively represent the roll angular velocity, pitch angular velocity, and yaw angular velocity in the body-axis system; phi, theta, and psi respectively represent the roll angle, pitch angle, and yaw angle. Denote the first derivative of the state variable \(x\) with respect to time \(t\). The control variable \(u\) includes the average rotor thrust throttle command \(dt\), the pitch throttle command \(de\), the roll throttle command \(da\), and the yaw throttle command \(dr\).

[0050] Add the rotor tilt installation error (or tolerance range) to the model. Here, two tolerance ranges are taken:

[0051] 1. Conventional error range: The absolute value of the total installation error of the coaxial power system on the eight arms shall not exceed 4.8 degrees, that is, on average, the absolute value of the installation error of the coaxial power system on each arm shall not exceed 0.6 degrees.

[0052] 2. Larger error range: The absolute value of the total installation error of the coaxial power system on the eight arms shall not exceed 8 degrees, that is, on average, the absolute value of the installation error of the coaxial power system on each arm shall not exceed 1 degree.

[0053] Then, design the optimization problem corresponding to the main iteration. Its design variables, objective function, and constraint equations are as follows:

[0054] Design variable: The rotor cross-tilt angle \(i\) n .

[0055] Objective function: Minimize the sum of the squares of the total throttle commands of the aircraft, that is:

[0056] \(\min J = dt\) 2 + de 2 + da 2 + dr 2

[0057] Constraint equation: Since the objective function is set to minimize the sum of the squares of the total throttle commands of the aircraft, the constraint on the rotor cross-tilt angle \(i\) n can be appropriately relaxed. After the rotor tilts, the tangential component of its thrust will generate a yaw moment on the center of gravity of the aircraft body.

[0058] If it is ensured that this yaw moment is in the same direction as the negative torque generated by the rotor on the aircraft body, the constraint equation is:

[0059] \(0^{\circ}\leq i\) n \(\leq 30^{\circ}\)

[0060] If it is not certain whether this yaw moment is in the same direction as the negative torque generated by the rotor on the aircraft body, the constraint range can be extended to:

[0061] \(-30^{\circ}\leq i\) n \(\leq 30^{\circ}\)

[0062] At this time, the numerical optimization time will slow down, but ultimately it can converge to the same optimal solution. The rotor cross-tilt angle generated by each main iteration will be assigned to the parameter \(i\) in the flight dynamics modeln 。

[0063] Next, design the optimization problem corresponding to the sub-iteration. Its design variables, objective function, initial and terminal conditions are as follows:

[0064] Design variables: state variable \(x\) and control variable \(u\).

[0065] Objective function: balance the right side of the flight dynamics mathematical model, that is, the aircraft reaches the steady-state level flight state.

[0066]

[0067] \(p = 0, q = 0, r = 0, \psi = 0\)

[0068] Initial value: The initial values of the state variable and the control variable are defaulted to 0; among them, the initial value of the body-axis system speed in the state variable can be given according to the flight mission or defaulted to 0.

[0069] Terminal value: The earth-axis system flight speeds \((V_x, V_y, V_z)\) required by the flight mission, \(V_y\) and \(V_z\) are 0 during forward flight.

[0070] After the sub-iteration ends, output the sum of squares \(J\) of the total throttle commands of the aircraft to the main iteration for further optimization calculation.

[0071] Both the main iteration and the sub-iteration use the sequential quadratic programming (SQP) algorithm for solution. The numerical optimization calculation process is as Figure 3 shown, including:

[0072] a) Give the initial iteration value of the main iteration design variable \(i\) n : Defaulted to 0 degrees.

[0073] b) Enter the main iteration calculation process: Use the current main iteration design variable \(i\) n to update the flight dynamics model of the multi-rotor aircraft, and add the rotor tilt installation error or tolerance range to the model.

[0074] c) Enter the sub-iteration calculation process: Give the initial value and the terminal value of the sub-iteration design variable (the initial value of the sub-iteration design variable is defaulted to 0, among which the initial value of the body-axis system speed in the state variable can be given according to the flight mission or defaulted to 0; the terminal value is the earth-axis system flight speed required by the flight mission). Use the SQP algorithm for iterative calculation, and the objective function is to balance the right side of the flight dynamics mathematical model. If the objective function converges (for example, the iteration accuracy is 10 -5 ), then output the sum of squares of the total throttle commands of the aircraft and enter the main iteration. Otherwise, continue to update the state variable and the control variable until convergence.

[0075] d) Then enter the main iterative calculation process: The main iteration uses the SQP algorithm to determine whether the objective function (the sum of the squares of the total throttle commands of the aircraft) converges (for example, the iteration accuracy is 10 -5 ), if it converges, output the current rotor cross-tilt angle i n , otherwise update the main iteration design variable i n , and return to step b).

[0076] The optimization results are shown in Table 1, where the speed is the speed in the earth axis system:

[0077] Table 1: Optimization results of the prototype rotor cross-tilt angle

[0078]

[0079] From the actual measurement results, it can be seen that the tilt of the propeller plane of this aircraft (initial error, before calibration) is generally between 0.6 degrees * 8 (conventional initial error) and 1.0 degrees * 8 (larger initial error). Combining with the requirements of the conventional flight mission of the aircraft: load range (0 - 50 kg), forward flight speed 4 - 5 m / s, and comparing with the optimization results, it can be known that: adopting a cross-tilt angle of 5 degrees, under the current installation accuracy, it can ensure a lower total throttle amount, while improving the yaw motion control efficiency of the multi-rotor aircraft, and minimizing its coupling with the attitude and lift control channels.

[0080] Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not used to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, for those skilled in the art, they can still modify the technical solutions described in the foregoing examples, or perform equivalent replacements for some of the technical features. All modifications, equivalent replacements, etc. made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims

1. A method for optimizing the cross-tilt angle of the rotors of a multi-rotor aircraft, characterized in that including: (1) Establish a flight dynamics model of a multi-rotor aircraft with the parameter of the cross-tilt angle i of the rotors n ; (2) adding the rotor tilt installation error or tolerance range to the above model; (3) designing a numerical optimization method with double iterative properties, taking the sum of the squares of the total throttle of each channel of the aircraft as the objective function, and optimizing to obtain the rotor cross-tilt angle under the current load, flight speed, and rotor tilt installation error or tolerance range; Among them, the design variable for the main iteration optimization is the rotor cross-tilt angle \(i\). n , the constraint of the design variable is the available range of the rotor cross-tilt angle, and the initial value of the iterative design variable \(i\). n is 0 degree, and the objective function is to minimize the sum of squares of the total throttle commands of the aircraft. The sum of squares of the total throttle commands of the aircraft is obtained by sub-iteration; the main iteration uses a numerical optimization method to determine whether the objective function converges. If it converges, the current rotor cross-tilt angle \(i\) is output. n , otherwise, according to the objective function and the current design variable, the rotor cross-tilt angle \(i\) is continuously updated. n until convergence. The design variables for the sub-iterative optimization are the state variables and control variables in the flight dynamics model, and the initial iteration value is defaulted to 0, where the initial value of the body-axis system speed can be given according to the flight mission or defaulted to 0; the end value is the earth-axis system flight speed required by the flight mission, and the objective function is the right-hand side of the trimmed flight dynamics model, so that the aircraft reaches a steady-state horizontal flight state; the sub-iteration uses a numerical optimization method to judge whether the objective function converges. If it converges, the sum of the squares of the total throttle commands of the aircraft is output and enters the main iteration. Otherwise, the state variables and control variables are continuously updated until convergence.

2. The method for optimizing the rotor cross-tilt angle of the multi-rotor aircraft according to claim 1, characterized in that, The rotor tilts around the direction of the arm, where the tilt angle directions between adjacent rotors are opposite and the magnitudes are the same; after tilting, the rotor generates a tangential tension component, thereby generating a yaw moment on the center of gravity of the fuselage; If it has been ensured that the yaw moment is in the same direction as the negative torque generated by the rotor on the fuselage, the constraint equation for the main iteration design variables is: 0°≤i n ≤30° If it is not certain whether the yaw moment is in the same direction as the negative torque generated by the rotor on the fuselage, the constraint equation for the main iteration design variables is: -30°≤i n ≤30°。 3. The method for optimizing the cross-tilt angle of the rotors of the multi-rotor aircraft according to claim 1, wherein Step (3) includes the following steps: (3.1) Give the initial value of the main iterative design variable i n , and the initial iteration value is defaulted to 0; (3.2) Enter the main iterative calculation process: Use the current main iterative design variable i n Update the flight dynamics model of the multi-rotor aircraft, and add the rotor tilt installation error or tolerance range to the model; (3.3) Enter the sub-iteration calculation process: give the initial value and end value of the sub-iteration design variables. The initial iteration value of the design variables is defaulted to 0, where the initial value of the body-axis system speed can be given according to the flight mission or defaulted to 0; the end value is the earth-axis system flight speed required by the flight mission; use a numerical optimization method to perform iterative calculations until the right-hand side of the trimmed flight dynamics mathematical model, and then output the sum of the squares of the total throttle commands of the aircraft to the main iteration; (3.4) Then enter the main iterative calculation process: Use the numerical optimization method to determine whether the sum of squares of the current total throttle commands of the aircraft converges. If so, output i n ; if not, update the main iterative design variable i n , and return to step (3.2).

4. The method for optimizing the cross-tilt angle of the rotors of the multi-rotor aircraft according to claim 1, characterized in that, The numerical optimization method is the sequential quadratic programming algorithm.

5. The method for optimizing the rotor cross-tilt angle of the multi-rotor aircraft according to claim 1, wherein The iteration accuracy of the main iterative objective function is 10 -5 .

6. The method for optimizing the rotor cross-tilt angle of the multi-rotor aircraft according to claim 1, characterized in that The iteration accuracy of the sub-iteration objective function is 10 -5 .

7. The method for optimizing the rotor cross-tilt angle of the multi-rotor aircraft according to claim 1, characterized in that The multi-rotor aircraft is an aircraft with four or more even-numbered rotors.

8. The method for optimizing the rotor cross-tilt angle of the multi-rotor aircraft according to claim 1, characterized in that The cross-tilt means that the rotor tilts around the direction of the arm, where the tilt angles between adjacent rotors are opposite.

9. The method for optimizing the rotor cross-tilt angle of the multi-rotor aircraft according to claim 1, wherein Analyze the rotor cross-tilt angles under different loads, different absolute values of the total rotor tilt installation error, and different flight speeds, and finally select a reasonable rotor cross-tilt angle with the flight mission as the goal.

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