A Cascade PID Parameter Tuning and Optimization Method for Multirotor Aircraft

Abstract

The present invention relates to the technical field of PID control optimization, and discloses a method for optimizing the tuning of cascade PID parameters of a multi-rotor aircraft, including: determining the expected altitude H corresponding to the flight mission according to the forward design requirements of the aircraft t , the expected speed V t , the expected natural frequency ω of the specified control channel of the aircraft sp and the expected damping ratio ζ of this channel sp ; establishing a non-linear flight dynamics model of the aircraft; performing trim calculations to obtain the state variables and control variables corresponding to the expected altitude and expected speed of the aircraft, and obtaining the trim result; linearizing the non-linear flight dynamics model based on the trim result to obtain a linear state equation; adding a PID control equation to the linear state equation, setting the PID parameters to be tuned as unknowns, and giving initial values, and obtaining the poles of the closed-loop control system of the specified control channel; automatically tuning the cascade PID parameters through an optimization method, thus getting rid of the dependence on engineering experience.

Description

Technical Field

[0001] The present invention relates to the technical field of PID control optimization, and more particularly to a method for optimizing the cascade PID parameter tuning of a multi-rotor aircraft. Background Art

[0002] In the control of multi-rotor aircraft, the cascade PID control law design method is widely adopted due to its significant advantages; this method realizes precise control of the aircraft attitude and position through the cascade of two or more PID controllers; the advantages of using the cascade PID control law design method include: enhancing the anti-interference ability of the system, improving the dynamic response, having strong robustness, and being convenient to implement, which makes it widely used in the field of engineering applications.

[0003] The general tuning process of cascade PID parameters is as follows: for small multi-rotor aircraft, first, the attitude and position of the aircraft are constrained by means such as hand-held, three-degree-of-freedom platform or suspension; subsequently, according to engineering experience or using the Ziegler-Nichols method, the cascade PID control parameters are directly debugged on the aircraft; for large multi-rotor aircraft, usually, a high-precision flight dynamics model is first established, and on this basis, through engineering experience or the Ziegler-Nichols method for simulation, the preliminary parameter tuning is completed, and ground tests are carried out through a three-degree-of-freedom platform or suspension, etc., and finally, flight tests are carried out for verification.

[0004] This kind of cascade PID parameter tuning method is simple, reliable, and widely used; however, there are still some limitations: the existing cascade PID parameter tuning method only depends on the parameter debugging based on engineering experience, and usually only a set of qualitative feasible parameters can be obtained, and it is impossible to guarantee obtaining the optimal parameter combination; such methods usually require the debugger to have rich experience, and the debugging process often takes a lot of time; this method cannot perform forward cascade PID parameter tuning through preset pole configuration (i.e., the desired natural frequency and damping ratio), which does not fully meet the requirements of the forward design process of large aircraft.

[0005] In view of this, the present invention proposes a method for optimizing the cascade PID parameter tuning of a multi-rotor aircraft, based on the forward design process, and obtaining the cascade PID parameters through an optimization method according to the desired frequency and damping to solve the above problems. Summary of the Invention

[0006] In order to overcome the above-mentioned defects of the prior art, the present invention provides a method for optimizing the cascade PID parameter tuning of a multi-rotor aircraft to solve the problems existing in the above-mentioned background art.

[0007] The present invention provides the following technical solution: a method for optimizing the cascade PID parameter tuning of a multi-rotor aircraft, including the following steps:

[0008] Step S01: Determine the expected altitude H corresponding to the flight mission according to the forward design requirements of the aircraft t , expected speed V t , expected natural frequency ω of the specified control channel of the aircraft spi and the expected damping ratio ζ of this channel spi ;

[0009] Step S02: Establish the non - linear flight dynamics model of the aircraft;

[0010] Step S03: Conduct trimming calculations, obtain the state variables and control variables corresponding to the aircraft at the expected altitude and expected speed, and acquire the trimming result;

[0011] Step S04: Linearize the non - linear flight dynamics model based on the trimming result to obtain the linear state equation;

[0012] Step S05: Add the PID control equation to the linear state equation, set the PID parameters to be tuned as unknowns and give initial values, and calculate the closed - loop control system poles of the specified control channel;

[0013] Step S06: Output the objective function J. If the objective function does not converge to the specified error range, call the optimization algorithm to recalculate a new set of cascade PID parameters, re - execute Step S05, and perform iteration; if the objective function converges to the specified error range, output the tuned cascade PID parameters.

[0014] Preferably, the specified control channel is any one of the attitude control channel and the speed control channel. The above - mentioned specified control channel is the pitch control channel. The attitude control channel includes the pitch control channel, roll control channel, and yaw control channel. The speed control channel includes the forward control channel, lateral control channel, and vertical control channel. The expected natural frequency and expected damping ratio of the specified control channel are the expected natural frequency and expected damping ratio of the corresponding control channel. The range of the expected damping ratio is selected from 0 to 1. The expected natural frequency and expected damping ratio can be converted into a pair of expected conjugate poles, expressed as: ; where a sp is the real part of the expected conjugate pole, and b sp is the imaginary part of the expected conjugate pole; the conversion formula is expressed as: .

[0015] Preferably, the formula for establishing the non - linear flight dynamics model of the aircraft in Step S02 is expressed as: , where Denote the first derivative of the state variable x with respect to time t, where t represents time and x is the state variable. The state variable x includes the body-axis system velocities (u b , v b , w b ), angular velocities (p, q, r), attitude angles ( , , ), and the earth-axis system velocities (Vx, Vy, Vz); u b , v b , w b represent the forward, lateral, and vertical velocities on the body-axis system respectively; p, q, r represent the roll angular velocity, pitch angular velocity, and yaw angular velocity under the body-axis system respectively; , , represent the roll angle, pitch angle, and yaw angle respectively; the control variable u includes the rotor thrust throttle command dt, pitch throttle command de, roll throttle command da, and yaw throttle command dr.

[0016] Preferably, the specific method of the trim calculation is as follows:

[0017] Initial values for trim calculation: The initial values of the state variables and control variables are defaulted to zero. Among them, the initial value of the body-axis system velocity in the state variables can be given according to the flight mission or defaulted to zero;

[0018] Constraints for trim calculation: The constraint formula for the aircraft to enter the steady-state level flight state is expressed as: ; where, represents the first derivative of the forward velocity on the body-axis system with respect to time t, represents the first derivative of the lateral velocity on the body-axis system with respect to time t, represents the first derivative of the vertical velocity on the body-axis system with respect to time t, represents the first derivative of the roll angular velocity under the body-axis system with respect to time t, represents the first derivative of the pitch angular velocity under the body-axis system with respect to time t, represents the first derivative of the yaw angular velocity under the body-axis system with respect to time t;

[0019] Through the initial values of the state variables and control variables, the steady-state constraints, and the non-linear flight dynamics model equations, call the sequential quadratic programming algorithm to obtain the state variables and control variables corresponding to the desired altitude and desired speed of the aircraft, and use them as the trim results.

[0020] Preferably, the PID parameters include the outer-loop proportional parameter P a , the inner-loop proportional parameter P r , the inner-loop integral parameter P I , and the inner-loop differential parameter Pd , the given initial values are: the initial proportional parameter P of the outer loop a0 = 1, the initial proportional parameter P of the inner loop r0 = 1, the initial integral parameter P of the inner loop I0 = 1 and the initial derivative parameter P of the inner loop d0 = 0.1.

[0021] Preferably, in the step S04, the linear state equation formula of the aircraft is expressed as: , where is the first derivative of the state increment, Δx represents the state increment under the trim state reference, Δu is the control increment under the trim state reference, A is the state quantity derivative matrix, and B is the control quantity derivative matrix;

[0022] Based on the linear state equation, only extract the control channels corresponding to the specified control channels, that is, the pitch control channel:

[0023] , where is the first derivative of Δx θq , Δx θq represents the pitch angle increment and pitch angular velocity increment under the trim state reference, , where Δθ is the pitch angle increment and Δq is the pitch angular velocity increment; Δd e is the pitch throttle command increment under the trim state reference, A θq represents the corresponding state matrix, and B θq represents the corresponding control matrix.

[0024] Preferably, the Laplace transform of the linear state equation is performed to obtain the pitch attitude transfer function P(s) of the flight dynamics model; the cascade PID control law of the aircraft in the pitch control channel is integrated to obtain the closed-loop control transfer function of the corresponding specified control channel, that is, the pitch control channel, and the formula is expressed as: , where x θq is the pitch angle and pitch angular velocity under the trim state reference, , , u pitch is the pitch attitude bar, s is the differential operator; the K is a constant, and the value range of u pitch is u pitch ∈ [-1, 1].

[0025] Preferably, the equation for obtaining the poles of the closed-loop control system of the specified control channel in the step S05 is expressed as: ; Solve the equation and take a pair of conjugate dominant poles a + bi; where a is the real part of the conjugate complex number and b is the imaginary part of the conjugate complex number; the conjugate dominant poles are a pair of conjugate complex poles among the closed-loop poles of the system that are the closest to the imaginary axis and have no closed-loop zeros around them.

[0026] Preferably, the formula of the objective function in step S06 is expressed as: ; The upper and lower limits of the cascade PID parameters to be tuned are expressed as: ; The meaning of the objective function J is expressed as calculating that the poles converge to the conjugate expected poles.

[0027] Technical effects and advantages of the present invention:

[0028] (1) By providing step S03 and step S04, the present invention is conducive to transforming a complex non-linear system into a relatively simple linear system through linearization processing, making mathematical processing and theoretical analysis easier and more intuitive; by analyzing the linearized model, it is easier to design flight control laws; at the same time, the linearized model requires fewer computing resources, so it can reduce computing latency and improve efficiency; and it is more easily applied to aircraft; during the trimming process, the balance point of the aircraft in the pending flight state can be found, making the linearized model more accurate near the trim point, thereby improving control accuracy and laying a foundation for subsequent tuning of cascade PID parameters.

[0029] (2) By providing step S05 and step S06, the present invention is conducive to automatically tuning the cascade PID parameters through an optimization method according to the expected frequency and damping preset in the forward design process, thereby getting rid of the dependence on engineering experience, reducing the workload of debuggers, improving debugging efficiency, reducing the burden on operators, meeting the requirements of the forward design process of large aircraft, and not relying on MATLAB non-linear control design tools. Brief Description of the Drawings

[0030] Figure 1 It is a flowchart of the cascade PID parameter tuning and optimization method for the multi-rotor aircraft of the present invention.

[0031] Figure 2 It is a schematic diagram of the integration of the cascade PID control law for the pitch attitude control channel of the present invention.

[0032] Figure 3 It is a schematic diagram of the integration of the cascade PID control law for the forward speed control channel.

[0033] Figure 4 It is the longitudinal channel control loop after the cascade PID parameter tuning and optimization of the pitch attitude loop is completed. Detailed Embodiments

[0034] The technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the present invention. In addition, the forms of each structure described in the following embodiments are merely examples, and a method for optimizing the cascade PID parameter tuning of a multi-rotor aircraft involved in the present invention is not limited to the structures described in the following embodiments. All other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0035] As Figure 1 shown, the present invention provides a method for optimizing the cascade PID parameter tuning of a multi-rotor aircraft, including the following steps:

[0036] Step S01: According to the forward design requirements of the aircraft, determine the expected altitude H t , expected speed V t , expected natural frequency ω sp of the specified control channel of the aircraft, and the expected damping ratio ζ sp of this channel. The specified control channel includes an attitude control channel and a speed control channel. The attitude control channel includes a pitch control channel, a roll control channel, and a yaw control channel. The speed control channel includes a forward control channel, a lateral control channel, and a vertical control channel. The expected natural frequency and expected damping ratio of the specified control channel are the expected natural frequency and expected damping ratio of the corresponding control channel. Exemplarily, when the specified control channel is the pitch control channel, the expected natural frequency and expected damping ratio of the aircraft pitch control channel are selected; when the specified control channel is the roll control channel, the expected natural frequency and expected damping ratio of the aircraft roll control channel are selected. In this embodiment, the pitch control channel is taken as an example for detailed description. The range of the expected damping ratio is selected from 0 to 1. The expected natural frequency and expected damping ratio can be converted into a pair of expected conjugate poles, expressed as: ; where a sp is the real part of the expected conjugate pole, and b sp is the imaginary part of the expected conjugate pole. The conversion formula is expressed as: ;

[0037] Step S02: Establish a non-linear flight dynamics model of the aircraft, the formula is expressed as: , where represents the first derivative of the state quantity x with respect to time t, t represents time, x is the state quantity, and the state quantity x includes the body-axis system speed (u b , v b , w b ), angular velocity (p, q, r), attitude angle ( , , ) and the earth axis system velocity (Vx, Vy, Vz); u b 、v b 、w b respectively represent the forward, lateral, and vertical velocities on the body axis system; p, q, and r respectively represent the roll angular velocity, pitch angular velocity, and yaw angular velocity under the body axis system; 、 、 respectively represent the roll angle, pitch angle, and yaw angle; the control quantity u includes the rotor thrust throttle command dt, pitch throttle command de, roll throttle command da, and yaw throttle command dr;

[0038] Step S03: Perform trim calculation to obtain the state quantities and control quantities corresponding to the aircraft at the desired altitude and desired speed. The specific method of the trim calculation is as follows:

[0039] Initial values for trim calculation: The initial values of the state quantities and control quantities are defaulted to zero. Among them, the initial value of the body axis system velocity in the state quantities can be given according to the flight mission or defaulted to zero;

[0040] Constraints for trim calculation: The constraint formula for the aircraft to enter the steady-state level flight state is expressed as: ; where, represents the first derivative of the forward velocity on the body axis system with respect to time t, represents the first derivative of the lateral velocity on the body axis system with respect to time t, represents the first derivative of the vertical velocity on the body axis system with respect to time t, represents the first derivative of the roll angular velocity under the body axis system with respect to time t, represents the first derivative of the pitch angular velocity under the body axis system with respect to time t, represents the first derivative of the yaw angular velocity under the body axis system with respect to time t;

[0041] Through the initial values of the state quantities and control quantities, steady-state constraints, and the non-linear flight dynamics model equations, call the sequential quadratic programming algorithm to obtain the state quantities and control quantities corresponding to the aircraft at the desired altitude and desired speed, and use them as the trim results;

[0042] Step S04: Linearize the non - linear flight dynamics model based on the trimming result to obtain a linear state equation. The purpose is to transform the complex non - linear system into a relatively simple linear system through linearization, making mathematical processing and theoretical analysis easier and more intuitive. By analyzing the linearized model, it is easier to design flight control laws. At the same time, the linearized model requires fewer computing resources, so it can reduce computational latency and improve efficiency. And it is more easily applied to aircraft. During the trimming process, the equilibrium point of the aircraft in the pending flight state can be found, making the linearized model more accurate near the trimming point, thereby improving control accuracy and laying a foundation for subsequent tuning of cascade PID parameters.

[0043] Step S05: Add a PID control equation based on the linear state equation. Let the PID parameters to be tuned be unknowns and give initial values, and calculate the closed - loop control system poles of the specified control channel. The PID parameters include the outer - loop proportional parameter P a , the inner - loop proportional parameter P r , the inner - loop integral parameter P I and the inner - loop derivative parameter P d . In this embodiment, the given initial values are: the outer - loop initial proportional parameter P a0 = 1, the inner - loop initial proportional parameter P r0 = 1, the inner - loop initial integral parameter P I0 = 1, and the inner - loop initial derivative parameter P d0 = 0.1.

[0044] Step S06: Output the objective function J. If the objective function does not converge to the specified error range, call the optimization algorithm to recalculate a new set of cascade PID parameters, re - execute Step S05, and perform iteration. If the objective function converges to the specified error range, output the tuned cascade PID parameters. The meaning of the objective function J is that the calculated poles converge to the conjugate desired poles. The optimization algorithm can be any one. In this embodiment, the sequential quadratic programming algorithm is used for optimization and solution. Each time a new set of cascade PID parameters is calculated by iteration, substitute them into Step S05 to find the conjugate dominant poles of the closed - loop control system, and substitute the conjugate dominant poles into the objective function until it converges within the error to obtain the finally tuned cascade PID parameters.

[0045] In this embodiment, it should be specifically noted that in Step S04, the formula of the linear state equation of the aircraft is expressed as: , where is the first - order derivative of the state increment, Δx represents the state increment under the trimming state reference, Δu is the control increment under the trimming state reference, A is the state quantity derivative matrix, and B is the control quantity derivative matrix.

[0046] Based on the linear state equation, ignoring the influence of other control channels except the specified control channel, only extracting the control channel corresponding to the specified control channel. In this embodiment, the specified control channel is the pitch control channel, so the influence of other control channels is ignored and only the pitch control channel is extracted:

[0047] , where is the first derivative of Δx θq , and Δx θq represents the pitch angle increment and pitch angular velocity increment under the trim state reference, , where Δθ is the pitch angle increment and Δq is the pitch angular velocity increment; Δd e is the pitch throttle command increment under the trim state reference, A θq represents the corresponding state matrix, and B θq represents the corresponding control matrix;

[0048] Taking the Laplace transform of the above linear state equation, the pitch attitude transfer function P(s) of the flight dynamics model is obtained; integrating the cascade PID control law of the aircraft in the specified control channel, the closed-loop control transfer function of the specified control channel is obtained. In this embodiment, taking the pitch control channel as an example, the cascade PID control law of the aircraft in the pitch control channel is integrated to obtain the closed-loop control transfer function of the pitch control channel; the formula is expressed as: , where x θq is the pitch angle and pitch angular velocity under the trim state reference, , , u pitch is the pitch attitude stick, and s is the differential operator; the purpose is to convert the pitch attitude stick into the desired pitch angle (in radian unit) θ com , where K is a constant that can be modified according to the actual situation, and the value range of the pitch attitude stick is [-1, 1]; if the specified control channel is the roll control channel, the corresponding roll attitude stick u roll is used to replace the pitch attitude stick. If the specified control channel is the yaw control channel, the corresponding yaw attitude stick u yaw is used to replace the pitch attitude stick. If the specified control channel is the forward control channel, the corresponding forward speed stick u vx is used to replace the pitch attitude stick...; the forward speed stick and the forward flight speed stick are different expressions of the same meaning;

[0049] The integration of the cascade PID control law of the pitch attitude control channel is as shown in Figure 2 .

[0050] In this embodiment, it should be specifically noted that in step S05, if the specified control channel is the pitch control channel, then step S05 can be to find the poles of the closed-loop control system of the pitch control channel. If it is other control channels, it is correspondingly changed to find the poles of the closed-loop control system of other control channels. The equation is expressed as: ; Solve this equation. This equation has many roots. Take a pair of conjugate dominant poles a + bi. Conjugate dominant poles refer to a pair of conjugate complex poles among the closed-loop poles of the system that are the closest to the imaginary axis and have no closed-loop zeros around them. In a control system, the dominant poles have the greatest influence on the dynamic performance of the system. Especially when they are located in the left half of the complex plane, they determine the stability and transient response characteristics of the system.

[0051] In this embodiment, it should be specifically noted that the formula of the objective function in step S06 is expressed as: ; a is the real part of the conjugate complex number, and b is the imaginary part of the conjugate complex number. The upper and lower limits of the cascade PID parameters to be tuned are expressed as: ;

[0052] The sequential quadratic programming algorithm is a method for solving nonlinear programming problems. This algorithm transforms the nonlinear programming problem into a series of quadratic programming sub-problems and gradually approaches the optimal solution of the original problem. The steps for optimizing and solving using the sequential quadratic programming algorithm are as follows:

[0053] Step 1: Calculate the gradient of the objective function and the Hessian matrix;

[0054] Step 2: Obtain the step size by solving the quadratic programming sub-problem;

[0055] Step 3: Update the solution vector;

[0056] Step 4: Determine whether the termination condition is satisfied. If it is satisfied, stop the iteration and return the optimal solution; otherwise, return to step 2;

[0057] In each iteration, the optimal solution of the original problem is approximated by solving a quadratic programming sub-problem.

[0058] In this embodiment, it should be specifically noted that the calculation of the gradient of the objective function and the Hessian matrix is prior art, and this embodiment will not elaborate on it too much;

[0059] The method for tuning and optimizing the cascade PID parameters of the roll and yaw attitude loops not detailed in this embodiment is the same as the method in this embodiment, that is, the method for tuning and optimizing the cascade PID parameters of the other two control channels of the attitude control channel is the same as the method in this embodiment, such as Figure 3 And Figure 4As shown, it is only necessary to replace the corresponding parameters related to the pitch control channel, such as the pitch angle and pitch angular velocity state variables, with the corresponding angle and angular velocity state variables; that is, when optimizing the cascade PID parameter tuning of the roll attitude loop, select the parameters related to the roll control channel, such as the roll angle and roll angular velocity state variables; when optimizing the cascade PID parameter tuning of the yaw attitude loop, select the parameters related to the yaw control channel, such as the yaw angle and yaw angular velocity state variables; the same applies to other control channels;

[0060] After the cascade PID parameter tuning of the pitch and roll attitude loops is completed, the PID parameters of the speed loop can be further tuned and optimized on this basis, that is, the PID parameters of the speed control channel, which is the same as the method in steps S04 and S06, and the corresponding parameters can be modified. Similarly, the cascade PID parameters of the altitude loop of the aircraft can be tuned and optimized, which will not be elaborated in this embodiment.

[0061] In this embodiment, it should be specifically noted that, compared with the existing technology, this embodiment can automatically tune the cascade PID parameters through an optimization method according to the expected frequency and damping preset in the forward design process, thus getting rid of the dependence on engineering experience, reducing the workload of the debugging personnel, improving the debugging efficiency, reducing the burden on the operators, meeting the requirements of the forward design process of large aircraft, and not relying on the MATLAB nonlinear control design tool.

[0062] Finally: The above are only the preferred embodiments of the present invention and are not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0063] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, and all of them should be covered by the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.

Claims

1. A cascade PID parameter tuning optimization method for a multi-rotor aircraft, characterized in that: The following steps are involved: Step S01: Determine the expected altitude H corresponding to the flight mission according to the forward design requirements of the aircraft t , expected speed V t 、The expected natural frequency of the aircraft's designated control channel ω sp and the desired damping ratio ζ of the channel sp ; Step S02: Establishing a nonlinear flight dynamics model of the aircraft; Step S03: Performing trim calculation to obtain the state quantity and control quantity corresponding to the aircraft at the desired altitude and desired speed, and obtaining the trim result; Step S04: linearizing the nonlinear flight dynamics model based on the trim result to obtain a linear state equation; Step S05: Add the PID control equation on the basis of the linear state equation, set the PID parameter to be adjusted as an unknown quantity, and give an initial value to find the closed-loop control system pole of the specified control channel; Step S06: Output the objective function J. If the objective function does not converge to the specified error range, call the optimization algorithm to recalculate a new set of cascade PID parameters, re-execute step S05, and iterate; if the objective function converges to the specified error range, output the adjusted cascade PID parameters.

2. The cascade PID parameter tuning optimization method for a multi-rotor aircraft according to claim 1, characterized in that: The designated control channel is any one of an attitude control channel and a velocity control channel. The designated control channel is a pitch control channel. The attitude control channel includes a pitch control channel, a roll control channel and a yaw control channel. The velocity control channel includes a forward control channel, a lateral control channel and a vertical control channel. The expected natural frequency and the expected damping ratio of the designated control channel are the expected natural frequency and the expected damping ratio of the corresponding control channel. The range of the expected damping ratio is selected from 0 to 1. The expected natural frequency and the expected damping ratio can be converted into a pair of expected conjugate poles, which can be expressed as: ; Among them, a sp is the real part of the desired conjugate pole, b sp is the imaginary part of the desired conjugate pole; the conversion formula is expressed as: .

3. The cascade PID parameter tuning optimization method for a multi-rotor aircraft according to claim 2, characterized in that: The formula for establishing the nonlinear flight dynamics model of the aircraft in step S02 is expressed as: ,in, The first-order derivative of the state quantity x with respect to time t is obtained, where t represents time and x is the state quantity. The state quantity x includes the body axis velocity (u b ,v b ,w b ), angular velocity (p, q, r), attitude angle ( , , ) and the Earth axis velocity (Vx, Vy, Vz); u b 、v b 、w b They represent the forward, lateral and vertical velocities on the body axis system respectively; p, q and r represent the roll angular velocity, pitch angular velocity and yaw angular velocity on the body axis system respectively; , , They represent the roll angle, pitch angle and yaw angle respectively; the control quantity u includes the rotor thrust throttle command dt, the pitch throttle command de, the roll throttle command da and the yaw throttle command dr.

4. The cascade PID parameter tuning optimization method for a multi-rotor aircraft according to claim 3, characterized in that: The specific method of the balancing calculation is: Initial value of trim calculation: The initial values ​​of state quantity and control quantity are set to zero by default. The initial value of the body axis velocity in the state quantity can be given according to the flight mission, or set to zero by default. Trim calculation constraint: The constraint formula for the aircraft to enter a steady-state horizontal flight state is expressed as: ;in, represents the first-order derivative of the forward velocity on the body axis system with respect to time t, represents the first-order derivative of the lateral velocity on the body axis system with respect to time t, It represents the first-order derivative of the vertical velocity on the body axis system with respect to time t, It represents the first-order derivative of the rolling angular velocity of the body axis system with respect to time t, It represents the first-order derivative of the pitch angular velocity of the body axis system with respect to time t, It represents the first-order derivative of the yaw angular velocity with respect to time t under the body axis system; Through the initial values ​​of state and control quantities, steady-state constraints, and nonlinear flight dynamics model equations, the sequential quadratic programming algorithm is called to obtain the state and control quantities corresponding to the aircraft at the desired altitude and desired speed, which are used as the balancing result.

5. The cascade PID parameter tuning optimization method for a multi-rotor aircraft according to claim 4, characterized in that: The PID parameters include the outer loop proportional parameter P a , Inner ring ratio parameter P r , inner loop integral parameter P I And the inner loop differential parameter P d , the given initial values ​​are: the initial proportional parameter P of the outer loop a0 =1, the initial proportional parameter of the inner loop P r0 =1, the initial integral parameter of the inner loop P I0 = 1 and the initial differential parameter P of the inner loop d0 =0.

1.

6. The cascade PID parameter tuning optimization method for a multi-rotor aircraft according to claim 5, characterized in that: In step S04, the linear state equation of the aircraft is expressed as: ,in, is the first-order derivative of the state increment, Δx represents the state increment under the trim state reference, Δu is the control increment under the trim state reference, A is the state quantity derivative matrix, and B is the control quantity derivative matrix; Based on the linear state equation, only the control channel corresponding to the specified control channel is extracted, that is, the pitch control channel: ,in, = Δx θq The first derivative of , Δx θq Indicates the pitch angle increment and pitch velocity increment under the trim state reference, , where Δθ is the pitch angle increment, Δq is the pitch angular velocity increment; Δd e is the pitch throttle command increment under the trim state reference, A θq represents the corresponding state matrix, B θq represents the corresponding control matrix.

7. The cascade PID parameter tuning optimization method for a multi-rotor aircraft according to claim 6, characterized in that: The linear state equation is Laplace transformed to obtain the pitch attitude transfer function P(s) of the flight dynamics model; the cascade PID control law of the aircraft in the pitch control channel is integrated to obtain the closed-loop control transfer function of the corresponding designated control channel, i.e., the pitch control channel, which is expressed as follows: , where x θq are the pitch angle and pitch rate under trimmed state reference, , ,u pitch is the pitch attitude bar, s is the differential operator; K is a constant, u pitch The value range is u pitch ∈[-1, 1].

8. The cascade PID parameter tuning optimization method for a multi-rotor aircraft according to claim 7, characterized in that: The equation for obtaining the pole of the closed-loop control system of the specified control channel in step S05 is expressed as: ; Solve the equation and take a pair of conjugate dominant poles a+bi; where a is the real part of the conjugate complex number and b is the imaginary part of the conjugate complex number; the conjugate dominant poles are a pair of conjugate complex poles in the closed-loop poles of the system that are closest to the imaginary axis and have no closed-loop zeros around them.

9. The cascade PID parameter tuning optimization method for a multi-rotor aircraft according to claim 8, characterized in that: The formula of the objective function in step S06 is expressed as: ; The upper and lower limits of the cascade PID parameters to be adjusted are expressed as: ; The meaning of the objective function J is that the calculated poles converge to the conjugate expected poles.

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