Cascade PID (Proportion Integration Differentiation) parameter setting optimization method for multi-rotor aircraft

Abstract

The invention relates to the technical field of PID (Proportion Integration Differentiation) control optimization, and discloses a cascade PID parameter setting optimization method for a multi-rotor aircraft, which comprises the following steps of: determining an expected height Ht and an expected speed Vt corresponding to a flight task, an expected inherent frequency omega sp of a specified control channel of the aircraft and an expected damping ratio zeta sp of the channel according to a forward design requirement of the aircraft; establishing a nonlinear flight dynamics model of the aircraft; balancing calculation is carried out, the corresponding state quantity and control quantity of the aircraft at the expected height and the expected speed are solved, and a balancing result is obtained; performing linearization processing on the nonlinear flight dynamics model based on the balancing result to obtain a linear state equation; adding a PID (Proportion Integration Differentiation) control equation on the basis of the linear state equation, setting a PID parameter to be set as an unknown quantity, giving an initial value, and solving a closed-loop control system pole of a specified control channel; cascade PID parameters are automatically set through an optimization method, thereby getting rid of dependence on engineering experience.

Description

Technical Field

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

[0002] In the control of multi-rotor aircraft, the cascade PID control law design method is widely used due to its significant advantages; this method achieves precise control of the aircraft's 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 system's anti-interference ability, improving dynamic response, having strong robustness and easy implementation, which makes it widely used in engineering application fields.

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

[0004] This cascade PID parameter tuning method is simple, reliable, and widely used; but it still has some limitations: the existing cascade PID parameter tuning method only relies on parameter debugging based on engineering experience, and usually can only obtain a set of qualitative feasible parameters, and cannot guarantee 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 expected natural frequency and damping ratio), which is not fully consistent with the requirements of the forward design process of large aircraft.

[0005] In view of this, the present invention proposes a cascade PID parameter tuning optimization method for a multi-rotor aircraft. Based on the forward design process, the cascade PID parameters are obtained through an optimization method according to the expected 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 cascade PID parameter tuning optimization method for a multi-rotor aircraft to solve the problems existing in the above-mentioned background technology.

[0007] The present invention provides the following technical solution: a cascade PID parameter tuning optimization method for a multi-rotor aircraft, comprising 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 、The expected natural frequency of the aircraft's designated control channel ω spi and the desired damping ratio ζ of the channel spi ;

[0009] Step S02: Establishing a nonlinear flight dynamics model of the aircraft;

[0010] 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;

[0011] Step S04: linearizing the nonlinear flight dynamics model based on the trim result to obtain a linear state equation;

[0012] 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;

[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 iterate; if the objective function converges to the specified error range, output the adjusted cascade PID parameters.

[0014] Preferably, the designated control channel is any one of an attitude control channel and a speed 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 speed 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, and the expected natural frequency and the expected damping ratio can be converted into a pair of expected conjugate poles, 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: .

[0015] Preferably, 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.

[0016] Preferably, the specific method of the balancing calculation is:

[0017] 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.

[0018] 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;

[0019] 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.

[0020] Preferably, 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.

[0021] Preferably, 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;

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

[0023] ,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.

[0024] Preferably, 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].

[0025] Preferably, the equation for obtaining the pole of the closed-loop control system of the designated 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.

[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 adjusted are expressed as: ; The meaning of the objective function J is that the calculated poles converge to the conjugate expected poles.

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

[0028] (1) The present invention is provided with step S03 and step S04, which is conducive to converting a complex nonlinear system into a simpler 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 the flight control law; at the same time, the linearized model requires less computing resources, so it can reduce computing delay and improve efficiency; and it is easier to be applied to aircraft; in the balancing process, the balance point of the aircraft in the pending flight state can be found, so that the linearized model is more accurate near the balancing point, thereby improving the control accuracy and laying a foundation for the subsequent adjustment of the cascade PID parameters.

[0029] (2) The present invention is provided with step S05 and step S06, which is conducive to automatically adjusting 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 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 The present invention is a flow chart of the cascade PID parameter tuning optimization method for a multi-rotor aircraft.

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

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

[0033] Figure 4 The longitudinal channel control loop after the pitch attitude loop cascade PID parameter tuning optimization is completed. DETAILED DESCRIPTION

[0034] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention. In addition, the forms of the various structures recorded in the following embodiments are merely illustrative. The cascade PID parameter tuning and optimization method for a multi-rotor aircraft involved in the present invention is not limited to the various structures recorded in the following embodiments. All other implementations obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

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

[0036] 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 , the designated 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 the expected damping ratio of the designated control channel are the expected natural frequency and the expected damping ratio of the corresponding control channel, illustratively, when the designated control channel is the pitch control channel, the expected natural frequency and the expected damping ratio of the pitch control channel of the aircraft are selected; when the designated control channel is the roll control channel, the expected natural frequency and the expected damping ratio of the roll control channel of the aircraft are selected; in this embodiment, the designated control channel is taken as an example for detailed description, the range of the expected damping ratio is selected from 0 to 1, and the expected natural frequency and the expected damping ratio can be converted into a pair of expected conjugate poles, 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: ;

[0037] Step S02: Establish a nonlinear flight dynamics model of the aircraft, which is expressed as follows: ,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;

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

[0039] 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.

[0040] 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;

[0041] 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;

[0042] Step S04: Based on the trimming result, the nonlinear flight dynamics model is linearized to obtain a linear state equation; the purpose is to transform a complex nonlinear system into a simpler linear system through linearization, so that mathematical processing and theoretical analysis become 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 less computing resources, so it can reduce computing delays and improve efficiency; and it is easier to be applied to aircraft; in the trimming process, the balance point of the aircraft in the pending flight state can be found, so that the linearized model is more accurate near the trimming point, thereby improving the control accuracy and laying the foundation for the subsequent adjustment of the cascade PID parameters;

[0043] Step S05: Add the PID control equation to the linear state equation, set the PID parameters to be adjusted as unknown quantities, and give initial values ​​to find the closed-loop control system poles of the specified control channel; 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 In this embodiment, the initial values ​​are given as follows: 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;

[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 iterate; if the objective function converges to the specified error range, output the adjusted cascade PID parameters; the meaning of the objective function J is expressed as the calculated poles converge to the conjugate expected poles; the optimization algorithm can be any one, and this embodiment uses the sequential quadratic programming algorithm for optimization and solution; each iteration calculates new cascade PID parameters, brings them into step S05 to find the conjugate dominant poles of the closed-loop control system, brings the conjugate dominant poles into the objective function until they converge to within the error, and obtains the final adjusted cascade PID parameters.

[0045] In this embodiment, it should be specifically explained 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;

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

[0047] ,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;

[0048] The above 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 specified control channel is integrated to obtain the closed-loop control transfer function of the specified control channel. In this embodiment, the pitch control channel is taken as an example, and 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 are the pitch angle and pitch rate under trimmed state reference, , ,u pitch is the pitch attitude bar, s is the differential operator; its purpose is to convert the pitch attitude bar into the desired pitch angle (in radians) θ com , K is a constant and can be modified according to actual conditions. The value range of the pitch attitude rod is [-1, 1]. If the designated control channel is the roll control channel, the corresponding roll attitude rod u roll Replace the pitch attitude stick. If the specified control channel is the yaw control channel, replace the corresponding yaw attitude stick u yaw Replace the pitch attitude stick. If the designated control channel is the forward control channel, replace the corresponding forward speed stick u vx Replace the pitch attitude lever...; the forward speed lever and the forward flight speed lever are different expressions of the same meaning;

[0049] The cascade PID control law of the pitch attitude control channel is integrated as follows: Figure 2 shown.

[0050] In this embodiment, it should be specifically explained that, in step S05 of this embodiment, the control channel specified is the pitch control channel, and step S05 can be to find the pole of the closed-loop control system of the pitch control channel. If it is other control channels, it is correspondingly transformed into finding the pole of the closed-loop control system of other control channels; the equation is expressed as: ; Solve the equation, which has many roots, and take a pair of conjugate dominant poles a+bi. The conjugate dominant poles refer to 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; In the control system, the dominant poles have the greatest impact 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 explained that the formula of the objective function in step S06 is expressed as: ; a is the real part of the conjugate complex number, b is the imaginary part of the conjugate complex number; the upper and lower limits of the cascade PID parameters to be adjusted are expressed as: ;

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

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

[0054] Step 2: Get 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 met. If so, stop the iteration and return to the optimal solution; otherwise, return to step 2;

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

[0058] In this embodiment, it should be specifically noted that the calculation of the objective function gradient and the Hessian matrix is ​​a prior art, and this embodiment will not go into detail about this.

[0059] The cascade PID parameter tuning optimization method of the roll and yaw attitude loops not described in detail in this embodiment is the same as the method of this embodiment, that is, the cascade PID parameter tuning optimization method of the other two control channels of the attitude control channel is the same as the method of 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 quantity with the corresponding angle and angular velocity state quantity; that is, when the cascade PID parameter tuning optimization of the roll attitude loop is performed, the parameters related to the roll control channel such as the roll angle and roll angular velocity state quantity are selected; when the cascade PID parameter tuning optimization of the yaw attitude loop is performed, the parameters related to the yaw control channel such as the yaw angle and yaw angular velocity state quantity are selected; other control channels are the same;

[0060] When the cascade PID parameters of the pitch and roll attitude loops are tuned and optimized, the PID parameters of the speed loop, that is, the PID parameters of the speed control channel, can be further tuned and optimized on this basis. The method of step S04 and step S06 is consistent with that of step S06. Just modify the corresponding parameters. Similarly, the cascade PID parameters of the altitude loop of the aircraft can be tuned and optimized. This embodiment will not be repeated here.

[0061] In this embodiment, it should be specifically explained that, compared with the existing technology, this embodiment can automatically adjust the cascade PID parameters through the 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 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 description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

[0063] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on 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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