Unmanned helicopter control method based on fuzzy neural network extended state observer

Abstract

This invention discloses a control method for unmanned helicopters based on a fuzzy neural network extended state observer, belonging to the field of flight control technology for tandem unmanned helicopters. The tandem unmanned helicopter flight controller structure includes an FNNESO-RBSC controller, a control strategy, and a tandem unmanned helicopter flight dynamics model. The FNNESO-RBSC controller calculates the lateral, longitudinal, heading, and vertical channel control quantities based on system input and output information, and distributes them to the control surfaces of the tandem unmanned helicopter via the control strategy. These control quantities act on the controlled object of the tandem unmanned helicopter, causing changes in the object's state response under aerodynamic effects, thus controlling it to the target flight state. This invention uses a fuzzy neural network to modify the extended state observer, improving its adaptability and thus more effectively acquiring the unknown total disturbance that needs to be compensated in the backstep control law.

Description

Technical Field

[0001] This invention belongs to the field of flight control technology for tandem unmanned helicopters, specifically relating to an unmanned helicopter control method based on a fuzzy neural network extended state observer. Background Technology

[0002] With the rapid development of microelectronics technology, unmanned helicopters are widely used in agricultural aviation operations such as seeding, remote sensing, and pesticide application. Compared with traditional symmetrical multi-rotor unmanned helicopters, tandem unmanned helicopters have the advantages of wider spraying area and higher wind-fog synchronization rate, thus having broader application prospects in the field of agricultural aviation. However, tandem unmanned helicopters are complex nonlinear strongly coupled systems. During flight, changes in weight, center of gravity, and inertia create internal disturbances within the uncertain system. Simultaneously, tandem unmanned helicopters are also affected or threatened by external wind disturbances, constituting external disturbances within the uncertain system. These complex internal and external disturbances severely affect the stability of the attitude and position control of tandem unmanned helicopters, which is detrimental to safe operational flight.

[0003] Researchers have proposed numerous control methods for the stable flight of tandem unmanned helicopters. Linear control methods, including Proportional-Integral-Derivative (PID) and Linear Quadratic Regulator (LQR), are renowned for their simple design and ease of engineering implementation. However, linear control faces challenges in effectively mitigating disturbances encountered by tandem unmanned helicopters. In contrast, nonlinear control methods offer more effective solutions to the effects of disturbances. For example, backstepping control, known for its robustness, stability, and fast response design, has gained widespread acceptance in unmanned helicopter flight control. Liu et al. designed a backstepping fault-tolerant control method to ensure cruise flight stability in the case of rotor tilt shaft jamming faults in tandem unmanned helicopters, but this method requires accurate fault information. While traditional backstepping control possesses good dynamic characteristics, its ability to overcome uncertain disturbances is still insufficient. To address this, Liang et al. designed an adaptive adjustment function to compensate for system uncertainties and a robust term function to solve the approximation error problem, improving the disturbance rejection capability of backstepping control. This method was effectively validated in attitude control simulations of tandem unmanned helicopters. Wang et al. proposed an adaptive command filtering backstepping sliding mode control method, which uses an adaptive control strategy to predict the upper limit of uncertainties and disturbances, thereby eliminating the impact of uncertainties and disturbances on the accuracy of backstepping control.

[0004] Although backstepping control is more robust to system uncertainties and disturbances compared to traditional control methods, it generally requires acquiring some unknown information to design the control law, which poses a challenge for practical applications. Therefore, it is necessary to explore alternative methods to reduce the dependence of backstepping control on the model information of the tandem unmanned helicopter. Considering the characteristics of internal and external disturbances, Han Jingqing designed Active Disturbance Rejection Control (ADRC). The basic concept of ADRC involves referring to internal and external disturbances collectively as the total disturbance and estimating its value using an Extended State Observer (ESO). ESO can effectively estimate the total disturbance without using the model information of the controlled object. ESO can eliminate the dependence of backstepping control on the model, enabling the backstepping controller to operate independently of the unmanned helicopter model. However, the adaptability of ESO needs to be enhanced, especially when the total disturbance exceeds a predetermined threshold, as inappropriate parameters lead to a decline in estimation performance. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by proposing a robust backstepping control method based on a fuzzy neural network extended state observer (FNNESO-RBSC). This invention integrates the advantages of neural networks, fuzzy control, extended state observers, and backstepping control. It modifies the extended state observer using a fuzzy neural network, enhancing its adaptability and thus more effectively acquiring the unknown total disturbance that needs to be compensated for in the backstepping control law. FNNESO-RBSC can overcome the influence of internal and external disturbances in tandem unmanned helicopters, meeting the flight stability control requirements of tandem unmanned helicopters.

[0006] This invention is implemented as follows:

[0007] A control method for unmanned helicopters based on a fuzzy neural network extended state observer is characterized by a tandem unmanned helicopter flight controller structure comprising an FNNESO-RBSC controller, a control strategy, and a tandem unmanned helicopter flight dynamics model. The FNNESO-RBSC controller calculates lateral, longitudinal, heading, and vertical channel control quantities based on system input and output information, and distributes them to each control surface of the tandem unmanned helicopter via the control strategy. These control quantities act on the controlled object of the tandem unmanned helicopter, causing changes in the object's state response under aerodynamic action, thereby controlling it to the target flight state.

[0008] Furthermore, in the aforementioned flight dynamics model: a tandem unmanned helicopter is adopted, whose aerodynamic components include rotors, wings, fuselage, and vertical tail. The left and right rotors have identical parameters except for their opposite rotation directions. The coordinate systems used for the flight dynamics model calculations include the ground coordinate system (O...).D X D Y D Z D ), body coordinate system (O) B X B Y B Z B ), wind axis system (O) V X V Y V Z V ) and propeller shaft system (O S X S Y S Z S ).

[0009] Furthermore, the rotor model is specifically as follows:

[0010] The model comprises three parts: a rotor induced velocity model, a blade flapping motion model, and rotor aerodynamic calculations. The rotor induced velocity model uses a first-order harmonic linear Pitt-Peters dynamic inflow model to calculate the rotor induced velocity; the induced velocity is expanded into a function of rotor spanwise position and azimuth using a first-order Fourier series.

[0011]

[0012] In the formula, v0, v c ,v s These are the time-averaged inflow dimensionless term, the first-order longitudinal inflow dimensionless term, and the first-order transverse inflow dimensionless term for the rotor induced velocity, respectively. Let ψ be the dimensionless term for the spanwise position of the blade. f The blade azimuth angle;

[0013] According to the Pitt-Peters dynamic inflow model, the induced velocity components of the rotor shaft disk do not change with time under steady flight conditions, that is:

[0014]

[0015] In the formula, C T C L C M These are the rotor lift coefficient, roll moment coefficient, and pitch moment coefficient, respectively, M and L. NL This is the gain matrix;

[0016] The blade flapping motion model is used to solve for the rotor flapping angle components. Considering only the first-order rigid flapping of the blades, the first-order dynamic model of the flapping angle β is:

[0017] β=a0+a 1s cosψ f b 1s sinψ f(3)

[0018] In the formula, a0, a 1s ,b 1s These are the rotor taper angle, rear chamfer angle, and side chamfer angle, respectively, and their expressions are:

[0019]

[0020] The Lock number γ is represented as:

[0021]

[0022] In the formula, a ∞ b7 is the airfoil lift line slope, b7 is the blade characteristic width, and ρ kq R is the air density, λ0 is the rotor radius, λ0 is the rotor inflow ratio, μ is the rotor advance ratio, θ0 is the rotor root installation angle, and I is the rotor root angle. β M β These are the moment of inertia of the blade flapping hinge and the moment of mass, respectively. A1 and B1 are the rotor collective pitch, lateral cyclic pitch and longitudinal cyclic pitch, respectively;

[0023] Based on the induced velocity model and the flapping model, the forces and moments of the rotor in the airframe coordinate system are calculated according to the blade element theory.

[0024] Furthermore, the wing model is specifically as follows:

[0025] Considering the aerodynamic interference of the rotor wake on the wing, the wing is divided into two parts: the slipstream region and the freestream region. The slipstream region is the part affected by the rotor wake, and the freestream region is the part unaffected by the rotor wake. The aerodynamic calculation process of the wing is as follows: First, the slipstream area of ​​the wing is calculated based on the rotor advance ratio. On this basis, the aerodynamic forces in the slipstream region and the freestream region under the wind axis system are calculated separately. The calculation method is the same for the front wing and the rear wing. Finally, the forces and moments of the front and rear wings under the wind axis system are projected onto the body axis system to obtain the total aerodynamic force of the wing.

[0026] Wing slipstream area S hl The calculation formula is as follows:

[0027]

[0028] Among them, the largest wing slipstream area R max Represented as:

[0029]

[0030] In the formula, μ max The forward velocity is the distance at which the rotor wake just leaves the wing, μ is the rotor forward velocity, R is the rotor radius, and C is the rotor radius. T Z is the rotor thrust coefficient. ris a dimensionless number representing the vertical distance from the rotor's rotation center to the wing;

[0031] Considering the influence of rotor induced velocity, the airflow velocity at the aerodynamic center of the wing slipstream region is:

[0032]

[0033] In the formula, V x V y V z ;ω x ,ω y ,ω z These represent the three-axis velocities and angular velocities of the tilt-rotor quadcopter UAV's center of mass in the body axis system, x w ,y w ,z w These are the coordinates of the wing's aerodynamic center in the three directions along the body axis, v. i The induced velocity of the rotor at the aerodynamic center of the wing;

[0034] The dynamic pressure q in the slipstream region of the wing w,hl for:

[0035]

[0036] Lift L in the wing slipstream region w,hl Resistance D w,hl And pitching moment M wz,hl for:

[0037] L w,hl =q w,hl S hl C Lw,hl (12)

[0038] D w,hl =q w,hl S hl C Dw,hl (13)

[0039] M wz,hl =q w,hl S hl c w C Mw,hl (14)

[0040] In the formula, C Lw,hl C Dw,hl C Mw,hl These are the lift coefficient, drag coefficient, and pitching moment coefficient of the wing under the wind axis system, respectively. hl c is the wing area in the slipstream region. w Let the wing chord length be denoted; then, based on coordinate projection, the forces and moments in the wing slipstream region in the body coordinate system are obtained;

[0041] The calculation methods for aerodynamics in the free flow region are the same as those in the slip flow region, except that the airflow velocity at the aerodynamic center of the wing in the free flow region does not include the rotor-induced velocity term.

[0042] Furthermore, the fuselage model specifically refers to:

[0043] The forces and torques on the fuselage are:

[0044]

[0045] In the formula, D F ,L F ,S F These are the drag, lift, and lateral force of the fuselage, M xF M yF M zF These are the fuselage's roll moment, yaw moment, and pitch moment, l F A is the characteristic length of the fuselage. F C represents the characteristic area of ​​the fuselage. DF C LF C SF These are the drag coefficient, lift coefficient, and lateral force coefficient of the fuselage, C. MxF C MyF C MzF These are the roll moment coefficient, yaw moment coefficient, and pitch moment coefficient of the fuselage, respectively; then, the forces and moments of the fuselage in the body coordinate system are obtained according to the coordinate projection.

[0046] Furthermore, the vertical tail model is specifically as follows:

[0047] The aerodynamic forces of the drooping tail section of the wind shaft system are:

[0048]

[0049] In the formula, D V ,L V ,S V These are the drag, lift, and lateral force of the vertical tail, C. LV C DV These are the lift coefficient and drag coefficient of the vertical tail, q. v The dynamic pressure of the vertical tail is determined; then, the force and torque of the vertical tail in the body coordinate system are obtained according to the coordinate projection.

[0050] Furthermore, the specific flight dynamics model of the tandem unmanned helicopter is as follows:

[0051] From the models of each aerodynamic component, the resultant aerodynamic force and resultant torque of the tilt-rotor UAV in the body axis system can be obtained:

[0052]

[0053] In the formula, F x ,F y ,F z M x M y M z These represent the resultant external forces and resultant external moments along all three axes of the entire aircraft. Based on the kinematic equations of the airframe, the following nonlinear flight dynamics model of the transverse unmanned helicopter is obtained:

[0054]

[0055] In the formula, ω x ,ω y ,ω z These are the angular velocities in the body coordinate system, V and V. x V y V z The values ​​are: linear velocity in the body coordinate system, φ, θ, and ψ, respectively; Euler angles for roll, pitch, and yaw, respectively; and X, Y, and Z, respectively, the three-axis position coordinates in the ground coordinate system. x ,I y ,I z Let I be the moment of inertia. xy Let g be the product of inertia, and g be the acceleration due to gravity.

[0056] Define X1=[φθψ], X2=[ω x ω y ω z ],X3=[V x V y V z ], X4=[XYZ], then equations (19) to (22) simplify to:

[0057]

[0058] In the formula, F i (·)(i=1,2,3,4) represents the unknown function of the relevant state variables, U a =[δ lat δ lon δ T ] represent the lateral, longitudinal, and yaw control parameters of the rotor, respectively. v =[δ φ δ θ δ col ] represent the virtual control values ​​for roll angle, pitch angle, and vertical channel control value, respectively. B a B v These represent the unknown control gain matrices for attitude and velocity, respectively.

[0059] Furthermore, the FNNESO-RBSC flight control law includes:

[0060] (1) Second-order nonlinear extended system

[0061] Consider a second-order nonlinear uncertain object subject to external disturbances:

[0062]

[0063] In the formula, u and y are the system input and output signals, f(x,w,t) is a nonlinear function containing unknown disturbances, and b(t) is an unknown compensation coefficient;

[0064] Let x3 = f(x,w,t) + (b(t) - b0)u be the new extended state variable, containing both internal and external disturbances, i.e., the total disturbance, and let b0 be a constant. Then system (24) becomes an extended system with 3 state variables, that is:

[0065]

[0066] (2) Fuzzy Neural Network Extended State Observer

[0067] The fuzzy neural network used to estimate the total perturbation is designed as a four-layer feedforward network containing 2-dimensional input (x = [x1 x2]), n fuzzy rules, and a one-dimensional output (total perturbation estimate);

[0068] First layer (input layer): Passes the input variable x = [x1 x2] to the next layer;

[0069] The second layer (membership function layer): also known as the fuzzification layer, receives the two outputs from the input layer. This paper uses a Gaussian function as the membership function to map the two variables x1 and x2 to n fuzzy rules respectively. The membership function value corresponding to the j-th input variable under the i-th fuzzy rule is:

[0070]

[0071] In the formula, Let represent the center and width of the membership function corresponding to the j-th input variable under the i-th fuzzy rule, respectively;

[0072] The third layer (fuzzy basis function layer): The fuzzy basis function corresponding to the i-th fuzzy rule is represented as:

[0073]

[0074] Fourth layer (output layer): Represented as the sum of the products of the fuzzy basis functions and the weights:

[0075]

[0076] In the formula, The output of the fuzzy neural network represents an estimate of the total system disturbance. To estimate the weight matrix.

[0077] The total disturbance x3 is estimated by the fuzzy neural network, and the state variables x1 and x2 are still estimated by the ESO. Therefore, the fuzzy neural network extended state observer (FNNESO) of the extended system (25) is:

[0078]

[0079] In the formula, λ,β i (i = 1, 2) are the gain coefficients, and ζ is the fixed step size. Then the output variable of FNNESO can track the state variables and total disturbance of system (25), i.e.:

[0080]

[0081] (3) Robust backstep control law

[0082] Define the error between the system's target quantity and the actual quantity:

[0083] e1 = x1 - x g (32)

[0084]

[0085] In the formula, x g For the system target quantity;

[0086] 1) Define the Lyapunov function:

[0087]

[0088] definition Where c1 is a positive constant and z1 is a virtual control term, then:

[0089]

[0090] and

[0091]

[0092] Define the switching function as follows:

[0093] σ=k1e1+z1 (38)

[0094] In the formula, k1>0;

[0095] because but:

[0096]

[0097] Since k1+c1>0, when σ=0, e1=0, z1=0 and Therefore, further design is required;

[0098] 2) Define the Lyapunov function:

[0099]

[0100] but:

[0101]

[0102] Design the backstep control law as follows:

[0103]

[0104] In the formula, h and c are positive constants;

[0105] Substituting the backstep control law (42) into equation (41), we get:

[0106]

[0107] Combined with the output of the fuzzy neural network extended state observer in equation (29) The estimation of the total system disturbance x3 is as follows:

[0108]

[0109] Pick

[0110]

[0111] Let τ T = [e1 z1], then:

[0112]

[0113] If Q is a positive definite matrix, then:

[0114]

[0115] because:

[0116]

[0117] By adjusting the values ​​of h, c1, and k1, we can make |Q| > 0, thus ensuring that Q is a positive definite matrix, and therefore guaranteeing...

[0118] According to the LaSalle invariance principle, when taking When t→∞, e1≡0, z1≡0, σ≡0, then when t→∞, e1→0, z1→0, σ→0, and thus x1→x g,

[0119] In summary, the FNNESO-RBSC controller is obtained;

[0120] (4) FNNESO-RBSC control law

[0121] Combining the nonlinear flight dynamics model of the tandem unmanned helicopter represented by equation (23), its corresponding attitude, velocity and position models can be transformed into second-order nonlinear uncertain objects as shown in equation (24); therefore, attitude, velocity and position control loops are designed.

[0122] Taking attitude control as an example, the control variable δ lat ,δ lon ,δ T The state variables φ, θ, and ψ form a single-input, single-output relationship; the control variable δ in the longitudinal channel... lon Designed as follows:

[0123]

[0124] In the formula, θ g The target pitch angle command signal is given, θ is the actual pitch angle of the tandem unmanned helicopter, and b is the target pitch angle command signal. 0θ To control the gain constant, These are estimates of the pitch angle state variables and pitch rate. This is the estimated total disturbance value for the pitch angle channel; similarly, the roll angle control value δ can be obtained. lat , heading angle control quantity δ T And the control quantities of the speed and position control channels.

[0125] Furthermore, the manipulation strategy is specifically as follows:

[0126] The roll angle and lateral velocity are adjusted by generating a rolling torque through differential collective pitch of the left and right rotors; the pitch angle and longitudinal velocity are adjusted by generating a pitch torque through the same longitudinal periodic pitch control of the left and right rotors; the heading angle is adjusted by generating a yaw torque through differential longitudinal periodic pitch control of the left and right rotors; and the vertical velocity is adjusted by changing the lift through the same collective pitch control of the left and right rotors. Thus, each control quantity is as shown in equation (50).

[0127]

[0128] In the formula, δ li ,δ ci (i = 1, 2) represent the longitudinal cyclic pitch and collective pitch control values ​​of the two rotors, respectively.

[0129] The advantages of this invention compared to the prior art are as follows:

[0130] (1) Fuzzy neural networks can effectively improve the adaptability of extended state observers and enhance the ability to estimate the unknown total disturbances faced by unmanned helicopters.

[0131] (2) The FNNESO-RBSC controller has a strong ability to resist uncertainties and internal and external disturbances, can quickly eliminate the influence of disturbances, ensure attitude stability, and ensure stable flight of tandem unmanned helicopters.

[0132] (3) Under the influence of strong internal and external disturbances, the FNNESO-RBSC controller can still ensure high-precision trajectory tracking control effect, and its anti-disturbance and robustness are better than traditional backstepping control and active disturbance rejection control. Attached Figure Description

[0133] Figure 1 This is a block diagram of the horizontal unmanned helicopter flight control system of the present invention;

[0134] Figure 2 This invention relates to the horizontally aligned unmanned helicopter configuration.

[0135] Figure 3 This is the transverse coordinate system for unmanned helicopters according to the present invention;

[0136] Figure 4 Calculation of rotor aerodynamic characteristics for this invention;

[0137] Figure 5 This is a flowchart of the wing aerodynamic calculation of the present invention;

[0138] Figure 6 This is a diagram of the fuzzy neural network structure of the present invention;

[0139] Figure 7 The FNNESO-RBSC controller of this invention;

[0140] Figure 8 This is a block diagram of the attitude control loop of the present invention;

[0141] Figure 9 This is a block diagram of the speed control loop of the present invention;

[0142] Figure 10 This is a block diagram of the position control loop of the present invention;

[0143] Figure 11 This is a schematic diagram of the manipulation strategy of the present invention;

[0144] Figure 12 The target trajectory curve of the present invention is shown; wherein (a) is a three-dimensional trajectory curve and (b) is a two-dimensional trajectory curve.

[0145] Figure 13The following are the flight state response curves of the present invention; where (a) is the position response curve, (b) is the velocity response curve, and (c) is the attitude response curve. Detailed Implementation

[0146] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the following examples provide a more detailed description of the invention. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention.

[0147] The structure of a horizontal unmanned helicopter flight controller is as follows: Figure 1 As shown, it consists of three parts: the FNNESO-RBSC controller, the control strategy, and the flight dynamics model of the tandem unmanned helicopter. The FNNESO-RBSC controller calculates the lateral, longitudinal, directional, and vertical channel control quantities based on the system input and output information. These are then distributed to the control surfaces of the tandem unmanned helicopter by the control strategy, acting on the controlled object. Under the influence of aerodynamics, this causes changes in the object's state response, enabling it to be controlled to the target flight state.

[0148] 1. Flight dynamics model

[0149] This paper studies tandem unmanned helicopters, such as... Figure 2 As shown, its aerodynamic components mainly consist of rotors, wings, fuselage and vertical tail. The left and right rotors are identical except for their rotation direction. Figure 3 The image shows the coordinate systems used in the model calculations, including the ground coordinate system (O). D X D Y D Z D ), body coordinate system (O) B X B Y B Z B ), wind axis system (O) V X V Y V Z V ) and propeller shaft system (O S X S Y S Z S The main structural parameters of the tandem unmanned helicopter are shown in Table 1.

[0150] Table 1. Main parameters of tandem unmanned helicopters

[0151]

[0152] (1) Rotor Model

[0153] The rotor model consists of three parts: the rotor induced velocity model, the blade flapping motion model, and the rotor aerodynamic calculation. Figure 4 As shown.

[0154] The rotor induced velocity model employs a first-order harmonic linear Pitt-Peters dynamic inflow model to calculate its induced velocity. The induced velocity is expanded into a function of rotor spanwise position and azimuth using a first-order Fourier series:

[0155]

[0156] In the formula, v0, v c ,v s These are the time-averaged inflow dimensionless term, the first-order longitudinal inflow dimensionless term, and the first-order transverse inflow dimensionless term for the rotor induced velocity, respectively. Let ψ be the dimensionless term for the spanwise position of the blade. f This is the blade azimuth angle.

[0157] According to the Pitt-Peters dynamic inflow model, the induced velocity components of the rotor shaft disk do not change with time under steady flight conditions, that is:

[0158]

[0159] In the formula, C T C L C M These are the rotor lift coefficient, roll moment coefficient, and pitch moment coefficient, respectively, M and L. NL This is the gain matrix.

[0160] The blade flapping motion model is used to solve for the rotor flapping angle components. Considering only the first-order rigid flapping of the blades, the first-order dynamic model of the flapping angle β is:

[0161] β=a0+a 1s cosψ f b 1s sinψ f (3)

[0162] In the formula, a0, a 1s ,b 1s These are the rotor taper angle, rear chamfer angle, and side chamfer angle, respectively, and their expressions are:

[0163]

[0164] The Lock number γ is represented as:

[0165]

[0166] In the formula, a ∞ b7 is the airfoil lift line slope, b7 is the blade characteristic width, and ρ kqR is the air density, λ0 is the rotor radius, λ0 is the rotor inflow ratio, μ is the rotor advance ratio, θ0 is the rotor root installation angle, and I is the rotor root angle. β M β These are the moment of inertia of the blade flapping hinge and the moment of mass, respectively. A1 and B1 represent the rotor collective pitch, lateral cyclic pitch, and longitudinal cyclic pitch, respectively.

[0167] Based on the induced velocity model and the flapping model, the forces and moments of the rotor in the airframe coordinate system are calculated according to the blade element theory.

[0168] (2) Wing Model

[0169] Considering the aerodynamic interference of the rotor wake on the wing, the wing is divided into two parts: the slipstream region and the freestream region. The slipstream region is the part affected by the rotor wake, while the freestream region is the part unaffected by the rotor wake. For example... Figure 5 The diagram illustrates the aerodynamic calculation process for an airfoil. First, the slipstream area of ​​the airfoil is calculated based on the rotor advance ratio. Then, the aerodynamic forces in the glide slope and free flow regions of the air axis system are calculated separately. The calculation methods for the front and rear airfoils are the same. Finally, the forces and moments of the front and rear airfoils under the air axis system are projected onto the body axis system to obtain the total aerodynamic forces of the airfoil.

[0170] Wing slipstream area S hl The calculation formula is as follows:

[0171]

[0172] Among them, the largest wing slipstream area R max Represented as:

[0173]

[0174] In the formula, μ max The forward velocity is the distance at which the rotor wake just leaves the wing, μ is the rotor forward velocity, R is the rotor radius, and C is the rotor radius. T Z is the rotor thrust coefficient. r is a dimensionless number representing the vertical distance from the rotor's rotation center to the wing.

[0175] Considering the influence of rotor induced velocity, the airflow velocity at the aerodynamic center of the wing slipstream region is:

[0176]

[0177] In the formula, V x V y V z ;ω x ,ω y ,ω z These represent the three-axis velocities and angular velocities of the tilt-rotor quadcopter UAV's center of mass in the body axis system, xw ,y w ,z w These are the coordinates of the wing's aerodynamic center in the three directions along the body axis, v. i The induced velocity of the rotor at the aerodynamic center of the wing.

[0178] The dynamic pressure q in the slipstream region of the wing w,hl for:

[0179]

[0180] Lift L in the wing slipstream region w,hl Resistance D w,hl And pitching moment M wz,hl for:

[0181] L w,hl =q w,hl S hl C Lw,hl (12)

[0182] D w,hl =q w,hl S hl C Dw,hl (13)

[0183] M wz,hl =q w,hl S hl c w C Mw,hl (14)

[0184] In the formula, C Lw,hl C Dw,hl C Mw,hl These are the lift coefficient, drag coefficient, and pitching moment coefficient of the wing under the wind axis system, respectively. hl c is the wing area in the slipstream region. w Let be the wing chord length. Then, based on coordinate projection, the forces and moments in the wing slipstream region in the body coordinate system are obtained.

[0185] The calculation methods for aerodynamic forces in the free flow region are the same as those in the slip flow region. However, the airflow velocity at the aerodynamic center of the wing in the free flow region does not include the rotor-induced velocity term, which will not be elaborated here.

[0186] (3) Fuselage Model

[0187] The forces and torques on the fuselage are:

[0188]

[0189] In the formula, D F ,L F ,S F These are the drag, lift, and lateral force of the fuselage, MxF M yF M zF These are the fuselage's roll moment, yaw moment, and pitch moment, l F A is the characteristic length of the fuselage. F C represents the characteristic area of ​​the fuselage. DF C LF C SF These are the drag coefficient, lift coefficient, and lateral force coefficient of the fuselage, C. MxF C MyF C MzF These are the fuselage's roll moment coefficient, yaw moment coefficient, and pitch moment coefficient, respectively. Then, the forces and moments of the fuselage in the body coordinate system are obtained based on coordinate projection.

[0190] (4) Vertical tail model

[0191] The aerodynamic forces of the drooping tail section of the wind shaft system are:

[0192]

[0193] In the formula, D V ,L V ,S V These are the drag, lift, and lateral force of the vertical tail, C. LV C DV These are the lift coefficient and drag coefficient of the vertical tail, q. v The dynamic pressure of the vertical tail is then calculated. The forces and moments of the vertical tail in the body coordinate system are then obtained based on coordinate projection.

[0194] (5) Nonlinear flight dynamics model of the whole aircraft

[0195] From the aerodynamic models of the above components, the resultant aerodynamic forces and moments of the tilt-rotor UAV in the body axis system can be obtained:

[0196]

[0197] In the formula, F x ,F y ,F z M x M y M z These represent the resultant external forces and resultant external moments along all three axes of the entire aircraft. Based on the kinematic equations of the airframe, the following nonlinear flight dynamics model of the transverse unmanned helicopter is obtained:

[0198]

[0199]

[0200] In the formula, ω x ,ω y,ω z These are the angular velocities in the body coordinate system, V and V. x V y V z The values ​​are: linear velocity in the body coordinate system, φ, θ, and ψ, respectively; Euler angles for roll, pitch, and yaw, respectively; and X, Y, and Z, respectively, the three-axis position coordinates in the ground coordinate system. x ,I y ,I z Let I be the moment of inertia. xy Let g be the inertial product, and g be the acceleration due to gravity.

[0201] Define X1=[φθψ], X2=[ω x ω y ω z ],X3=[V x V y V z ], X4=[XYZ], then equations (19) to (22) simplify to:

[0202]

[0203] In the formula, F i (·)(i=1,2,3,4) represents the unknown function of the relevant state variables, U a =[δ lat δ lon δ T ] represent the lateral, longitudinal, and yaw control parameters of the rotor, respectively. v =[δ φ δ θ δ col ] represent the virtual control values ​​for roll angle, pitch angle, and vertical channel control value, respectively. B a B v These represent the unknown control gain matrices for attitude and velocity, respectively.

[0204] 2. FNNESO-RBSC Flight Control Law

[0205] (1) Second-order nonlinear extended system

[0206] Consider a second-order nonlinear uncertain object subject to external disturbances:

[0207]

[0208] In the formula, u and y are the system input and output signals, f(x,w,t) is a nonlinear function containing unknown disturbances, and b(t) is an unknown compensation coefficient.

[0209] Let x3 = f(x,w,t) + (b(t) - b0)u be the new extended state variable, containing both internal and external disturbances, i.e., the total disturbance, and let b0 be a constant. Then system (24) becomes an extended system with 3 state variables, that is:

[0210]

[0211] (2) Fuzzy Neural Network Extended State Observer

[0212] The fuzzy neural network used to estimate the total perturbation is designed as a four-layer feedforward network, such as... Figure 6 As shown, it contains 2-dimensional input (x = [x1 x2]), n fuzzy rules, and a one-dimensional output (total perturbation estimate).

[0213] First layer (input layer): Pass the input variable x = [x1 x2] to the next layer.

[0214] The second layer (membership function layer): also known as the fuzzification layer, receives the two outputs from the input layer. This paper uses a Gaussian function as the membership function to map the two variables x1 and x2 to n fuzzy rules respectively. The membership function value corresponding to the j-th input variable under the i-th fuzzy rule is:

[0215]

[0216] In the formula, Let represent the center and width of the membership function corresponding to the j-th input variable under the i-th fuzzy rule, respectively.

[0217] The third layer (fuzzy basis function layer): The fuzzy basis function corresponding to the i-th fuzzy rule is represented as:

[0218]

[0219] Fourth layer (output layer): Represented as the sum of the products of the fuzzy basis functions and the weights:

[0220]

[0221] In the formula, The output of the fuzzy neural network represents an estimate of the total system disturbance. To estimate the weight matrix.

[0222] The total disturbance x3 is estimated by the fuzzy neural network, and the state variables x1 and x2 are still estimated by the ESO. Therefore, the fuzzy neural network extended state observer (FNNESO) of the extended system (25) is:

[0223]

[0224] In the formula, λ,β i (i = 1, 2) are the gain coefficients, and ζ is the fixed step size. Then the output variable of FNNESO can track the state variables and total disturbance of system (25), i.e.:

[0225]

[0226] (3) Robust backstep control law

[0227] Define the error between the system's target quantity and the actual quantity:

[0228] e1 = x1 - x g (32)

[0229]

[0230] In the formula, x g This is the target quantity of the system.

[0231] 1) Define the Lyapunov function:

[0232]

[0233] definition Where c1 is a positive constant and z1 is a virtual control term, then:

[0234]

[0235] and

[0236]

[0237] Define the switching function as follows:

[0238] σ=k1e1+z1 (38)

[0239] In the formula, k1>0.

[0240] because but:

[0241]

[0242] Since k1+c1>0, when σ=0, e1=0, z1=0 and Therefore, further design work is required.

[0243] 2) Define the Lyapunov function:

[0244]

[0245] but:

[0246]

[0247] Design the backstep control law as follows:

[0248]

[0249] In the formula, h and c are positive constants.

[0250] Substituting the backstep control law (42) into equation (41), we get:

[0251]

[0252] Combined with the output of the fuzzy neural network extended state observer in equation (29) The estimation of the total system disturbance x3 is as follows:

[0253]

[0254] Pick

[0255]

[0256] Let τ T = [e1 z1], then:

[0257]

[0258] If Q is a positive definite matrix, then:

[0259]

[0260] because:

[0261]

[0262] By adjusting the values ​​of h, c1, and k1, we can make Q > 0, thus ensuring that Q is a positive definite matrix, and therefore guaranteeing...

[0263] According to the LaSalle invariance principle, when taking When t→∞, e1≡0, z1≡0, σ≡0, then when t→∞, e1→0, z1→0, σ→0, and thus x1→x g ,

[0264] In summary, the FNNESO-RBSC controller is as follows: Figure 7 As shown.

[0265] (4) FNNESO-RBSC control law

[0266] Combining the nonlinear flight dynamics model of the tandem unmanned helicopter represented by equation (23), its corresponding attitude, velocity, and position models can be transformed into second-order nonlinear uncertain objects as shown in equation (24). Therefore, designing such... Figures 8 to 10 The attitude, velocity, and position control loops are shown.

[0267] Taking attitude control as an example, the control variable δ lat ,δ lon ,δ T It forms a single-input, single-output relationship with the state variables φ, θ, and ψ. The control variable δ in the longitudinal channel... lon Designed as follows:

[0268]

[0269] In the formula, θ g The target pitch angle command signal is given, θ is the actual pitch angle of the tandem unmanned helicopter, and b is the target pitch angle command signal. 0θ To control the gain constant, These are estimates of the pitch angle state variables and pitch rate. This is the estimated total disturbance value for the pitch angle channel.

[0270] Similarly, the roll angle control value δ can be obtained. lat , heading angle control quantity δ T The control parameters for the speed and position control channels will not be elaborated upon further.

[0271] 3. Manipulation strategy

[0272] Horizontal unmanned helicopter control strategy, such as Figure 11 As shown, the roll angle and lateral velocity are adjusted by generating a rolling torque through differential collective pitch control of the left and right rotors; the pitch angle and longitudinal velocity are adjusted by generating a pitch torque through the same longitudinal periodic pitch control of the left and right rotors; the yaw angle is adjusted by generating a yaw torque through differential longitudinal periodic pitch control of the left and right rotors; and the vertical velocity is adjusted by changing the magnitude of lift through the same collective pitch control of the left and right rotors. Thus, each control parameter is as shown in equation (50).

[0273]

[0274] In the formula, δ li ,δ ci (i = 1, 2) represent the longitudinal cyclic pitch and collective pitch control values ​​of the two rotors, respectively.

[0275] 4. Simulation verification experiment

[0276] To verify the effectiveness of the FNNESO-RBSC controller designed in this paper, attitude control simulation experiments were conducted in the MATLAB / Simulink environment. Figure 12As shown, the target trajectory includes two parts: a figure-eight maneuver and a skiing maneuver. In the simulation experiment, the controllers used were a BSC controller, an ADRC controller, and the FNNESO-RBSC controller designed in this invention. A rectangular wind with a speed of 9 m / s and a pulse width of 1 second was introduced as an external disturbance in the direction of the incoming airflow along all three rotor axes. The total weight and triaxial inertial product of the tandem unmanned helicopter were uniformly reduced by 15% over the initial 30 seconds. The simulation results are as follows. Figure 13 As shown in the figure, the position tracking curves reveal that all three controllers can track the target's flight path well, but the position error curve indicates that the FNNESO-RBSC controller has the smallest tracking error and the highest tracking accuracy. Meanwhile, due to the influence of external wind disturbances and internal disturbances, the velocity and attitude response curves of all three controllers exhibit some degree of oscillation and fluctuation, but the FNNESO-RBSC controller shows the least impact from disturbances and the smoothest flight. The above analysis demonstrates that the FNNESO-RBSC controller has superior trajectory tracking control performance, effectively overcomes the influence of internal and external disturbances, and possesses strong robustness and disturbance rejection capabilities.

[0277] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

[0278] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A control method for an unmanned helicopter based on a fuzzy neural network extended state observer, characterized in that, The tandem unmanned helicopter flight controller structure includes the FNNESO-RBSC controller, control strategy, and tandem unmanned helicopter flight dynamics model; The FNNESO-RBSC controller calculates the lateral, longitudinal, heading, and vertical channel control quantities based on the system input and output information, and distributes them to each control surface of the tandem unmanned helicopter through the control strategy. This affects the controlled object of the tandem unmanned helicopter, causing the object's state response to change under aerodynamic action, thus controlling it to the target flight state. The flight dynamics model described above employs a tandem unmanned helicopter, whose aerodynamic components include a rotor, wings, fuselage, and vertical tail. The coordinate systems used for the flight dynamics model calculations include the ground coordinate system (O...). D X D Y D Z D ), body coordinate system (O) B X B Y B Z B ), wind axis system (O) V X V Y V Z V ) and propeller shaft system (O S X S Y S Z S ); The rotor model mentioned above is specifically: The model comprises three parts: a rotor induced velocity model, a blade flapping motion model, and rotor aerodynamic calculations. The rotor induced velocity model uses a first-order harmonic linear Pitt-Peters dynamic inflow model to calculate the rotor induced velocity; the induced velocity is expanded into a function of rotor spanwise position and azimuth using a first-order Fourier series. In the formula, v0, v c ,v s These are the time-averaged inflow dimensionless term, the first-order longitudinal inflow dimensionless term, and the first-order transverse inflow dimensionless term for the rotor induced velocity, respectively. Let ψ be the dimensionless term for the spanwise position of the blade. f The blade azimuth angle; According to the Pitt-Peters dynamic inflow model, the induced velocity components of the rotor shaft disk do not change with time under steady flight conditions, that is: In the formula, C T C L C M These are the rotor lift coefficient, roll moment coefficient, and pitch moment coefficient, respectively, M and L. NL This is the gain matrix; The blade flapping motion model is used to solve for the rotor flapping angle components; considering only the first-order rigid flapping of the blades, the first-order dynamic model of the flapping angle β is: β=a0+a 1s cosψ f b 1s sinψ f (3) In the formula, a0, a 1s ,b 1s These are the rotor taper angle, rear chamfer angle, and side chamfer angle, respectively, and their expressions are: The Lock number γ is represented as: In the formula, a ∞ b7 is the airfoil lift line slope, b7 is the blade characteristic width, and ρ kq R is the air density, λ0 is the rotor radius, λ0 is the rotor inflow ratio, μ is the rotor advance ratio, θ0 is the rotor root installation angle, and I is the rotor root angle. β M β These are the moment of inertia of the blade flapping hinge and the moment of mass, respectively. A1 and B1 are the rotor collective pitch, lateral cyclic pitch and longitudinal cyclic pitch, respectively; Based on the induced velocity model and the flapping model, the forces and moments of the rotor in the airframe coordinate system are calculated according to the blade element theory.

2. The unmanned helicopter control method based on a fuzzy neural network extended state observer according to claim 1, characterized in that, The wing model mentioned above is specifically: Considering the aerodynamic interference of the rotor wake on the wing, the wing is divided into two parts: the slipstream region and the freestream region. The slipstream region is the part affected by the rotor wake, and the freestream region is the part unaffected by the rotor wake. The aerodynamic calculation process of the wing is as follows: First, the slipstream area of ​​the wing is calculated based on the rotor advance ratio. On this basis, the aerodynamic forces in the slipstream region and the freestream region under the wind axis system are calculated separately. The calculation method is the same for the front wing and the rear wing. Finally, the forces and moments of the front and rear wings under the wind axis system are projected onto the body axis system to obtain the total aerodynamic force of the wing. Wing slipstream area S hl The calculation formula is as follows: Among them, the largest wing slipstream area R max Represented as: In the formula, μ max The forward velocity is the distance at which the rotor wake just leaves the wing, μ is the rotor forward velocity, R is the rotor radius, and C is the rotor radius. T Z is the rotor thrust coefficient. r is a dimensionless number representing the vertical distance from the rotor's rotation center to the wing; Considering the influence of rotor induced velocity, the airflow velocity at the aerodynamic center of the wing slipstream region is: In the formula, V x V y V z ;ω x ,ω y ,ω z These represent the three-axis velocities and angular velocities of the tilt-rotor quadcopter UAV's center of mass in the body axis system, x w ,y w ,z w These are the coordinates of the wing's aerodynamic center in the three directions along the body axis, v. i The induced velocity of the rotor at the aerodynamic center of the wing; The dynamic pressure q in the slipstream region of the wing w,hl for: Lift L in the wing slipstream region w,hl Resistance D w,hl And pitching moment M wz,hl for: L w,hl =q w,hl S hl C Lw,hl (12) D w,hl =q w,hl S hl C Dw,hl (13) M wz,hl =q w,hl S hl c w C Mw,hl (14) In the formula, C Lw,hl C Dw,hl C Mw,hl These are the lift coefficient, drag coefficient, and pitching moment coefficient of the wing under the wind axis system, respectively. hl c is the wing area in the slipstream region. w Let the wing chord length be denoted; then, based on coordinate projection, the forces and moments in the wing slipstream region in the body coordinate system are obtained; The calculation methods for aerodynamics in the free flow region are the same as those in the slip flow region, except that the airflow velocity at the aerodynamic center of the wing in the free flow region does not include the rotor-induced velocity term.

3. The unmanned helicopter control method based on a fuzzy neural network extended state observer according to claim 1, characterized in that, The fuselage model is specifically as follows: The forces and torques on the fuselage are: In the formula, D F ,L F ,S F These are the drag, lift, and lateral force of the fuselage, M xF M yF M zF These are the fuselage's roll moment, yaw moment, and pitch moment, l F A is the characteristic length of the fuselage. F C represents the characteristic area of ​​the fuselage. DF C LF C SF These are the drag coefficient, lift coefficient, and lateral force coefficient of the fuselage, C. MxF C MyF C MzF These are the roll moment coefficient, yaw moment coefficient, and pitch moment coefficient of the fuselage, respectively; then, the forces and moments of the fuselage in the body coordinate system are obtained according to the coordinate projection.

4. The unmanned helicopter control method based on a fuzzy neural network extended state observer according to claim 1, characterized in that, The vertical tail model is specifically as follows: The aerodynamic forces of the drooping tail section of the wind shaft system are: In the formula, D V ,L V ,S V These are the drag, lift, and lateral force of the vertical tail, C. LV C DV These are the lift coefficient and drag coefficient of the vertical tail, q. v The dynamic pressure of the vertical tail is determined; then, the force and torque of the vertical tail in the body coordinate system are obtained according to the coordinate projection.

5. The unmanned helicopter control method based on a fuzzy neural network extended state observer according to claim 1, characterized in that, The aforementioned tandem unmanned helicopter flight dynamics model is as follows: The aerodynamic resultant force and resultant torque of the tilt-rotor UAV in the body axis system can be obtained from the models of each aerodynamic component. In the formula, F x ,F y ,F z M x M y M z The resultant external forces and resultant external moments of each component of the entire aircraft are defined along three axes. Based on the kinematic equations of the airframe, the following nonlinear flight dynamics model of the transverse unmanned helicopter is obtained: In the formula, ω x ,ω y ,ω z These are the angular velocities in the body coordinate system, V and V. x V y V z The values ​​are: linear velocity in the body coordinate system, φ, θ, and ψ, respectively; Euler angles for roll, pitch, and yaw, respectively; and X, Y, and Z, respectively, the three-axis position coordinates in the ground coordinate system. x ,I y ,I z Let I be the moment of inertia. xy Let g be the product of inertia, and g be the acceleration due to gravity. Define X1=[φ θ ψ], X2=[ω x ω y ω z ],X3=[V x V y V z ], X4=[XYZ], then equations (19) to (22) simplify to: In the formula, F i (·)(i=1,2,3,4) represents the unknown function of the relevant state variables, U a =[δ lat δ lon δ T ] represent the lateral, longitudinal, and yaw control parameters of the rotor, respectively. v =[δ φ δ θ δ col ] represent the virtual control values ​​for roll angle, pitch angle, and vertical channel control value, respectively. B a B v These represent the unknown control gain matrices for attitude and velocity, respectively.

6. The unmanned helicopter control method based on a fuzzy neural network extended state observer according to claim 1, characterized in that, The FNNESO-RBSC flight control law includes: (1) Second-order nonlinear extended system Consider a second-order nonlinear uncertain object subject to external disturbances: In the formula, u and y are the system input and output signals, f(x,w,t) is a nonlinear function containing unknown disturbances, and b(t) is an unknown compensation coefficient; Let x3 = f(x,w,t) + (b(t) - b0)u be the new extended state variable, containing both internal and external disturbances, i.e., the total disturbance, and let b0 be a constant. Then system (24) becomes an extended system with 3 state variables, that is: (2) Fuzzy Neural Network Extended State Observer The fuzzy neural network used to estimate the total perturbation is designed as a four-layer feedforward network containing 2-dimensional input (x = [x1 x2]), n fuzzy rules, and a one-dimensional output (total perturbation estimate); First layer (input layer): Passes the input variable x = [x1 x2] to the next layer; The second layer (membership function layer): also known as the fuzzification layer, receives the two outputs from the input layer. This paper uses a Gaussian function as the membership function to map the two variables x1 and x2 to n fuzzy rules respectively. The membership function value corresponding to the j-th input variable under the i-th fuzzy rule is: In the formula, Let represent the center and width of the membership function corresponding to the j-th input variable under the i-th fuzzy rule, respectively; The third layer (fuzzy basis function layer): The fuzzy basis function corresponding to the i-th fuzzy rule is represented as: Fourth layer (output layer): Represented as the sum of the products of the fuzzy basis functions and the weights: In the formula, The output of the fuzzy neural network represents an estimate of the total system disturbance. To estimate the weight matrix; The total disturbance x3 is estimated by the fuzzy neural network, and the state variables x1 and x2 are still estimated by the ESO. Then the fuzzy neural network extended state observer (FNNESO) of the extended system (25) is: In the formula, λ,β i (i = 1, 2) are the gain coefficients, and ζ is the fixed step size; then the output variable of FNNESO can track the state variables and total disturbance of system (25), that is: (3) Robust backstep control law Define the error between the system's target quantity and the actual quantity: e1=x1-x g (32) In the formula, x g For the system target quantity; 1) Define the Lyapunov function: definition Where c1 is a positive constant and z1 is a virtual control term, then: and Define the switching function as follows: σ=k1e1+z1 (38) In the formula, k1>0; because but: Since k1+c1>0, when σ=0, e1=0, z1=0 and Therefore, further design is required; 2) Define the Lyapunov function: but: Design the backstep control law as follows: In the formula, h and χ are positive constants; Substituting the backstep control law (42) into equation (41), we get: Combined with the output of the fuzzy neural network extended state observer in equation (29) The estimation of the total system disturbance x3 is as follows: Pick Let τ T = [e1 z1], then: If Q is a positive definite matrix, then: because: By adjusting the values ​​of h, c1, and k1, we can make |Q| > 0, thus ensuring that Q is a positive definite matrix, and therefore guaranteeing... According to the LaSalle invariance principle, when taking When t→∞, e1≡0, z1≡0, σ≡0, then when t→∞, e1→0, z1→0, σ→0, and thus x1→x g , In summary, the FNNESO-RBSC controller is obtained; (4) FNNESO-RBSC control law Combining the nonlinear flight dynamics model of the tandem unmanned helicopter represented by equation (23), its corresponding attitude, velocity and position models can be transformed into second-order nonlinear uncertain objects as shown in equation (24); therefore, attitude, velocity and position control loops are designed. Taking attitude control as an example, the control variable δ lat ,δ lon ,δ T The state variables φ, θ, and ψ form a single-input, single-output relationship; the control variable δ in the longitudinal channel... lon Designed as follows: In the formula, θ g The target pitch angle command signal is given, θ is the actual pitch angle of the tandem unmanned helicopter, and b is the target pitch angle command signal. 0θ To control the gain constant, These are estimates of the pitch angle state variables and pitch rate. This is the estimated total disturbance value for the pitch angle channel; similarly, the roll angle control variable δ can be obtained. lat , heading angle control quantity δ T And the control quantities of the speed and position control channels.

7. The unmanned helicopter control method based on a fuzzy neural network extended state observer according to claim 1, characterized in that, The manipulation strategy is as follows: The roll angle and lateral velocity are adjusted by generating a rolling torque through differential collective pitch of the left and right rotors; the pitch angle and longitudinal velocity are adjusted by generating a pitch torque through the same longitudinal periodic pitch control of the left and right rotors; the heading angle is adjusted by generating a yaw torque through differential longitudinal periodic pitch control of the left and right rotors; and the vertical velocity is adjusted by changing the lift through the same collective pitch control of the left and right rotors. Thus, each control quantity is as shown in equation (50). In the formula, δ li ,δ ci (i = 1, 2) represent the longitudinal cyclic pitch and collective pitch control values ​​of the two rotors, respectively.

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