Continuous sliding mode fault-tolerant control method for small unmanned helicopter

Abstract

The invention relates to a fault-tolerant control technology for a small single-rotor unmanned helicopter, and aims to provide a nonlinear fault-tolerant control design method for the fault-tolerant control problem of the small single-rotor unmanned helicopter with model uncertainty when an actuator validity loss fault occurs. Therefore, the technical scheme adopted by the invention is as follows: the continuous sliding mode fault-tolerant control method for the small unmanned helicopter comprises the following steps: determining a kinetic model of the single-rotor unmanned helicopter, and expressing the attitude tracking error of the single-rotor unmanned helicopter as a rotation matrix form; introducing the effectiveness loss fault of the actuator and the uncertainty of the model into the kinetic model of the unmanned helicopter, and rewriting the kinetic model based on an incremental nonlinear dynamic inverse method; and designing a fault-tolerant controller in combination with a superhelix control algorithm to realize the fault-tolerant control of the unmanned helicopter. The method is mainly applied to fault-tolerant flight control occasions of small single-rotor unmanned helicopters.

Description

Technical Field

[0001] The present invention relates to a fault-tolerant control technology for a small single-rotor unmanned helicopter, and in particular to attitude fault-tolerant tracking control of a helicopter in the presence of actuator effectiveness loss failure and modeling uncertainty. Background Art

[0002] In recent years, UAVs have played an important role in military and civilian fields such as battlefield reconnaissance, search and rescue, and remote sensing mapping. According to the different power structures, UAVs can be divided into fixed-wing UAVs and rotary-wing UAVs. Compared with fixed-wing UAVs, rotary-wing UAVs have the functions of fixed-point hovering and vertical take-off and landing, high flight agility and strong maneuverability, and can perform tasks in complex environments. Among them, single-rotor unmanned helicopters mainly rely on the main propeller, tail propeller and variable pitch structure to provide power. Their structure is more compact, the weight distribution is more concentrated, and they can quickly change their attitude with a shorter lever arm, thereby improving flight efficiency. However, the flight control development of unmanned helicopters faces many challenges, including open-loop instability as a rotary-wing aircraft, model uncertainty of the dynamic system, and various possible faults.

[0003] In recent years, the control research of unmanned helicopters has attracted widespread attention from scholars. Xian Bin et al. combined reinforcement learning with the superhelical control algorithm to design a nonlinear control algorithm for the control problem of a small unmanned helicopter with modeling uncertainty and unknown external wind disturbance. The experiment proved that the proposed algorithm has good robustness and control effect (Journal: Control and Decision; Author: Xian Bin, Lin Jiayu; Publication Year: 2020; Article Title: Finite Time Convergence Control Design of Small Unmanned Helicopters Based on Reinforcement Learning; Pages: 2646–2653). Hou Jie et al. combined the radial basis function neural network with the extended state observer, and used the output of the observer to design an effective robust adaptive controller, which improved the anti-interference ability of the system and weakened the system's dependence on the accurate model (Journal: Control Theory and Applications; Author: Hou Jie, Chen Mou, Liu Nan; Publication Year: 2021; Article Title: Unmanned Helicopter Control Based on Radial Basis Function Neural Network and Extended State Observer; Pages: 2646–2653). Haoxiang Ma et al. used fuzzy logic system and second-order nonlinear disturbance observer to estimate system uncertainty and external disturbance respectively, and finally minimized the cost function of the attitude loop through the inverse optimal control method to achieve safe tracking flight of unmanned helicopter (Journal: IEEE Transactions on Fuzzy Systems; Author: Haoxiang Ma , Mou Chen , Gang Feng; Publication Year: 2022; Article Title: Disturbance observer-based adaptive fuzzy tracking control for unmanned autonomous helicopter with flight boundary constraints; Pages: 184–198). Yao Zou et al. proposed a saturation control scheme based on differential hyperbolic tangent function in the design of position loop controller, established the criteria for selecting controller parameters, and ensured the extraction of non-singular command attitude for finite time position tracking. In the design of attitude loop controller, based on barrier Lyapunov function and backstepping method, a non-singular attitude loop controller with corresponding initial condition constraints was proposed to achieve bounded trajectory tracking control of small helicopters (Journal: IEEE Transactions on Aerospace and Electronic Systems; Author: Yao Zou, Wei Huo; Publication Year: 2017; Article Title: Nonlinear robust controller for miniature helicopters without singularity; Pages: 1402–1411). However, the above control scheme does not take into account the possibility of failure. In actual flight, the high-speed operation of unmanned helicopters and the long-term operation of the transmission mechanism inevitably lead to mechanical wear, thereby increasing the probability of actuator failure.

[0004] Since the above control scheme ignores this risk, the safety of the unmanned helicopter during operation will be affected. In the field of unmanned helicopter control, designing effective fault-tolerant control is one of the key research directions. Fault-tolerant control can be divided into two categories: active fault-tolerant control and passive fault-tolerant control. The main difference is whether they include a fault diagnosis link. Active fault-tolerant control is a fault-tolerant control scheme that adjusts the controller online through the fault information obtained by the fault diagnosis link when a fault occurs. Sohrab Mokhtar et al. designed an adaptive observer based on neural network and extended Kalman filter, combined with the dynamic model of the unmanned helicopter to detect faults in the actuator and navigation sensor, and designed an active fault-tolerant controller to compensate for the faults in real time (Journal: Remote Sensing; Author: Sohrab Mokhtari, Alireza Abbaspour, Kang K.Yen; Publication Year: 2021; Article Title: Neural network-based active fault-tolerant control design for unmanned helicopter with additive faults; Page Number: 2396). Xin Qiet al. proposed a self-healing control method based on fault diagnosis, which analyzes and ensures the safety of unmanned helicopters under actuator faults by solving a set of linear matrices at one time (Journal of Intelligent & Robotic Systems; Author: Xin Qi, Juntong Qi, Didier Therlliol; Year of publication: 2016; Article title: Self-healing control design under actuator fault occurrence on single-rotor unmanned helicopters.; Pages: 21-35). Guillermo Heredia et al. proposed a sensor fault detection and diagnosis scheme for small unmanned helicopters based on redundancy analysis, using the observer-Kalman filter identification method to determine the occurrence of fault behavior, and tested the system using real unmanned helicopter flight data (Journal of Mathematical Problems in Engineering; Author: Guillermo Heredia, A.Ollero; Year of publication: 2011; Article title: Detection of Sensor Faults in Small Helicopter UAVs Using Observer / Kalman Filter Identification; Pages: 21-35).

[0005] Active fault-tolerant control is highly dependent on the accuracy and timeliness of fault diagnosis, which may increase potential risks. Passive fault-tolerant control is more robust in this regard because it does not rely on the fault diagnosis link. Passive fault-tolerant control mainly relies on the robustness of the controller itself, and adopts a control scheme that is set in advance and fixed during operation. Kun Yan et al. used a disturbance observer to process an unknown continuous function composed of actuator faults, and based on the linear quadratic regulator control technology, gave an optimal fault-tolerant control law that ensures the convergence of the tracking error. The simulation results show the effectiveness and practicality of the proposed fault-tolerant controller (Conference: 2018IEEE 7th Data Driven Control and Learning Systems Conference; Author: Kun Yan , Qingxian Wu , Mou Chen; Publication Year: 2018; Article Title: LQR-based optimal tracking fault tolerant control for a helicopter with actuator faults; Pages: 1022–1027). Kun Yan et al. also proposed an adaptive compensation fault-tolerant control scheme for a medium-sized unmanned helicopter system with input saturation and faults. Adaptive control is used to compensate for external disturbances, and compensatory control inputs are designed to reduce the impact of actuator faults and input saturation. Simulation results verify the effectiveness of the proposed algorithm (Journal: Chinese Journal of Aeronautics; Author: Kun Yan , Mou Chen , Qingxian Wu ; Publication Year: 2019; Article Title: Robust adaptive compensation control for unmanned autonomous helicopter with input saturation and actuator faults; Pages: 2299–2310). Summary of the invention

[0006] Aiming at the fault-tolerant control problem of a small single-rotor unmanned helicopter with model uncertainty under the condition of actuator effectiveness loss failure, a nonlinear fault-tolerant control design method is proposed. To this end, the technical solution adopted by the present invention is that the continuous sliding mode fault-tolerant control method of the small unmanned helicopter determines the dynamic model of the single-rotor unmanned helicopter, and the attitude tracking error of the single-rotor unmanned helicopter is expressed in the form of a rotation matrix; the actuator effectiveness loss failure and model uncertainty are introduced into the unmanned helicopter dynamic model, and the dynamic model is rewritten based on the incremental nonlinear dynamic inverse method; the fault-tolerant controller is designed in combination with the super-helical control algorithm to realize the fault-tolerant control of the unmanned helicopter.

[0007] The specific steps are as follows:

[0008] Step 1) determining the dynamic model of the single-rotor unmanned helicopter;

[0009] Define two orthogonal coordinate systems: (1) Inertial coordinate system {I} = {O I ,X I ,Y I ,Z I}, where X I Pointing to geographic north, Y I Pointing to geographic east, Z I Then the vertical plane {X I ,Y I} points downward; (2) body coordinate system {B} = {O B ,X B ,Y B ,Z B}, where the origin of the coordinate system is O B Located at the center of gravity of the unmanned helicopter, X B Point to the front of the aircraft, Y B Point to the right of the body, Z B Then it is perpendicular to the body and points directly below the unmanned helicopter. The unmanned helicopter attitude dynamics model based on the rotation matrix is ​​expressed as follows:

[0010]

[0011] in represents the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, represents the inertia matrix of the unmanned helicopter, Defined in the body coordinate system {B}, it represents the input torque generated by the rotation of the helicopter's main rotor and tail rotor, represents the angular velocity of the unmanned helicopter defined in the body coordinate system {B}, the symbol × represents the cross product of two vectors, and S(ω) represents the product of ω=[ω1,ω2,ω3] T Zhang Cheng's antisymmetric matrix is ​​specifically expressed as follows

[0012]

[0013] The helicopter uses the unique cross-plate structure and the change of the tail rotor collective pitch to adjust the flapping angle of the main rotor in the roll direction and the pitch direction and the thrust of the tail rotor, so as to achieve the purpose of adjusting the center of mass input torque and define the virtual control input v c (t) = [a s (t) b s (t) T t (t)] T , where a s (t) and b s (t) represents the flapping angle of the main rotor in the rolling and pitching directions, T t (t) is the thrust generated by the tail rotor, v c The relationship between (t) and the center of mass input torque τ(t) is expressed as:

[0014] τ=A(T m )v c +B(T m ) (3)

[0015] Where A(T m ) and B(T m ) is expressed as follows:

[0016]

[0017]

[0018] In (4) and (5), x m ,y m and z m They represent the distance from the main rotor to the center of mass at X in the body coordinate system {B}. B , Y B and Z B Distance in direction, x t With z t They represent the distance from the tail rotor to the center of mass at X in the body coordinate system {B}. B With Z B Distance in direction, K β is the constant coefficient related to the main rotor, T m =mg, where m is the mass of the unmanned helicopter, g is the gravity coefficient, Q m (T m ) is specifically expressed as

[0019] Q m (T m )=C M (T m ) 1.5 +D M (6)

[0020] Among them C M and D M represents the constant coefficient related to aerodynamics;

[0021] The helicopter's flapping angle changes slowly during flight, so the actual control input With virtual control input v c The transformation relationship between (t) is expressed as:

[0022]

[0023] Among them A c , C lon , A lon , B D , D lat , B lat and K ped are all positive numbers, δ lon , δ lat and δ ped They represent the regularized roll servo input, the regularized pitch servo input, and the regularized tail control input respectively;

[0024] Based on the rotation matrix form, the error function is defined Attitude error e R (t) and the angular velocity error e ω (t) is:

[0025]

[0026] in and represents the rotation matrix and the desired angular velocity of the desired posture, tr[·] represents the trace of the matrix, (·) ∨ represents the inverse transformation of S(·);

[0027] Step 2) determining an incremental nonlinear dynamic inverse model with actuator faults and model uncertainty;

[0028] The mathematical model of actuator effectiveness loss failure is expressed as follows:

[0029]

[0030] in is the identity matrix, ρ i (t)∈(0,1](i=1,2,3) represents the effectiveness loss factor, ρ i = 1 indicates a fault-free situation, diag{·} represents a diagonal matrix, t represents the operating time, and tf is the time when a fault occurs;

[0031] Taking the actual situation into consideration, the actuator effectiveness loss failure and model uncertainty are further introduced into the unmanned helicopter dynamics model. Combining (1) and (3), (9) is further rewritten as follows:

[0032]

[0033] where τ d (t) represents model uncertainty;

[0034] Let △t be the data sampling time interval, perform Taylor expansion on the second equation in equation (10) at the time t-△t, and ignore its high-order terms to obtain:

[0035]

[0036] △v c =v c -v c0 (12)

[0037] The variables at time t-△t are represented by subscript 0, and the variables without subscript 0 are sampled at time t. is the virtual control input v c The increment of

[0038] Step 3) Fault-tolerant controller design;

[0039] For (8) R (t) Take the first-order derivative and we get:

[0040]

[0041] For ω (t) Take the first-order derivative and we get:

[0042]

[0043] The matrix in (13) Is a reversible matrix, and the designed sliding surface s(t) is in the following form:

[0044]

[0045] in, s1, s2 and s3 represent the sliding surfaces of the three attitude channels of the unmanned helicopter respectively. is the Hurwitz matrix to be designed, k Ri (i=1,2,3) is a positive constant;

[0046] When s = 0, we know from (15)

[0047]

[0048] Substituting (16) into (13), we can obtain:

[0049]

[0050] Calculate (17) and we get

[0051]

[0052] where e R (t) represents the attitude error at time t, e R (0) represents the attitude error at the initial moment. From (18), we know that on the designed sliding surface, the attitude error converges rapidly in an exponential form;

[0053] Take the first-order derivative of (15) and rearrange (11), (13) and (14) to obtain;

[0054]

[0055] Among them, Ω(t) is a function related to known and measurable quantities, and D(t) is a parameter related to unknown and unmeasurable quantities. The specific expressions of the two are as follows:

[0056]

[0057] D=-J -1 d (21)

[0058] D=[D1D2D3] T is globally bounded and satisfies the following inequalities:

[0059]

[0060] In the above inequality, δ1, δ2 and δ3 are unknown constants, and δ i 0, i=1,2,3;

[0061] Based on (19) and combined with the superhelical control algorithm, the increment of the virtual control input is designed as follows:

[0062] △v c =A -1 J(X+Ω) (23)

[0063] (23) where X = X1 + X2, the first-order derivatives of X1 and X2 are expressed as follows:

[0064]

[0065]

[0066] where sgn(·) represents the sign function, k 11 , k 12 , k 13 , k 21 , k 22 and k 23 are all positive gains and satisfy the following inequality

[0067]

[0068] In the above formula, i = 1, 2, 3;

[0069] Combining (11) and (23), we can see that the virtual control input is:

[0070] v c =A -1 J(X+Ω)+v c0 (27)

[0071] where v c0 Represents the virtual control input at the previous sampling moment;

[0072] Substituting (23) into (19), the closed-loop system dynamic equation is obtained as follows:

[0073]

[0074] The characteristics and beneficial effects of the present invention are:

[0075] 1. The present invention introduces the geometric control method into the fault-tolerant control of unmanned helicopters, defines the tracking error in the form of a rotation matrix, and improves the smoothness of the control effect;

[0076] 2. Aiming at the problem that fault-tolerant control has a strong dependence on model knowledge and that system uncertainty increases with the occurrence of faults, the present invention adopts an incremental nonlinear dynamic inversion method, which effectively solves the strong chattering caused by sliding mode control when a fault occurs and improves the response speed of the system;

[0077] 3. The present invention introduces a superhelical fault-tolerant control algorithm and designs a nonlinear fault-tolerant controller to further enhance the system robustness. Based on the Lyapunov analysis method, the stability of the closed-loop system and the finite-time convergence of the attitude tracking error are proved.

[0078] 4. The present invention has been verified by real-time control experiments on a hardware-in-the-loop experimental platform, proving the effectiveness of the designed controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is the defined coordinate system diagram of single-rotor unmanned helicopter;

[0080] Figure 2 It is a small single-rotor unmanned helicopter hardware-in-the-loop experimental platform used in the present invention;

[0081] Figure 3 is the attitude curve of the unmanned helicopter corresponding to the super spiral control algorithm;

[0082] Figure 4 is the control input curve of the unmanned helicopter corresponding to the super spiral control algorithm;

[0083] Figure 5 is the attitude curve of the unmanned helicopter corresponding to the geometric control algorithm;

[0084] Figure 6 It is the control input curve of the unmanned helicopter corresponding to the geometric control algorithm. DETAILED DESCRIPTION

[0085] The technical problem to be solved by the present invention is to realize fault-tolerant control of a small single-rotor unmanned helicopter in view of the situation that the small single-rotor unmanned helicopter has actuator effectiveness loss failure and model uncertainty.

[0086] The technical solution adopted by the present invention is: in view of the existence of actuator effectiveness loss failure and model uncertainty, a geometric control strategy for a small single-rotor unmanned helicopter is designed based on incremental nonlinear dynamic inversion, and the robustness of the control effect is further enhanced in combination with a superhelical control algorithm, thereby achieving fault-tolerant control of a small single-rotor unmanned helicopter.

[0087] According to the concept of geometric control, the attitude tracking error of the helicopter is expressed in the form of a rotation matrix to enhance the smoothness of the control effect. Based on the incremental nonlinear dynamic inversion method, the nonlinear dynamic model considering the actuator failure is processed. On the basis of the above, the super-helical control design method is further introduced, and a nonlinear robust fault-tolerant control algorithm is designed to improve the robustness of the control system to the actuator effectiveness loss failure.

[0088] The specific steps are as follows:

[0089] Step 1) determining the dynamic model of the single-rotor unmanned helicopter;

[0090] The coordinate system of a single-rotor unmanned helicopter is defined as follows: Figure 1 As shown, two orthogonal coordinate systems are defined: (1) Inertial coordinate system {I} = {O I ,X I ,Y I ,Z I}, where X I Pointing to geographic north, Y I Pointing to geographic east, Z I Then the vertical plane {X I ,Y I} points downward; (2) body coordinate system {B} = {O B ,X B ,Y B ,Z B}, where the origin of the coordinate system is O B Located at the center of gravity of the unmanned helicopter, X B Point to the front of the aircraft, Y B Point to the right of the body, Z B Then it is perpendicular to the body and points directly below the unmanned helicopter. The unmanned helicopter attitude dynamics model based on the rotation matrix can be expressed as follows

[0091]

[0092] in represents the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, represents the inertia matrix of the unmanned helicopter, Defined in the body coordinate system {B}, it represents the input torque generated by the rotation of the helicopter's main rotor and tail rotor, represents the angular velocity of the unmanned helicopter defined in the body coordinate system {B}, the symbol × represents the cross product of two vectors, and S(ω) represents the product of ω=[ω1,ω2,ω3] T Zhang Cheng's antisymmetric matrix is ​​specifically expressed as follows

[0093]

[0094] The helicopter uses the unique cross-plate structure and the change of the tail rotor collective pitch to adjust the flapping angle of the main rotor in the roll direction and the pitch direction and the thrust of the tail rotor, so as to achieve the purpose of adjusting the center of mass input torque. Define the virtual control input v c (t) = [a s (t) b s (t) T t (t)] T , where a s (t) and b s (t) represents the flapping angle of the main rotor in the rolling and pitching directions, T t (t) represents the thrust generated by the tail rotor. c The relationship between (t) and the center of mass input torque τ(t) is expressed as

[0095] τ=A(T m )v c +B(T m ) (31)

[0096] Where A(T m ) and B(T m ) is expressed as follows:

[0097]

[0098]

[0099] In (4) and (5), x m ,y m and z m They represent the distance from the main rotor to the center of mass at X in the body coordinate system {B}. B , Y B and Z B Distance in direction, x t With z t They represent the distance from the tail rotor to the center of mass at X in the body coordinate system {B}. B With Z B Distance in direction, K β is the constant coefficient related to the main rotor, T m =mg, where m is the mass of the unmanned helicopter, g is the gravity coefficient, Q m (Tm ) is specifically expressed as

[0100] Q m (T m )=C M (T m ) 1.5 +D M (34)

[0101] Among them C M and D M Represents a constant coefficient related to aerodynamics.

[0102] To facilitate the design of control strategies, it is assumed that the helicopter flapping angle changes slowly during flight and the actual control input With virtual control input v c The transformation relationship between (t) can be expressed as

[0103]

[0104] Among them A c , C lon , A lon , B D , D lat , B lat and K ped are all positive numbers, δ lon , δ lat and δ ped They represent the regularized roll servo input, the regularized pitch servo input, and the regularized tail control input respectively.

[0105] Step 2) determining an incremental nonlinear dynamic inverse model with actuator faults and model uncertainty;

[0106] Due to the high-speed operation and long-term transmission of the helicopter during operation, the actuator will inevitably wear out, resulting in a decrease in efficiency. This decrease in efficiency is called actuator effectiveness loss failure, which is a common type of failure in unmanned helicopters during flight. Its mathematical model can be expressed as follows

[0107]

[0108] in is the identity matrix, ρ i (t)∈(0,1](i=1,2,3) represents the effectiveness loss factor, ρ i =1 indicates no fault, t indicates the running time, t f is the time when the failure occurred.

[0109] Considering the actual situation, the actuator effectiveness loss failure and model uncertainty are further introduced into the unmanned helicopter dynamics model. Combining (1) and (3), (8) can be further rewritten as follows:

[0110]

[0111] where τ d (t) represents the model uncertainty.

[0112] Let △t be the data sampling time interval, perform Taylor expansion on the second equation in equation (9) at time t-△t, and ignore its high-order terms to obtain

[0113]

[0114] △v c =v c -v c0 (39)

[0115] The variables at time t-△t are represented by subscript 0, and the variables without subscript 0 are sampled at time t. is the virtual control input v c increment.

[0116] Step 3) Fault-tolerant controller design;

[0117] For subsequent controller design, the error function is defined here Attitude error e R (t) and the angular velocity error e ω (t) is

[0118]

[0119] in and represents the rotation matrix and the desired angular velocity formed by the desired posture, tr(·) represents the trace of the matrix, (·) ∨ represents the inverse transformation of S(·).

[0120] For R (t) Taking the first-order derivative we get

[0121]

[0122] For ω (t) Taking the first-order derivative we get

[0123]

[0124] Assume that the matrix in 1(13) is a reversible matrix.

[0125] The design sliding surface s(t) is as follows

[0126]

[0127] in, s1, s2 and s3 represent the sliding surfaces of the three attitude channels of the unmanned helicopter respectively. is the Hurwitz matrix to be designed, k Ri (i=1,2,3) is a normal number.

[0128] When s = 0, we know from (15)

[0129]

[0130] Substituting (16) into (13}, we can get

[0131]

[0132] Calculating (17) yields

[0133]

[0134] where e R (t) represents the attitude error at time t, e R (0) represents the attitude error at the initial moment. From (18), we can see that on the designed sliding surface, the attitude error converges rapidly in an exponential form.

[0135] Taking the first-order derivative of (15), and rearranging (10), (13) and (14) into (15), we obtain

[0136]

[0137] Where Ω(t) is a function related to known and measurable quantities, and D(t) is a parameter related to unknown and unmeasurable quantities. The specific expressions of the two are as follows:

[0138]

[0139] D=-J -1 d (49)

[0140] Assume 2D = [D1D2D3] T is globally bounded and satisfies the following inequality

[0141]

[0142] In the above inequality, δ1, δ2 and δ3 are unknown constants, and δ i 0, i=1,2,3.

[0143] Based on (19), the increment of the virtual control input is designed as follows

[0144] △v c =A -1 J(X+Ω) (51)

[0145] (23) where X = X1 + X2, the first-order derivatives of X1 and X2 are expressed as follows

[0146]

[0147]

[0148] where sgn(·) represents the sign function, k 11 , k 12 , k 13 , k 21 , k 22 and k 23 are all positive gains and satisfy the following inequality

[0149]

[0150] In the above formula, i=1,2,3.

[0151] Combining (11) and (23), we can see that the virtual control input is

[0152] v c =A -1 J(X+…)+v c0 (55)

[0153] where v c0 Represents the virtual control input at the previous sampling moment.

[0154] Substituting (23) into (19), the closed-loop system dynamic equation is obtained as follows:

[0155]

[0156] The present invention is further described in detail below with reference to the accompanying drawings and specific examples.

[0157] The technical solution adopted by the present invention is: in view of the existence of actuator effectiveness loss failure and model uncertainty, a geometric control strategy for a small single-rotor unmanned helicopter is designed based on incremental nonlinear dynamic inversion, and the robustness of the control effect is further enhanced in combination with a superhelical control algorithm, thereby achieving fault-tolerant control of a small single-rotor unmanned helicopter.

[0158] The specific steps are as follows:

[0159] Step 1) determining the dynamic model of the single-rotor unmanned helicopter;

[0160] The coordinate system of a single-rotor unmanned helicopter is defined as follows: Figure 1 As shown, two orthogonal coordinate systems are defined: (1) Inertial coordinate system {I} = {O I ,X I ,Y I ,Z I}, where X I Pointing to geographic north, Y I Pointing to geographic east, Z I Then the vertical plane {X I ,Y I} points downward; (2) body coordinate system {B} = {O B ,X B ,Y B ,Z B}, where the origin of the coordinate system is O B Located at the center of gravity of the unmanned helicopter, X B Point to the front of the aircraft, Y B Point to the right of the body, Z B Then it is perpendicular to the body and points directly below the unmanned helicopter. The unmanned helicopter attitude dynamics model based on the rotation matrix can be expressed as follows

[0161]

[0162] in represents the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, represents the inertia matrix of the unmanned helicopter, Defined in the body coordinate system {B}, it represents the input torque generated by the rotation of the helicopter's main rotor and tail rotor, represents the angular velocity of the unmanned helicopter defined in the body coordinate system {B}, the symbol × represents the cross product of two vectors, and S(ω) represents the product of ω=[ω1,ω2,ω3] T Zhang Cheng's antisymmetric matrix is ​​specifically expressed as follows

[0163]

[0164] The helicopter uses the unique cross-plate structure and the change of the tail rotor collective pitch to adjust the flapping angle of the main rotor in the roll direction and the pitch direction and the thrust of the tail rotor, so as to achieve the purpose of adjusting the center of mass input torque. Define the virtual control input v c (t) = [a s (t) b s (t) T t (t)] T , where a s (t) and b s(t) represents the flapping angle of the main rotor in the rolling and pitching directions, T t (t) represents the thrust generated by the tail rotor. c The relationship between (t) and the center of mass input torque τ(t) is expressed as

[0165] τ=A(T m )v c +B(T m ) (3)

[0166] Where A(T m ) and B(T m ) is expressed as follows:

[0167]

[0168]

[0169] In (4) and (5), x m ,y m and z m They represent the distance from the main rotor to the center of mass at X in the body coordinate system {B}. B , Y B and Z B Distance in direction, x t With z t They represent the distance from the tail rotor to the center of mass at X in the body coordinate system {B}. B With Z B Distance in direction, K β is the constant coefficient related to the main rotor, T m =mg, where m is the mass of the unmanned helicopter, g is the gravity coefficient, Q m (T m ) is specifically expressed as

[0170] Q m (T m )=C M (T m ) 1.5 +D M (6)

[0171] Among them C M and D M Represents a constant coefficient related to aerodynamics.

[0172] To facilitate the design of control strategies, it is assumed that the helicopter flapping angle changes slowly during flight and the actual control input With virtual control input v c The transformation relationship between (t) can be expressed as

[0173]

[0174] Among them A c , C lon , A lon , B D , D lat , B lat and K ped are all positive numbers, δ lon , δ lat and δ ped They represent the regularized roll servo input, the regularized pitch servo input, and the regularized tail control input respectively.

[0175] Step 2) determining an incremental nonlinear dynamic inverse model with actuator faults and model uncertainty;

[0176] Due to the high-speed operation and long-term transmission of the helicopter during operation, the actuator will inevitably wear out, resulting in a decrease in efficiency. This decrease in efficiency is called actuator effectiveness loss failure, which is a common type of failure in unmanned helicopters during flight. Its mathematical model can be expressed as follows

[0177]

[0178] in is the identity matrix, ρ i (t)∈(0,1](i=1,2,3) represents the effectiveness loss factor, ρ i =1 indicates no fault, t indicates the running time, t f is the time when the failure occurred.

[0179] Considering the actual situation, the actuator effectiveness loss failure and model uncertainty are further introduced into the unmanned helicopter dynamics model. Combining (1) and (3), (8) can be further rewritten as follows:

[0180]

[0181] where τ d (t) represents the model uncertainty.

[0182] Let △t be the data sampling time interval, perform Taylor expansion on the second equation in equation (9) at time t-△t, and ignore its high-order terms to obtain

[0183]

[0184] △v c =v c -v c0 (11)

[0185] The variables at time t-△t are represented by subscript 0, and the variables without subscript 0 are sampled at time t. is the virtual control input v c increment.

[0186] Step 3) Fault-tolerant controller design;

[0187] For subsequent controller design, the error function is defined here Attitude error e R (t) and the angular velocity error e ω (t) is

[0188]

[0189] in and represents the rotation matrix and the desired angular velocity formed by the desired posture, tr(·) represents the trace of the matrix, (·) ∨ represents the inverse transformation of S(·).

[0190] For R (t) Taking the first-order derivative we get

[0191]

[0192] For ω (t) Taking the first-order derivative we get

[0193]

[0194] Assume that the matrix in 1(13) is a reversible matrix.

[0195] The design sliding surface s(t) is as follows

[0196]

[0197] in, s1, s2 and s3 represent the sliding surfaces of the three attitude channels of the unmanned helicopter respectively. is the Hurwitz matrix to be designed, k Ri (i=1,2,3) is a normal number.

[0198] When s = 0, we know from (15)

[0199]

[0200] Substituting (16) into (13}, we can get

[0201]

[0202] Calculating (17) yields

[0203]

[0204] where e R (t) represents the attitude error at time t, e R (0) represents the attitude error at the initial moment. From (18), we can see that on the designed sliding surface, the attitude error converges rapidly in an exponential form.

[0205] Taking the first-order derivative of (15), and rearranging (10), (13) and (14) into (15), we obtain

[0206]

[0207] Where Ω(t) is a function related to known and measurable quantities, and D(t) is a parameter related to unknown and unmeasurable quantities. The specific expressions of the two are as follows:

[0208]

[0209] D=-J -1 d (21)

[0210] Assume 2D = [D1D2D3] T is globally bounded and satisfies the following inequality

[0211]

[0212] In the above inequality, δ1, δ2 and δ3 are unknown constants, and δ i 0, i=1,2,3.

[0213] Based on (19), the increment of the virtual control input is designed as follows

[0214] △v c =A -1 J(X+Ω) (23)

[0215] (23) where X = X1 + X2, the first-order derivatives of X1 and X2 are expressed as follows

[0216]

[0217]

[0218] where sgn(·) represents the sign function, k 11 , k 12 , k 13 , k 21 , k 22 and k 23 are all positive gains and satisfy the following inequality

[0219]

[0220] In the above formula, i=1,2,3.

[0221] Combining (11) and (23), we can see that the virtual control input is

[0222] v c =A -1 J(X+Ω)+v c0 (27)

[0223] where v c0 Represents the virtual control input at the previous sampling moment.

[0224] Substituting (23) into (19), the closed-loop system dynamic equation is obtained as follows:

[0225]

[0226] The present invention is described in detail below with reference to specific examples and accompanying drawings.

[0227] 1. Introduction to the experimental platform

[0228] In order to verify the effectiveness and practicality of the fault-tolerant control method proposed in the present invention, the present invention used a small single-rotor unmanned helicopter hardware-in-the-loop experimental platform independently designed and developed by the research group to conduct a fault simulation flight experiment, and conducted a comparative experiment under the same conditions. Figure 2 As shown in the figure, the host computer uses MATLAB / Simulink modules to design fault-tolerant controllers and real-time control of the target machine. The target machine uses the xPC real-time kernel to execute the fault-tolerant control algorithm and completes the control of the unmanned helicopter through communication equipment. The small single-rotor unmanned helicopter of the YATO TREX-450 class is fixed on a low-damping universal ball, and the attitude and acceleration information of each channel of the unmanned helicopter is transmitted back to the target machine at a frequency of 500Hz through the inertial navigation unit carried by the airborne flight control system.

[0229] 2. Experimental Verification and Analysis

[0230] The superhelical fault-tolerant controller designed by the present invention is compared with a geometric control method, and a set of comparative experiments are carried out on the above-mentioned experimental platform. The controller design of the geometric control method is as follows

[0231]

[0232] Among them, k r =diag{[k r1 ,k r2 ,k r3 ]T}, k ω =diag{[k ω1 ,k ω2 ,k ω3 ] T} and k I =diag{[k I1 ,k I2 ,k I3 ] T} are all positive diagonal matrices.

[0233] (1) Parameter selection

[0234] The expected attitude of the experiment is φ=0°, θ=0° and ψ=0°. To simulate the actuator efficiency loss failure, the tail rotor actuator is set to lose 5% of its effectiveness at 20 seconds, 8% at 50 seconds, and 10% at 80 seconds. The fault matrix is ​​as follows:

[0235]

[0236] In the experiment, the relevant parameters of the superhelix controller designed by the present invention are selected as follows: R1 =0.6, k R2 =0.3, k R3 =0.5, k 11 =1500, k 12 =1500, k 13 =120, k 21 =0.1, k 22 =0.1, k 23 =0.1. The parameters related to the geometric controller are selected as follows: k r1 =2900, k r2 =2700, k r3 =70, k ω1 =35, k ω2 =25, k ω3 =1.7, k I1 =50, k I2 =50, k I3 =30,

[0237] (2) Results Analysis

[0238] The results of the unmanned helicopter fault simulation experiment based on the super spiral controller are as follows: Figure 3 and Figure 4 shown. Figure 3Indicates the change of attitude angle in the fault-tolerant control experiment. In the experiment, the tail servo lost 5% of its effectiveness at the 20th second, resulting in a fluctuation of about 18° in the yaw angle, and a smaller fluctuation in the roll angle and pitch angle. At the 50th second, due to the loss of 8% of the effectiveness of the tail servo, the yaw angle fluctuated by about 43°. At the 80th second, the loss of the effectiveness of the tail servo reached 10%, which led to a sharp fluctuation of about 72° in the yaw angle. However, when the above faults occurred, the attitude of the unmanned helicopter could be quickly restored within 10 seconds, and it could maintain a stable flight state after restoration. Since the three attitude channels of the small single-rotor unmanned helicopter are strongly coupled, the fluctuation of the yaw channel will affect the pitch and roll channels. At the 50th and 80th seconds, the loss of effectiveness of the yaw channel and the rapid restoration process caused certain fluctuations in the pitch and roll channels, but they were all within a reasonable range of ±4°. Figure 4 The actual control input curve in the experiment is shown, and it can be seen that the actual control input fluctuates within a reasonable range.

[0239] The results of the unmanned helicopter fault simulation experiment based on geometric control are as follows: Figure 5 and Figure 6 At the 80th second, the effectiveness loss of the tail servo reached 10%, causing the geometric control algorithm to collapse. The unmanned helicopter began to oscillate violently and lost control, so the data recording was terminated before it diverged. Figure 5 The attitude angle change of the simulated fault experiment based on geometric control is shown. At the 20th second, the yaw angle fluctuated by about 22°, and at the 50th second, the fluctuation of the yaw angle increased to about 90°, with a significant increase in severity. At the 80th second, the effectiveness loss of the tail servo reached 10%, which directly led to the collapse of the unmanned helicopter system. It can be seen from the curve that after the fault occurred at the 20th and 50th seconds, the attitude angle converged very slowly and did not return to a stable state. Figure 6 The actual control input curve of the simulated fault experiment based on geometric control is shown. It can be seen that at the moment of the fault, the actual control input corresponding to the yaw channel was adjusted accordingly, but this adjustment did not effectively suppress the impact caused by the fault.

[0240] In order to further compare the fault tolerance effects of the two control algorithms, the recovery time, maximum error and steady-state error of the yaw channel after a fault occurs are analyzed, and the specific values ​​are shown in Table 1. Where ° represents the absence of this value.

[0241] Table 1: Control effect comparison

[0242]

[0243]

[0244] The experimental results show that, compared with the fault-tolerant effect of geometric control, the fault-tolerant controller designed by the present invention can respond quickly when a fault occurs, suppress the negative impact of the fault, and reduce the attitude angle fluctuation caused by the fault. In addition, the controller can quickly restore the unmanned helicopter to a stable range and has the ability to tolerate more serious faults.

[0245] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed in the present invention should be covered within the protection scope of the present invention.

Claims

1. A continuous sliding mode fault-tolerant control method for a small unmanned helicopter, characterized in that: Determine the dynamic model of the single-rotor unmanned helicopter, and express the attitude tracking error of the single-rotor unmanned helicopter in the form of a rotation matrix; introduce the actuator effectiveness loss failure and model uncertainty into the unmanned helicopter dynamic model, and rewrite the dynamic model based on the incremental nonlinear dynamic inverse method; design a fault-tolerant controller in combination with the superhelical control algorithm to achieve fault-tolerant control of the unmanned helicopter.

2. The continuous sliding mode fault-tolerant control method for a small unmanned helicopter as claimed in claim 1, characterized in that: The detailed steps are as follows: Step 1) determining the dynamic model of the single-rotor unmanned helicopter; Define two orthogonal coordinate systems: (1) Inertial coordinate system {I} = {O I ,X I ,Y I ,Z I }, where X I Pointing to geographic north, Y I Pointing to geographic east, Z I Then the vertical plane {X I ,Y I } points downward; (2) body coordinate system {B} = {O B ,X B ,Y B ,Z B }, where the origin of the coordinate system is O B Located at the center of gravity of the unmanned helicopter, X B Point to the front of the aircraft, Y B Point to the right of the body, Z B Then it is perpendicular to the body and points directly below the unmanned helicopter. The unmanned helicopter attitude dynamics model based on the rotation matrix is ​​expressed as follows: in represents the rotation matrix from the body coordinate system {B} to the inertial coordinate system {I}, represents the inertia matrix of the unmanned helicopter, Defined in the body coordinate system {B}, it represents the input torque generated by the rotation of the helicopter's main rotor and tail rotor, represents the angular velocity of the unmanned helicopter defined in the body coordinate system {B}, the symbol × represents the cross product of two vectors, and S(ω) represents the product of ω=[ω1,ω2,ω3] T Zhang Cheng's antisymmetric matrix is ​​specifically expressed as follows The helicopter uses the unique cross-plate structure and the change of the tail rotor collective pitch to adjust the flapping angle of the main rotor in the roll direction and the pitch direction and the thrust of the tail rotor, so as to achieve the purpose of adjusting the center of mass input torque and define the virtual control input v c (t) = [a s (t) b s (t) T t (t)] T , where a s (t) and b s (t) represents the flapping angle of the main rotor in the rolling and pitching directions, T t (t) is the thrust generated by the tail rotor, v c The relationship between (t) and the center of mass input torque τ(t) is expressed as: τ=A(T m )v c +B(T m ) (3) Where A(T m ) and B(T m ) is expressed as follows: In (4) and (5), x m ,y m and z m They represent the distance from the main rotor to the center of mass at X in the body coordinate system {B}. B , Y B and Z B Distance in direction, x t With z t They represent the distance from the tail rotor to the center of mass at X in the body coordinate system {B}. B With Z B Distance in direction, K β is the constant coefficient related to the main rotor, T m =mg, where m is the mass of the unmanned helicopter, g is the gravity coefficient, Q m (T m ) is specifically expressed as Q m (T m )=C M (T m ) 1.5 +D M (6) Among them C M and D M represents the constant coefficient related to aerodynamics; The helicopter's flapping angle changes slowly during flight, so the actual control input With virtual control input v c The transformation relationship between (t) is expressed as: Among them A c , C lon , A lon , B D , D lat , B lat and K ped are all positive numbers, δ lon , δ lat and δ ped They represent the regularized roll servo input, the regularized pitch servo input, and the regularized tail control input respectively; Based on the rotation matrix form, the error function is defined Attitude error e R (t) and the angular velocity error e ω (t) is: in and represents the rotation matrix and the desired angular velocity of the desired posture, tr[·] represents the trace of the matrix, (·) ∨ represents the inverse transformation of S(·); Step 2) determining an incremental nonlinear dynamic inverse model with actuator faults and model uncertainty; The mathematical model of actuator effectiveness loss failure is expressed as follows: in is the identity matrix, ρ i (t)∈(0,1](i=1,2,3) represents the effectiveness loss factor, ρ i =1 indicates a fault-free situation, diag{·} indicates a diagonal matrix, t indicates the running time, t f is the time when the failure occurred; Taking the actual situation into consideration, the actuator effectiveness loss failure and model uncertainty are further introduced into the unmanned helicopter dynamics model. Combining (1) and (3), (9) is further rewritten as follows: where τ d (t) represents model uncertainty; Let Δt be the data sampling time interval, perform Taylor expansion on the second equation in equation (10) at time t-Δt, and ignore its high-order terms to obtain: Δv c =v c -v c0 (12) The variables at time t-Δt are represented by subscript 0, and the variables without subscript 0 are sampled at time t. is the virtual control input v c The increment of Step 3) Fault-tolerant controller design; For (8) R (t) Take the first-order derivative and we get: For ω (t) Take the first-order derivative and we get: The matrix in (13) Is a reversible matrix, and the designed sliding surface s(t) is in the following form: in, s1, s2 and s3 represent the sliding surfaces of the three attitude channels of the unmanned helicopter respectively. is the Hurwitz matrix to be designed, k Ri (i=1,2,3) is a positive constant; When s = 0, we know from (15) Substituting (16) into (13), we can obtain: Calculate (17) and we get where e R (t) represents the attitude error at time t, e R (0) represents the attitude error at the initial moment. From (18), we know that on the designed sliding surface, the attitude error converges rapidly in an exponential form; Take the first-order derivative of (15) and rearrange (11), (13) and (14) to obtain; Among them, Ω(t) is a function related to known and measurable quantities, and D(t) is a parameter related to unknown and unmeasurable quantities. The specific expressions of the two are as follows: D-J -1 d (21) D=[D1D2D3] T is globally bounded and satisfies the following inequalities: In the above inequality, δ1, δ2 and δ3 are unknown constants, and δ i ≥0, i=1,2,3; Based on (19) and combined with the superhelical control algorithm, the increment of the virtual control input is designed as follows: Δv c =A -1 J(X+Ω) (23) (23) where X = X1 + X2, the first-order derivatives of X1 and X2 are expressed as follows: where sgn(·) represents the sign function, k 11 , k 12 , k 13 , k 21 , k 22 and k 23 are all positive gains and satisfy the following inequality In the above formula, i = 1, 2, 3; Combining (11) and (23), we can see that the virtual control input is: v c =A -1 J(X+Ω)+v c0 (27) where v c0 Represents the virtual control input at the previous sampling moment; Substituting (23) into (19), the closed-loop system dynamic equation is obtained as follows:

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