Control method for suppressing measurement interference of height and attitude system of unmanned helicopter

Abstract

The invention discloses a control method for suppressing measurement interference of an unmanned helicopter height attitude system. The control method comprises the following steps: firstly, establishing a nonlinear dynamic model of the unmanned helicopter height attitude system under measurement interference; then designing a disturbance observer to estimate measurement disturbance, establishing a state observer for a system with uncertain output by using the cleaned measurement output, and designing an output feedback controller to suppress the influence of the measurement disturbance; and finally, analyzing the stability of an error system, including a state estimation error system and a tracking error system, determining a gain matrix of the observer by using a linear matrix inequality LMI, and ensuring the bounded stability of the error system and the stability of the unmanned helicopter in the flight process. According to the invention, the problem of insufficient consideration of measurement interference in research of an anti-interference control problem in the prior art is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of unmanned helicopter flight tracking control, and in particular relates to a control method for suppressing measurement interference of an unmanned helicopter altitude attitude system. Background Art

[0002] With the rapid development of UAV technology, aerial vehicles represented by unmanned helicopters have emerged in the military, civil and industrial fields due to their flexible operation and wide application. Considering the complexity of the flight environment of unmanned helicopters and their strong nonlinearity and strong coupling, fully considering the changes in the internal and external environment in the process of building the control model can provide more information for the design of the controller and effectively enhance the stability of the closed-loop system. In recent years, most of the control schemes based on disturbance observers have been designed to eliminate the adverse effects of external disturbances, estimate unknown disturbances using disturbance observers, and then compensate them through feedback control to improve the control performance and stability of the system.

[0003] Existing research has launched a series of discussions on the process interference problem of the nonlinear system of unmanned helicopters, considering the influence of interference force and interference torque on the position and attitude of unmanned helicopters due to changes in the external environment. Due to the combined effects of sensor drift and the external environment, measurement interference is inevitably mixed into the control signal measurement and execution process. The present invention fully considers the influence of measurement interference and proposes an anti-interference control strategy for measurement interference of the altitude attitude control system of unmanned helicopters. The main idea is to first design an interference observer to estimate the measurement interference, use its estimated value to clean the measurement output, and then construct a state observer with the cleaned measurement output information, and finally design a flight tracking controller that suppresses measurement interference, effectively improving the flight stability of the unmanned helicopter. Summary of the invention

[0004] The purpose of the present invention is to provide a control method for suppressing measurement interference of an unmanned helicopter altitude attitude system, thereby solving the problem of insufficient consideration of measurement interference in the research of anti-interference control problems in the prior art.

[0005] The technical solution adopted by the present invention is a control method for suppressing interference in measuring the altitude attitude system of an unmanned helicopter, which is specifically implemented according to the following steps:

[0006] Step 1: Establish a nonlinear dynamic model of the altitude attitude system of the unmanned helicopter under measurement interference;

[0007] Step 2: Design a disturbance observer to estimate the measurement disturbance, and use the cleaned measurement output to establish a state observer for the system with uncertain output, and design an output feedback controller to suppress the influence of the measurement disturbance;

[0008] Step 3: Analyze the stability of the error system, including the state estimation error system and the tracking error system, and use the linear matrix inequality (LMI) to determine the gain matrix of the observer to ensure the boundedness of the error system and the stability of the flight process of the unmanned helicopter.

[0009] The features of the present invention also lie in that

[0010] Step 1 is specifically implemented according to the following steps:

[0011] Analyze the dynamic model of the altitude and attitude system of the unmanned helicopter under measurement interference:

[0012] Step 1.1: Establish a mathematical description of the system according to the dynamic model of the unmanned helicopter:

[0013]

[0014] Where represents the derivative of the vertical altitude of the unmanned helicopter in the inertial coordinate system, v(t) represents the velocity of the inertial coordinate system along the z-axis, represents the derivative of the velocity of the inertial coordinate system along the z-axis, m is the mass of the unmanned helicopter, g is the gravitational acceleration constant, F(t, Ω(t)) represents the resultant external force along the z-axis direction, H(Ω(t)) represents the attitude motion matrix, Ω(t) = (φ(t) θ(t) ψ(t)) T represents the Euler angles of the unmanned helicopter, represents the derivative of the Euler angles of the unmanned helicopter, φ(t), ψ(t) respectively represent the roll angle, pitch angle and yaw angle of the unmanned helicopter, J = diag{J xx J yy J zz} represents the inertia matrix of the unmanned helicopter, J xx , J yy , J zz represents the moments of inertia of the airframe about the x, y, and z axes, w(t) = (p(t) q(t) r(t)) T represents the roll angular velocity, pitch angular velocity and yaw angular velocity, represents the roll angular acceleration, pitch angular acceleration and yaw angular acceleration, w(t) × represents the cross product operator matrix, τ(t) represents the torque, which is the control input of the altitude and attitude system of the unmanned helicopter and is mainly used for adjusting the attitude angles,

[0015] F(t, Ω(t)) is specifically expressed as:

[0016] F(t, Ω(t)) = cosφ(t)cosθ(t)T m (t) - mg

[0017] Among them, T m (t) represents the main rotor thrust, which is the control input of the altitude attitude system of the unmanned helicopter, and cos(·) represents the cosine function of the trigonometric function.

[0018] H(Ω(t)) is specifically expressed as:

[0019]

[0020] Among them, sin(·) represents the sine function of the trigonometric function, cos(·) represents the cosine function of the trigonometric function, tan(·) represents the tangent function of the trigonometric function, and sec(·) represents the secant function of the trigonometric function.

[0021] w(t) × is specifically expressed as:

[0022]

[0023] Step 1.2: Express the dynamic model obtained in Step 1.1 as a state-space equation:

[0024]

[0025] y(t) = x 1 (t) + d(t)

[0026] Among them, represents the derivative of the system state, x 1 (t) = (h(t) Ω(t) T ) T represents the pose and attitude state of the unmanned helicopter system, f 1 (x 1 ) is a matrix function, x 2 (t) = (v(t) w(t) T ) T represents the speed and angular velocity state of the system, represents the derivative of the system speed and angular velocity state, f 2 (x 2 ) is a matrix function, is a constant matrix, u(t) = (T m (t) τ(t) T ) T is the control input, y(t) represents the measured output of the system, and d(t) represents the measurement disturbance.

[0027] The matrix function is specifically expressed as:

[0028] and

[0029] The constant matrix is specifically expressed as:

[0030]

[0031] The measurement disturbance d(t) is described by an external system and is specifically expressed as:

[0032]

[0033] where is the internal state of the system, is the derivative of the internal state of the system, and W and M are constant disturbance coefficient matrices with appropriate dimensions.

[0034] Step 2 is specifically implemented according to the following steps:

[0035] Step 2.1: Estimate the unmeasurable state output by constructing a state observer using the measurement output;

[0036] Step 2.2: Design a disturbance observer based on the state observer using the system output and the state estimate;

[0037] Step 2.3: Define the state estimation error and the disturbance estimation error of the observer;

[0038] Step 2.4: Design an output feedback controller using the backstepping method and the barrier Lyapunov function.

[0039] Step 2.1 is specifically implemented according to the following steps:

[0040] The state observer is designed as:

[0041]

[0042] where and respectively represent the estimates of the states x 1 (t) and x 2 (t), represents the derivative of the state , the estimate of the matrix function f 1 (x 1 ), the estimate of the matrix function f 2 (x 2 ), L 1 and L 2 represent the observation gain matrices of the state observer, y(t) represents the measurement output of the system, represents the estimate of the measurement output of the observer, is a constant matrix, u(t) is the control input, and d(t) represents the estimate of the measurement output of the observer, Represents the estimated value of the measurement interference.

[0043] In step 2.2, the disturbance observer is designed using the system output and the state estimated value as follows:

[0044]

[0045] Where, Represents the estimated value of the measurement interference, Represents the internal state of the measurement interference The estimated value of, σ(t) is an auxiliary variable, and K represents the gain matrix of the disturbance observer, Is the derivative of the auxiliary variable, and W and M are constant disturbance coefficient matrices with appropriate dimensions, And Respectively represent the state x 1 (t) and x 2 (t) estimated values, The estimated value of the matrix function f 2 (x 2 ).

[0046] In step 2.3, the system state estimation error is defined as And The disturbance estimation error is represented by the error of the internal state Of as Then the state estimation error and the disturbance estimation error are represented as:

[0047]

[0048] Where, Represents the state estimation error Derivative of, Represents the state estimation error Derivative of, And Respectively represent the state x 1 (t) and x 2 (t) estimated values, The estimated value of the matrix function f 1 (x 1 ). The estimated value of the matrix function f 2 (x 2 ). L 1 And L 2 Represent the observation gain matrices of the state observer, Represents the estimated error of the measurement interference, Represents the state estimation error Derivative of, K represents the gain matrix of the disturbance observer, and W and M are constant disturbance coefficient matrices with appropriate dimensions.

[0049] Define the tracking error in Step 2.4:

[0050]

[0051] where and represent the estimated values of the states x 1 (t) and x 2 (t) respectively, x d (t) represents the expected trajectory of the unmanned helicopter, and x 2d (t) represents the virtual control law to be designed.

[0052] Design the flight tracking controller:

[0053] To achieve the constraint on the system state, select the following barrier Lyapunov function V 1 (t):

[0054]

[0055] where k 1bi represents the error boundary, satisfying |e 1i (0)| ≤ k 1bi , i = 1, 2, 3, 4, ln(·) represents the natural logarithm, and e 1i (t) is the i-th variable of the tracking error e 1 (t);

[0056] At this time,

[0057] where represents the derivative of the barrier Lyapunov function V 1 (t), represents the transpose of the tracking error e 1 (t), is the derivative of the tracking error e 1 (t), the estimated value of the matrix function f 1 (x 1 ), e 2 (t) is the tracking error, x 2d (t) represents the virtual control law to be designed, L 1 represents the observation gain matrix of the state observer, represents the estimated error of the measurement interference, represents the state estimation error, represents the derivative of the expected trajectory,

[0058] According to the Young's inequality, there exist constant parameters ε1 , ε 2 satisfies ε 1 > 0, ε 2 > 0 such that,

[0059]

[0060] where, represents the transpose of the tracking error e 1 (t), Θ 1 is a variable matrix, L 1 represents the observation gain matrix of the state observer, represents the state estimation error, represents the disturbance estimation error, ε 1 , ε 2 is a positive constant parameter, is ε 1 , ε 2 's inverse, is the transpose of the gain matrix L 1 's transpose, is the transpose of the variable matrix Θ 1 's transpose, represents the transpose of the state estimation error 's transpose, represents the transpose of the disturbance estimation error 's transpose.

[0061] Since is an invertible matrix function, the virtual control law x 2d (t) is obtained:

[0062]

[0063] where, is 's inverse function, k 1 is a positive constant, e 1 (t) is the tracking error, is the desired trajectory 's derivative, is the transpose of the variable matrix Θ 1 's transpose, is the transpose of the gain matrix L 1 's transpose, ε 1 , ε 2 is a positive constant;

[0064] The obtained virtual control law x 2d (t) is substituted into e 2 (t):

[0065]

[0066] Define the barrier Lyapunov function V 2 (t):

[0067]

[0068] Among them, k 2bi represents the error bound, satisfying |e 2i (0)|≤k 2bi ,i=1,2,3,4,ln(·) represents the natural logarithm,e 2i (t) is the tracking error e 2 The i-th variable of (t);

[0069] Barrier Lyapunov function V 2 The derivative of (t) is:

[0070]

[0071] in, Represents the barrier Lyapunov function V 2 The derivative of (t), represents the tracking error e 2 The transpose of (t), is the tracking error e 2 The derivative of (t), Matrix function f 2 (x 2 ), is a constant matrix, u is the control input, L 2 represents the observation gain matrix of the state observer, represents the estimated error of the measurement disturbance, represents the state estimation error, represents the derivative of the virtual control law;

[0072] According to Young's inequality, there exists a constant parameter ε 3 ,ε 4 Satisfy ε 3 >0,ε 4 >0 makes,

[0073]

[0074] in, represents the tracking error e 2 The transpose of (t), Θ 2 is the variable matrix, L 2 represents the observation gain matrix of the state observer, represents the state estimation error, represents the interference estimation error, ε 3 ,ε 4is a positive constant parameter, is ε 3 , ε 4 is the inverse of, is the gain matrix L 2 is the transpose of, is the variable matrix Θ 2 is the transpose of, represents the transpose of the state estimation error is the transpose of, represents the transpose of the disturbance estimation error is the transpose of;

[0075] Design the controller u(t):

[0076]

[0077] where, is a constant matrix is the inverse matrix of, is the derivative of the virtual control law x 2d (t), The matrix function f 2 (x 2 ) is the estimated value, ε 3 , ε 4 is a positive parameter, is the variable matrix Θ 2 is the transpose of, is the gain matrix L 2 is the transpose of, u a (t) is the additive controller to be designed;

[0078] Define a new barrier Lyapunov function V 12 (t) = V 1 (t) + V 2 (t):

[0079]

[0080] where, is the derivative of the barrier Lyapunov function V 12 (t), k 1 , k 2 is a positive constant, represents the transpose of the tracking error e 1 (t), Θ 1 is a variable matrix, represents the transpose of the tracking error e 2 (t), Θ 2 is a variable matrix, The matrix function f 1 (x 1 ) is the estimated value, is the constant ε1 , ε 2 , ε 3 , ε 4 the inverse of represents the state estimation error the transpose of represents the disturbance estimation error the transpose of, u a (t) is the additive controller to be designed;

[0081] At this time, determine the barrier Lyapunov function V 12 (t) satisfies:

[0082]

[0083] where, k 1bi represents the boundary of the error e 1i (t), e 1i (t) is the tracking error e 1 (t) is the i-th variable of the tracking error e 2bi represents the boundary of the error e 2i (t), e 2i (t) is the tracking error e 2 (t) is the i-th variable of the tracking error e is the constant ε 1 , ε 2 , ε 3 , ε 4 the inverse of represents the state estimation error the transpose of represents the disturbance estimation error the transpose of.

[0084] Step 3 is specifically implemented according to the following steps:

[0085] Step 3.1. Conduct a stability analysis of the estimation error system:

[0086] Define a new state variable: and the Lyapunov function: where,

[0087] According to the variables, the Lyapunov function expands to:

[0088]

[0089] where, represents the state estimation error the transpose of represents the state estimation error the transpose of represents the disturbance estimation error The transpose of, P 1 , P 2 , P 3 is a diagonal matrix variable;

[0090] To determine the feasible observer gain, the estimation error is expressed as:

[0091]

[0092] where, represents the state estimation error of the derivative, represents the state estimation error of the derivative, represents the disturbance estimation error of the derivative, L 1 and L 2 represent the observation gain matrix of the state observer, K represents the gain matrix of the disturbance observer, W and M are constant disturbance coefficient matrices with appropriate dimensions, and respectively represent the estimates of the state x 1 (t) and x 2 (t), The matrix function f 1 (x 1 , x 2 ) estimate, The matrix function f 2 (x 2 ) estimate, K -1 represents the inverse matrix of the gain K;

[0093] At this time, the dynamics of the Lyapunov function V 3 (t) is expressed as:

[0094]

[0095] where, P′ is expressed as a non - linear matrix, represents the state estimation error, represents the transpose of the state estimation error, represents the state estimation error, represents the transpose of the state estimation error, represents the disturbance estimation error, represents the transpose of the disturbance estimation error, L 1 and L 2 represent the observation gain matrix of the state observer, K represents the gain matrix of the disturbance observer, W and M are constant disturbance coefficient matrices with appropriate dimensions, P 1,P 2 ,P 3 is a diagonal matrix variable;

[0096] Since F 1 (t), F 2 (t) and F 3 (t) satisfy the local Lipschitz condition, there exists a constant λ i > 0 such that:

[0097]

[0098] where, represents the state estimation error, represents the transpose of the state estimation error, represents the state estimation error, represents the transpose of the state estimation error, represents the disturbance estimation error, represents the transpose of the disturbance estimation error, is the inverse of the positive constant λ 1 , λ 2 , λ 3 of, T i > 0 is determined by the parameter and state constraint conditions of the unmanned helicopter, I is a diagonal matrix with appropriate dimensions, K represents the gain matrix of the disturbance observer, P 1 , P 2 , P 3 is a diagonal matrix variable;

[0099] Then, P′ is reformulated as:

[0100]

[0101] and

[0102] where, Π ij represents the element in the i-th row and j-th column, sym{X} = X T + X, is the inverse of the positive constant λ 1 , λ 2 , λ 3 of, P 1 , P 2 , P 3 is a diagonal matrix variable, L 1 and L 2 represent the observation gain matrices of the state observer, and represent the transposes of the gain matrices L 1 and L 2 respectively, K represents the gain matrix of the disturbance observer, K Tdenotes the transpose of the gain matrix K, W and M are constant disturbance coefficient matrices with appropriate dimensions, T i denotes a constant determined by the constraint conditions of the parameters and states of the unmanned helicopter, I is a diagonal matrix with appropriate dimensions, and * can take any matrix;

[0103] Step 3.2. Conduct a stability analysis of the tracking error system:

[0104] Consider the Lyapunov function: V(t) = V 12 (t) + V 3 (t)

[0105] According to the tracking error obtained in Step 2, the derivative of V(t) is expressed as:

[0106]

[0107] where k 1bi denotes the boundary of the error e 1i (t), e 1i (t) is the i-th variable of the tracking error e 1 (t), k 2bi denotes the boundary of the error e 2i (t), e 2i (t) is the i-th variable of the tracking error e 2 (t). is the transpose of the state variable , Φ is expressed as a non-linear matrix.

[0108] When there exists a positive constant γ such that Φ < -γI, the global asymptotic stability of the closed-loop system can be guaranteed;

[0109]

[0110] where Π ij denotes the element in the i-th row and j-th column, is the constant ε 1 , ε 2 , ε 3 , ε 4 's inverse, P 1 , P 2 , P 3 is a diagonal matrix variable, and denote the transposes of the diagonal matrices P 2 and P 3 , L 1 and L 2 denote the observation gain matrices of the state observer, and denote the gain matrices L 1 and L2 is the transpose of, K represents the gain matrix of the disturbance observer, K T represents the transpose of the gain matrix K, W and M are constant disturbance coefficient matrices with appropriate dimensions, W T represents the transpose of the constant matrix W, T i is a positive constant, I is a diagonal matrix with appropriate dimensions, γ is a positive constant, * means that any matrix can be taken.

[0111] Define X 1 = P 1 L 1 , X 2 = P 2 L 2 , X 3 = P 3 K to obtain a new nonlinear matrix Φ′:

[0112]

[0113] where, Π′ ij represents the element of Π ij after one change, and represent the transpose of the variables X 2 and X 3 , W and M are constant matrices, W T represents the transpose of the constant matrix W, Π ij represents the element of the i-th row and j-th column, T i is a positive constant, I is a diagonal matrix with appropriate dimensions, γ is a positive constant, P 1 T , and represent the transpose of the diagonal matrices P 1 , P 2 and P 3 , is the constant ε 1 , ε 2 , ε 3 , ε 4 , ε T + X, λ 1 , λ 2 , λ 3 is a positive constant;

[0114] Step 3.3, Apply the Schur complement theorem to convert the nonlinear inequality into a linear inequality, define X 1 = P 1 L 1 , X 2 = P 2 L 2 , X 3=P 3 K results in:

[0115]

[0116] where, Π″ 11 =-sym{X 1}+λ 1 T 1 I+λ 3 T 1 I+γI, Π 14 =(P 1 I I),

[0117] Π′ 22 =-sym{P 2}+λ 1 T 2 I+λ 2 T 4 I+λ 3 T 4 I+γI, Π 36 =(X 3 W T W T )

[0118] Π′ 33 =sym{P 3 M-X 3 WM}+γI, Π 44 =diag{-λ 1 I -ε 1 I -ε 3 I}

[0119] Π 66 =diag{-λ 3 I -ε 2 I -ε 4 I}。

[0120] where, Π ij represents the element in the i-th row and j-th column, Π″ ij represents the element of Π ij after the second transformation, X 1 , X 2 and X 3 are defined new linear variables, represents the transpose of the variable X 3 , W and M are constant matrices, W T represents the transpose of the constant matrix W, I is a diagonal matrix with appropriate dimensions, γ is a positive constant, P 1 T , and represent the diagonal matrix P1 , P 2 and P 3 transpose, is the constant ε 1 , ε 2 , ε 3 , ε 4 inverse, sym{X} = X T + X, diag{·} represents a diagonal matrix, λ 1 , λ 2 , λ 3 is a positive constant, T i is a positive constant;

[0121] Step 3.4. Conduct stability analysis on the altitude and attitude closed-loop system of the unmanned aerial vehicle:

[0122] The linear matrix inequality holds, ensuring that the derivative of the Lyapunov function is negative definite:

[0123]

[0124] Satisfy and γ 0 = min{1, γ, k 1 , k 2};

[0125] Among them, is the derivative of the Lyapunov function V(t), γ 0 , γ, k 1 , k 2 are all positive constants, k 1bi represents the boundary of the error e 1i (t), e 1i (t) is the i-th variable of the tracking error e 1 (t), k 2bi represents the boundary of the error e 2i (t), e 2i (t) is the i-th variable of the tracking error e 2 (t), represents the error variable, represents the transpose of the error variable;

[0126] Step 3.5. For the altitude and attitude system of the unmanned helicopter, use the linear matrix inequality LMI toolbox to solve the above matrices, and obtain the corresponding state observer and disturbance observer gain matrices respectively. At this time, the altitude and attitude control system of the unmanned helicopter can achieve the expected control goal under the designed flight output feedback tracking controller.

[0127] The beneficial effects of the present invention are as follows. The control method for suppressing measurement interference in the altitude and attitude system of an unmanned helicopter realizes the precise tracking of a predetermined trajectory by the unmanned helicopter under measurement interference. The effective estimation of measurement interference enables the unmanned helicopter to quickly resume its normal flight state when the measurement output is abnormal. This method effectively suppresses the interference in the output measurement signal, improves the robustness of the unmanned helicopter system, and thus ensures the flight control performance of the unmanned helicopter. BRIEF DESCRIPTION OF THE DRAWINGS

[0128] Figure 1 FIG. 1 is the overall flowchart of the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0129] FIG. 2(a) shows the tracking curve and error curve of altitude in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter under measurement interference according to the present invention;

[0130] FIG. 2(b) shows the tracking curve and error curve of roll angle in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0131] FIG. 2(c) shows the tracking curve and error curve of pitch angle in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0132] FIG. 2(d) shows the tracking curve and error curve of yaw angle in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0133] FIG. 3(a) shows the tracking curve and error curve of speed in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0134] FIG. 3(b) shows the tracking curve and error curve of roll angular velocity in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0135] FIG. 3(c) shows the tracking curve and error curve of pitch angular velocity in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0136] FIG. 3(d) shows the tracking curve and error curve of yaw angular velocity in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0137] FIG. 4(a) shows the measurement interference in the anti-interference flight tracking control method for the altitude and attitude system of an unmanned helicopter based on measurement interference according to the present invention;

[0138] Figure 4(b) shows the measurement interference in the anti-interference flight tracking control method of the unmanned helicopter altitude and attitude system based on measurement interference of the present invention;

[0139] Figure 4(c) shows the measurement interference in the anti-interference flight tracking control method of the unmanned helicopter altitude and attitude system based on measurement interference of the present invention;

[0140] Figure 4(d) shows the measurement interference in the anti-interference flight tracking control method of the unmanned helicopter altitude and attitude system based on measurement interference of the present invention;

[0141] Figure 5(a) shows the control input in the anti-interference flight tracking control method of the unmanned helicopter altitude and attitude system based on measurement interference of the present invention;

[0142] Figure 5(b) shows the control input in the anti-interference flight tracking control method of the unmanned helicopter altitude and attitude system based on measurement interference of the present invention;

[0143] Figure 5(c) shows the control input in the anti-interference flight tracking control method of the unmanned helicopter altitude and attitude system based on measurement interference of the present invention;

[0144] Figure 5(d) shows the control input in the anti-interference flight tracking control method of the unmanned helicopter altitude and attitude system based on measurement interference of the present invention. Detailed implementation manners

[0145] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0146] Example 1

[0147] The control method of the present invention for suppressing the measurement interference of the unmanned helicopter altitude and attitude system has a flowchart as Figure 1 shown, and is specifically implemented according to the following steps:

[0148] Step 1: Establish a non-linear dynamic model of the unmanned helicopter altitude and attitude system under measurement interference;

[0149] Step 1 is specifically implemented according to the following steps:

[0150] Analyze the dynamic model of the unmanned helicopter altitude and attitude system under measurement interference:

[0151] Step 1.1: Establish a mathematical description of the system according to the dynamic model of the unmanned helicopter:

[0152]

[0153] Among them, represents the derivative of the vertical direction height of the unmanned helicopter in the inertial coordinate system, v(t) represents the velocity of the inertial coordinate system along the z-axis, Denote the derivative of the velocity of the inertial coordinate system along the z-axis, m is the mass of the unmanned helicopter, g is the gravitational acceleration constant, F(t,Ω(t)) represents the resultant external force along the z-axis direction, H(Ω(t)) represents the attitude motion matrix, and Ω(t)=(φ(t) θ(t) ψ(t)) T Denote the Euler angles of the unmanned helicopter, Denote the derivative of the Euler angles of the unmanned helicopter, φ(t), ψ(t) represent the roll angle, pitch angle and yaw angle of the unmanned helicopter respectively, J = diag{J xx J yy J zz} represents the inertia matrix of the unmanned helicopter, J xx , J yy , J zz represent the moments of inertia of the airframe about the x, y, z axes, w(t)=(p(t) q(t) r(t)) T represent the roll angular velocity, pitch angular velocity and yaw angular velocity, represent the roll angular acceleration, pitch angular acceleration and yaw angular acceleration, w(t) × represent the cross product operator matrix, τ(t) represents the torque, which is the control input of the altitude attitude system of the unmanned helicopter and is mainly used for adjusting the attitude angles,

[0154] F(t,Ω(t)) is specifically expressed as:

[0155] F(t,Ω(t)) = cosφ(t)cosθ(t)T m (t) - mg

[0156] where, T m (t) represents the main rotor thrust, which is the control input of the altitude attitude system of the unmanned helicopter, and cos(·) represents the cosine function of the trigonometric function.

[0157] H(Ω(t)) is specifically expressed as:

[0158]

[0159] where, sin(·) represents the sine function of the trigonometric function, cos(·) represents the cosine function of the trigonometric function, tan(·) represents the tangent function of the trigonometric function, and sec(·) represents the secant function of the trigonometric function.

[0160] w(t) × is specifically expressed as:

[0161]

[0162] Step 1.2. Represent the dynamic model obtained in Step 1.1 as a state-space equation:

[0163]

[0164] y(t) = x 1 (t) + d(t)

[0165] wherein, represents the derivative of the system state, x 1 (t) = (h(t) Ω(t) T ) T represents the position and attitude state of the unmanned helicopter system, f 1 (x 1 ) is a matrix function, x 2 (t) = (v(t) w(t) T ) T represents the speed and angular velocity state of the system, represents the derivative of the system speed and angular velocity state, f 2 (x 2 ) is a matrix function, is a constant matrix, u(t) = (T m (t) τ(t) T ) T is the control input, y(t) represents the measured output of the system, and d(t) represents the measurement disturbance.

[0166] The matrix function is specifically expressed as:

[0167] and

[0168] The constant matrix is specifically expressed as:

[0169]

[0170] The measurement disturbance d(t) is described by an external system and is specifically expressed as:

[0171]

[0172] wherein, is the internal state of the system, is the derivative of the internal state of the system, and W and M are constant disturbance coefficient matrices with appropriate dimensions.

[0173] Step 2: Design an interference observer to estimate the measurement interference, establish a state observer for the system with uncertain output using the cleaned measurement output, and design an output feedback controller to suppress the influence of the measurement interference;

[0174] Step 2 is specifically implemented according to the following steps:

[0175] Step 2.1: Estimate the unmeasurable state output by constructing a state observer using the measurement output;

[0176] Step 2.1 is specifically implemented according to the following steps:

[0177] The state observer is designed as:

[0178]

[0179] where, and respectively represent the estimated values of states x 1 (t) and x 2 (t), represents the derivative of state , the estimated value of the matrix function f 1 (x 1 ), the estimated value of the matrix function f 2 (x 2 ), L 1 and L 2 represent the observation gain matrices of the state observer, y(t) represents the measurement output of the system, represents the estimated value of the measurement output of the observer, is a constant matrix, u(t) is the control input, d(t) represents the estimated value of the measurement output of the observer, represents the estimated value of the measurement disturbance.

[0180] Step 2.2: Design a disturbance observer based on the state observer using the system output and the state estimated value;

[0181] In Step 2.2, the design of the disturbance observer using the system output and the state estimated value is as follows:

[0182]

[0183] where, represents the estimated value of the measurement disturbance, represents the estimated value of the internal state of the measurement disturbance, σ(t) is an auxiliary variable, K represents the gain matrix of the disturbance observer, is the derivative of the auxiliary variable, W and M are constant disturbance coefficient matrices with appropriate dimensions, and respectively represent the estimated values of states x 1 (t) and x 2 (t), the estimated value of the matrix function f 2 (x 2 ).

[0184] Step 2.3: Define the state estimation error and disturbance estimation error of the observer;

[0185] In Step 2.3, define the system state estimation error as and the disturbance estimation error is represented by the error of the internal state of the error system as Then the state estimation error and disturbance estimation error are expressed as:

[0186]

[0187] where represents the derivative of the state estimation error , represents the derivative of the state estimation error , and represent the estimated values of the state x 1 (t) and x 2 (t) respectively, the estimated value of the matrix function f 1 (x 1 ), the estimated value of the matrix function f 2 (x 2 ), L 1 and L 2 represent the observation gain matrices of the state observer, represents the estimated error of the measured disturbance, represents the derivative of the state estimation error , K represents the gain matrix of the disturbance observer, and W and M are constant disturbance coefficient matrices with appropriate dimensions.

[0188] Step 2.4: Design an output feedback controller using the backstepping method and the barrier Lyapunov function.

[0189] Define the tracking error in Step 2.4:

[0190]

[0191] where and represent the estimated values of the state x 1 (t) and x 2 (t) respectively, x d (t) represents the expected trajectory of the unmanned helicopter, and x 2d (t) represents the virtual control law to be designed.

[0192] Design a flight tracking controller:

[0193] To achieve the constraint of the system state, the following barrier Lyapunov function \(V\) is selected 1 (t):

[0194]

[0195] where \(k\) 1bi represents the error boundary, satisfying \(|e\) 1i (0)|\(\leq k\) 1bi , \(i = 1, 2, 3, 4\), \(\ln(\cdot)\) represents the natural logarithm, \(e\) 1i (t) is the \(i\)-th variable of the tracking error \(e\) 1 (t);

[0196] At this time,

[0197] where, represents the derivative of the barrier Lyapunov function \(V\) 1 (t), represents the transpose of the tracking error \(e\) 1 (t), is the derivative of the tracking error \(e\) 1 (t), The estimated value of the matrix function \(f\) 1 (x 1 ), \(e\) 2 (t) is the tracking error, \(x\) 2d (t) represents the virtual control law to be designed, \(L\) 1 represents the observation gain matrix of the state observer, represents the estimated error of the measurement disturbance, represents the state estimation error, represents the derivative of the desired trajectory,

[0198] According to the Young's inequality, there exist constant parameters \(\varepsilon\) 1 , \(\varepsilon\) 2 satisfying \(\varepsilon\) 1 \(> 0\), \(\varepsilon\) 2 \(> 0\) such that,

[0199]

[0200]

[0201] where, represents the transpose of the tracking error \(e\) 1 (t), \(\Theta\) 1 is the variable matrix, \(L\) 1 represents the observation gain matrix of the state observer, represents the state estimation error, represents the disturbance estimation error, \(\varepsilon\)1 , ε 2 is a positive constant parameter, is ε 1 , ε 2 's inverse, is the gain matrix L 1 's transpose, is the variable matrix Θ 1 's transpose, represents the state estimation error 's transpose, represents the disturbance estimation error 's transpose.

[0202] Since is an invertible matrix function, the virtual control law x 2d (t):

[0203]

[0204] where, is 's inverse function, k 1 is a positive constant, e 1 (t) is the tracking error, is the desired trajectory 's derivative, is the variable matrix Θ 1 's transpose, is the gain matrix L 1 's transpose, ε 1 , ε 2 is a positive constant;

[0205] The obtained virtual control law x 2d (t), substituting into e 2 (t):

[0206]

[0207] Define the barrier Lyapunov function V 2 (t):

[0208]

[0209] where, k 2bi represents the error boundary, satisfying |e 2i (0)| ≤ k 2bi , i = 1, 2, 3, 4, ln(·) represents the natural logarithm, e 2i (t) is the i-th variable of the tracking error e 2 (t);

[0210] The barrier Lyapunov function V 2The derivative of (t) is:

[0211]

[0212] where denotes the derivative of the barrier Lyapunov function V 2 (t), denotes the tracking error e 2 (t) transpose, is the derivative of the tracking error e 2 (t), matrix function f 2 (x 2 ), is a constant matrix, u is the control input, L 2 denotes the observation gain matrix of the state observer, denotes the estimated error of the measurement disturbance, denotes the state estimation error, denotes the derivative of the virtual control law;

[0213] According to Young's inequality, there exist constant parameters ε 3 , ε 4 satisfying ε 3 > 0, ε 4 > 0 such that,

[0214]

[0215] where denotes the transpose of the tracking error e 2 (t), Θ 2 is a variable matrix, L 2 denotes the observation gain matrix of the state observer, denotes the state estimation error, denotes the disturbance estimation error, ε 3 , ε 4 are positive constant parameters, is the inverse of ε 3 , ε 4 , is the transpose of the gain matrix L 2 , is the transpose of the variable matrix Θ 2 , denotes the transpose of the state estimation error , denotes the transpose of the disturbance estimation error ;

[0216] Design the controller u(t):

[0217]

[0218] Among them, is a constant matrix of the inverse matrix, is the derivative of the virtual control law x 2d (t), matrix function f 2 (x 2 ) of the estimated value, ε 3 , ε 4 is a positive parameter, is the variable matrix Θ 2 of the transpose, is the gain matrix L 2 of the transpose, u a (t) is the additive controller to be designed;

[0219] Define a new barrier Lyapunov function V 12 (t) = V 1 (t) + V 2 (t):

[0220]

[0221] Among them, is the derivative of the barrier Lyapunov function V 12 (t), k 1 , k 2 is a positive constant, represents the tracking error e 1 (t) of the transpose, Θ 1 is the variable matrix, represents the tracking error e 2 (t) of the transpose, Θ 2 is the variable matrix, matrix function f 1 (x 1 ) of the estimated value, is the constant ε 1 , ε 2 , ε 3 , ε 4 of the inverse, represents the state estimation error of the transpose, represents the disturbance estimation error of the transpose, u a (t) is the additive controller to be designed;

[0222] At this time, determine the barrier Lyapunov function V 12 (t) satisfies:

[0223]

[0224] Among them, k 1bi represents the boundary of the error e 1i (t), e 1i (t) is the tracking error e 1 (t)'s i-th variable, k 2bi represents the boundary of the error e 2i (t), e 2i (t) is the tracking error e 2 (t)'s i-th variable, is the constant ε 1 , ε 2 , ε 3 , ε 4 's inverse, represents the transpose of the state estimation error , represents the transpose of the disturbance estimation error .

[0225] Step 3: Analyze the stability of the error system, including the state estimation error system and the tracking error system, and use the linear matrix inequality LMI to determine the observer gain matrix to ensure the boundedness of the error system and the stability of the flight process of the unmanned helicopter.

[0226] Step 3 is specifically implemented according to the following steps:

[0227] Step 3.1: Analyze the stability of the estimation error system:

[0228] Define a new state variable: and the Lyapunov function: Among them,

[0229] According to the variables, the Lyapunov function expands to:

[0230]

[0231] Among them, represents the transpose of the state estimation error , represents the transpose of the state estimation error , represents the transpose of the disturbance estimation error , P 1 , P 2 , P 3 is a diagonal matrix variable;

[0232] To determine the feasible observer gain, the estimation error is expressed as:

[0233]

[0234] Among them, represents the derivative of the state estimation error , represents the derivative of the state estimation error , represents the derivative of the disturbance estimation error , L 1 and L 2 represent the observation gain matrix of the state observer, K represents the gain matrix of the disturbance observer, W and M are constant disturbance coefficient matrices with appropriate dimensions, and respectively represent the estimated values of the state x 1 (t) and x 2 (t), The matrix function f 1 (x 1 , x 2 )'s estimated value, The matrix function f 2 (x 2 )'s estimated value, K -1 represents the inverse matrix of the gain K;

[0235] At this time, the dynamics of the Lyapunov function V 3 (t) is expressed as:

[0236]

[0237] Among them, P′ is expressed as a non - linear matrix, represents the state estimation error, represents the transpose of the state estimation error, represents the state estimation error, represents the transpose of the state estimation error, represents the disturbance estimation error, represents the transpose of the disturbance estimation error, L 1 and L 2 represent the observation gain matrix of the state observer, K represents the gain matrix of the disturbance observer, W and M are constant disturbance coefficient matrices with appropriate dimensions, P 1 , P 2 , P 3 are diagonal matrix variables;

[0238] Since F 1 (t), F 2 (t) and F 3 (t) satisfy the local Lipschitz condition, there exists a constant λ i > 0 such that:

[0239]

[0240] wherein, represents the state estimation error, represents the transpose of the state estimation error, represents the state estimation error, represents the transpose of the state estimation error, represents the disturbance estimation error, represents the transpose of the disturbance estimation error, is the positive constant λ 1 , λ 2 , λ 3 is the inverse of, T i > 0 is determined by the parameter and state constraint conditions of the unmanned helicopter, I is a diagonal matrix with appropriate dimensions, K represents the gain matrix of the disturbance observer, P 1 , P 2 , P 3 is a diagonal matrix variable;

[0241] Then, P′ is reformulated as:

[0242]

[0243] and

[0244] wherein, Π ij represents the element in the i-th row and j-th column, sym{X} = X T + X, is the positive constant λ 1 , λ 2 , λ 3 is the inverse of, P 1 , P 2 , P 3 is a diagonal matrix variable, L 1 and L 2 represent the observation gain matrix of the state observer, and represent the transpose of the gain matrix L 1 and L 2 represent the transpose of the gain matrix L T represents the transpose of the gain matrix K, W and M are constant disturbance coefficient matrices with appropriate dimensions, T i represents a constant determined by the parameter and state constraint conditions of the unmanned helicopter, I is a diagonal matrix with appropriate dimensions, * can take any matrix;

[0245] Step 3.2. Conduct a stability analysis of the tracking error system:

[0246] Consider the Lyapunov function: V(t) = V 12 (t) + V 3 (t)

[0247] According to the tracking error obtained in step 2, the derivative of V(t) is expressed as:

[0248]

[0249] where k 1bi represents the boundary of the error e 1i (t), e 1i (t) is the i-th variable of the tracking error e 1 (t), k 2bi represents the boundary of the error e 2i (t), e 2i (t) is the i-th variable of the tracking error e 2 (t). is the transpose of the state variable , and Φ is expressed as a non-linear matrix.

[0250] When there exists a positive constant γ such that Φ < -γI, the global asymptotic stability of the closed-loop system can be guaranteed;

[0251]

[0252] where Π ij represents the element in the i-th row and j-th column, is the constant ε 1 , ε 2 , ε 3 , ε 4 is the inverse of P 1 , P 2 , P 3 is a diagonal matrix variable, and represent the transposes of the diagonal matrices P 2 and P 3 , L 1 and L 2 represent the observation gain matrices of the state observer, and represent the transposes of the gain matrices L 1 and L 2 , K represents the gain matrix of the disturbance observer, K T represents the transpose of the gain matrix K, W and M are constant disturbance coefficient matrices with appropriate dimensions, W T represents the transpose of the constant matrix W, T i is a positive constant, I is a diagonal matrix with appropriate dimensions, γ is a positive constant, and * means that any matrix can be taken.

[0253] Define X 1 =P 1 L 1 , X 2 =P 2 L 2 , X 3 =P 3 K to obtain a new non - linear matrix Φ′:

[0254]

[0255]

[0256] where, Π′ ij denotes the element of Π ij after one change, and denote the transpose of the variable X 2 and X 3 , W and M are constant matrices, W T denotes the transpose of the constant matrix W, Π ij denotes the element of the i - th row and j - th column, T i is a positive constant, I is a diagonal matrix with appropriate dimension, γ is a positive constant, P 1 T , and denote the transposes of the diagonal matrices P 1 , P 2 and P 3 , is the constant ε 1 , ε 2 , ε 3 , ε 4 's inverse, sym{X}=X T +X, λ 1 , λ 2 , λ 3 is a positive constant;

[0257] Step 3.3, apply the Schur complement theorem to convert the non - linear inequality into a linear inequality. To handle the non - linear terms, define X 1 =P 1 L 1 , X 2 =P 2 L 2 , X 3 =P 3 K to obtain:

[0258]

[0259] where, Π″ 11 =-sym{X1}+λ 1 T 1 I+λ 3 T 1 I+γI,Π 14 =(P 1 II),

[0260] Π′ 22 =-sym{P 2}+λ 1 T 2 I+λ 2 T 4 I+λ 3 T 4 I+γI,Π 36 =(X 3 W T W T )

[0261] Π′ 33 =sym{P 3 MX 3 WM}+γI,Π 44 =diag{-λ 1 I-ε 1 I-ε 3 I}

[0262] Π 66 =diag{-λ 3 I-ε 2 I-ε 4 I}.

[0263] Among them, ij represents the element in the i-th row and j-th column, Π″ ij Represents Π ij After the second transformation, X 1 , X 2 and X 3 is a new linear variable defined, Represents variable X 3 The transpose of W and M is a constant matrix, W T represents the transpose of the constant matrix W, I is a diagonal matrix of appropriate dimension, γ is a positive constant, P 1 T , and Denotes the diagonal matrix P 1 , P 2 and P 3 The transpose of is the constant ε 1 ,ε 2 ,ε 3 ,ε4 Inverse of, sym{X} = X T +X, diag{·} represents a diagonal matrix, λ 1 , λ 2 , λ 3 is a positive constant, T i is a positive constant;

[0264] Step 3.4. Conduct stability analysis on the altitude and attitude closed-loop system of the unmanned aerial vehicle:

[0265] The linear matrix inequality holds, ensuring that the derivative of the Lyapunov function is negative definite:

[0266]

[0267] Satisfy and γ 0 = min{1, γ, k 1 , k 2};

[0268] Among them, is the derivative of the Lyapunov function V(t), γ 0 , γ, k 1 , k 2 are all positive constants, k 1bi represents the boundary of the error e 1i (t), e 1i (t) is the i-th variable of the tracking error e 1 (t), k 2bi represents the boundary of the error e 2i (t), e 2i (t) is the i-th variable of the tracking error e 2 (t), represents the error variable, represents the transpose of the error variable;

[0269] Step 3.5. For the altitude and attitude system of the unmanned helicopter, use the linear matrix inequality (LMI) toolbox to solve the above matrices, and obtain the corresponding state observer and disturbance observer gain matrices respectively. At this time, the altitude and attitude control system of the unmanned helicopter can achieve the expected control goal under the designed flight output feedback tracking controller.

[0270] Example 2

[0271] A control method for suppressing measurement interference in the altitude and attitude system of an unmanned helicopter, the flowchart is as Figure 1 shown, and it is specifically implemented according to the following steps:

[0272] Step 1. Establish a nonlinear dynamic model of the altitude and attitude system of the unmanned helicopter under measurement interference;

[0273] Step 2: Design an interference observer to estimate the measurement interference, and use the cleaned measurement output to establish a state observer for the system with uncertain output, and design an output feedback controller to suppress the influence of the measurement interference;

[0274] Step 3: Analyze the stability of the error system, including the state estimation error system and the tracking error system, and use the linear matrix inequality (LMI) to determine the gain matrix of the observer to ensure the boundedness of the error system and the stability of the flight process of the unmanned helicopter.

[0275] Embodiment 3

[0276] The control method for suppressing the measurement interference of the altitude attitude system of an unmanned helicopter according to the present invention has a flow chart as Figure 1 shown, and is specifically implemented according to the following steps:

[0277] Step 1: Establish a nonlinear dynamic model of the altitude attitude system of an unmanned helicopter under measurement interference;

[0278] Step 1 is specifically implemented according to the following steps:

[0279] Analyze the dynamic model of the altitude attitude system of an unmanned helicopter under measurement interference:

[0280] Step 1.1: Establish a mathematical description of the system according to the dynamic model of the unmanned helicopter:

[0281]

[0282] where represents the derivative of the vertical direction altitude of the unmanned helicopter in the inertial coordinate system, v(t) represents the velocity of the inertial coordinate system along the z-axis, represents the derivative of the velocity of the inertial coordinate system along the z-axis, m is the mass of the unmanned helicopter, g is the gravitational acceleration constant, F(t,Ω(t)) represents the resultant external force along the z-axis direction, H(Ω(t)) represents the attitude motion matrix, Ω(t)=(φ(t)θ(t)ψ(t)) T represents the Euler angles of the unmanned helicopter, represents the derivative of the Euler angles of the unmanned helicopter, φ(t), ψ(t) respectively represent the roll angle, pitch angle and yaw angle of the unmanned helicopter, J = diag{J xx J yy J zz} represents the inertia matrix of the unmanned helicopter, J xx , J yy , J zz represents the moments of inertia of the airframe about the x, y, and z axes, w(t)=(p(t)q(t)r(t))T represent the roll angular velocity, pitch angular velocity and yaw angular velocity, represent the roll angular acceleration, pitch angular acceleration and yaw angular acceleration, w(t) × represents the cross product operator matrix, and τ(t) represents the torque, which is the control input of the unmanned helicopter altitude attitude system and is mainly used for the adjustment of the attitude angle.

[0283] F(t, Ω(t)) is specifically expressed as:

[0284] F(t, Ω(t)) = cosφ(t)cosθ(t)T m (t) - mg

[0285] where, T m (t) represents the main rotor thrust, which is the control input of the unmanned helicopter altitude attitude system, and cos(·) represents the cosine function of the trigonometric function.

[0286] H(Ω(t)) is specifically expressed as:

[0287]

[0288] where, sin(·) represents the sine function of the trigonometric function, cos(·) represents the cosine function of the trigonometric function, tan(·) represents the tangent function of the trigonometric function, and sec(·) represents the secant function of the trigonometric function.

[0289] w(t) × is specifically expressed as:

[0290]

[0291] Step 1.2. Represent the dynamic model obtained in Step 1.1 as a state - space equation:

[0292]

[0293] y(t) = x 1 (t) + d(t)

[0294] where, represents the derivative of the system state, x 1 (t) = (h(t) Ω(t) T ) T represents the pose and attitude state of the unmanned helicopter system, f 1 (x 1 ) is a matrix function, x 2 (t) = (v(t) w(t) T ) T represents the speed and angular velocity state of the system, Denote the derivative of the system speed and angular velocity states, f 2 (x 2 ) is a matrix function, is a constant matrix, u(t) = (T m (t)τ(t) T ) T is the control input, y(t) represents the measured output of the system, and d(t) represents the measurement disturbance.

[0295] The matrix function is specifically expressed as: and

[0296] The constant matrix is specifically expressed as:

[0297] The measurement disturbance d(t) is described by an external system and is specifically expressed as: where, is the internal state of the system, is the derivative of the internal state of the system, and W and M are constant disturbance coefficient matrices with appropriate dimensions.

[0298] Step 2: Design an interference observer to estimate the measurement interference, establish a state observer for the system with uncertain output using the cleaned measurement output, and design an output feedback controller to suppress the influence of the measurement interference;

[0299] Step 3: Analyze the stability of the error system, including the state estimation error system and the tracking error system, and use the linear matrix inequality LMI to determine the gain matrix of the observer to ensure the boundedness of the error system and the stability of the flight process of the unmanned helicopter.

[0300] Example 4

[0301] The control method for suppressing the measurement interference of the altitude attitude system of an unmanned helicopter according to the present invention has a flowchart as Figure 1 shown and is specifically implemented according to the following steps:

[0302] Step 1: Establish a nonlinear dynamic model of the altitude attitude system of the unmanned helicopter under measurement interference;

[0303] Step 2: Design an interference observer to estimate the measurement interference, establish a state observer for the system with uncertain output using the cleaned measurement output, and design an output feedback controller to suppress the influence of the measurement interference;

[0304] Step 2 is specifically implemented according to the following steps:

[0305] Step 2.1: Estimate the unmeasurable state output by constructing a state observer using the measurement output;

[0306] Step 2.2: Design an interference observer based on the state observer, using the system output and the state estimation value;

[0307] Step 2.3: Define the state estimation error and the interference estimation error of the observer;

[0308] Step 2.4: Design an output feedback controller using the backstepping method and the barrier Lyapunov function.

[0309] Step 3: Analyze the stability of the error system, including the state estimation error system and the tracking error system, and use the linear matrix inequality (LMI) to determine the gain matrix of the observer to ensure the boundedness of the error system and the stability of the flight process of the unmanned helicopter.

[0310] Embodiment 5

[0311] The control method for suppressing measurement interference in the altitude attitude system of an unmanned helicopter according to the present invention has a flowchart as Figure 1 shown, and is specifically implemented according to the following steps:

[0312] Step 1: Establish a nonlinear dynamic model of the altitude attitude system of an unmanned helicopter under measurement interference;

[0313] Step 2: Design an interference observer to estimate the measurement interference, and use the cleaned measurement output to establish a state observer for the system with uncertain output, and design an output feedback controller to suppress the influence of the measurement interference;

[0314] Step 2 is specifically implemented according to the following steps:

[0315] Step 2.1: Construct a state observer by using the measurement output to estimate the unmeasurable state output;

[0316] Step 2.2: Design an interference observer based on the state observer, using the system output and the state estimation value;

[0317] Step 2.3: Define the state estimation error and the interference estimation error of the observer;

[0318] Step 2.4: Design an output feedback controller using the backstepping method and the barrier Lyapunov function.

[0319] Step 2.1 is specifically implemented according to the following steps:

[0320] The state observer is designed as:

[0321]

[0322] Wherein, and respectively represent the state x 1 (t) and x 2The estimated value of (t), represents the state derivative, The matrix function f 1 (x 1 )'s estimated value, The matrix function f 2 (x 2 )'s estimated value, L 1 and L 2 represent the observation gain matrix of the state observer, y(t) represents the measured output of the system, represents the estimated value of the measured output of the observer, is a constant matrix, u(t) is the control input, d(t) represents the estimated value of the measured output of the observer, represents the estimated value of the measurement disturbance.

[0323] Step 3: Analyze the stability of the error system, including the state estimation error system and the tracking error system, and use the linear matrix inequality LMI to determine the gain matrix of the observer to ensure the boundedness of the error system and the stability of the unmanned helicopter flight process.

[0324] Example 6

[0325] Specific parameters are selected for the altitude attitude control system of the unmanned helicopter:

[0326] J xx = 0.26 kg·m 2 ; J yy = 0.35 kg·m 2 ; J zz = 0.29 kg·m 2 ; m = 8 kg

[0327] λ 1 = 1; λ 2 = 4; λ 3 = 10; ε 1 = 1; ε 2 = 1; ε 3 = 1; ε 4 = 1; T 1 = 0.1; T 2 = 0.4; T 3 = 0.1

[0328]

[0329] Using the LMI toolbox in MATLAB, the observer gain matrix is obtained:

[0330]

[0331] Based on the above settings, for the anti-interference flight tracking control method of the UAV altitude and attitude system with the proposed output feedback, the simulation results are as shown in the accompanying drawings of the specification.

[0332] Figures 2(a) to 2(d) It shows the desired trajectory, estimated value and estimated error curve of the unmanned helicopter system. Figure 2(a) represents the altitude curve of the unmanned helicopter, Figure 2(b) represents the roll angle curve of the unmanned helicopter, Figure 2(c) represents the pitch angle curve of the unmanned helicopter, and Figure 2(d) represents the yaw angle curve of the unmanned helicopter. By comparing the desired trajectory and the estimated trajectory, it can be clearly seen the tracking performance of the unmanned helicopter system when performing tasks.

[0333] Figures 3(a) to 3(d) They are the curves of the expected value, estimated value and error change of the speed and angular velocity states of the unmanned helicopter. Figure 3(a) represents the vertical speed curve of the unmanned helicopter, Figure 3(b) represents the roll angular velocity curve of the unmanned helicopter, Figure 3(c) represents the pitch angular velocity curve of the unmanned helicopter, and Figure 3(d) represents the yaw angular velocity curve of the unmanned helicopter. As shown in the figure, the state estimated values of the speed and angular velocity well track the expected system state, and the estimation error always remains within a small range, indicating that both the speed error and angular velocity error of the unmanned helicopter are well constrained.

[0334] Figures 4(a) to 4(d) It further shows the role of the measurement disturbance observer. Figure 4(a), Figure 4(b), Figure 4(c) and Figure 4(d) respectively represent the disturbances acting on the measurement output of the unmanned helicopter system and the estimation results of the measurement disturbance observer coincide with the actual disturbance d(t), indicating that the designed disturbance observer can effectively estimate the measurement disturbance and achieve an accurate dynamic response to external measurement disturbances.

[0335] Figure 5(a), Figure 5(b), Figure 5(c) and Figure 5(d) depict the change curves of the input u(t) of the unmanned helicopter altitude and attitude system, fully demonstrating the adjustment process of the anti-interference output feedback controller to the system dynamic characteristics, indicating that the designed controller can effectively suppress the influence of measurement disturbances on the unmanned helicopter altitude and attitude system.

[0336] The simulation results show that the proposed control strategy can effectively estimate the uncertain states and disturbances of the nonlinear helicopter altitude and attitude system and achieve accurate tracking of the expected signal. The above simulation results confirm that the control scheme proposed in the present invention can effectively eliminate the adverse effects brought by measurement disturbances and ensure that the unmanned helicopter altitude and attitude system has good flight tracking performance.

Claims

1. A control method for suppressing interference in measurement of an unmanned helicopter altitude attitude system, characterized in that: Follow the steps below to implement it: Step 1: Establish a nonlinear dynamic model of the altitude attitude system of the unmanned helicopter under measurement interference; Step 2: Design a disturbance observer to estimate the measurement disturbance, and use the cleaned measurement output to establish a state observer for the system with uncertain output, and design an output feedback controller to suppress the influence of the measurement disturbance; Step 3: Analyze the stability of the error system, including the state estimation error system and the tracking error system, and use the linear matrix inequality LMI to determine the gain matrix of the observer to ensure the boundedness of the error system and the stability of the unmanned helicopter flight process.

2. The control method for suppressing measurement interference of an unmanned helicopter altitude attitude system according to claim 1 is characterized in that: The step 1 is specifically implemented according to the following steps: The dynamic model of the altitude attitude system of the unmanned helicopter under measurement interference is analyzed: Step 1.1: Establish a mathematical description of the system based on the dynamic model of the unmanned helicopter: in, represents the derivative of the vertical height of the unmanned helicopter in the inertial coordinate system, v(t) represents the velocity of the inertial coordinate system along the z-axis, represents the derivative of the velocity of the inertial coordinate system along the z-axis, m is the mass of the unmanned helicopter, g is the gravitational acceleration constant, F(t,Ω(t)) represents the resultant external force along the z-axis, H(Ω(t)) represents the attitude motion matrix, Ω(t)=(φ(t)θ(t)ψ(t)) T represents the Euler angle of the unmanned helicopter, represents the derivative of the Euler angle of the unmanned helicopter, φ(t), ψ(t) represents the roll angle, pitch angle and yaw angle of the unmanned helicopter, J = diag{J xx J yy J zz } represents the inertia matrix of the unmanned helicopter, J xx ,J yy ,J zz Represents the moment of inertia of the body around the x, y, and z axes, w(t) = (p(t)q(t)r(t)) T represents the roll angular velocity, pitch angular velocity and yaw angular velocity, represents the roll acceleration, pitch acceleration and yaw acceleration, w(t) × represents the cross product operator matrix, τ(t) represents the torque, which is the control input of the altitude attitude system of the unmanned helicopter, mainly used for the adjustment of the attitude angle. F(t,Ω(t)) is specifically expressed as: F(t,Ω(t))=cosφ(t)cosθ(t)T m (t)-mg Among them, T m (t) represents the main rotor thrust, which is the control input of the altitude attitude system of the unmanned helicopter, and cos(·) represents the cosine function of the trigonometric function; H(Ω(t)) is specifically expressed as: Among them, sin(·) represents the sine function of the trigonometric function, cos(·) represents the cosine function of the trigonometric function, tan(·) represents the tangent function of the trigonometric function, and sec(·) represents the secant function of the trigonometric function; w(t) × Specifically expressed as: Step 1.2: Express the dynamic model obtained in step 1.1 as a state space equation: y(t)=x1(t)+d(t) in, represents the derivative of the system state, x1(t)=(h(t)Ω(t) T ) T represents the position and attitude state of the unmanned helicopter system, f1(x1) is a matrix function, x2(t)=(v(t)w(t) T ) T represents the velocity and angular velocity state of the system, represents the derivative of the system velocity and angular velocity state, f2(x2) is a matrix function, is a constant matrix, u(t)=(T m (t)τ(t) T ) T is the control input, y(t) represents the measured output of the system, and d(t) represents the measured disturbance; The matrix function is specifically expressed as: and The constant matrix is ​​specifically expressed as: The measurement disturbance d(t) is described by the external system and is specifically expressed as: in, is the internal state of the system, is the derivative of the internal state of the system, and W and M are constant interference coefficient matrices with appropriate dimensions.

3. The control method for suppressing measurement interference of an unmanned helicopter altitude attitude system according to claim 2 is characterized in that: The step 2 is specifically implemented according to the following steps: Step 2.1, estimate the unmeasurable state output by constructing a state observer using the measured output; Step 2.2, based on the state observer, design a disturbance observer using the system output and state estimation value; Step 2.3, define the state estimation error and disturbance estimation error of the observer; Step 2.4: Design the output feedback controller using the backstepping method and the barrier Lyapunov function.

4. The control method for suppressing measurement interference of an unmanned helicopter altitude attitude system according to claim 3 is characterized in that: The step 2.1 is specifically implemented according to the following steps: The state observer is designed to: in, and denote the estimated values ​​of states x1(t) and x2(t), respectively. Indicates status The derivative of The estimated value of the matrix function f1(x1), The estimated value of the matrix function f2(x2), L1 and L2 represent the observation gain matrices of the state observer, y(t) represents the measured output of the system, represents the estimated value of the observer's measured output, is a constant matrix, u(t) is the control input, d(t) represents the estimated value of the observer's measured output, Represents an estimate of the measurement interference.

5. The control method for suppressing measurement interference of an unmanned helicopter altitude attitude system according to claim 4 is characterized in that: The design of the disturbance observer using the system output and state estimation value in step 2.2 is as follows: in, represents an estimate of the measurement interference, Indicates that the measurement disturbs the internal state The estimated value of , σ(t) is an auxiliary variable, K represents the gain matrix of the disturbance observer, are derivatives of the auxiliary variables, W and M are constant interference coefficient matrices of appropriate dimensions, and denote the estimated values ​​of states x1(t) and x2(t), respectively. Estimated value of the matrix function f2(x2).

6. The control method for suppressing measurement interference of an unmanned helicopter altitude attitude system according to claim 5 is characterized in that: In step 2.3, the system state estimation error is defined as and The disturbance estimation error is calculated by the internal state of the error system The error is expressed as Then the state estimation error and disturbance estimation error are expressed as: in, represents the state estimation error The derivative of represents the state estimation error The derivative of and denote the estimated values ​​of states x1(t) and x2(t), respectively. The estimated value of the matrix function f1(x1), The estimated value of the matrix function f2(x2), L1 and L2 represent the observation gain matrix of the state observer, represents the estimated error of the measurement disturbance, represents the state estimation error The derivative of , K represents the gain matrix of the disturbance observer, and W and M are constant disturbance coefficient matrices with appropriate dimensions.

7. The control method for suppressing measurement interference of an unmanned helicopter altitude attitude system according to claim 6 is characterized in that: The tracking error is defined in step 2.4: in, and They represent the estimated values ​​of states x1(t) and x2(t), respectively. d (t) represents the expected trajectory of the unmanned helicopter, x 2d (t) represents the virtual control law to be designed; Design a flight tracking controller: In order to realize the constraint on the system state, the following barrier Lyapunov function V1(t) is selected: Among them, k 1bi represents the error bound, satisfying |e 1i (0)|≤k 1bi ,i=1,2,3,4,ln(·) represents the natural logarithm,e 1i (t) is the i-th variable of the tracking error e1(t); at this time, in, represents the derivative of the barrier Lyapunov function V1(t), represents the transpose of the tracking error e1(t), is the derivative of the tracking error e1(t), The estimated value of the matrix function f1(x1), e2(t) tracking error, x 2d (t) represents the virtual control law to be designed, L1 represents the observation gain matrix of the state observer, represents the estimated error of the measurement disturbance, represents the state estimation error, represents the derivative of the expected trajectory, According to Young's inequality, there exist constant parameters ε1,ε2 that satisfy ε1>0,ε2>0 such that, in, represents the transpose of the tracking error e1(t), Θ1 is the variable matrix, L1 represents the observation gain matrix of the state observer, represents the state estimation error, represents the interference estimation error, ε1, ε2 are positive constant parameters, is the inverse of ε1,ε2, is the transpose of the gain matrix L1, is the transpose of the variable matrix Θ1, represents the state estimation error The transpose of The interference estimation error The transpose of because is a reversible matrix function, and the virtual control rate x is obtained 2d (t): in, yes is the inverse function, k1 is a positive constant, e1(t) is the tracking error, The expected trajectory The derivative of is the transpose of the variable matrix Θ1, is the transpose of the gain matrix L1, ε1, ε2 are positive constants; The obtained virtual control rate x 2d (t), substitute into e2(t): Define the barrier Lyapunov function V2(t): Among them, k 2bi represents the error bound, satisfying |e 2i (0)|≤k 2bi ,i=1,2,3,4,ln(·) represents the natural logarithm,e 2i (t) is the i-th variable of the tracking error e2(t); The derivative of the barrier Lyapunov function V2(t) is: in, represents the derivative of the barrier Lyapunov function V2(t), represents the transpose of the tracking error e2(t), is the derivative of the tracking error e2(t), The estimated value of the matrix function f2(x2), is a constant matrix, u is the control input, L2 represents the observation gain matrix of the state observer, represents the estimated error of the measurement disturbance, represents the state estimation error, represents the derivative of the virtual control law; According to Young's inequality, there exist constant parameters ε3, ε4 that satisfy ε3>0, ε4>0 such that, in, represents the transpose of the tracking error e2(t), Θ2 is the variable matrix, L2 represents the observation gain matrix of the state observer, represents the state estimation error, represents the interference estimation error, ε3, ε4 are positive constant parameters, is the inverse of ε3,ε4, is the transpose of the gain matrix L2, is the transpose of the variable matrix Θ2, represents the state estimation error The transpose of The interference estimation error The transpose of Design controller u(t): in, is a constant matrix The inverse matrix of is the virtual control law x 2d The derivative of (t), The estimated value of the matrix function f2(x2), ε3, ε4 are positive parameters, is the transpose of the variable matrix Θ2, is the transpose of the gain matrix L2, u a (t) is the additive controller that needs to be designed; Define a new barrier Lyapunov function V 12 (t) = V1(t) + V2(t): in, is the barrier Lyapunov function V 12 The derivative of (t), k1, k2 are positive constants, represents the transpose of the tracking error e1(t), Θ1 is the variable matrix, represents the transpose of the tracking error e2(t), Θ2 is the variable matrix, The estimated value of the matrix function f1(x1), is the inverse of the constants ε1, ε2, ε3, ε4, represents the state estimation error The transpose of The interference estimation error The transpose of u a (t) is the additive controller that needs to be designed; At this point, determine the barrier Lyapunov function V 12 (t)Satisfy: Among them, k 1bi Indicates the error e 1i The boundary of (t), e 1i (t) is the ith variable of the tracking error e1(t), k 2bi Indicates the error e 2i The boundary of (t), e 2i (t) is the ith variable of the tracking error e2(t), is the inverse of the constants ε1, ε2, ε3, ε4, represents the state estimation error The transpose of The interference estimation error The transpose of .

8. The control method for suppressing measurement interference of an unmanned helicopter altitude attitude system according to claim 7, characterized in that: The step 3 is specifically implemented according to the following steps: Step 3.1: Perform stability analysis on the estimated error system: Define a new state variable: And the Lyapunov function: in, In terms of variables, the Lyapunov function is expanded as: in, represents the state estimation error The transpose of represents the state estimation error The transpose of The interference estimation error The transpose of , P1, P2, P3 are diagonal matrix variables; To determine the feasible observer gain, the estimation error is expressed as: in, represents the state estimation error The derivative of represents the state estimation error The derivative of The interference estimation error The derivative of , L1 and L2 represent the observation gain matrix of the state observer, K represents the gain matrix of the disturbance observer, W and M are constant disturbance coefficient matrices with appropriate dimensions, and denote the estimated values ​​of states x1(t) and x2(t), respectively. The estimated value of the matrix function f1(x1,x2), The estimated value of the matrix function f2(x2), K -1 represents the inverse matrix of gain K; At this time, the dynamic representation of the Lyapunov function V3(t) is: Among them, P′ is represented as a nonlinear matrix, represents the state estimation error, represents the transpose of the state estimation error, represents the state estimation error, represents the transpose of the state estimation error, represents the interference estimation error, represents the transpose of the disturbance estimation error, L1 and L2 represent the observation gain matrices of the state observer, K represents the gain matrix of the disturbance observer, W and M are constant disturbance coefficient matrices with appropriate dimensions, and P1, P2, and P3 are diagonal matrix variables; Since F1(t), F2(t) and F3(t) satisfy the local Lipschitz condition, there exists a constant λ i >0 makes: in, represents the state estimation error, represents the transpose of the state estimation error, represents the state estimation error, represents the transpose of the state estimation error, represents the interference estimation error, represents the transpose of the disturbance estimation error, is the inverse of the normal constants λ1,λ2,λ3, T i >0 is determined by the parameters and state constraints of the unmanned helicopter, I is a diagonal matrix with appropriate dimensions, K represents the gain matrix of the disturbance observer, and P1, P2, P3 are diagonal matrix variables; Then, P′ can be restated as: and Among them, ij represents the element in the i-th row and j-th column, sym{X}=X T +X, is the inverse of the positive constants λ1,λ2,λ3, P1,P2,P3 are diagonal matrix variables, L1 and L2 represent the observation gain matrices of the state observer, and represents the transpose of the gain matrices L1 and L2, K represents the gain matrix of the disturbance observer, K T represents the transpose of the gain matrix K, W and M are constant interference coefficient matrices with appropriate dimensions, and T i represents the constant determined by the parameters and state constraints of the unmanned helicopter, I is a diagonal matrix with appropriate dimensions, and * can be any matrix; Step 3.2: Perform stability analysis on the tracking error system: Consider the Lyapunov function: V(t) = V 12 (t)+V3(t) According to the tracking error obtained in step 2, the derivative of V(t) is expressed as: Among them, k 1bi Indicates the error e 1i The boundary of (t), e 1i (t) is the ith variable of the tracking error e1(t), k 2bi Indicates the error e 2i The boundary of (t), e 2i (t) is the i-th variable of the tracking error e2(t); is a state variable The transpose of , Φ is represented as a nonlinear matrix; When there is a positive constant γ such that Φ<-γI, the closed-loop system can be guaranteed to be globally asymptotically stable; Among them, ij represents the element in row i and column j, is the inverse of the constants ε1, ε2, ε3, ε4, P1, P2, P3 are diagonal matrix variables, and represents the transpose of the diagonal matrices P2 and P3, L1 and L2 represent the observation gain matrices of the state observer, and represents the transpose of the gain matrices L1 and L2, K represents the gain matrix of the disturbance observer, K T represents the transpose of the gain matrix K, W and M are constant interference coefficient matrices with appropriate dimensions, W T represents the transpose of the constant matrix W, T i is a normal constant, I is a diagonal matrix with appropriate dimension, γ is a normal constant, and * indicates that any matrix can be used; Define X1=P1L1,X2=P2L2,X3=P3K to get the new nonlinear matrix Φ′: Among them, Π′ ij Represents Π ij After a change, the element and represents the transpose of variables X2 and X3, W and M are constant matrices, W T represents the transpose of the constant matrix W, Π ij represents the element in row i and column j, T i is a positive constant, I is a diagonal matrix of appropriate dimension, γ is a positive constant, P1 T , and represents the transpose of the diagonal matrices P1, P2, and P3, is the inverse of the constants ε1, ε2, ε3, ε4, sym{X}=X T +X, λ1, λ2, λ3 are positive constants; Step 3.3, use Schur's complement theorem to convert the nonlinear inequality into a linear inequality, define X1 = P1L1, X2 = P2L2, X3 = P3K to obtain: Among them, P″ 11 =-sym{X1}+λ1T1I+λ3T1I+γI,Π 14 =(P1 II),Π2′2=-sym{P2}+λ1T2I+λ2T4I+λ3T4I+γI,Π 36 =(X3 W T W T ) Π3′3=sym{P3M-X3WM}+γI,Π 44 =diag{-λ1I-ε1I-ε3I} P 66 =diag{-λ3I-ε2I-ε4I}; Among them, ij represents the element in the i-th row and j-th column, Π′ ij ′ represents Π ij After the quadratic transformation, X1, X2 and X3 are the new linear variables defined. represents the transpose of variable X3, W and M are constant matrices, W T represents the transpose of the constant matrix W, I is a diagonal matrix of appropriate dimension, γ is a positive constant, P1 T , and represents the transpose of the diagonal matrices P1, P2, and P3, is the inverse of the constants ε1, ε2, ε3, ε4, sym{X}=X T +X, diag{·} represents a diagonal matrix, λ1,λ2,λ3 are positive constants, T i is a positive constant; Step 3.4: Perform stability analysis on the UAV altitude attitude closed-loop system: The linear matrix inequality holds, ensuring that the derivative of the Lyapunov function is negative definite: satisfy And γ0=min{1,γ,k1,k2}; in, is the derivative of the Lyapunov function V(t), γ0,γ,k1,k2 are all positive constants, k 1bi Indicates the error e 1i The boundary of (t), e 1i (t) is the ith variable of the tracking error e1(t), k 2bi Indicates the error e 2i The boundary of (t), e 2i (t) is the ith variable of the tracking error e2(t), represents the error variable, represents the transpose of the error variable; Step 3.5: For the unmanned helicopter altitude attitude system, use the linear matrix inequality LMI toolbox to solve the above matrices and obtain the corresponding state observer and disturbance observer gain matrices respectively. At this time, the unmanned helicopter altitude attitude control system can achieve the expected control target under the designed flight output feedback tracking controller.

Images