An optimization method for gliding missile controller based on improved Gray Wolf

Abstract

The present invention belongs to the field of trajectory control optimization, and specifically relates to an optimization method for a gliding missile controller based on an improved Gray Wolf algorithm. The method comprises the following steps: Step (1): Based on the dynamic characteristics analysis of the gliding missile, a disturbance motion equation of the missile body is established and simplified; Step (2): Based on the simplified disturbance motion equation of the missile body, under the conditions of zero interference and zero initialization, a suitable input control quantity and state vector are selected to construct its longitudinal state equation; Step (3): Based on the system state equation, an LQR linear quadratic regulator is constructed: the parameters of the weighting matrix Q matrix and the R matrix in the LQR linear quadratic regulator are optimized using the Gray Wolf algorithm with a nonlinear convergence factor to obtain the feedback gain matrix K, thereby improving the system response time and the stability of the new control system. The present invention optimizes the trajectory and improves the system response by selecting some parameters in the longitudinal disturbance equation as state variables and optimizing the feedback gain, thereby improving the stability margin of the system.

Description

Technical Field

[0001] The invention belongs to the field of trajectory control optimization, and in particular relates to an optimization method for a gliding projectile controller based on an improved Gray Wolf. Background Art

[0002] Gliding missiles, a key area of ​​guided weapon research in various countries, are of great practical and strategic significance. As the core component of a glide missile, the onboard computer system (IMU) uses the inertial navigation system (INS) and GPS to obtain parameters such as target and missile coordinates, geomagnetic information, and roll angle information. This information is then processed using a program embedded in the onboard computer to generate control signals. With the development of modern guided weapons, the onboard computer must possess robust data processing and logical computing capabilities. While optimizing system hardware, achieving trajectory optimization, improving range and accuracy, and designing a more stable and reliable trajectory are crucial. Summary of the Invention

[0003] The purpose of the present invention is to provide an optimization method for a gliding missile controller based on an optimized gray wolf algorithm, thereby improving the stability margin of the system, optimizing the trajectory, and thus increasing the longitudinal and lateral overloads.

[0004] The technical solution to achieve the purpose of the present invention is: an optimization method based on the improved Gray Wolf gliding bomb controller, comprising the following steps:

[0005] Step (1): Based on the dynamic characteristics analysis of the gliding missile, the disturbance motion equation of the missile body is established and simplified;

[0006] Step (2): Based on the simplified perturbation motion equation of the projectile, under the conditions of zero disturbance and zero initialization, select appropriate input control variables and state vectors to construct its longitudinal state equation;

[0007] Step (3): Based on the system state equation, construct an LQR linear quadratic regulator: use the Grey Wolf algorithm with nonlinear convergence factor to optimize the parameters of the weighting matrices Q and R in the LQR linear quadratic regulator to obtain the feedback gain matrix K, thereby improving the system response time and improving the stability of the new control system.

[0008] Furthermore, step (1) is simplified as follows:

[0009] Step (11): Based on the “small perturbation hypothesis” and the coefficient freezing method, the dynamic equations of the gliding missile are linearized to eliminate the relevant influence of the velocity bias in the equation group, and the perturbation motion equation group can be obtained by simplification:

[0010]

[0011] Where: is the pitch angle, α is the attack angle, β is the sideslip angle, is the yaw angle, θ is the trajectory inclination angle, is the ballistic deviation angle, δ z0 and δ y0 The rudder deflection angle in the pitch and yaw directions is is the pitch damping moment coefficient, is the pitching moment coefficient, is the partial derivative of the pitching moment with respect to the sideslip angle, is the pitch rudder moment coefficient, is the yaw damping moment coefficient, is the partial derivative of the yawing moment with respect to the angle of attack, is the yaw rudder moment coefficient, Y α is the slope of the lift line, is the pitch rudder efficiency, Z α is the partial derivative of the side force with respect to the angle of attack, is the yaw rudder efficiency, J x 、J y and J z are the moments of inertia of the projectile around the x, y and z axes of the coordinate system respectively;

[0012] Step (12): Ignore the influence of Magnus moment and gyroscopic moment, simplify the dynamic characteristics analysis of the projectile, use the dynamic coefficient symbols to represent the coefficients in the simplified perturbation motion equation group (1) obtained in step (11) and simplify the perturbation motion equation group:

[0013]

[0014] The aerodynamic parameters in formula (2) mainly change with the change of speed. The longitudinal motion parameters are calculated as follows:

[0015] Aerodynamic damping coefficient Static stability coefficient Control torque coefficient Projectile lift coefficient rudder lift coefficient

[0016] Furthermore, step (2) is specifically as follows: select the pitch angle derivative and the angle of attack α as the state vector, the longitudinal rudder deflection angle δ z0 As the control variable, the longitudinal state equation is constructed, which includes the following steps:

[0017] Step (21): By selecting the pitch channel related equations in the simplified perturbation motion equations, the longitudinal perturbation motion related state equations are established:

[0018]

[0019] Where the state matrix and input matrix are and The control input is u=[δ z0 ], where δ z0 is the longitudinal rudder angle, and the state variable is

[0020] Step (22): Select performance indicator function:

[0021]

[0022] Where Q matrix and R matrix are the weighted matrices of the diagonal matrix, and Q matrix and R matrix are matrices related to state error and control energy consumption, respectively.

[0023] Furthermore, in step (3), the improved grey wolf algorithm is used to optimize the parameters of the Q array and R array in the LQR regulator. The specific steps are as follows:

[0024] The parameters q1, q2 and r1 in the Q array and R array are brought into the position vector dimension of the gray wolf in the gray wolf algorithm. According to the pre-determined value range of the wolf pack, the coefficient vectors A1 and C, the linear convergence factor in the original gray wolf algorithm is changed to a nonlinear convergence factor to improve the convergence speed in the middle and late stages. The nonlinear convergence factor η1 selects the sigmoid function, that is, η1=1 / 1+e -t The fitness function selects the absolute error integral criterion with strong ability to suppress small deviations According to the fitness function, the three optimal solutions and other solutions are selected as the optimal solution alpha1, the second optimal solution beta1, and the third optimal solution delta1, the gray wolf ∞;

[0025] The actions in the Grey Wolf Algorithm are defined as follows:

[0026] D=|C·Y P (t)-Y(t)|

[0027] D represents the distance between the individual and the prey, Y p (t) and Y(t) represent the positions of the target and the gray wolf, respectively;

[0028] Gray Wolves Position Update:

[0029] Y(t+1)=Y P (t)-A1·D

[0030] In the formula |r1| and |r2| are random numbers in the interval [0, 1];

[0031] D α1 =|C1·Y α1- Y|

[0032] D β1 =|C2·Y β1 -Y|

[0033] D δ1 =|C3·Y δ1 -Y|

[0034] D α1 D β1 D δ1 are the positions of the three wolves and the gray wolf of the optimal solution;

[0035] Y1=Y α1 -A 11 ·D α1

[0036] Y2=Y β1 -A 12 ·D β1

[0037] Y3=Y δ1 -A 13 ·D δ1

[0038] Y(t+1)=(Y1+Y2+Y3) / 3

[0039] Y1, Y2, and Y3 are the directions of the gray wolf affected by the three optimal solutions and the step length Y(t+1), which is the position after one iteration;

[0040] The optimization process is as follows: the system first completes the initialization of the gray wolf population, nonlinear convergence factor η1, coefficient vectors A1 and C; calculates the fitness of the gray wolf individuals, saves the three optimal solutions α1, β1 and δ1, and updates the gray wolf position, η1, A1 and C through the gray wolf algorithm definition; calculates the fitness of all gray wolves, updates the position and fitness of the optimal solution leader α1, the suboptimal solution β1 and the third optimal solution; then determines whether the termination condition is met to reach the optimal solution. If the termination condition is not met, it returns to update the gray wolf position, η1, A1 and C, and continues to iterate until the termination condition is met. Finally, the fitness and position of the leader are output; the data in the optimal solution position dimension are brought into the Q matrix and R matrix of the LQR linear quadratic regulator;

[0041] The LQR controller obtains the steady-state solution P through the Riccati equation, which is as follows:

[0042] PA+A T PP T BR -1 B T P+Q=0

[0043] K=-R -1 B TP solves the feedback gain matrix K;

[0044] Substitute the input state relationship u=-Kx into A new state equation is obtained to optimize the system performance. When t approaches ∞, the closed-loop system improves the system stability margin and tracking accuracy and eliminates some errors.

[0045] Compared with the prior art, the present invention has the following significant advantages:

[0046] The present invention linearizes the glide bomb system and establishes a mathematical model. A linear quadratic regulator is designed, and the Grey Wolf algorithm of the nonlinear convergence factor is used. While ensuring a relatively fast convergence speed and a certain ability to escape the local optimal solution in the later stage, the Q matrix and R matrix parameters in the linear quadratic regulator LQR are tuned, and the optimal feedback gain matrix K is output, which accelerates the system response while maintaining a stable margin that meets the requirements, improves control stability, and reduces system errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a schematic diagram of the application process of the optimized gray wolf algorithm of the present invention.

[0048] Figure 2 2 is a schematic structural diagram of the onboard computer device according to the present invention. DETAILED DESCRIPTION

[0049] The present invention is further described in detail below with reference to the accompanying drawings.

[0050] An optimization method for a gliding missile controller based on an optimized gray wolf algorithm comprises the following steps in sequence:

[0051] Step (1): Based on the dynamic characteristics analysis of a gliding missile, the missile body disturbance motion equation is established and simplified.

[0052] Step (2): Based on the simplified perturbation motion equation of the projectile, under the conditions of zero disturbance and zero initialization, select appropriate input control variables and state variables to construct its longitudinal state equation.

[0053] Step (3): Based on the system state equation, construct an LQR linear quadratic regulator. Use the Grey Wolf algorithm with nonlinear convergence factor to optimize the parameters of the weighting matrices Q and R in the LQR linear quadratic regulator and obtain the feedback gain matrix K, thereby improving the system response time and enhancing the stability of the new control system.

[0054] The glider missile is ruddered for a certain period of time after leaving the muzzle, and the two pairs of rudder wings are perpendicular to each other. The rudder is used to change the pitch angle and yaw angle of the missile body to play a control role. In step (1), the dynamic equations of the glider missile are linearized based on the "small perturbation assumption" and the coefficient freezing method, eliminating the relevant influence of the velocity deviation in the equation group, and simplifying the perturbation motion equation group to obtain:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] Where: is the pitch angle, α is the attack angle, β is the sideslip angle, is the yaw angle, θ is the trajectory inclination angle, is the ballistic deviation angle, δ z0 and δ y0 is the rudder deflection angle of the rudder in the pitch and yaw directions. is the pitch damping moment coefficient, is the pitching moment coefficient, is the partial derivative of the pitching moment with respect to the sideslip angle, is the pitch rudder moment coefficient, is the yaw damping moment coefficient, is the partial derivative of the yawing moment with respect to the angle of attack, is the yaw rudder moment coefficient, Y α is the slope of the lift line, is the pitch rudder efficiency, Z α is the partial derivative of the side force with respect to the angle of attack, is the yaw rudder efficiency, J x 、J y and J z are the moments of inertia of the projectile around the x, y and z axes of the coordinate system respectively.

[0062] Due to the aerodynamic layout characteristics of the missile, the Magnus moment on the missile is only one ten-millionth of the aerodynamic stability moment, so the influence of the Magnus moment can be ignored. x It is also much smaller than J y and J z, ignoring the influence of gyroscopic torque, simplifying the dynamic characteristics analysis of the projectile, using the dynamic coefficient symbols to represent the coefficients in the equation group (1) and simplifying the perturbation motion equation group as follows:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] The aerodynamic parameters in formula (2) mainly change with the change of speed. The longitudinal motion parameters are calculated as follows:

[0070] Aerodynamic damping coefficient Static stability coefficient Control torque coefficient Projectile lift coefficient rudder lift coefficient

[0071] The transfer function is used to characterize the dynamic characteristics of the system. Since the longitudinal and lateral motion characteristics of the guided projectile are similar, the longitudinal motion is mainly analyzed. Under zero interference and zero initial conditions, the longitudinal motion equations (2) are Laplace transformed and sorted to obtain:

[0072]

[0073] Using Cramer's theorem θ(s) and α(s) are respectively expressed and brought into the adjoint matrix Δθ(s), Δα(s), to obtain the transfer function of the longitudinal disturbance motion:

[0074]

[0075]

[0076]

[0077] Introducing longitudinal overload on the missile

[0078] According to the above two equations, the transfer function of longitudinal overload can be obtained:

[0079]

[0080] According to step (2), from equations 1, 3, and 5 in equation (2), select the pitch angle derivative and the angle of attack α as the state vector, the longitudinal rudder deflection angle δ x0 As the control quantity, the state equation related to the longitudinal disturbance motion is obtained:

[0081]

[0082] Where the state matrix and input matrix are and Rudder deflection angle u=[δ z0 ] as the control input, the state variable is

[0083] Select performance indicator function:

[0084]

[0085] Where Q matrix and R matrix are diagonal weighted matrices, and Q matrix and R matrix are matrices related to state error and control energy consumption, respectively. The q1, q2 and r1 in the Q matrix and R matrix are brought into the position vector dimension of the gray wolf in the gray wolf algorithm. According to the pre-determined value range of the wolf pack, coefficient vectors A1 and C, the linear convergence factor in the original gray wolf algorithm is changed to a nonlinear convergence factor to improve the convergence speed in the middle and late stages. The nonlinear convergence factor η1 selects the sigmoid function, that is, η1 = 1 / 1 + e -1 The fitness function selects the absolute error integral criterion with strong ability to suppress small deviations According to the fitness function, the three optimal solutions and other solutions are selected as the optimal solution alpha1, the suboptimal solution beta1, the third optimal solution delta1, and the gray wolf ∞.

[0086] The actions in the Grey Wolf Algorithm are defined as follows:

[0087] D=|C·Y P (t)-Y(t)| (9)

[0088] D represents the distance between the individual and the prey, Y p (t) and Y(t) represent the positions of the target and the gray wolf respectively.

[0089] Gray Wolves Position Update:

[0090] Y(t+1)=Y P (t)-A1·D (10)

[0091] In the formula |r1| and |r2| are random numbers in the interval [0, 1].

[0092] D α1 =|C1·Yα1 -Y|

[0093] D β1 =|C2·Y β1 -Y|

[0094] D δ1 =|C3·Y δ1 -Y| (11)

[0095] D α1 D β1 D δ1 These are the positions of the three wolves and the gray wolf for the optimal solution.

[0096] Y1=Y α1 -A 11 ·D α1

[0097] Y2=Y β1 -A 12 ·D β1

[0098] Y3=Y δ1 -A 13 ·D δ1 (12)

[0099] Y(t+1)=(Y1+Y2+Y3) / 3 (13)

[0100] Y1, Y2, and Y3 are the directions and step sizes of the wolf affected by the three optimal solutions. Y(t+1) is the position after one iteration.

[0101] Optimization process such as Figure 1 The system first initializes the gray wolf population, the nonlinear convergence factor η1, and the coefficient vectors A1 and C. The fitness of individual gray wolves is calculated, and the three optimal solutions α1, β1, and δ1 are saved. The gray wolf algorithm defines the updated positions of the gray wolves, η1, A1, and C. The fitness of all gray wolves is calculated, and the positions and fitness of the optimal alpha wolf α1, the suboptimal solution β1, and the third-optimal solution δ1 are updated. It then determines whether the termination criteria have been met to reach the optimal solution. If not, the system returns to updating the gray wolf positions, η1, A1, and C, and continues iterating until the termination criteria are met. Finally, the fitness and position of the alpha wolf are output. The data in the optimal solution position dimension is fed into the Q and R matrices of the LQR linear quadratic regulator.

[0102] The LQR controller obtains the steady-state solution P through the Riccati equation, which is as follows:

[0103] PA+A T PP T BR -1 B TP+Q=0(14)

[0104] K=-R -1 B T P solves the feedback matrix K.

[0105] Substitute the input state relationship u=-Kx into A new state equation is obtained to optimize the system response when the closed-loop system approaches ∞, improve the system stability margin and tracking accuracy, and eliminate some errors.

[0106] The onboard computer device used in the present invention is as follows Figure 2 The system primarily consists of a measurement input unit, a control and data processing unit, a program and data storage unit, and a servo control output unit. The measurement input unit is used to acquire real-time information about the missile, such as its position and rudder angle. It includes a GPS module and a separate board containing MEMS inertial devices. Communication is achieved through the sensor's serial interface, transmitting data such as attitude and acceleration.

[0107] The control and data processing unit is used to process parameters such as the projectile posture to complete the trajectory calculation. The control and data processing unit includes a reset circuit, a power supply circuit, a clock circuit, a JTAG circuit, a master chip, and a slave chip.

[0108] The program and data storage unit is used to control program and data storage.

[0109] The steering gear control output unit is used to output the control signal output by the main control unit to the steering gear to realize steering control.

Claims

1. An optimization method for a gliding bomb controller based on an improved Gray Wolf, characterized in that: The steps include: Step (1): Based on the dynamic characteristics analysis of the gliding missile, the disturbance motion equation of the missile body is established and simplified; Step (2): Based on the simplified perturbation motion equation of the projectile, under the conditions of zero disturbance and zero initialization, select appropriate input control variables and state vectors to construct its longitudinal state equation; Step (3): Based on the system state equation, construct an LQR linear quadratic regulator: use the Grey Wolf algorithm with nonlinear convergence factor to optimize the parameters of the weighting matrices Q and R in the LQR linear quadratic regulator to obtain the feedback gain matrix K, thereby improving the system response time and improving the stability of the new control system.

2. The method according to claim 1, characterized in that Step (1) is simplified as follows: Step (11): Based on the "small perturbation assumption" and the coefficient freezing method, the dynamic equations of the gliding missile are linearized to eliminate the relevant influence of the velocity bias in the equation group, and the perturbation motion equation group can be obtained by simplification: Where: is the pitch angle, α is the attack angle, β is the sideslip angle, is the yaw angle, θ is the trajectory inclination angle, is the ballistic deviation angle, δ z0 and δ y0 are the rudder deflection angles of the rudder in the pitch and yaw directions respectively, is the pitch damping moment coefficient, is the pitching moment coefficient, is the partial derivative of the pitching moment with respect to the sideslip angle, is the pitch rudder moment coefficient, is the yaw damping moment coefficient, is the partial derivative of the yawing moment with respect to the angle of attack, is the yaw rudder moment coefficient, Y α is the slope of the lift line, is the pitch rudder efficiency, Z α is the partial derivative of the side force with respect to the angle of attack, is the yaw rudder efficiency, J x 、J y and J z are the moments of inertia of the projectile around the x, y and z axes of the coordinate system respectively; Step (12): Ignore the influence of Magnus moment and gyroscopic moment, simplify the dynamic characteristics analysis of the projectile, use the dynamic coefficient symbols to represent the coefficients in the simplified perturbation motion equation group (1) obtained in step (11) and simplify the perturbation motion equation group: The aerodynamic parameters in formula (2) mainly change with the change of speed. The longitudinal motion parameters are calculated as follows: Aerodynamic damping coefficient Static stability coefficient Control torque coefficient Projectile lift coefficient rudder lift coefficient 3. The method according to claim 2, characterized in that Step (2) is as follows: Select the pitch angle derivative and the angle of attack α as the state vector, the longitudinal related pitch rudder deflection angle δ z0 As the control variable, the longitudinal state equation is constructed, which includes the following steps: Step (21): By selecting the pitch channel related equations in the simplified perturbation motion equations, the longitudinal perturbation motion related state equations are established: Where the state matrix and input matrix are and Rudder deflection angle u=[δ z0 ] as the control input, the state variable is Step (22): Select performance indicator function: Where Q matrix and R matrix are the weighted matrices of the diagonal matrix, and Q matrix and R matrix are matrices related to state error and control energy consumption, respectively.

4. The method according to claim 3, characterized in that In step (3), the improved grey wolf algorithm is used to optimize the parameters of the Q array and R array in the LQR regulator. The specific steps are as follows: The parameters q1, q2 and r1 in the Q array and R array are brought into the position vector dimension of the gray wolf in the gray wolf algorithm. According to the pre-determined value range of the wolf pack, the coefficient vectors A1 and C, the linear convergence factor in the original gray wolf algorithm is changed to a nonlinear convergence factor to improve the convergence speed in the middle and late stages. The nonlinear convergence factor η1 selects the sigmoid function, that is, η1=1 / (1+e -t ), the fitness function selects the absolute error integral criterion with strong ability to suppress small deviations According to the fitness function, the three optimal solutions and other solutions are selected as the optimal solution alpha1, the second optimal solution beta1, and the third optimal solution delta1, the gray wolf ω; The actions in the Grey Wolf Algorithm are defined as follows: D=|C·Y P (t)-Y(t)| D represents the distance between the individual and the prey, Y p (t) and Y(t) represent the positions of the target and the gray wolf, respectively; Gray Wolves Position Update: Y(t+1)=Y P (t)-A1·D In the formula |r1| and |r2| are random numbers in the interval [0,1]; D α1 =|C1·Y α1 -Y| D β1 =|C2·Y β1 -And| D δ1 =|C3·Y δ1 -Y| D α1 D β1 D δ1 are the distances between the three wolves of the optimal solution and the gray wolf; Y1=Y α1 -A 11 ·D α1 Y2=Y β1 -A 12 ·D β1 Y3=Y δ1 -A 13 ·D δ1 Y(t+1)=(Y1+Y2+Y3) / 3 Y1, Y2, and Y3 are the direction and step length of the gray wolf affected by the three optimal solutions, and Y(t+1) is the position of the gray wolf after one iteration; The optimization process is as follows: the system first completes the gray wolf population, nonlinear convergence factor η1, coefficient vectors A1 and C; calculates the fitness of individual gray wolves, updates and saves the three optimal solutions α1, β1 and δ1, and updates the gray wolf position, η1, A1 and C through the gray wolf algorithm definition. Calculate the fitness of all gray wolves, update the position and fitness of the optimal solution alpha1, the suboptimal solution β1 and the third optimal solution δ1; then determine whether the termination condition is met to reach the optimal solution. If the termination condition is not met, return to update the gray wolf position, η1, A1 and C, continue to iterate until the termination condition is met, and finally output the fitness and position of the alpha wolf; bring the data in the optimal solution position dimension into the Q matrix and R matrix of the LQR linear quadratic regulator; The LQR controller obtains the steady-state solution P through the Riccati equation, which is as follows: PA+A T P-P T BR -1 B T P+Q=0 K=-R -1 B T P solves the feedback gain matrix K; Substitute the input state relationship u=-Kx into A new state equation is obtained to optimize the system performance. When t approaches ∞, the closed-loop system improves the system stability margin and tracking accuracy and eliminates some errors.

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