CN105022881B - A kind of carrier-borne aircraft autonomous landing on the ship Guidance Law Design method based on dove group optimization - Google Patents

Abstract

The present invention is a kind of carrier-borne aircraft autonomous landing on the ship Guidance Law Design method based on dove group optimization, and implementation step is：Step 1：Build carrier-borne aircraft and stern flow Simulink emulation modules；Step 2：Initialize dove colony optimization algorithm parameter；Step 3：Design cost function；Step 4：Guidance law parameter to be optimized is set in Simulink；Step 5：Optimizing is carried out using the map compass operator of dove colony optimization algorithm；Step 6：Optimizing is carried out using the terrestrial reference operator of dove colony optimization algorithm；Step 7：Store results are simultaneously verified.This method can effectively reduce the work difficulty for flying control designer, and improve robustness of the carrier landing guidance rule to stern flow interference.

Description

A Design Method of Guidance Law for Carrier Aircraft Autonomous Landing Based on Pigeon Group Optimization

technical field

The invention relates to a design method of a carrier-based aircraft's autonomous landing guidance law based on pigeon group optimization, and belongs to the technical field of carrier-based aircraft.

Background technique

Carrier-based aircraft is an important force in national defense and plays an important role in the navies of various countries. Carrier-based aircraft technology is a research hotspot in various countries, reflecting a country's national defense technical strength. Many scholars at home and abroad have conducted in-depth research on various technologies related to carrier-based aircraft. There is a big difference between carrier-based aircraft and land-based aircraft. The special environment at sea brings huge challenges to carrier-based aircraft landing. The carrier aircraft provides a greater rolling distance, so the carrier aircraft must successfully hook one of the four arresting cables when landing to achieve the purpose of deceleration. The aircraft carrier will be affected by the waves at sea, which will cause its deck to move in six degrees of freedom. If compensation is not added, it will cause deviations in the contact point of the carrier-based aircraft. In addition, a factor that has a great impact on carrier-based aircraft landing is the influence of the aircraft carrier's wake. When the aircraft carrier is moving on the sea, or when the wind blows across the deck, it will interfere with the airflow behind the aircraft carrier. The wake will make the carrier-based aircraft Deviation from a given glide path will affect the safety of the ship.

Manual landing will be affected by weather factors and human factors, and it cannot guarantee the safety of landing under harsh conditions. Therefore, autonomous landing technology has emerged, which can realize carrier-based aircraft autonomously landing around the clock. Guidance law optimization design is an important part of autonomous ship landing technology. When designing the landing guidance law of a carrier-based aircraft, it is necessary to optimize the guidance law, so that the robustness of the landing guidance law to wake interference can be enhanced, and the tracking accuracy of the carrier-based aircraft on the glide slope can be improved to achieve safe landing. purpose of the ship. Different guidance law parameters will be used in different phases of landing according to specific requirements. It is difficult to achieve optimal results by manual tuning of these parameters, and it will also bring a huge workload to designers. Therefore, a It is a very necessary technology to adjust the parameters of the guidance law with this automatic optimization method, which can not only reduce the workload of the designer, but also improve the system performance.

Swarm intelligence is an important branch of bionic intelligence. People are inspired by the behavior of biological groups in nature through observation of biological groups in nature. On this basis, they are generally improved, and their behavior patterns are described mathematically. On the basis of the swarm intelligence model, people put forward the concept of swarm intelligence optimization algorithm, which uses the behavior patterns of biological groups to solve optimization problems. Pigeon Inspired Optimization (PIO) is a new heuristic swarm intelligence optimization algorithm proposed by Haibin Duan in 2014. The algorithm is inspired by the group behavior of pigeons. Based on the behavior characteristics of landmarks and landmarks, two algorithm mechanisms of map compass and landmarks are established.

In the process of finding the destination, the pigeon flock will first refer to the sun and the magnetic field for preliminary positioning, and then perform precise positioning according to the landmarks. According to this characteristic, the pigeon flock algorithm proposes two corresponding operators, which are map compass calculation The operator and the landmark mechanism are used to simulate this characteristic of the pigeon flock, and these two operators are combined to solve the optimization problem.

(1) Map compass operator

In the map and compass operator, the group of pigeons advances according to the guidance of the map and compass. In the D-dimensional space, the position information X _i and velocity information V _i of the i-th pigeon are updated every generation. The specific update criteria are as follows: Shown:

V _i (t) = V _i (t-1) e - ^Rt + rand (X _g -X _i (t-1)) (1)

X _i (t)=X _i (t-1)+V _i (t) (2)

In the formula, R is the map and compass factor, rand is a random number generated randomly from 0 to 1, and X _g is the global optimal position under the current number of iterations, which is obtained by comparing the position information of all pigeons. The schematic diagram of the map compass operator is shown in Figure 1. The pigeon on the far right in the figure is the pigeon with the global optimal position information. The thin arrow indicates the previous speed vector of the pigeon, and the thick arrow indicates the adjustment vector of the pigeon's speed under the action of this mechanism. direction, the result of the superposition of the two speed vectors is the current speed vector of the pigeon.

(2) Landmark operator

Since the pigeon mainly relies on the landmarks to guide the target in the later stage of finding the destination, a landmark operator is proposed according to its behavior characteristics. The operator stipulates that the number of pigeons in each generation is halved, and in order to reach the destination faster, the remaining pigeons fly directly to the destination. The specific update criteria are as follows:

X _i (t)=X _i (t-1)+rand (X _c (t)-X _i (t-1)) (5)

In the above formula, N _p is the number of pigeon flocks, fitness is the cost function of pigeon position information, in order to obtain the minimum value of the cost function, f _min can be taken as the objective function, and X _c is the weighted position center of the pigeon flock. The schematic diagram of the landmark operator is shown in Figure 2. The pigeons outside the circle leave the group, the pigeons in the center are the destination of the remaining pigeons, and the remaining pigeons quickly move towards the center of the target. The overall flowchart of the pigeon swarm algorithm is shown in Figure 3.

Contents of the invention

1. Purpose of the invention:

The present invention proposes a design method for autonomous landing guidance law of carrier-based aircraft based on pigeon group optimization. Robustness of gravitational law to ship wake disturbance.

This method uses the Simulink control simulation model of the ship-borne aircraft, constructs a typical ship wake interference module in the control model, and obtains the error of the closed-loop system of the ship-borne aircraft deviating from the given glide slope under the interference of the ship wake through simulation. The objective function of the optimization problem is constructed on the above, and the optimal guidance law parameter value is obtained by using the pigeon group optimization algorithm.

2. Technical solution:

The present invention utilizes the characteristics of strong global search capability and wide applicability of the swarm intelligence optimization algorithm, and develops a carrier-based aircraft autonomous landing guidance law optimization design method based on the pigeon swarm optimization algorithm. The steps of the method are as follows:

Step 1: Build the Simulink simulation module of carrier aircraft and ship wake

The ship wake model in this method considers the following four components: atmospheric turbulence, steady-state aircraft carrier wake disturbance, periodic aircraft carrier wake disturbance and random aircraft carrier wake disturbance.

U ₁ and W ₁ are the horizontal atmospheric turbulence component and the vertical atmospheric turbulence component, respectively. The unit white noise is obtained by filtering with a shaping filter, and their spatial power spectral densities are shown in the following formula:

U ₂ and W ₂ are the steady-state component of the horizontal wake and the steady-state component of the vertical wake, respectively. They can be obtained by piecewise linearization, and the specific shape of the curve is shown in Figure 4.

U ₃ and W ₃ are the periodic component of the horizontal wake and the periodic component of the vertical wake respectively, which can be obtained by formula calculation, and the specific calculation formula is shown in the following formula:

in,

In the formula, ω _s is the pitch frequency, θ _s is the pitch amplitude, V _wod is the deck wind, V = 10m/s carrier aircraft approach speed, X is the distance of the aircraft from the ship, and P is the random phase.

U ₄ and W ₄ are the random component of the horizontal wake and the random component of the vertical wake, respectively. The unit white noise is obtained by filtering with a shaping filter, and its calculation formula is shown in the following formula:

Among them, rand is a random number, σ(x) and τ(x) are coefficients related to distance, and their shapes are given in Figure 5.

The carrier aircraft model and the inner ring autopilot it uses are given by specific design requirements.

Step 2: Initialize the parameters of the pigeon group optimization algorithm

(1) Initialize the optimization parameter dimension D

The parameters optimized in this method are the parameters in the guidance law of the autonomous landing of the carrier-based aircraft, which can be changed according to the form of the guidance law.

(2) Initialize the population size M

The population size M of the swarm intelligence optimization algorithm has a great influence on the optimization effect. The selection of the general population size is 3-5 times the dimension of the optimization problem.

(3) Initialize the attenuation coefficient R

The attenuation coefficient R is applied in the map compass operator of the pigeon swarm algorithm, and it affects the attenuation speed of the particle's own velocity.

(4) Initialize the population position and speed

The upper limit P _max and the lower limit P _min of the position, the upper limit V _max and the lower limit V _min of the speed of the group are not set in the search space. Initialize an initial position x _i and initial velocity V _i for each particle in the population.

(5) Set Algorithm Algebra

The pigeon swarm optimization algorithm has two operators, namely the map compass operator and the landmark operator. Before the algorithm operation, it is necessary to set the maximum algebra NC ₁ and NC ₂ of the two algorithms respectively.

Step 3: Design the cost function

The setting of the cost function is very critical in the optimization of the landing guidance law, and its setting directly affects the optimization effect. In this method, the goal of optimizing the parameters of the guidance law is to minimize the displacement of the carrier-based aircraft from the designated glide path under the interference of the ship's wake during the landing process, and the control input should be as small as possible. So define the following cost function:

Among them, hc is the specified glide _{slope height command, h is the height of the carrier aircraft, θ c is} the pitch angle command for the inner ring autopilot, θ _css is the pitch angle command in steady state, w ₁ and w ₂ are weights , t ₁ and t ₂ are the time periods concerned by the designer.

Step 4: Set the guidance law parameters to be optimized in Simulink

Pass the parameters in the optimization algorithm to the Simulink model, load the .mat file with the parameter value of the guidance law in the initialization function of the Simulink module, and write the defined guidance law in the guidance law parameter gain module in Simulink Parameter variable name.

Step 5: Use the PIO map compass operator to optimize

Using the initialized group position and velocity, select the global optimal position X _g according to the initial individual cost function value. According to the formula V _i (t) = V _i (t-1) · e ^-Rt + rand · (X _g -X _i (t-1)) (1) and the formula Xi ₍ t) = Xi ₍ t- 1) The formula in +V _i (t) (2) updates the velocity V _i and position x _i of each individual, and calculates the cost function value of the newly generated particle. If the cost function value of the new particle is lower than the cost of the global optimal position If the function value is lower, the newly generated particle position is defined as the new global optimal position X _g . Repeatedly apply the map compass operator to optimize until the running algebra is greater than the maximum algebra NC ₁ of the map compass operator and stop.

Step 6: Use the PIO landmark operator to optimize

Using the optimization result of the map compass operator as the initial population of the landmark operator, according to the formula X _c (t)=∑X _i (t)·fitness(X _i (t))/∑fitness(X _i (t)) The formula in (4) and the formula X _i (t)=X _i (t-1)+rand (X _c (t)-X _i (t-1)) (5) updates the velocity V _i of each individual and position x _i , calculate the cost function value of the newly generated particle, if the cost function value of the new particle is lower than the cost function value of the global optimal position, define the newly generated particle position as the new global optimal position X _g . According to the formula N _p (t) = N _p (t-1)/2 (3) to calculate the population size of the new population, according to the calculation results of the formula (3), discard some individuals with a larger cost function in the population, and select The better group is used as the reserved group for the next round of optimization, and the landmark operator is repeatedly used for optimization until the number of running algebra is greater than the maximum number of NC ₂ of the landmark operator.

Step 7: Store the result and verify

The result of landmark operator optimization is regarded as the final guidance law optimization result. This result is saved in a .mat file, and the .mat file is called in the Simulink module, and the optimized guidance law parameters are used for simulation. The tracking accuracy of the aircraft on the specified glideslope under the wake disturbance is evaluated to evaluate the results of the optimization of the guidance law. If you are not satisfied with the optimization result, you can adjust the cost function used in optimization, restart the algorithm for optimization, until you get a satisfactory optimization result.

3. Advantages and effects:

The present invention proposes a design method for the autonomous landing guidance law of a carrier-based aircraft based on pigeon group optimization, and aims to provide an intelligent parameter setting method for the landing guidance law. This method effectively reduces the work difficulty of the control law designers, and improves the robustness of the guidance law to the ship's wake disturbance. In different landing environments, the performance requirements of the guidance law are different. By modifying the cost function of the optimization problem, this method can quickly design the guidance law parameters that meet the requirements according to the specific requirements, and reduce the workload of designers.

Description of drawings

Figure 1 Schematic diagram of the map compass operator of the pigeon swarm optimization algorithm.

Fig. 2 Schematic diagram of the landmark operator of the pigeon swarm optimization algorithm.

Figure 3 The overall flow chart of the pigeon group optimization algorithm.

Fig. 4a Schematic diagram of the steady-state components of the horizontal wake.

Fig. 4b Schematic diagram of the steady-state component of the vertical wake.

Figure 5. Schematic diagram of the variation curve of aσ(x) with ship distance.

Figure 5b Schematic diagram of the curve of τ(x) changing with the distance from the ship.

Figure 6 The overall block diagram of carrier aircraft landing control.

Fig. 7a Schematic diagram of synthetic horizontal wake interference.

Fig. 7b Schematic diagram of the synthesized vertical wake interference.

Figure 8 Schematic diagram of the evolution curve of the cost function.

Figure 9. Schematic diagram of glide slope deviation under ship wake interference.

Figure 10 is a schematic diagram of the angle of attack response during landing.

Fig. 11 Schematic diagram of velocity response during landing.

Fig. 12 Schematic diagram of pitch angle response during landing.

Figure 13 Schematic diagram of autopilot command input during landing. Fig. 14 is a flow chart of the present invention.

The labels and symbols in the figure are explained as follows:

Nc - the number of iterations of the optimization algorithm

N - does not meet the conditions (no)

Y - meet the conditions (yes)

θ _c ——autopilot pitch angle command

δ _e ——elevator command

T——throttle thrust command

h _{error ——height} error

α——angle of attack

V - speed

θ——pitch angle

Detailed ways

See Fig. 1-Fig. 14, verify the effectiveness of the design method proposed by the present invention through a specific carrier-based aircraft autonomous landing guidance law optimization example below, the ship wake disturbance used in this example comes from the U.S. military standard The airflow disturbance model given in MIL28785C, the carrier aircraft model used is the F-18 longitudinal nonlinear model, the inner ring autopilot used is in the form of pitch angle command, and the approach power compensation is also used in the longitudinal control of the carrier aircraft system. In this example, the speed of the carrier-based aircraft is 70m/s, and the landing is completed around 84s. The experimental computer configuration is i5-4210M processor, 2.60Ghz main frequency, 4G memory, and the software is MATLAB 2013b version.

See Figure 14, the specific implementation steps of this example are as follows:

Step 1: Build the Simulink simulation module of carrier aircraft and ship wake

The ship wake model in this example considers four components: atmospheric turbulence, steady-state aircraft carrier wake disturbance, periodic aircraft carrier wake disturbance, and random aircraft carrier wake disturbance.

U ₁ and W ₁ are the horizontal atmospheric turbulence component and the vertical atmospheric turbulence component, respectively. The unit white noise is obtained by filtering with a shaping filter, and their spatial power spectral densities are shown in the following formula:

U ₂ and W ₂ are the steady-state component of the horizontal wake and the steady-state component of the vertical wake, respectively. They can be obtained by piecewise linearization, and the specific shape of the curve is shown in Figure 4.

U ₃ and W ₃ are the periodic component of the horizontal wake and the periodic component of the vertical wake respectively, which can be obtained by formula calculation, and the specific calculation formula is shown in the following formula:

in,

In the formula, ω _s = 0.7rad/s is the pitch frequency, θ _s = 1.414rad is the pitch amplitude, V _wod = 10m/s is the deck wind, V = 10m/s is the approach speed of the carrier aircraft, and X is The distance from the aircraft to the ship, the range is [-5000,0]m, P is the random phase, and its value is between [0,2π].

U ₄ and W ₄ are the random component of the horizontal wake and the random component of the vertical wake, respectively. The unit white noise is obtained by filtering with a shaping filter, and its calculation formula is shown in the following formula:

Among them, rand is a random number, σ(x) and τ(x) are coefficients related to distance, and their shapes are given in Figure 5. The overall block diagram of carrier-based aircraft landing control is shown in Figure 6, and the synthesized ship wake disturbance used in the simulation is shown in Figure 7.

Step 2: Initialize the parameters of the pigeon group optimization algorithm

(1) Initialize the optimization parameter dimension D

The optimized parameters in this example are the parameters in the guidance law of the autonomous landing of the carrier-based aircraft. The default guidance law is in the form of PID-DD (proportional, integral, differential, second-order differential), so there are 4 parameters to be optimized , set the optimization parameter dimension D=4.

(2) Initialize the population size M

The population size M of the swarm intelligence optimization algorithm has a great influence on the optimization effect. The selection of the general population size is 3-5 times the dimension of the optimization problem. The default value of population size in this example is 15.

(3) Initialize the attenuation coefficient R

The attenuation coefficient R is applied in the map compass operator of the pigeon swarm algorithm, and it affects the attenuation speed of the particle's own velocity. The default value of the attenuation coefficient R in this example is 0.1.

(4) Initialize the population position and speed

The upper limit of position P _max =[3,3,5,5] and the lower limit of position P _min =[0,0,0,0] of the group are not set in the search space, and the upper limit of velocity V _max =0.2(P _max -P _min ) and the lower speed limit V _min =0.2(P _min −P _max ). Initialize an initial position x _i and initial velocity V _i for each particle in the population.

(5) Set Algorithm Algebra

The pigeon swarm optimization algorithm has two operators, namely the map compass operator and the landmark operator. Before the algorithm operation, it is necessary to set the maximum algebra NC ₁ =15 and NC ₂ =20 respectively.

Step 3: Design the cost function

The setting of the cost function is very critical in the optimization of the landing guidance law, and its setting directly affects the optimization effect. In this method, the goal of optimizing the parameters of the guidance law is to minimize the displacement of the carrier-based aircraft from the designated glide path under the interference of the ship's wake during the landing process, and the control input should be as small as possible. So define the following cost function:

Among them, h _c is the specified glide path height command, which is a straight line with a constant slope, the initial value is 305.8m, and the slope is -4.2706m/s. h is the height of the carrier aircraft, θ _c is the pitch angle command for the inner ring autopilot, θ _css = -3.2deg is the pitch angle command in steady state, w ₁ = 1 and w ₂ = 0.2 are the weight coefficients, t ₁ = 20s and t ₂ =83s are the time periods concerned by the designer.

Step 4: Set the guidance law parameters to be optimized in Simulink

Pass the parameters in the optimization algorithm to the Simulink model, load the "Kopt.mat" file with the value of the guidance law parameter in the initialization function of the Simulink module, and write the defined value in the guidance law parameter gain module in Simulink Guidance law parameter variables Kopt(1), Kopt(2), Kopt(3), Kopt(4), these four variables correspond to the gain of proportional, integral, differential and second order differential respectively.

Step 5: Use the PIO map compass operator to optimize

Using the initialized group position and velocity, select the global optimal position X _g according to the initial individual cost function value. Update the velocity V _i and position _xi of each individual, and calculate the cost function value of the newly generated particle. If the cost function value of the new particle is lower than the cost function value of the global optimal position, the newly generated particle position is defined as The new global optimal position X _g . Repeatedly apply the map compass operator to optimize until the running algebra is greater than the maximum algebra NC ₁ of the map compass operator and stop.

Step 6: Use the PIO landmark operator to optimize

Use the optimization results of the map compass operator as the initial population of the landmark operator, update the velocity V _i and position _xi of each individual, and calculate the cost function value of the newly generated particles. If the cost function value of the new particle is better than the global optimal If the cost function value of the position is lower, the newly generated particle position is defined as the new global optimal position X _g . Calculate the number of groups in the new population according to the formula (3), discard some individuals with a larger cost function in the group according to the calculation result of the formula (3), and select the better group in the current group as the reserved group for the next round of optimization, repeat Apply the landmark operator to optimize until the running algebra is greater than the maximum algebra NC ₂ of the landmark operator and stop.

Step 7: Store the result and verify

The result of landmark operator optimization is regarded as the final guidance law optimization result. The result of this optimization is Kopt(1)=2.156, Kopt(2)=0.403, Kopt(3)=2.974, Kopt(4)=3.185 . Save this result in the "Kopt.mat" file, call the "Kopt.mat" file in the Simulink module, use the optimized guidance law parameters for simulation, and observe the behavior of the carrier-based aircraft on the specified glide slope under wake disturbance. Tracking accuracy, evaluating the results of guidance law optimization. The evolution curve of the cost function in the optimization process is shown in Figure 8, the error of deviation from the glideslope is shown in Figure 9, and the angle of attack response, velocity response and pitch angle response during the landing process are shown in Figure 10-Figure 12 As shown, the pitch angle command input of the inner ring is shown in Figure 13. If you are not satisfied with the optimization result, you can adjust the cost function used in optimization, restart the algorithm for optimization, until you get a satisfactory optimization result.

Through the above optimization process, a set of guidance law parameters with strong robustness to the ship’s wake can be obtained. The evolution curve of the cost function during optimization is shown in Figure 8, and the landing simulation results are shown in Figure 9-13 As shown, it can be seen from the simulation results that the displacement of the carrier-based aircraft from the glideslope during the landing process is small, and the overall performance of the system is satisfactory.

Claims (1)

1. A carrier-based aircraft autonomous landing guidance law design method based on pigeon swarm optimization, is characterized in that: the specific steps of the method are as follows: Step 1: Build the Simulink simulation module of carrier aircraft and ship wake The ship wake model considers the following four components: atmospheric turbulence, steady-state aircraft carrier wake disturbance, periodic aircraft carrier wake disturbance and random aircraft carrier wake disturbance; U ₁ and W ₁ are the horizontal atmospheric turbulence component and the vertical atmospheric turbulence component, respectively, which are obtained by filtering with unit white noise through a shaping filter, and their spatial power spectral densities are shown in the following formula: <mrow><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>&amp;Phi;</mi><msub><mi>U</mi>mi><mn>1</mn></msub></msub><mo>=</mo><mfrac><mn>5.663</mn><mrow><mn>1</mn><mo>+</mo><msup><mrow><mo>(</mo><mn>30.48</mn><mi>&amp;Omega;</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>&amp;Phi;</mi><msub><mi>W</mi><mn>1</mn></msub></msub><mo>=</mo><mfrac><mn>2.0275</mn><mrow><mn>1</mn><mo>+</mo><msup><mrow><mo>(</mo><mn>30.48</mn><mi>&amp;Omega;</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfrac></mrow></mtd></mtr></mtable></mfenced><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow> U ₂ and W ₂ are the steady-state components of the horizontal wake and the steady-state components of the vertical wake, respectively, which are obtained by piecewise linearization; U ₃ and W ₃ are the periodic component of the horizontal wake and the periodic component of the vertical wake respectively, which are obtained by formula calculation, and the specific calculation formula is shown in the following formula: <mrow><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>U</mi><mn>3</mn></msub><mo>=</mo><msub><mi>&amp;theta;</mi><mi>s</mi></msub><msub><mi>V</mi><mrow><mi>w</mi><mi>o</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mn>2.22</mn><mo>+</mo><mn>0.0009</mn><mi>X</mi><mo>)</mo></mrow><mi>C</mi></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>W</mi><mn>3</mn></msub><mo>=</mo><msub><mi>&amp;theta;</mi><mi>s</mi></msub><msub><mi>V</mi><mrow><mi>w</mi><mi>o</mi><mi>d</mi></mrow></msub><mrow><mo>(</mo><mn>4.98</mn><mo>+</mo><mn>0.0018</mn><mi>X</mi><mo>)</mo></mrow><mi>C</mi></mrow></mtd></mtr></mtable></mfenced><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mrow> in, <mrow><mi>C</mi><mo>=</mo><mi>c</mi><mi>o</mi><mi>s</mi><mo>{</mo><msub><mi>&amp;omega;</mi><mi>s</mi></msub><mo>&amp;lsqb;</mo><mi>t</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mi>V</mi><mo>-</mo><msub><mi>V</mi><mrow><mi>w</mi><mi>o</mi><mi>d</mi></mrow></msub></mrow><mrow><mn>0.85</mn><msub><mi>V</mi><mrow><mi>w</mi><mi>o</mi><mi>d</mi></mrow></msub></mrow></mfrac><mo>)</mo></mrow><mo>+</mo><mfrac><mi>X</mi><mrow><mn>0.85</mn><msub><mi>V</mi><mrow><mi>w</mi><mi>o</mi><mi>d</mi></mrow></msub></mrow></mfrac><mo>&amp;rsqb;</mo><mo>+</mo><mi>P</mi><mo>}</mo><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>8</mn><mo>)</mo></mrow></mrow> In the formula, ω _s is the pitch frequency, θ _s is the pitch amplitude, V _wod is the deck wind, V = 10m/s carrier aircraft approach speed, X is the distance of the aircraft from the ship, and P is the random phase; U ₄ and W ₄ are the random component of the horizontal wake and the random component of the vertical wake respectively, which are obtained by using unit white noise and filtered by a shaping filter, and their calculation formula is shown in the following formula: <mrow><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>U</mi><mn>4</mn></msub><mo>=</mo><mo>&amp;lsqb;</mo><mi>r</mi><mi>a</mi><mi>n</mi><mi>d</mi><mo>&amp;rsqb;</mo><mo>&amp;CenterDot;</mo><mo>&amp;lsqb;</mo><mfrac><mi>s</mi><mrow><mi>s</mi><mo>+</mo><mn>0.1</mn></mrow></mfrac><mo>&amp;rsqb;</mo><mi>sin</mi><mrow><mo>(</mo><mn>10</mn><mi>&amp;pi;</mi><mi>t</mi><mo>)</mo></mrow><mfrac><mrow><mi>&amp;sigma;</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msqrt><mrow><mn>2</mn><mi>&amp;tau;</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></msqrt></mrow><mrow><mi>&amp;tau;</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>s</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>V</mi><mn>4</mn></msub><mo>=</mo><msub><mi>W</mi><mn>4</mn></msub><mo>=</mo><mo>&amp;lsqb;</mo><mi>r</mi><mi>a</mi><mi>n</mi><mi>d</mi><mo>&amp;rsqb;</mo><mo>&amp;CenterDot;</mo><mo>&amp;lsqb;</mo><mfrac><mi>s</mi><mrow><mi>s</mi><mo>+</mo><mn>0.1</mn></mrow></mfrac><mo>&amp;rsqb;</mo><mi>sin</mi><mrow><mo>(</mo><mn>10</mn><mi>&amp;pi;</mi><mi>t</mi><mo>)</mo></mrow><mfrac><mrow><mn>0.035</mn><msub><mi>V</mi><mrow><mi>w</mi><mi>o</mi><mi>d</mi></mrow></msub><msqrt><mn>6.66</mn></msqrt></mrow><mrow><mn>3.33</mn><mi>s</mi><mo>+</mo><mn>1</mn></mrow></mfrac></mrow></mtd></mtr></mtable></mfenced><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow> Among them, rand is a random number, σ(x) and τ(x) are coefficients related to distance, and the carrier aircraft model and the inner ring autopilot used by it are given by specific design requirements; Step 2: Initialize the parameters of the pigeon group optimization algorithm (1) Initialize the optimization parameter dimension D The optimized parameters are the parameters in the guidance law of the autonomous landing of the carrier-based aircraft, which vary according to the form of the guidance law; (2) Initialize the population size M The population size M of the swarm intelligence optimization algorithm has a great influence on the optimization effect, and the selection of the general population size is 3-5 times the dimension of the optimization problem; (3) Initialize the attenuation coefficient R The attenuation coefficient R is applied in the map compass operator of the pigeon group algorithm, which affects the attenuation speed of the particle's own velocity; (4) Initialize the population position and speed Set the upper limit P _max and the lower limit P _min of the group in the search space, as well as the upper limit V _max and the lower limit V _min of the speed; assign initial values to the position x _i and speed V _i of each individual in the population; <mrow><mfenced open = "{" close = ""><mtable><mtr><mtd><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>=</mo><msub><mi>P</mi><mi>min</mi></msub><mo>+</mo><mi>r</mi><mi>a</mi><mi>n</mi><mi>d</mi><mo>&amp;CenterDot;</mo><mrow><mo>(</mo><msub><mi>P</mi><mi>max</mi></msub><mo>-</mo><msub><mi>P</mi><mi>min</mi></msub><mo>)</mo></mrow></mrow></mtd></mtr><mtr><mtd><mrow><msub><mi>V</mi><mi>i</mi></msub><mo>=</mo><msub><mi>V</mi><mi>min</mi></msub><mo>+</mo><mi>r</mi><mi>a</mi><mi>n</mi><mi>d</mi><mo>&amp;CenterDot;</mo><mrow><mo>(</mo><msub><mi>V</mi><mi>max</mi></msub><mo>-</mo><msub><mi>V</mi><mi>min</mi></msub><mo>)</mo></mrow></mrow></mtd></mtr></mtable></mfenced><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>10</mn><mo>)</mo></mrow></mrow> (5) Set Algorithm Algebra The pigeon group optimization algorithm has two operators, which are the map compass operator and the landmark operator. Before the algorithm operation, the maximum algebra NC ₁ and NC ₂ of the two algorithms need to be set respectively; Step 3: Design the cost function The setting of the cost function is very critical in the optimization of the landing guidance law, and its setting directly affects the optimization effect; the goal of optimizing the parameters of the guidance law is to make the carrier-based aircraft deviate from the The displacement of the specified glideslope is the smallest, and the control input is as small as possible, so the following cost function is defined: <mrow><mi>cos</mi><mi></mi><mi>t</mi><mo>=</mo><msub><mi>w</mi><mn>1</mn></msub><munderover><mo>&amp;Integral;</mo><msub><mi>t</mi><mn>1</mn></msub><msub><mi>t</mi><mn>2</mn></msub></munderover><mo>|</mo><mrow><msub><mi>h</mi><mi>c</mi></msub><mo>-</mo><mi>h</mi></mrow><mo>|</mo><mi>d</mi><mi>t</mi><mo>+</mo><msub><mi>w</mi><mn>2</mn></msub><munderover><mo>&amp;Integral;</mo><msub><mi>t</mi><mn>1</mn></msub><msub><mi>t</mi><mn>2</mn></msub></munderover><mo>|</mo><mrow><msub><mi>&amp;theta;</mi><mi>c</mi></msub><mo>-</mo><msub><mi>&amp;theta;</mi><mrow><mi>c</mi><mi>s</mi><mi>s</mi></mrow></msub></mrow><mo>|</mo><mi>d</mi><mi>t</mi><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>11</mn><mo>)</mo></mrow></mrow> Among them, hc is the specified glide _{slope height command, h is the height of the carrier aircraft, θ c is} the pitch angle command for the inner ring autopilot, θ _css is the pitch angle command in steady state, w ₁ and w ₂ are weights , t ₁ and t ₂ are the time periods concerned by the designer; Step 4: Set the guidance law parameters to be optimized in Simulink Pass the parameters in the optimization algorithm to the Simulink model, load the .mat file with the parameter value of the guidance law in the initialization function of the Simulink module, and write the defined guidance law in the guidance law parameter gain module in Simulink parameter variable name; Step 5: Use the pigeon group to optimize the map compass operator for optimization Using the initialized group position and velocity, select the global optimal position X _g according to the initial individual cost function value; according to the formula V _i (t)=V _i (t-1) e ^-Rt +rand (X _g - The formula in Xi(t-1))(1) and the formula Xi(t)=Xi(t-1)+ _{Vi (} t)(2 _{) updates each individual's velocity V i and position} x _i , calculate the cost function value of newly generated particles, if the cost function value of the new particle is lower than the cost function value of the global optimal position, then define the position of the newly generated particle as the new global optimal position X _g ; repeatedly apply the map The compass operator performs optimization until the running algebra is greater than the maximum algebra NC ₁ of the map compass operator; Step 6: Use pigeon group optimization landmark operator to optimize Using the optimization result of the map compass operator as the initial population of the landmark operator, according to the formula X _c (t)=∑X _i (t)·fitness(X _i (t))/∑fitness(X _i (t)) The formula in (4) and the formula X _i (t)=X _i (t-1)+rand (X _c (t)-X _i (t-1)) (5) updates the velocity V _i of each individual and position x _i , calculate the cost function value of the newly generated particle, if the cost function value of the new particle is lower than the cost function value of the global optimal position, define the newly generated particle position as the new global optimal position X _g ; According to the formula X _p (t) = N _p (t-1)/2 (3) to calculate the population size of the new population, according to the result calculated by the formula (3), discard a part of individuals with a larger cost function in the population, and select the current population The better group among them is used as the reserved group for the next round of optimization, and the landmark operator is repeatedly used for optimization until the running algebra is greater than the maximum algebra NC ₂ of the landmark operator; Step 7: Store the result and verify The result of landmark operator optimization is regarded as the final guidance law optimization result. This result is saved in a .mat file, and the .mat file is called in the Simulink module, and the optimized guidance law parameters are used for simulation. The tracking accuracy of the designated glideslope under wake interference is evaluated to evaluate the results of the optimization of the guidance law; if the optimization results are not satisfied, the cost function used in the optimization is adjusted, and the algorithm is restarted for optimization until a satisfactory optimization result is obtained.