CN106125549A - Between a kind of overhead weapon station is advanced, burst-firing gun muzzle vibrates substep suppressing method - Google Patents

Abstract

The invention provides burst-firing gun muzzle vibration substep suppressing method between a kind of overhead weapon station traveling, comprise the steps: step one, given bracing frame elastic modelling quantity, cartridge box quality, the scope of buffer rigidity；Step 2, employing Latin hypercube EXPERIMENTAL DESIGN choose acquisition N group sample point；Step 3, the calculating vibration integrated parameter of gun muzzle；Step 4, associating N group sample point and the vibration integrated parameter of N number of gun muzzle constitute initial training sample point set；Step 5, use genetic algorithm carry out optimizing to kriging agent model, find out optimum point and greatest hope improves point；Step 6, based on dual kriging Model sequence iteration optimization algorithms structure parameter optimizing problem carried out optimizing until convergence；Step 7, various external drives and internal nonlinearity factor are considered as summation disturbance in the lump, by the state variable of expansion, it are estimated, finally by feedback mechanism, it is compensated suppression.

Description

Between a kind of overhead weapon station is advanced, burst-firing gun muzzle vibrates substep suppressing method

Technical field

The invention belongs to weapon station technical field, burst-firing gun muzzle vibration between advancing particularly to a kind of overhead weapon station Suppressing method step by step.

Background technology

During Canon launching, the TRANSIENT HIGH TEMPERATURE of powder burning generation, pushed at high pressure bullet high-speed motion in thorax, cannon in addition Effect of inertia, make cannon produce high vibration, cause gun muzzle point to change, have a strong impact on fire accuracy.Research cannon The gun muzzle disturbance launched and Changing Pattern thereof, for evaluating and examine cannon performance, identifying that the cannon quality of production, raising cannon are penetrated Hit precision and there is important theory significance.Make gun muzzle disturbance minimum by overhead weapon station structural parameters are optimized.

Summary of the invention

The present invention has designed and developed burst-firing gun muzzle vibration substep suppressing method between the traveling of a kind of overhead weapon station, passes through Optimization to structural parameters and the optimization to controller, solve the big problem affecting fire accuracy of gun muzzle disturbance amount.

The technical scheme that the present invention provides is:

Between a kind of overhead weapon station is advanced, burst-firing gun muzzle vibrates substep suppressing method, comprises the steps:

Step one, the scope E ∈ [E of given overhead weapon station bracing frame elastic modulus E_a,E_b], scope m of cartridge box quality m ∈[m_a,m_b], the scope K ∈ [K of buffer stiffness K_a,K_b]；

Step 2, employing Latin hypercube EXPERIMENTAL DESIGN choose the value of E, m, K, obtain N group sample point (E_i,m_i,K_i), i= 1,2,...,N；

Step 3, overhead weapon station bracing frame elastic modelling quantity, cartridge box quality, buffer rigidity are respectively set as E_i、m_i、 K_i, overhead weapon station is carried out gun muzzle disturbance test, obtains height to linear velocity mean-square value D_i(v_z), level mean square to linear velocity Value D_i(v_y), height to angular displacement mean-square value D_i(θ_z) and level to angular displacement mean-square value D_i(θ_y), calculate gun muzzle vibration integrated Parameter F_i

F_i=w₁D(v_z)+w₂D(θ_z)+w₃D(v_y)+w₄D(θ_y)

Wherein, w₁、w₂、w₃、w₄For weight coefficient；

Step 4, associating N group sample point (E_i,m_i,K_i) and vibration integrated parameter F of N number of gun muzzle_iConstitute initial training sample Point set, builds kriging agent model；

Step 5, use genetic algorithm carry out optimizing to kriging agent model, find out optimum point and greatest hope improves Point；

Step 6, the optimum point obtained in step 5 and greatest hope are improved two variance smallest point of point as to be added Sampled point, re-start kriging agent model optimizing, until optimum point restrain；The weapon station bracing frame bullet now obtained Property modulus E₀, cartridge box quality m₀, buffer K₀It is overhead weapon station structure optimization parameter.

Step 7, various external drives and internal nonlinearity factor are considered as summation disturbance in the lump, become by the state of expansion It is estimated by amount, finally by feedback mechanism, it is compensated suppression.

Preferably, in step 3, w₁=w₃=1, w₂=w₄=10.

Preferably, in step 6, convergence criterion is:

Wherein,It is respectively kth generation, the optimal value of kth+1 generation kriging model.

Preferably, in step 2, Latin hypercube test is used to extract 35 groups of sample points.

In step 5, Population in Genetic Algorithms quantity is 44, and crossover probability is 0.7, and mutation probability is 0.05, and convergence threshold values is 0.001。

Preferably, the scope E ∈ [1.5,2.5] of bracing frame elastic modulus E.

Preferably, the scope m ∈ [50,130] of cartridge box quality m.

Preferably, the scope K ∈ [500,750] of buffer stiffness K.

Preferably, in step 7, can be by a unknown non-thread by weapon station Internal dynamics characteristic and external disturbance Property functionThen weapon station mechanical system can be reduced to a second order controlled system:

In formula, y, x₁Expression system exports, i.e. overhead weapon station pitching segment angle speed,x₂For angular acceleration,For Angle acceleration；

It is used in extended state observer and system unmodel parts and unknown external disturbance are considered as summation disturbance, and pass through The state variable of expansion is observed.Extraction system output variable y and input variable u, input extended state observer:

Then state variable z₁It is the tracking amount to weapon station pitching segment angle speed, z₂It is the tracking amount of angular acceleration, z₃ It it is the tracking amount to summation disturbance；

Draw controlled quentity controlled variable u₀After, together with summation disturbance z₃, use following feedback rates that controlled system is compensated:

U=u₀-z₃

Finally give overhead weapon station big gun Ore-controlling Role height to steady working condition Active Disturbance Rejection Control model.

The invention has the beneficial effects as follows: the invention provides burst-firing gun muzzle vibration point between a kind of overhead weapon station traveling Step suppressing method, by designing the optimization of bracing frame elastic modelling quantity, cartridge box quality, buffer rigidity, with to controlling the excellent of its Change, make gun muzzle disturbance amount minimum.

Accompanying drawing explanation

Fig. 1 is burst-firing gun muzzle vibration substep suppressing method flow chart between overhead weapon station of the present invention is advanced.

Fig. 2 is overhead weapon station structural representation of the present invention.

Fig. 3 is that overhead weapon station big gun Ore-controlling Role of the present invention height is to steady working condition Active Disturbance Rejection Control model.

Detailed description of the invention

The present invention is described in further detail below in conjunction with the accompanying drawings, to make those skilled in the art with reference to description literary composition Word can be implemented according to this.

As it is shown in figure 1, the invention provides burst-firing gun muzzle vibration substep suppression side between a kind of overhead weapon station traveling Method, comprises the following steps:

Step one: select bracing frame elastic modulus E, cartridge box quality m, buffer stiffness K these three structural parameters as excellent The design variable of change problem, shown in the span chart 1 of these three parameter:

Table 1

Step 2: use Latin hypercube EXPERIMENTAL DESIGN to choose the value of E, m, K, obtain 35 groups of sample point (E_i,m_i,K_i), i =1,2 ..., 35.

Step 3, overhead weapon station bracing frame elastic modelling quantity, cartridge box quality, buffer rigidity are respectively set as E_i、m_i、 K_i, overhead weapon station is carried out gun muzzle disturbance test, obtains height to linear velocity mean-square value D_i(v_z), level mean square to linear velocity Value D_i(v_y), height to angular displacement mean-square value D_i(θ_z) and level to angular displacement mean-square value D_i(θ_y), calculate gun muzzle vibration integrated Function

MinF=min (w₁D(v_z)+w₂D(θ_z)+w₃D(v_y)+w₄D(θ_y))

Wherein, w₁、w₂、w₃、w₄For weight coefficient, effect is that the dimension to Vibration Parameter is unified, and value is: w₁=w₃= 1, w₂=w₄=10.

Step 4: generate initial training sample space.By 35 groups of sample point (E_i,m_i,K_i), i=1,2 ..., 35 together with big gun The vibration integrated parameter of mouth generates initial training sample space, and part sample space is as shown in table 2

Table 2

Step 5: on the basis of initial training sample space, utilizes " DACE " Toolbox structure first in Matlab For kriging model, regression function selects binary quadratic polynomial, and correlation function selects Gaussian function, and considers anisotropy Effect, individually gives θ value to each design variable, and scope takes [0.1,20], and initial value is unified is set to 10.Select genetic algorithm As optimized algorithm, arranging population quantity is 44, and crossover probability is 0.7, and mutation probability is 0.05, and convergence threshold values is 0.001.

Kriging agent model is substantially a kind of approximate model [139] based on theory of statistics, its effectiveness and accurately Property is affected little by random error.Kriging agent model, when being predicted unknown point, needs by the most known sampling The information of point, estimates unknown point by this information is weighted combination, and method of weighting is then according to minimizing estimated value error Variance determine, it is therefore contemplated that kriging model is optimum linear unbiased estimate.

Kriging, as the approximate model of a kind of half parametric, is made up of linear regression part and nonparametric part:

In formula, F (β, x) for returning part, multinomial and regression coefficient β by a series of x together decide on:

In Interpolation Process, (β, x) provides overall situation approximation to F, and the polynomial form of x can be chosen as 0 rank, 1 rank or 2 rank.

Z (x) is nonparametric part, provides the approximation of partial deviations in Interpolation Process, has a following statistical property:

In formula, E is expectation, and Var is variance, and Cov is covariance, and R is correlation function, and θ is associated vector.

Assume that the sample point set comprising n design variable number known to a group is X=[x¹,x²,…,xⁿ]^T, it is corresponding Functional value be Y=[y¹,y²,…,yⁿ]^T, then after using kriging to carry out interpolation, to any one unknown point response value It is estimated as:

In formula, c is interpolation coefficient.The estimation difference of agent model is:

In formula, F=[f₁,f₂,…,f_n]^T, Z=[z₁,z₂,…,z_n]^T。

In order to ensure the unbiasedness of estimated result, need to make above-mentioned estimation difference is desired for 0:

I.e. have:

F^TC-f (x)=0

Now, the mean square deviation of estimated value is:

In formula,

Kriging model needsMinimum, therefore coefficient c can minimize mean square deviation Optimized model by foundation and solves Draw:

Introducing Lagrange multiplier obtains:

L (c, λ)=σ²(1+c^TRc-2c^Tr)-λ^T(F^Tc-f(x))

Above formula about the gradient of c is:

Can obtain system equation in conjunction with constraints is:

Can derive further:

Above formula is substituted into:

The parameter estimation maximum likelihood function of logarithmic form is:

After θ initial value is given, by maximum likelihood function respectively to β and σ²Differentiate, and make it be equal to 0, then can obtain Maximum-likelihood estimation to two parameters is:

Now, kriging is minimum dispersion linear unbiased estimator to the estimation of unknown point:

Step 6: according to above-mentioned initial condition, based on dual kriging Model sequence iteration optimization algorithms to weapon station Structure parameter optimizing problem carries out optimizing, and convergence criterion is:

In formula,It is respectively kth generation, the optimal value of kth+1 generation kriging model.

Result as shown in table 3, table 4, wherein x₁、x₂、x₃The most corresponding bracing frame elastic modelling quantity, cartridge box quality and buffering Device rigidity.

Table 3

Table 4

From characteristic point history, in the searching process of weapon station gun muzzle vibration optimization problem, optimal value is not one Diminish taste, but fluctuate back and forth between-40 to 40, cause the kriging agent model that the reason of this phenomenon is to simulate There is several close minimum points, when the pattern search of epicycle kriging to optimum point through add some points raising accuracy after, separately One close minimum point highlights, and becomes the optimum point of next round kriging model, optimizing the most repeatedly, adds some points, and one Until these several minimum points " are filled and led up ", globe optimum is retained.

Knowable to table 3, table 4, whole optimization process experienced by 26 renewals taking turns kriging model, altogether adds some points 26, The global optimum of convergence is 1.965 eventually, has compared initial value, and objective function optimization amplitude is 24.7%, corresponding structure ginseng Number optimal solution is: bracing frame elastic modelling quantity is 1.913GPa, cartridge box quality is 122.506kg, buffer rigidity 615.69N/mm.

Using said structure parameters optimization as the structural parameters of weapon station, build weapon station and the model on road surface.Such as Fig. 2 institute Showing, certain type overhead weapon station mainly includes part and overhead part in car, wherein internal point of car include control crank, display, Bench board, fire control computer etc., overhead part then includes armament systems, sees and take aim at system, gun turret system etc..Then set up 8 etc. Level road surface model, i.e. A～H level road surface model.

Burst-firing gun muzzle vibration characteristics between advancing under existing PID controller for investigation overhead weapon station, to weapon station Burst-firing dynamics simulation between advancing, driving cycle is 27km/h speed difference road surface (A～F level), for avoiding crawler belt Gun muzzle is impacted by chassis from the static desired speed that accelerates to, and five burst-firings load when advancing 14 seconds, and radio frequency is 300 Send out/point, different road surfaces gun muzzle vibration height can represent with displacement curve to angular displacement.Additionally, whether advance to even for embodying Launch the impact hitting gun muzzle vibration, carry out burst-firing dynamics simulation between weapon station stopping, and its bullet is gone out gun muzzle moment Gun muzzle angle of site displacement mean-square value is listed in the lump with running result, as shown in table 5.

Table 5

As shown in Table 5, for inferior grade road surface (corresponding to A, B level road surface), PID controller can cause in road pavement excitation Barrel height carry out stability contorting to skew, wherein, A level, B level road surface advance between burst-firing gun muzzle vibration height to position, angle The 0.065mil that shifting mean-square value is respectively between 0.069mil, 0.08mil, and stopping is close, shows big gun control system under this driving cycle System can carry out effective stability contorting to barrel, thus inhibits the oscillating component caused in gun muzzle vibration by road excitation, makes Under this operating mode, gun muzzle vibration is mainly caused by shooting load；Along with the aggravation (corresponding to C level road surface) of driving cycle, controller pair The rejection ability of road disturbance gradually weakens, gun muzzle vibration that gun muzzle vibration that traveling process causes has caused with burst-firing Quite, between advancing under C level road surface, burst-firing gun muzzle vibration height is 0.109mil to angular displacement mean-square value simultaneously, is about and stops Between 2 times of burst-firing, show that the influence degree that under this operating mode, gun muzzle is vibrated by burst-firing load and pavement loading is suitable；With After, when driving cycle is further exacerbated by (corresponding to D～F level road surface), gun muzzle vibration that burst-firing causes falls into oblivion the most completely In gun muzzle vibration caused in road excitation, and between under E level, F level road surface, weapon station is advanced burst-firing gun muzzle vibration height to Angular displacement mean-square value respectively may be about 11 times and 38 times of burst-firing between stopping, shows that under this operating mode, PID controller cannot be right Road disturbance effectively suppresses, and load, in other words, now gun muzzle are significantly larger than shot in the contribution that gun muzzle is vibrated by complex road condition Vibration is mainly caused by road excitation.Therefore, for meeting the barrel stability contorting demand of more driving cycle, suppressing acute further Under strong driving cycle, the road disturbance component of gun muzzle vibration, present invention introduces Auto Disturbances Rejection Control Technique.

In overhead weapon station work process, external drive and internal nonlinearity factor act on jointly, penetrate between causing advancing Hit the overhead weapon station under operating mode and there is the complication system characteristic of strong nonlinearity, variable element, it is difficult to accurate controlled system mould Type is lumped together.To this end, introducing Auto Disturbances Rejection Control Technique, directly by various external drives (outside in Active Disturbance Rejection Control Portion's disturbance) and internal nonlinearity factor (unmodel parts corresponding in Active Disturbance Rejection Control) be considered as summation disturbance in the lump, with expansion It is estimated by the state variable opened, and finally by certain feedback mechanism, it is compensated suppression.

On the basis of original weapon station big gun Ore-controlling Role current-velocity double-loop control structure, speed ring PID controller is changed Cause Active Disturbance Rejection Control.After weapon station mechanical system is considered as the black box of a unknown properties, all Internal dynamics characteristics And external disturbance can be with a unknown nonlinear functionRepresent, then weapon station mechanical system can be reduced to a second order Controlled system:

In formula, y, x₁Expression system exports, i.e. overhead weapon station pitching segment angle speed,x₂For angular acceleration,For (weapon station machinery system dynamics characteristic, external disturbance all can be equivalent to a unknown nonlinear function f to angle acceleration (x₁,x₂) act on this).

Effect in view of Nonlinear Tracking Differentiator is desired signal is carried out noise filtering, transition process arranging and is given The differential signal of desired signal, works to big gun Ore-controlling Role fax operating mode and tracking operating mode；And this subject study purpose is to protect Hold barrel space point to constant, suppression advance between road excitation cause gun muzzle vibration, i.e. stablizing mainly for big gun Ore-controlling Role Operating mode, it is desirable to signal is 0, therefore, for simplifying control process, does not the most use Nonlinear Tracking Differentiator.

It is used in extended state observer and system unmodel parts and unknown external disturbance are considered as summation disturbance, and pass through The state variable of expansion is observed.Extraction system output variable y and input variable u, input extended state observer:

Then state variable z₁It is the tracking amount to weapon station pitching segment angle speed, z₂It is the tracking amount of angular acceleration, z₃ It it is the tracking amount to summation disturbance.

Nonlinear feedback rate error nonlinear combination form:

Draw controlled quentity controlled variable u₀After, together with summation disturbance z₃, use following feedback rates that controlled system is compensated:

U=u₀-z₃

Finally give overhead weapon station big gun Ore-controlling Role height to steady working condition Active Disturbance Rejection Control model, as shown in Figure 3.

For investigating burst-firing gun muzzle dynamic response between the traveling under automatic disturbance rejection controller effect of the overhead weapon station, carry out Burst-firing dynamics simulation between the traveling of different driving cycles.Control to satisfy the need with PID to contrast Active Disturbance Rejection Control intuitively The inhibition of face disturbance, remove burst-firing when calculating lasting accuracy between traveling during, gun muzzle vibration of (14～15 seconds) is high Low to angular displacement data；Meanwhile, bullet is used to go out gun muzzle moment gun muzzle vibration height to angular displacement mean-square value as weapon station even Launching the token state hitting gun muzzle vibration, this token state is owing to occurring when marching fire, it is possible to shooting is carried by reflection controller Lotus and the comprehensive rejection ability of the dual disturbance of road excitation, under different driving cycle difference controllers, weapon station is stable smart between advancing It is as shown in table 6 to the contrast of angular displacement mean-square value that degree and bullet go out gun muzzle moment gun muzzle vibration height.

Table 6

From simulation result, for lasting accuracy between advancing, between after using automatic disturbance rejection controller, overhead weapon station is advanced Lasting accuracy all has a greater degree of improvement under different driving cycles, and average improvement amplitude is 7.6%, wherein, on A level road surface Under improvement amplitude the highest, reach 9.9%, show that Active Disturbance Rejection Control controls to be effectively improved weapon station big gun control system compared with PID System barrel stability under different driving cycles；Going out gun muzzle moment gun muzzle angular displacement mean-square value for bullet, it averagely changes Kind amplitude is 15.3%, and wherein, the improvement amplitude under C level road surface is the highest, reaches 21.7%, under minimum F level road surface 8.4%, show to improve in effect general trend and weaken with the raising of pavement grade.It should be noted that under identical road surface from Disturbance rejection control is compared PID and is controlled the amplitude that the improvement degree of diagonal displacement mean-square value generally to be improved more than lasting accuracy, such as A level After being ADRC by replacing PID under road surface, between traveling, lasting accuracy improves 9.9%, and between advancing, burst-firing bullet goes out gun muzzle Moment gun muzzle angular displacement mean-square value improves 21.7%, in showing that gun muzzle is not only vibrated under this driving cycle by Active Disturbance Rejection Control Road disturbance component suppresses, and shooting load disturbance component is also created inhibitory action, suppresses the most to a certain extent Gun muzzle vibration caused by burst-firing, enhances the inhibition that gun muzzle is vibrated by structure parameter optimizing, fully demonstrates Carried structure parameter optimizing combines the effectiveness of the substep suppressing method improving control strategy herein.

Although embodiment of the present invention are disclosed as above, but it is not restricted in description and embodiment listed Using, it can be applied to various applicable the field of the invention completely, for those skilled in the art, and can be easily Realizing other amendment, therefore under the general concept limited without departing substantially from claim and equivalency range, the present invention does not limit In specific details with shown here as the legend with description.

Claims (9)

1. burst-firing gun muzzle vibration substep suppressing method between an overhead weapon station is advanced, it is characterised in that include walking as follows Rapid:

Step one, the scope E ∈ [E of given overhead weapon station bracing frame elastic modulus E_a,E_b], the scope m ∈ of cartridge box quality m [m_a,m_b], the scope K ∈ [K of buffer stiffness K_a,K_b]；

Step 2, employing Latin hypercube EXPERIMENTAL DESIGN choose the value of E, m, K, obtain N group sample point (E_i,m_i,K_i), i=1, 2,...,N；

Step 3, overhead weapon station bracing frame elastic modelling quantity, cartridge box quality, buffer rigidity are respectively set as E_i、m_i、K_i, right Overhead weapon station carries out gun muzzle disturbance test, obtains height to linear velocity mean-square value D_i(v_z), level is to linear velocity mean-square value D_i (v_y), height to angular displacement mean-square value D_i(θ_z) and level to angular displacement mean-square value D_i(θ_y), calculate the vibration integrated parameter of gun muzzle F_i

F_i=w₁D(v_z)+w₂D(θ_z)+w₃D(v_y)+w₄D(θ_y)

Wherein, w₁、w₂、w₃、w₄For weight coefficient；

Step 4, associating N group sample point (E_i,m_i,K_i) and vibration integrated parameter F of N number of gun muzzle_iConstitute initial training sample point set, Build kriging agent model；

Step 5, use genetic algorithm carry out optimizing to kriging agent model, find out optimum point and greatest hope improves point；

Step 6, the optimum point obtained and greatest hope are improved two variance smallest point of point adopt as to be added in step 5 Sampling point, re-starts kriging agent model optimizing, until optimum point restrains；The weapon station bracing frame springform now obtained Amount E₀, cartridge box quality m₀, buffer K₀It is overhead weapon station structure optimization parameter；

Step 7, weapon station mechanical system can be reduced to a second order controlled system:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_1=x_2\\ {\stackrel{\·}{x}}_2=f(x_1,x_2)+u\\ y=x_1\end{array}\right.$

In formula, y, x₁Expression system exports, i.e. overhead weapon station pitching segment angle speed,x₂For angular acceleration,Add for angle Speed；

Various external drives and internal nonlinearity factor are considered as summation disturbance in the lump, by the state variable of expansion, it are estimated Meter, draws disturbance compensation value finally by feedback mechanism.

Between overhead weapon station the most according to claim 1 is advanced, burst-firing gun muzzle vibrates substep suppressing method, its feature It is, in step 3, w₁=w₃=1, w₂=w₄=10.

Between overhead weapon station the most according to claim 2 is advanced, burst-firing gun muzzle vibrates substep suppressing method, its feature Being, in step 6, convergence criterion is:

$\frac{{\hat{y}}_{\min }^{k+1}-{\hat{y}}_{\min }^k}{{\hat{y}}_{\min }^k}\≤1\%$

Wherein,It is respectively kth generation, the optimal value of kth+1 generation kriging model.

Between overhead weapon station the most according to claim 3 is advanced, burst-firing gun muzzle vibrates substep suppressing method, its feature It is, in step 2, uses Latin hypercube test to extract 35 groups of sample points.

Between overhead weapon station the most according to claim 4 is advanced, burst-firing gun muzzle vibrates substep suppressing method, its feature Being, in step 5, Population in Genetic Algorithms quantity is 44, and crossover probability is 0.7, and mutation probability is 0.05, and convergence threshold values is 0.001。

Between overhead weapon station the most according to claim 5 is advanced, burst-firing gun muzzle vibrates substep suppressing method, its feature It is, the scope E ∈ [1.5,2.5] of bracing frame elastic modulus E.

Between overhead weapon station the most according to claim 5 is advanced, burst-firing gun muzzle vibrates substep suppressing method, its feature It is, the scope m ∈ [50,130] of cartridge box quality m.

Between overhead weapon station the most according to claim 5 is advanced, burst-firing gun muzzle vibrates substep suppressing method, its feature It is, the scope K ∈ [500,750] of buffer stiffness K.

Between overhead weapon station the most according to claim 1 is advanced, burst-firing gun muzzle vibrates substep suppressing method, its feature It is, in step 7, extraction system output variable y and input variable u, input extended state observer:

$\left\{\begin{array}{c}e=z_1-y,fe=fal(e,0.5,\mathrm{\δ}),{\mathrm{fe}}_1=fal(e,0.25,\mathrm{\δ})\\ {\stackrel{\·}{z}}_1=z_2-{\mathrm{\β}}_{1}e\\ {\stackrel{\·}{z}}_2=z_3-{\mathrm{\β}}_{2}fe+u\\ {\stackrel{\·}{z}}_3=-{\mathrm{\β}}_3{\mathrm{fe}}_1\end{array}\right.$

Then state variable z₁It is the tracking amount to weapon station pitching segment angle speed, z₂It is the tracking amount of angular acceleration, z₃It is right The tracking amount of summation disturbance；

Draw controlled quentity controlled variable u₀After, together with summation disturbance z₃, use following feedback rates that controlled system carries out disturbance compensation:

U=u₀-z₃。