CN110673473B - Error Sign Integral Robust Adaptive Control Method for Two-Axis Coupled Tank Gun System - Google Patents

Abstract

The invention discloses an error sign integral robust adaptive control method for a two-axis coupled tank gun system, and the error sign integral robust adaptive control algorithm can be used to control such systems with strong uncertainty and nonlinearity. control. The present invention is proposed in the following context: Since the development of the tank gun has higher requirements for its precision control, the previous modeling method of pitch and direction and the method of separately controlling it are no longer sufficient for the whole system. Good control effect, and the two-axis coupled modeling scheme can effectively restore the actual movement of the tank gun. However, for such two-axis coupled tank gun systems, due to its coupling characteristics and nonlinearity, the control difficulty of such systems is greatly increased. The control method disclosed in the invention effectively solves the problem of the two-axis coupling tank gun system, improves the control precision of the entire system, and obtains good tracking performance.

Description

Error Sign Integral Robust Adaptive Control Method for Two-Axis Coupled Tank Gun System

technical field

The invention relates to the technical field of motion control, in particular to an error symbol integral robust adaptive control method of a two-axis coupled tank gun system.

Background technique

In modern road-based weapon systems, tanks are still one of the main combat weapons on the ground. The main attack method of the tank comes from the tank gun weapon carried by the tank. As the new generation of armored weapons and equipment tends to be integrated, systematic, automated, lightweight and unmanned, the unmanned turret system has been developed and developed in many military powers in the process of development, but its overall performance is inferior to manned turrets Not a lot. Unmanned turret, also known as overhead weapon turret, means that the weapon system of a tank or armored vehicle is installed on the top of the vehicle body, there is no crew in the turret, and all crew members are located in the vehicle body. The development of the unmanned turret of the tank has greatly improved the safety of the crew and the maintenance effect of the battlefield, regardless of the internal environment of the occupants. Therefore, the control of the unmanned turret carried by this road-based mobile platform is very important in the future army war, especially for the development and manufacture of the fifth-generation tanks. However, for this type of two-axis coupled tank gun system, due to its uncertainty, unmodeled error and nonlinearity, it greatly increases the control difficulty of this type of system. Therefore, if the traditional control method is adopted, the expected control goal may not be achieved. If the disturbance is relatively large, the traditional control method may even lead to system instability.

Therefore, the control methods for the two-axis coupling system of this kind of tank gun have been continuously proposed. The PID algorithm can achieve a certain degree of control for the entire system, but the accuracy of tracking, the time for error convergence, and especially the impact of external disturbances on the entire system, these factors make the control performance of the PID algorithm for the entire control system not reach a very good level. status. Then someone proposed to use the Synovial Variable Structure Control (SMC) algorithm to control such a system with large external disturbance. However, due to the discontinuity of SMC control, its actual disconnection is reflected in the shear plane as the boundary, the driving direction of the synovial trajectory above the switching plane and the driving direction of the synovial film below the switching plane are opposite, and intersect the switching plane, This intersection is discontinuous. Therefore, in the actual system, especially in the two-axis coupling system of the tank gun used in this paper, this shortcoming will be continuously amplified, resulting in more obvious system tremor effect, so the specific adjustment of the gun angle will increase the muzzle jitter. It has a great impact on the overall control accuracy. Active Disturbance Rejection Control (ADRC) can achieve a good control for this control system, but the control performance of ADRC is very dependent on the setting of the algorithm gain parameters. If the modeling parameters of the system are inaccurate, or there are many If the factors are not taken into account, the control performance of ADRC will be greatly reduced. The Extended State Observer (ESO) used in the ADRC control system is mainly based on the output error of the model, so it is often impossible to observe the external error. In the actual system of this model, the external disturbance is also a factor that cannot be ignored, so it is also It will reduce the control performance of the ADRC control algorithm.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide an error symbol integral robust adaptive control method for a two-axis coupled tank gun system. Based on the traditional RISE control method and integrating the idea of adaptive control, it can not only effectively deal with modeling uncertainty , and can obtain continuous control input and asymptotic tracking performance. In the adaptive part, it can better solve the influence of the coefficient of the model uncertainty, and then have better control performance. At the same time, it solves the problems of nonlinearity, model uncertainty, external interference, etc., and meets the requirements of system control accuracy.

The technical solution for realizing the object of the present invention is: a method for robust self-adaptive control method of error sign integral of two-axis coupled tank gun system, comprising the following steps:

Step 1, establish a mathematical model of the dynamics of the two-axis coupled tank gun system;

Step 2, designing a robust adaptive controller of error sign integral;

In step 3, the Lyapunov stability theory is used to prove the stability, and the Barbalat lemma is introduced to obtain the result of the global asymptotic stability of the system.

Compared with the prior art, the present invention has significant advantages as follows: it effectively solves the problems of the traditional control method for the two-axis coupled tank gun in this paper, and for the control accuracy, the reduction of error convergence time, the tracking performance and the anti-interference ability for external errors Both are greatly improved; the simulation results verify its effectiveness.

Description of drawings

Fig. 1 is the principle schematic diagram of the error sign integral robust adaptive (RISEA) control method of the two-axis coupling tank gun system of the present invention;

Figure 2 is a schematic diagram of a two-axis coupled tank gun system;

Fig. 3 is the tracking process diagram of the system high and low direction output to the desired command under the action of the RISEA controller designed by the present invention;

Fig. 4 is a tracking process diagram of the desired command output in the horizontal direction of the system under the action of the RISEA controller designed by the present invention;

Fig. 5 is a curve diagram of the tracking error of the system in the high and low directions with time under the action of the RISEA controller;

Fig. 6 is the curve diagram of the tracking error in the horizontal direction of the system under the action of the RISEA controller as a function of time;

时RISEA、RISE、PID三种控制器分别作用下系统水平方向的跟踪误差的对比曲线图；Figure 7 shows the system interference as

The comparison curve of the tracking error in the horizontal direction of the system under the action of RISEA, RISE and PID controllers respectively;

时RISEA、RISE、PID三种控制器分别作用下系统水平方向的跟踪误差的对比曲线图；Figure 8 shows the system interference as

The comparison curve of the tracking error in the horizontal direction of the system under the action of RISEA, RISE and PID controllers respectively;

FIG. 9 is a graph of the estimated value of the parameter θ ₁₁ in the RISEA controller as a function of time;

Figure 10 is a graph of the estimated value of the parameter θ ₁₂ in the RISEA controller as a function of time;

Figure 11 is a graph of the estimated value of the parameter θ ₁₃ in the RISEA controller as a function of time;

Figure 12 is a graph of the estimated value of the parameter θ ₂₁ in the RISEA controller as a function of time;

Figure 13 is a graph of the estimated value of the parameter θ ₂₂ in the RISEA controller as a function of time;

Figure 14 is a graph of the estimated value of the parameter θ ₂₃ in the RISEA controller as a function of time;

时RISEA控制器分别作用下系统高低方向的输入图；Figure 15 is the system interference as

When the RISEA controller acts on the input diagram of the high and low directions of the system respectively;

时RISEA控制器分别作用下系统水平方向的输入图。Figure 16 is the system interference as

When the RISEA controller acts on the input map of the horizontal direction of the system respectively.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

1-2, the error symbol integral robust adaptive control method of the two-axis coupled tank gun system according to the present invention includes the following steps:

Step 1, establish the mathematical model of the dynamics of the two-axis coupled gun system, as follows:

Step 1.1. Consider the modeling idea of the dynamic model, and use the Lagrange-Euler method to build the dynamic model of the tank gun:

Therefore, according to the Lagrange-Euler method, the dynamic equation of the two-axis coupled tank gun system is:

In formula (1), the rotation angle is q=[q ₁ q ₂ ] ^T , where q ₁ is the rotation angle in the horizontal direction of the two-axis coupling tank gun system, and q ₂ is the rotation angle in the height direction of the two-axis coupling tank gun system; M _a ∈R ^2×2 is an inertial symmetric positive definite matrix; M _b ∈ R ^{2 ×2} is a Coriolis centrifugal matrix; M _g ∈ R ^2×1 is a gravitational moment vector, M _g =[T _g1 T _g2 ] ^T , T _g1 The two-axis coupled tank gun system is the gravitational moment in the horizontal direction, T _g1 = 0, T _g2 is the gravitational moment in the height direction of the two-axis coupled tank gun system; the tank gun system input T = [T ₁ T ₂ ] ^T , where T ₁ is the input in the horizontal direction of the two-axis coupling tank gun system, T ₂ is the input torque in the vertical direction of the two-axis coupling tank gun system; friction torque T _f = [T _f1 T _f2 ], T _f1 is the two-axis coupling tank gun system The resistance torque generated by the friction force in the horizontal direction of the system, T _f2 is the resistance torque generated by the friction force in the high and low directions of the two-axis coupled tank gun system, and T _f is fitted and approximated by the lugre model:

i＝1,2，其中，l_ij为摩擦力参数，i＝1,2，j＝1,2,3，v_j为摩擦形状参数；两轴耦合坦克炮系统的总干扰d＝[d₁ d₂]^T，其中d₁为两轴耦合坦克炮系统的水平方向干扰，其中d₂为两轴耦合坦克炮系统的高低方向干扰；

其中A₁₁，A₁₂，A₂₁和A₂₂为惯性正定矩阵的惯性项；

其中B₁₂，B₂₁和B₂₂为科氏离心矩阵的科氏离心项；令sinq_i＝s_i，cosq_i＝c_i，i＝1,2；

i=1,2, where l _ij is the friction parameter, i=1,2, j=1,2,3, v _j is the friction shape parameter; the total disturbance of the two-axis coupled tank gun system d=[d ₁ d ₂ ] ^T , where d ₁ is the horizontal direction interference of the two-axis coupled tank gun system, and d ₂ is the high and low direction interference of the two-axis coupled tank gun system;

where A ₁₁ , A ₁₂ , A ₂₁ and A ₂₂ are the inertial terms of the inertial positive definite matrix;

where B ₁₂ , B ₂₁ and B ₂₂ are the Coriolis centrifugal terms of the Coriolis centrifugal matrix; let sinq _i =s _i , cosq _i =ci , _i =1,2;

Therefore, the parameters of M _a and M _b are expressed by the following formulas:

Wherein I _yy1 , I _xx2 , I _yy2 and I _zz2 are moments of inertia; I _xz2 , I _yz2 , and I _xy2 are inertia tensors.

且令u＝T_i+T_gi，i＝1,2，则式(1)运动方程转化为状态方程：Step 1.2, define state variables:

And let u=T _i +T _gi , i=1,2, then the equation of motion of equation (1) is transformed into the equation of state:

i＝1,2，j＝1,2,3，且定义参数估计为

j＝1,2,3，

是对于θ_j的参数估计值；定义摩擦函数中的函数部分为：

In formula (2), the friction function parameter is defined as

i=1,2, j=1,2,3, and the parameter estimation is defined as

j=1,2,3,

is the parameter estimate for θ _j ; the function part in the definition of the friction function is:

x₁表示坦克炮水平转动角度和方向转动角度所构成的列向量，x₂表示坦克炮水平转动角速度和方向转动角速度所构成的列向量；

x ₁ represents the column vector formed by the horizontal rotation angle and direction rotation angle of the tank gun, and x ₂ represents the column vector formed by the horizontal rotation angular velocity and the direction rotation angular velocity of the tank gun;

To facilitate controller design, the following assumptions are made:

均存在并有界即：Suppose 1 that the total disturbance d=[d ₁ d ₂ ] ^T of the two-axis coupled tank gun system is smooth enough such that

Both exist and are bounded:

具有不确定的上界，In formula (3), the upper bound parameters δ _1i , δ _2i , i=1, 2 are unknown constants, namely

has an indeterminate upper bound,

Go to step 2.

Among them, the total interference of the tank gun system includes external load interference, unmodeled friction, unmodeled dynamics, and the disturbance caused by the deviation of the actual parameters of the system from the modeled parameters.

Step 2. Design the error symbol integral robust adaptive controller, the steps are as follows:

选取x₂为虚拟控制，使方程

趋于稳定状态；令x_2eq为虚拟控制的期望值，x_2eq与真实状态x₂的误差为z₂＝x₂-x_2eq，对z₁求导可得：Step 2.1. Define z ₁ =x ₁ -x _1d as the tracking error of the tank gun system, x _1d is the position command that the tank gun system expects to track, and the command is second-order continuous and differentiable, according to the first in formula (2) equation

Choose x ₂ as the dummy control so that the equation

tends to a stable state; let x _2eq be the expected value of virtual control, the error between x _2eq and the real state x ₂ is z ₂ =x ₂ -x _2eq , and derivation for z ₁ can be obtained:

Design a virtual control law:

k₁₁、k₁₂均为正数，则：Adjustable gain in formula (5)

Both k ₁₁ and k ₁₂ are positive numbers, then:

Since z ₁ (s)=G(s)z ₂ (s), where G(s)=1/(s+k ₁ ) is a stable transfer function, when z ₂ tends to 0, z ₁ also must tend to 0;

Step 2.2. To obtain an additional controller design freedom, define an auxiliary error signal r:

k₂₁、k₂₂均为正数；Adjustable gain in formula (7)

k ₂₁ and k ₂₂ are both positive numbers;

According to equations (2) and (7), there are the following expansions of r:

According to equation (8), the model-based controller can be designed as:

其中k_r1，k_r2均为正的反馈增益，I_m为单位对角阵,u_a为基于模型的补偿项，u_s为鲁棒控制律且其中u_s1为线性鲁棒反馈项，u_s2为非线性鲁棒项用于克服建模不确定性对系统性能的影响，定义参数估计的残差为

j＝1,2,3，将式(9)代入式(8)中得：Formula (9)

where k _r1 and k _r2 are positive feedback gains, _Im is a unit diagonal matrix, u _a is a model-based compensation term, u _s is a robust control law and where u _s1 is a linear robust feedback term, u _s2 For the nonlinear robust term used to overcome the influence of modeling uncertainty on system performance, the residual error of parameter estimation is defined as

j=1, 2, 3, substituting formula (9) into formula (8), we get:

In formula (10), the design parameter adaptive law is:

Γ _i is the adaptive gain, which is constant; since the state of r is unknown, the integral by parts method is used to process it, and then the actual adaptive law is obtained:

According to the error symbol integral robust controller design method, the integral robust term u _s2 is designed as:

β需满足以下条件：Controller gain in equation (11)

β must meet the following conditions:

Among them, β ₁ is the gain in the horizontal direction, and β ₂ is the gain in the high and low directions.

Differentiating both sides of equation (10) and applying equations (7), (12) and (13), we get:

定义误差参量为Z＝[z₁ z₂ r]^T，由

结构可得，一定存在全局可逆非减正函数ρ(||Z||)∈R⁺使得：In the formula, the unestimable term

Define the error parameter as Z=[z ₁ z ₂ r] ^T , given by

The structure can be obtained, there must be a globally invertible non-decreasing positive function ρ(||Z||)∈R ⁺ such that:

Go to step 3.

Step 3. Use the Lyapunov stability theory to prove the stability, and introduce the Barbalat lemma to obtain the result of the global asymptotic stability of the system, as follows:

Define auxiliary functions L(t), P(t):

分别表示z₂和

的初始值；z ₂ (0),

denote z ₂ and

the initial value of ;

时，P(t)≥0。proven when

When , P(t)≥0.

Proof of this lemma:

Integrate both sides of Equation (19) and apply Equation (7) to get:

Integrating Eq. (20) by parts can get:

Therefore

所示的条件时，P(t)≥0成立，即引理得证。It can be seen from formula (22) that if the selection of β satisfies the formula

When the conditions shown, P(t)≥0 is established, that is, the lemma is proved.

P(t)≥0，因此定义李雅普诺夫函数如下：According to the above proof, it can be seen that when

P(t)≥0, so the Lyapunov function is defined as follows:

Taking the derivative of equation (23) and substituting equations (6), (7), (16), and (22) into equations (23), we can get:

则：also because

but:

为保证

的半负定行，需要r≥0，即

由式(25)可知

V(t)≤V(0)，因此V∈L_∞范数，进而可以得出z₁，z₂，r均有界。where parameters

to guarantee

The semi-negative definite line of , requires r ≥ 0, i.e.

From formula (25), it can be known that

V(t)≤V(0), so V∈L _∞ norm, and it can be concluded that z ₁ , z ₂ , and r are bounded.

Integrating Equation (25) can get:

From equation (25), it can be known that z ₁ , z ₂ , r∈L ₂ norm, and according to equations (6), (7), (13) and assumption 1, we can get:

范数，因此W是一致连续的，由Barbalat引理可知：t→∞时，W→0。故t→∞时，z₁→0。

norm, so W is consistent and continuous, according to Barbalat's lemma: when t→∞, W→0. Therefore, when t→∞, z ₁ →0.

Therefore, there is a conclusion: the error symbol integral robust controller designed for the two-axis coupled tank gun (2) can make the system obtain a globally asymptotically stable result, and adjusting the gains k ₁ , k ₂ , k _r and β can make the system track The error tends to zero under the condition that time tends to infinity. The schematic diagram of the control principle of the two-axis coupled tank gun system error sign integral robust self-adjustment (RISEA) is shown in Figure 2.

Example

In order to evaluate the performance of the designed controller, the following parameters are taken to model the two-axis coupled tank gun system in the simulation:

The inertia tensor matrix parameters are: I _yy1 =2547kg·m ² , I _xx2 =5400kg·m ² , I _yy2 =5443kg, I _zz2 =224kg·m ² , I _xy2 =-2.8kg·m ² , I _yz2 =13.7 kg·m ² , I _zx2 =0.8kg·m ² ; the shape parameters in the lugre friction model are: v ₁ =200, v ₂ =10, v ₃ =160.

The expected instructions for a given system are

The system operating conditions of this simulation are time-varying disturbances:

Take the following controllers for comparison:

Error Sign Integral Robust Self-Adjusting (RISEA) controller: take the controller parameters k ₁₁ =150, k ₁₂ =15, k _r =50000; β ₁ =100, k ₁₁ =150, k ₁₂ =10, k _r = 50000, β ₂ =100; the adaptive gain is Γ ₁ =diag[80 300], Γ ₂ =diag[8 25], Γ ₁ =diag[1.8 8].

PID controller: The selection steps of the PID controller parameters are as follows: first, in the case of ignoring the nonlinear dynamics of the two-axis coupled tank gun system, a set of controller parameters are obtained through the PID parameter self-tuning function in Matlab, and then the system is adjusted. After the nonlinear dynamic is added, the obtained self-tuning parameters are fine-tuned so that the system can obtain the best tracking performance. The controller parameters of the selected high and low directions are k _P =318000, k _I =100, k _D =120000; the selected controller parameters of the horizontal direction are k _P =220000,k _I =100,k _D =850000;

The tracking of the system output to the desired command under the action of the RISEA controller is shown in Figure 3 and Figure 4. It can be seen that the expected command and the system output basically overlap and have good tracking performance; the tracking error of the RISEA controller, the RISE controller and the PID control The tracking errors of the sensors are compared in Figure 5, Figure 6, Figure 7, and Figure 8, respectively. It can be seen from Figure 5 and Figure 6 that under the action of the RISEA controller, the position output of the direct drive motor system has a high tracking accuracy for the command, and the amplitude of the steady-state tracking error is about 1×10 ^-4 (rad). 7 and Fig. 8 compare the tracking errors of the two controllers, it can be seen that the tracking error of the RISEA controller proposed by the present invention is much smaller than that of the PID controller, and the magnitude of the steady-state tracking error of the PID controller is about 2.1×10 ^-2 (rad), and compared with the RISE algorithm, its tremor is also reduced a lot.

Figures 9 to 14 are the curves of the estimated value of the gain θ of the RISEA controller of the present invention changing with time. It can be seen from the figures that although the initial value of the gain is given by people based on experience, due to the effect of the adaptive law, The gain value will automatically converge to an appropriate value over time, so on the basis of the traditional RISE algorithm, the friction parameters of the model can be more perfected, and the performance can be improved for practical system applications.

时RISEA控制器作用下两轴耦合坦克炮控制输入随时间变化的曲线图。从图中可以看出，所获得的控制输入是低频连续的信号，更利于在实际应用中的执行。Figure 15 and Figure 16 are the system interference as

The curve diagram of the control input of the two-axis coupled tank gun under the action of the RISEA controller over time. As can be seen from the figure, the obtained control input is a low-frequency continuous signal, which is more conducive to the implementation in practical applications.

Claims (2)

1. An error sign integral robust self-adaptive control method of a two-axis coupling tank gun system is characterized by comprising the following steps of:

Step 1, establishing a mathematical model of dynamics of a two-axis coupling gun system, which comprises the following steps:

step 1.1, considering a dynamic model modeling thought, integrating a modeling thought of a mechanical arm, and establishing a dynamic model of the tank gun by adopting a Lagrange-Euler method:

therefore, according to the Lagrange-Euler method, the kinetic equation of a two-axis coupled tank gun system is as follows:

in the formula (1), the rotation angle is q ═ q₁ q₂]^TWherein q is₁For the horizontal rotation angle, q, of a two-axis coupled tank gun system₂The two shafts are coupled with the rotation angle of the tank gun system in the height direction; m is a group of_a∈R^2×2Is an inertia symmetric positive definite matrix; m_b∈R^2×2Is a Coriolis force centrifugation matrix; m_g∈R^2×1Is a moment of gravity vector, M_g＝[T_g1 T_g2]^T，T_g1The two-axis coupled tank gun system is the gravity moment, T, in the horizontal direction_g1＝0，T_g2Coupling the gravity moment of the tank gun system in the height direction for two shafts; tank gun system input T ═ T₁ T₂]^TWherein T is₁For horizontal input, T, of a two-axis coupled tank gun system₂The input torque in the height direction of the two-axis coupling tank gun system is obtained; friction torque T_f＝[T_f1 T_f2]，T_f1Moment of resistance, T, generated by friction in the horizontal direction of a two-axis coupled tank gun system_f2Resistance moment generated by friction force in high and low directions of two-shaft coupled tank gun system, T_fAdopting a lugre model to carry out fitting approximation:

Wherein l_ijThe friction parameter is i-1, 2, j-1, 2,3, the friction shape parameter v_j(ii) a Total interference d ═ d of system error of two-axis coupling tank gun₁ d₂]^TWherein d is₁For horizontal interference of a two-axis coupled tank gun system, where d₂The two shafts are coupled with the interference of the tank gun system in the high and low directions;

wherein A is₁₁、A₁₂、A₂₁And A₂₂The inertia terms are inertia positive definite matrixes;

wherein B is₁₂、B₂₁And B₂₂A coriolis centrifuge term that is a coriolis centrifuge matrix; let sin q_i＝s_i，cos q_i＝c_i，i＝1,2；

Therefore M_aAnd M_bWherein the parameters are expressed by the formula:

A₁₂(q)＝A₂₁(q)＝s₂I_yz2-c₂I_xy2，A₂₂＝I_yy2；

wherein I_yy1、I_xx2、I_yy2And I_zz2Are rotational inertia; i is_xz2、I_yz2、I_xy2Are all inertia tensors;

step 1.2, defining state variables:

and let u be T_i+T_giAnd i is 1,2, the equation of motion of formula (1) is converted into an equation of state:

in the formula (2), the friction function parameter is defined as

And defining a parameter estimate of

Is for theta_jThe parameter estimation value of (2); the functional part of the friction function is defined as:

x₁a column vector, x, representing the horizontal and directional angles of rotation of the tank gun₂A column vector which represents the horizontal rotation angular velocity and the direction rotation angular velocity of the tank gun;

for the controller design, assume the following:

assume that 1: total interference d ═ d of two-axis coupling tank gun system₁ d₂]^TIs sufficiently smooth to make

Are present and bounded i.e.:

The upper bound parameter in formula (3) is δ_1i、δ_2iI is 1 and 2 are unknown normal numbers, i.e.

If the upper bound is uncertain, the step 2 is carried out;

step 2, designing an error symbol integral robust self-adaptive controller, comprising the following steps:

step 2.1, defining the tracking error z of the tank gun system₁＝x₁-x_1d，x_1dIs a position instruction which is expected to be tracked by the tank gun system and the second order of the instruction can be continuously microminiaturized according to the first equation in the formula (2)

Selecting x₂For virtual control, let equation

Tends to a stable state; let x_2eqFor desired values of virtual control, x_2eqAnd the true state x₂Has an error of z₂＝x₂-x_2eqTo z is to₁The derivation can be:

designing a virtual control law:

adjustable gain in formula (5)

k₁₁、k₁₂Are positive numbers, then:

due to z₁(s)＝G(s)z₂(s) wherein G(s) is 1/(s + k)₁) Is a stable transfer function when z₂When going to 0, z₁Also necessarily tends to 0;

step 2.2, to obtain an additional degree of freedom of controller design, defining an auxiliary error signal r:

adjustable gain in formula (7)

k₂₁、k₂₂Are all positive numbers;

according to equations (2) and (7), there is an expansion of r as follows:

according to equation (8), the model-based controller is designed to:

in the formula (9)

Wherein k is_r1，k_r2All are positive feedback gains, I_mIs a unit diagonal matrix, u_aFor model-based compensation terms, u_sIs a robust control law, and u _s1For a linear robust feedback term, u_s2Is a nonlinear robust term for overcoming the influence of modeling uncertainty on the system performance, and the residual error of parameter estimation is defined as

Substituting formula (9) into formula (8) to obtain:

the parameter adaptation law is designed in equation (10) as follows:

Γ_iare adaptive gains, all are constants; since the state of r is unknown, the state is processed by a fractional integration method, and an actual adaptive law is obtained:

according to the design method of an error sign integral robust controller, an integral robust term u_s2The design is as follows:

controller gain in equation (11)

Beta should satisfy the following condition:

wherein beta is₁For the controller gain in the horizontal direction, beta₂Gain is the high and low direction of the controller;

the two-sided derivation of the equation of equation (10) and the use of equations (7), (12) and (13) can be obtained:

in the formula, the term is not estimated

Defining an error parameter as Z ═ Z₁ z₂ r]^TFrom

The structure can be obtained, and a global reversible non-subtractive function rho (| | Z |) is formed for R⁺Such that:

turning to the step 3;

step 3, stability is proved by applying Lyapunov stability theory, and a global asymptotic stability result of the system is obtained by introducing barbalt theorem, which is concretely as follows:

defining the auxiliary functions L (t), P (t):

z₂(0)、

respectively represents z₂And

an initial value of (1);

is proved to be when

When P (t) ≧ 0, the Lyapunov function is thus defined as follows:

The Lyapunov stability theory is applied to carry out stability verification, and the Barbalt theorem is applied to obtain the global asymptotic stability result of the system, so that the gain k is adjusted₁、k₂、k_rThe tracking error of the tank gun system tends to zero under the condition that the time tends to infinity.

2. The adaptive control method for the error sign integral robustness of the two-axis coupling tank gun system according to claim 1, characterized in that: in step 1.2, the total interference of the tank gun system comprises the interference caused by external load interference, unmodeled friction, unmodeled dynamic state and the deviation of the actual parameters and the modeling parameters of the system.

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