Hyperbolic continuous robust control method for vertical system of special vehicle launching tube

Abstract

The invention discloses a hyperbolic continuous robust control method for a vertical system of a special vehicle launching tube, which is based on the characteristic of external interference suppression in traditional sliding mode control, combines the smooth characteristic of a hyperbolic tangent function, and achieves the robust control of the vertical system of the launching tube under the condition that strong uncertainty nonlinearity and strong external interference exist in the system. The system flutter phenomenon can be prevented while nonlinearity is compensated and interference is suppressed, the control precision is effectively improved, the error convergence time is shortened, the tracking performance is improved, and finally an exponential stable error convergence result is obtained. Compared with the prior art, the control method disclosed by the invention effectively solves the problems caused by strong nonlinearity and strong external interference of the vertical stabilization system of the special vehicle launching tube, so that the control precision of the whole system is improved, and good tracking performance is obtained.

Description

Technical Field

[0001] The invention relates to the technical field of motion control, and in particular to a hyperbolic continuous robust control method for a vertical stabilization system of a launch tube of a special vehicle. Background Art

[0002] Special vehicles are tracked armored combat vehicles that are mainly used by the army for ground assaults. They have high mobility and off-road capabilities, hard armor protection, and strong firepower. They are one of the main weapons and equipment for modern land warfare. Special vehicles mainly attack targets by launching shells through the special vehicle launch tubes they carry. It can undertake combat missions in a variety of complex terrains. It is mainly used to fight against enemy armored vehicles. It can also suppress other launch tube equipment, destroy enemy field fortifications, and annihilate enemy manpower. Digitalization, high mobility, and high precision will definitely be the development direction of the next generation of main combat special vehicles. It is necessary to further improve the fire control computer's control performance of the launch tube, as well as the ability to capture and process battlefield information. This is of great significance to improving the survivability of special vehicles on the battlefield and improving the first-shot hit capability under high mobility conditions.

[0003] In the prior art, the control methods for the special vehicle launch tube vertical system are: (1) PID controller designed based on classical control theory. The PID algorithm can achieve a certain control effect for the entire system, but it cannot effectively compensate for the random disturbances generated by the outside world during the travel process, thereby restricting the performance of the special vehicle launch tube vertical system; (2) Adaptive control method. The adaptive control method is a very effective method for dealing with parameter uncertainty problems and can obtain steady-state performance of asymptotic tracking. However, it is powerless when facing uncertainty nonlinearities such as reducer tooth backlash in the special vehicle launch tube vertical system. When the uncertainty nonlinearity is too large, the system may become unstable. (3) Sliding mode control method. Classical sliding mode control can effectively deal with any bounded modeling uncertainty and obtain steady-state performance of asymptotic tracking. However, the discontinuous controller designed by classical sliding mode control is prone to cause the flutter problem of the sliding mode surface. Therefore, in the actual system, especially the special vehicle launch tube vertical system adopted in this paper, this shortcoming will be continuously amplified, resulting in a more obvious system flutter effect. The muzzle jitter will increase during the adjustment of the launch tube firing angle, which has a great impact on the overall control accuracy.

[0004] In summary, the existing control methods have the problem of being unable to simultaneously achieve multiple control effects such as effectively suppressing external interference, dealing with backlash nonlinearity, and solving system chatter. In actual systems, the existence of each problem will have a great impact on control accuracy. Summary of the invention

[0005] In view of the above problems, the present invention provides a hyperbolic continuous robust control method for the vertical system of a special vehicle launch tube. Based on the hyperbolic continuous robust control method, the influence of tooth clearance nonlinearity is taken into account in the presence of external interference, and the problem of system flutter existing in the classical sliding film control in the control of the vertical system of the special vehicle is solved.

[0006] The technical solution to achieve the purpose of the present invention is: a hyperbolic continuous robust control method for a special vehicle launch tube vertical system, comprising the following steps:

[0007] Step 1, establishing a mathematical model of the dynamics of the vertical system of the special vehicle launch tube;

[0008] Step 2: Design a hyperbolic continuous robust controller; the control input u of the controller is:

[0009]

[0010] Where k is the gain, is the measurement parameter, z 2 is the virtual error, -kz 2 is the linear robust feedback term, is the model compensation term, is the derivative of the expected value of the virtual control, θ T is the determination parameter vector, x 1 is the state variable 1, x 2 is state variable 2, is a function of the state variable, u s is the interference suppression term;

[0011] Step 3: Use Lyapunov stability theory to prove the stability and introduce Barbalat’s lemma to obtain the result of global asymptotic stability of the system.

[0012] Compared with the prior art, the present invention has the following significant advantages: the present invention is based on the hyperbolic continuous robust controller design method,

[0013] The precise control of the special vehicle launch tube vertical system is achieved, which solves the problem that the traditional control method cannot simultaneously achieve multiple control effects such as effectively suppressing external interference, handling tooth gap nonlinearity, and solving system flutter for the special vehicle launch tube vertical system in this article. It effectively improves the control accuracy, reduces the error convergence time, and improves the tracking performance and the ability to resist external errors. The simulation results verify its effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic diagram of the principle of the hyperbolic continuous robust control method of the vertical system of the launch tube of a special vehicle of the present invention;

[0015] Figure 2 It is a schematic diagram of the vertical system of the launch tube of a special vehicle;

[0016] Figure 3 A diagram showing the tracking process of the system's vertical output to the desired command under the action of the hyperbolic continuous robust controller designed by the present invention;

[0017] Figure 4 It is a curve diagram of the tracking error of the system in the vertical direction changing with time under the action of the hyperbolic continuous robust controller;

[0018] Figure 5 It is a comparison curve of the tracking error in the vertical direction of the system under the action of hyperbolic continuous robust controller and PID controller respectively when the system disturbance is D(t)=50sin2πt(N·m). DETAILED DESCRIPTION

[0019] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Combination Figure 1-Figure 2 The hyperbolic continuous robust control method of the special vehicle launch tube vertical system of the present invention comprises the following steps:

[0021] Step 1: Establish a mathematical model of the dynamics of the vertical system of the special vehicle launch tube, as follows:

[0022] Step 1.1, considering the dynamic coupling characteristics between the servo motor-reducer-screw-cradle, the dynamic model of the special vehicle launch tube is established using classical mechanics theory:

[0023] Therefore, according to Newton's second law, the moment balance equation of the cradle is:

[0024]

[0025] In formula (1), q, They respectively represent the pitch angle, angular velocity and angular acceleration of the cradle; J represents the moment of inertia of the pitch part relative to the ear axis; F represents the thrust of the electric cylinder; Δ(q) represents the force arm of the electric cylinder thrust F, which is a variable that changes with the pitch angle; m represents the total mass of the pitch part; g represents the acceleration of gravity; l represents the distance from the total center of mass of the pitch part to the ear axis of the pitch part.

[0026] The force arm Δ(q) of the electric cylinder can be expressed as follows according to the geometric relationship:

[0027]

[0028] In the formula, l 1 and l 2 Respectively represent the distance between the rotary axis and the ear axis of the upper and lower fulcrums of the electric cylinder; l0 It is the initial installation length of the electric cylinder; is the initial installation angle of the electric cylinder.

[0029] The push-out distance y of the electric cylinder can be expressed as:

[0030]

[0031] Ignoring the influence of the flexibility factor of the special vehicle launch tube, the load dynamic equation of the vertical stabilizer of the special vehicle launch tube is established:

[0032]

[0033] In the formula, q, The meanings of parameters such as J, F, Δ(q), m, g, and l are the same as those in formula (1); B is the viscous friction coefficient; d(t) represents the unmodeled error and external disturbance.

[0034] Establish the dynamic equation on the output shaft of the electric cylinder servo motor:

[0035]

[0036] In formula (5), q m , and Respectively represent the angle, angular velocity and angular acceleration of the servo motor output shaft; J m Indicates the motor shaft moment of inertia; B m is the viscous friction coefficient of the motor shaft; T m is the gear reducer input torque; T e is the electromagnetic torque of the motor, which is proportional to the motor armature current i, that is,

[0037] T e =k t i(6)

[0038] In the formula, k t is the motor torque coefficient, and i is the motor armature current.

[0039] Define the stator voltage u as the control input, and the motor equivalent voltage balance equation can be listed as:

[0040]

[0041] Where, u represents the motor control input voltage (control input); R and L represent the motor armature resistance and inductance respectively; k e Represents the motor back electromotive force coefficient. In the actual system, if is small, then the derivative of the current is tends to 0, so the motor electromagnetic torque of equation (7) can be further expressed as:

[0042]

[0043] There is a gear reducer inside the electric cylinder. In order to ensure the normal rotation of the gears, a small gap is usually left between the gears. In order to facilitate the design of the controller, the influence of the nonlinearity of the tooth gap is regarded as the transmission error of the transmitted torque, and the output torque τ(t) of the gear reducer can be expressed by the following formula:

[0044] τ(t)=NT m +d t (t) (9)

[0045] Where N is the reduction ratio of the gear reducer; d t (t) represents the transmission error caused by the nonlinearity of tooth backlash.

[0046] Next, the equation for the ball screw in the electric cylinder to convert the torque τ(t) into thrust F can be expressed as:

[0047]

[0048] Where, η represents the total efficiency of the electric cylinder; p h Indicates the lead of the screw.

[0049] The corresponding relationship between the rotation angle of the servo motor output shaft and the pitch angle is as follows:

[0050]

[0051] In the formula, q m represents the angle of rotation of the servo motor output shaft, N is the deceleration of the gear reducer, and y represents the distance pushed out by the electric cylinder, see formula (3). By taking the derivative of formula (11) twice, we can get the angular velocity of the servo motor output shaft: and angular acceleration for:

[0052]

[0053]

[0054] Finally, combining equations (5), (8) to (10), (12) and (13), we can get the thrust F of the electric cylinder as:

[0055]

[0056] In the formula,

[0057]

[0058] f 1 、f 2 、f3 Define variables for the intermediate.

[0059] Substituting equation (14) into equation (4) yields the input-load dynamic equation:

[0060]

[0061] Step 1.2, define state variables: Then the equation of motion in formula (18) can be rewritten as the following state space equation form:

[0062]

[0063] In the formula, are all measurement parameters, They are state variables x 1 、x 2 The derivative of represents the total unmodeled disturbance of the system.

[0064] To facilitate controller design, the following assumptions are made:

[0065] Assumption 1: The total disturbance D(t) of the vertical system of the special vehicle launch tube has an upper bound:

[0066] |D(t)|≤δ (20)

[0067] Assume that δ in equation (3) is a known constant and proceed to step 2.

[0068] Among them, the total interference of the special vehicle gun system includes the unmodeled error and external disturbance d(t), the transmission error d caused by the nonlinearity of the tooth gap t (t).

[0069] Step 2: Design a hyperbolic continuous robust controller. The steps are as follows:

[0070] Step 2.1: Define the tracking error z of the special vehicle launch tube vertical system 1 =x 1 -x 1d , x 1d is the position command that the special vehicle launch tube vertical system expects to track, and the command is second-order continuously differentiable. According to the first equation in equation (19): Select x 2 For virtual control, make the equation Tend to a stable state; let x 2eq is the expected value of the virtual control, x 2eq With the real state x 2 The error is z 2 =x 2 -x 2eq , for z1 The derivative is:

[0071]

[0072] Design of virtual control law:

[0073]

[0074] In formula (22), the adjustable gain k is a positive number, then:

[0075]

[0076] Because z 1 (s) = G(s)z 2 (s), where G(s) = 1 / (s+k) is a stable transfer function. 2 When z approaches 0, 1 It will inevitably tend to 0;

[0077] Right 2 The derivative is:

[0078]

[0079] In formula (24), θ T =[g 2 g 3 g 4 ], g 1 , g 2 , g 3 , g 4 The meaning is the same as formula (19);

[0080] Step 2.2, design the control input u:

[0081]

[0082] In formula (25), k is the gain, which can be adjusted according to the control effect. is the measurement parameter, z 2 is the virtual error, -kz 2 is the linear robust feedback term, is the model compensation term, is the derivative of the expected value of the virtual control, θ T is the determination parameter vector, x 1 is the state variable 1, x 2 is state variable 2, is a function of the state variable, u s is the interference suppression term;

[0083] is the model compensation term, substituting formula (25) into formula (24) to obtain:

[0084]

[0085] According to the hyperbolic continuous robust controller design method, the disturbance rejection term u s Designed for:

[0086]

[0087] In formula (27), δ is the upper bound of the known interference, and γ is a positive constant. Go to step 3.

[0088] Step 3: Use Lyapunov stability theory to prove the stability and get the result of exponential stability of the system. The details are as follows: Use Lyapunov stability theory to prove the stability and use Barbalat lemma to get the result of global asymptotic stability of the system. Therefore, adjust the gain k 1 , k 2 Make the tracking error of the special vehicle gun system approach zero when time approaches infinity. Specifically:

[0089] The Lyapunov function is defined as follows:

[0090]

[0091] Deriving equation (28) and substituting equations (23), (26), and (27) into equation (28) yields:

[0092]

[0093] And because of the following inequality:

[0094] z 2 D-δtanh(δz 2 / γ)≤γκ 0

[0095]

[0096] In the formula, γ is an adjustable parameter and the constant κ is 0 =0.2785, using formula (30):

[0097]

[0098] Right now:

[0099]

[0100] Design Gain Solving inequality (32) yields:

[0101]

[0102] From formula (33), we can know V gradually decreases to 0 in exponential form. When t→∞, V→0, so when t→∞, z 1 →0,z 2 →0.

[0103] Therefore, it is concluded that the hyperbolic continuous robust controller designed for the special vehicle launch tube vertical system can make the system obtain a global asymptotically stable result, and adjusting the gains k and γ can make the system error approach zero under the condition that the actual value approaches infinity. Figure 2 shown.

[0104] Example

[0105] In order to evaluate the performance of the designed controller, the following parameters are taken in the simulation to model the vertical system of the special vehicle launch tube: m = 2048.7 kg, g = 9.8 kg·m / s, J = 3448 kg·m 2 , l=0.12m,l 0 =0.40m,l 1 =0.32m,l 2 =0.44m, η=0.85, N=5, P h =16mm, k t =1.54N·m / A, k e =0.89V·s / rad, R=0.41Ω, B=0.0015N·m·s / rad, B m =0.001N·m·s / rad, J m =0.002kg·m 2 .

[0106] Given a system with the expected instruction x 1d =0.1sin(t)(rad).

[0107] The system condition of this simulation is time-varying disturbance: D(t) = 50sin2πt(N·m)

[0108] Take the following controller for comparison:

[0109] Hyperbolic continuous robust controller: Take controller parameters k=26, γ=0.5.

[0110] PID controller: The steps for selecting PID controller parameters are: first, ignoring the nonlinear dynamics of the vertical system of the special vehicle launch tube, a set of controller parameters are obtained through the PID parameter self-tuning function in Matlab, and then the self-tuning parameters are fine-tuned after adding the nonlinear dynamics of the system to obtain the best tracking performance. The selected vertical controller parameters are k P =-2000,k I =-180,k D =-1200.

[0111] The tracking of the system output to the expected command under the action of the hyperbolic continuous robust controller is as follows: Figure 3 As shown in Figure 1, it can be seen that the expected command and system output basically coincide with each other, and it has good tracking performance. The tracking error comparison between the hyperbolic continuous robust controller and the PID controller is shown in Figure 1. Figure 4 , Figure 5 As shown. Figure 4 It can be seen that under the action of the hyperbolic continuous robust 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 3.5×10 -4 (rad), from Figure 5 The comparison of the tracking errors of the two controllers shows that the tracking error of the hyperbolic continuous robust controller proposed in this invention is much smaller than that of the PID controller. The amplitude of the steady-state tracking error of the PID controller is about 6.4×10 -3 (rad).

Claims

1. A hyperbolic continuous robust control method for a special vehicle launch tube vertical system, characterized in that: The following steps are involved: Step 1, establishing a mathematical model of the dynamics of the vertical system of the special vehicle launch tube; Step 2: Design a hyperbolic continuous robust controller; the control input u of the controller is: Where k is the gain, is the measured parameter, z2 is the virtual error, -kz2 is the linear robust feedback term, is the model compensation term, is the derivative of the expected value of the virtual control, θ T is the measured parameter vector, x1 is state variable 1, x2 is state variable 2, is a function of the state variable, u s is the interference suppression term; Step 3: Use Lyapunov stability theory to prove the stability and introduce Barbalat’s lemma to obtain the result of global asymptotic stability of the system.

2. The hyperbolic continuous robust control method for the vertical system of the launch tube of a special vehicle according to claim 1 is characterized in that: In step 1, the input-load dynamic equation of the special vehicle launch tube vertical system is established as: Where, J represents the moment of inertia of the pitch part relative to the ear axis; F represents the thrust of the electric cylinder; Δ(q) represents the force arm of the electric cylinder thrust F, which is a variable that changes with the pitch angle; m represents the total mass of the pitch part; g represents the gravitational acceleration; l represents the distance between the total center of mass of the pitch part and the ear axis of the pitch part, q, They represent the cradle pitch angle, angular velocity and angular acceleration respectively, Δ(q) is the force arm of the electric cylinder, η represents the total efficiency of the electric cylinder; p h represents the lead of the screw, N is the reduction ratio of the gear reducer; k t is the motor torque coefficient, u is the motor control input voltage; R and L are the motor armature resistance and inductance respectively; B is the viscous friction coefficient; d(t) is the unmodeled error and external disturbance, d t (t) represents the transmission error caused by nonlinear backlash; f1, f2, and f3 are intermediate defined variables.

3. The hyperbolic continuous robust control method for the vertical system of the special vehicle launch tube according to claim 2 is characterized in that: In the vertical system of the special vehicle launch tube, there is a gear reducer inside the electric cylinder. In order to ensure the normal rotation of the gears, a gap is set between the gears. In order to facilitate the design of the controller, the nonlinear influence of the gear gap is regarded as the transmission error of the transmitted torque. The output torque τ(t) of the gear reducer is expressed by the following formula: τ(t)=NT m +d t (t) Where, T m is the input torque of the gear reducer, N is the reduction ratio of the gear reducer; d t (t) represents the transmission error caused by the nonlinearity of tooth backlash; The equation for converting the torque τ(t) into thrust F by the ball screw is expressed as: Where, η represents the total efficiency of the electric cylinder; p h Indicates the lead of the screw.

4. The hyperbolic continuous robust control method for the vertical system of the launch tube of a special vehicle according to claim 2 is characterized in that: Define the state variables: Then the state space equation of the vertical system of the special vehicle launch tube is: In the formula, represents the total unmodeled disturbance of the system.

5. The hyperbolic continuous robust control method for the vertical system of the launch tube of a special vehicle according to claim 4 is characterized in that: In step 2, the tracking error z1 of the vertical system of the special vehicle launch tube is defined as 1d , x 1d It is the position instruction that the vertical system of the special vehicle launch tube expects to track, and the instruction is second-order continuously differentiable. Select x2 as the virtual control, so that the equation Tend to a stable state; let x 2eq is the expected value of the virtual control, x 2eq The error from the true state x2 is z2 = x2-x 2eq , and take the derivative of the tracking error z1 to obtain: Design of virtual control law: In the formula, the gain k is a positive number.

6. The hyperbolic continuous robust control method for the vertical system of the launch tube of a special vehicle according to claim 1 is characterized in that: Interference suppression term u s for: Where δ is the upper bound of the known interference and γ is a positive constant.

7. The hyperbolic continuous robust control method for the vertical system of the launch tube of a special vehicle according to claim 1 is characterized in that: In step 3, the Lyapunov function is: In the formula, V gradually decreases to 0 in an exponential form. When t→∞, V→0, so when t→∞, z1→0, z2→0.

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