A predetermined time dynamic surface control method for a special vehicle horizontal system

Abstract

The application discloses a predetermined time dynamic surface control method for a horizontal system of a special vehicle, introduces a time-varying coordination function and a first-order filter to construct a dynamic surface error, and guarantees that the system reaches an expected state within any predetermined time. The control method is proposed for the following problems: as modern combat puts forward higher requirements for the control of the horizontal system of the special vehicle, the requirements cover high precision, high aiming speed and strong disturbance resistance capability. However, the control methods used by the horizontal system of the special vehicle in the past do not have the capability of tracking a specified signal at any time, some control methods have the problem of discontinuous control input, and few of them have the strong disturbance resistance capability. Compared with the prior art, the control method disclosed by the application effectively solves the problems of the high precision, the high aiming speed, the strong disturbance resistance capability and the continuous control input of the horizontal system of the special vehicle, so that the control precision of the system is improved, and good tracking performance is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of motion control, and particularly relates to a predetermined time dynamic surface control (DSCPT) method of a horizontal system of a special vehicle. BACKGROUND

[0002] With the informatization and unmannedization of future battlefields, special vehicles are required to develop towards high mobility, high precision and high stability, which puts forward higher requirements for the stability of the launch rotating body and the rapid aiming of the special vehicle in the process of high-speed driving. The horizontal system of the modern special vehicle is divided into hydraulic type and electric type. The traditional hydraulic stabilization system has the outstanding shortcomings of low efficiency, large noise and high heat. The electric type not only overcomes the above-mentioned shortcomings, but also has low cost and high efficiency, and is the main development direction of the horizontal stabilization system at present. However, the horizontal system of the electric special vehicle has stronger nonlinearity and electromechanical coupling. In addition, the combat environment of the special vehicle on the battlefield is particularly complex, and the first enemy fire will bring significant tactical advantages, and even directly affect the battle result. This puts forward higher requirements for the rapidity and stability of the horizontal system.

[0003] In the past few decades, researchers have made many contributions to the design of the controller of the horizontal system. The PID controller is the most classic controller, and its design is based on the linear system. It is one of the controllers widely used in the horizontal system of the special vehicle at present. So far, researchers have proposed a series of control strategies to improve the PID controller, such as fuzzy PID control, adaptive PID control, fractional order PID control, etc. However, in the actual horizontal stabilization system, the PID control is difficult to compensate for a large number of nonlinear factors. Therefore, the nonlinear controller based on the model has become the research direction of the control of the horizontal system of the special vehicle at present. In order to solve the problem of unknown parameters in the system, nonlinear adaptive control has been widely applied to the special vehicle system. However, adaptive control depends on the accuracy of the model. When there is a large external disturbance in the horizontal system, the model will produce a certain error, which makes the system unstable.

[0004] In order to solve the above-mentioned problems and further enhance the robustness when dealing with parameter uncertainty and uncertain nonlinearity, various robust control methods have been applied to adaptive control. Adaptive robust control combines adaptive control and nonlinear robust terms to deal with the parameter uncertainty and unmodeled disturbance of the horizontal system respectively. This strategy not only retains the advantages of adaptive control, but also overcomes external disturbances by carefully designing nonlinear robust terms.

[0005] However, in the presence of disturbance, adaptive robust control can only guarantee the tracking error to be bounded. To solve this problem, a robust integral feedback control of error sign is proposed, which obtains asymptotic control effect for bidirectional stabilization system with various uncertainties. But this control strategy requires the second derivative of disturbance to be bounded. In addition, in order to effectively deal with various uncertainties of special vehicle stabilization system, a method based on state observer is proposed. The adaptive anti-disturbance control strategy combines adaptive control and active disturbance rejection control organically. This strategy uses adaptive principle to deal with unknown parameters, and the remaining uncertainties of the system are estimated by the extended state observer. In addition, other control strategies such as RBF neural network control and fuzzy sliding mode control are also used to compensate for unknown disturbance, and have been applied to other mechanical power systems. However, all the above control methods can only ensure to meet the performance requirements as time tends to infinity. SUMMARY

[0006] The present application aims to provide a predetermined time dynamic surface control method for a special vehicle horizontal system, which is based on the backstepping method and combines the dynamic surface control method to design a controller that can predefine the time for the tracking error to reach a specified range, and the controller gain contains a continuous hyperbolic tangent function to suppress the total disturbance, effectively solving the rapid aiming problem of the special vehicle horizontal system and obtaining better tracking performance.

[0007] The technical solution for achieving the purpose of the present application is a predetermined time dynamic surface control method for a special vehicle horizontal system, comprising the following steps:

[0008] Step 1, establishing a mathematical model of the special vehicle horizontal system;

[0009] Step 2, designing a predetermined time dynamic surface controller; a composite dynamic surface error is introduced into the controller to realize the stabilization of the special vehicle horizontal system in any predetermined time;

[0010] Step 3, using Lyapunov stability theory to prove stability and obtain the result of global stability of the system in predetermined time.

[0011] Compared with the prior art, the present application has the following advantages:

[0012] (1) By introducing dynamic surface error and time-varying coordination function, the problem that the existing control method cannot realize the stabilization of the special vehicle horizontal system in any predetermined time is effectively solved.

[0013] (2) By constructing a hyperbolic tangent term, the problems of continuous input and anti-disturbance of the controller are solved. BRIEF DESCRIPTION OF DRAWINGS

[0014] Figure 1 is a schematic diagram of the predetermined time dynamic surface (DSCPT) control method for the special vehicle horizontal system of the present application;

[0015] Figure 2 is a schematic diagram of a special vehicle horizontal system;

[0016] Figure 3 is a tracking process diagram of a sinusoidal expected command under the action of four predetermined time DSCPT controllers designed by the present application;

[0017] Figure 4 is a tracking error diagram of a sinusoidal expected command under the action of four predetermined time DSCPT controllers;

[0018] Figure 5 is a tracking process diagram of a straight line expected command under the action of four predetermined time DSCPT controllers designed by the present application;

[0019] Figure 6 is a tracking error diagram of a straight line expected command under the action of four predetermined time DSCPT controllers;

[0020] Figure 7 is a tracking error diagram of a straight line expected command under the action of four predetermined time DSCPT controllers when the disturbance is 1000 times;

[0021] Figure 8 is a tracking error diagram of a straight line expected command under the action of 1s predetermined time;

[0022] Figure 9 is a tracking error diagram of a straight line expected command under the action of 2s predetermined time;

[0023] Figure 10 is a tracking error diagram of a straight line expected command under the action of 3s predetermined time;

[0024] Figure 11 is a tracking error diagram of a straight line expected command under the action of 6s predetermined time; DETAILED DESCRIPTION

[0025] The present application will be further described in detail below in combination with the accompanying drawings and specific embodiments.

[0026] In combination with Figures 1-2 , the predetermined time dynamic surface control method of the special vehicle horizontal system includes the following steps:

[0027] Step 1, establishing a mathematical model of the special vehicle horizontal system;

[0028] Step 1.1, the servo motor in the special vehicle horizontal system considered by the present application has a very small ratio of actual inductance to resistance, and the derivative of current with respect to time tends to zero.

[0029] Therefore, according to Newton's second law, the electrical coupling dynamics equation of the special vehicle horizontal system machine is:

[0030]

[0031] q and respectively represent the azimuth angle of the launching gyro and the elevation angle of the launching tube; is the angular velocity of the launching gyro rotation; is the angular acceleration of the launching gyro rotation; J0is the moment of inertia of the load relative to the rotation axis of the launching gyro at a certain fixed elevation angle of the launching tube; J m is the moment of inertia of the motor shaft; N is the gear reduction ratio; u is the control input voltage; R is the motor armature resistance; k t is the motor torque coefficient; k e is the motor back electromotive force coefficient; B m is the motor shaft viscous friction coefficient; B is the raceway viscous friction coefficient; d t (t) is the gear backlash nonlinear error; d r (t) is the external disturbance and unmodeled error; is the difference between the actual moment of inertia and J0.

[0032] Step 1.2, define state variables: Then the equation of motion of formula (1) is converted into the state equation:

[0033]

[0034] In formula (2), θ1=k t N / (J0R+J m N 2 R), θ2=(k e N 2 / R+B m N 2 +B) / (J0+J m N 2 are all defined combination constants and known; x1 and x2 are state variables 1 and 2 respectively; is the defined combination of the total disturbance of the system, including gear backlash nonlinearity, external disturbance, unmodeled error, and launching tube nonlinear disturbance.

[0035] In order to facilitate controller design, the following assumptions are made:

[0036] Assumption 1: the system expected angle command x 1d is a second-order continuous differentiable, and the expected angle command, the expected angular velocity command, and the expected angular acceleration command are all bounded.

[0037] Assumption 2: the total disturbance D(t) has a known upper bound δ, that is

[0038] |D(t)|≤δ (3)

[0039] Step 2, design the scheduled time dynamic surface controller, the steps are as follows:

[0040] Step 2.1, controller design preparation:

[0041] Define e1=x1-x 1d is the tracking error of the system, x 1d is the position command that the system is expected to track and the command is second-order continuous differentiable, based on the backstepping design idea, the compound dynamic surface error is introduced:

[0042]

[0043] In formula (4), z1 and z2 are compound dynamic surface errors 1 and 2 respectively, μ1(t) is a time-varying tuning function, satisfies a first-order filter:

[0044]

[0045] wherein is the filter output, β2 is a virtual control law, τ2 is a positive constant parameter. In addition, the time-varying tuning function in (4) should also satisfy the following three conditions:

[0046] Condition 1, when t≥0, the second derivative of the time-varying tuning function is continuous and bounded;

[0047] Condition 2, μ1(0)=0 is always true when t≥T, wherein t is time and T is a predetermined time;

[0048] Condition 3, μ1(0) and satisfy the condition:

[0049]

[0050] In formula (6), m1, q1∈R are constants determined by the initial conditions of the system state and the expected trajectory.

[0051] In formula (4), if |x1-x 1d -μ1(t)|≤ε, then when t≥T, μ1(0)=0, e1=|x1-x 1d |≤ε, wherein ε is a set boundary. Therefore, in the following design, the main design goal will be to limit z1 within the set boundary ε.

[0052] Step 2.2, tracking error definition and controller design:

[0053] Define the tracking error of the first-order filter as follows:

[0054]

[0055] In formula (7), y2 is a first-order filter error.

[0056] To provide parameters for stability proof, the derivation of z1 and z2 in formula (4) is combined with formula (2) to have the following expansion formula:

[0057]

[0058] According to formula (8), the model-based virtual control law β2 and the controller u can be designed as:

[0059]

[0060] In formula (9), c1, c2, and γ are normal numbers, and the hyperbolic tangent term tanh(δz2 / γ) is used to ensure the continuity of the controller input signal. Substituting formula (9) into formula (8) gives

[0061]

[0062] In formula (10), z1 and z2 are the compound dynamic surface error 1 and the compound dynamic surface error 2 respectively, and are the derivatives of z1 and z2 respectively.

[0063] Step 2.3, define the conditions required for proof:

[0064] Define Γ = 1 / 4 + κ0Γ, κ0, and κ0 are constants, where κ0 = 0.2785. Based on the Lyapunov stability proof process, τ2, Γ, ε, c1, and c2 should satisfy:

[0065]

[0066] Step 3, use the Lyapunov stability theory to prove the stability of the horizontal system of the special vehicle, and obtain the predetermined time global stability result of the system, as follows:

[0067] Define the Lyapunov function as follows:

[0068]

[0069] Derive formula (12) and substitute formula (5), (7), and (8) to obtain:

[0070]

[0071] In formula (13), Γ = 1 / 4 + κ0κ0 = 0.2785, and the hyperbolic tangent term tanh(δz / γ) effectively suppresses the disturbance.

[0072] Define the vector where is the real set, the boundary set Ω is defined to prove the stability of the system signal:

[0073]

[0074] The proof can be completed by the following four steps:

[0075] Step 3.1, prove the boundedness of all closed-loop system signals under the condition of the boundary set Ω.

[0076] From Assumption 1, Condition 1, we can get x 1d (t), μ1(t), is bounded when t≥0. From the condition of equation (14), z1, z2, y2 are bounded. From equation (4), x1(z1, x 1d , μ1) is bounded, so combined with equation (9), we can know that is bounded. From equations (4), (7), x2(z2, β2, y2) is bounded. So u(x2, z1, z2, y2) is bounded. Therefore, all signals of the closed-loop system are bounded under the condition of the set Ω.

[0077] Step 3.2, prove the boundedness under the condition of the boundary set Ω.

[0078] Differentiate β2 in equation (9) and combine equations (2), (4), (5), (7), we can get:

[0079]

[0080] Using the conclusion in Step 1, we can get is bounded. Therefore, select the parameter τ2 to make the following inequality:

[0081]

[0082] Step 3.3, select the parameter to make Ω hold.

[0083] From equation (5) we can get y2(0) = 0. Substitute equations (6), (9) into equation (4), we can get:

[0084]

[0085] From equation (12), we can get z1(0) = 0, z2(0) = 0, V(0) = 0

[0086] Select the parameter to make the following inequality hold:

[0087]

[0088] From equation (12), (13), (16), (18), we have

[0089]

[0090] Under the condition of set Ω, equation (19) is always true. Equation (19) shows that when V = ε 2 / 2, V(t) = 0. Therefore, from V(0) = 0 < ε 2 / 2, we have V(t) ≤ ε 2 / 2 for t ≥ 0. All sets Ω are true. From equation (14), we have |z1(t)| ≤ ε for t ≥ 0.

[0091] Step 3.4, analyze the preset time T of the system.

[0092] From condition 2, μ1(t) = 0 for t ≥ T, combined with equation (4), we have |x1(t)-x 1d (t)| ≤ ε for t ≥ T.

[0093] Therefore, by applying the predetermined time dynamic surface control method, it can be guaranteed that the tracking error e(t) = x1(t)-x 1d (t) is bounded in the predefined time, and the user can arbitrarily preset the tracking time T, which verifies the predetermined time performance of the control method, which can guarantee the rapid aiming of the tank.

[0094] Embodiment

[0095] In order to examine the performance of the designed controller, the following parameters are taken in the simulation to model the horizontal system of special vehicles:

[0096] The model parameters of the horizontal system of special vehicles are: k t = 1.89 (N·m / A), N = 400, J0= 10526.3 (kg·m 2 ), R = 0.607 (Ω), J m = 0.0002 (kg·m 2 ), k e = 1.09 (V·s / rad), B m = 0.0012 (N·m·s / rad), B = 710 (N·m·s / rad), g = 9.8 (m / s 2 ).

[0097] According to two different system working conditions, the simulation process is divided into three parts:

[0098] ① The expected command x 1d(t) = sint (rad), when the time-varying disturbance D(t) = 0.15 sint (N·m)

[0099] This operating condition verifies the dynamic tracking performance of the pre-set time dynamic surface controller (DSCPT), comparing controllers with different pre-set times:

[0100] The four DSCPT controllers have the same parameters: c1=55, c2=55, [δ]=0.65, γ=1, τ2=0.01, m1=1, ε=0.001, q1=1, Γ=0.5285.

[0101] The scheduled times for the four DSCPT controllers are T = 1, 2, 3, and 6 seconds, respectively.

[0102] The system output tracking of the desired command, tracking error, and other parameters under the action of four different time-delayed DSCPT controllers are as follows: Figure 3 and Figure 4 As shown. By Figure 3 and Figure 4 It can be seen that, under the action of the DSCPT controller, the position output of the special vehicle's leveling system has a very high tracking accuracy to the command. Furthermore, from... Figure 3 and Figure 4 As can be seen, under four different preset times, the system reached stability according to its respective preset time, which fully verifies the preset time performance of the DSCPT controller. The amplitude of the steady-state tracking error was strictly limited to 3 × 10⁻⁶. -4 In (rad), this verifies the good tracking performance of the DSCPT controller.

[0103] ②Expected instruction x 1d (t)=0.2t+5(rad), when the time-varying disturbance D(t)=0.15sint(N·m)

[0104] This operating condition verifies the stability of the DSCPT controller. The parameter settings for the four types of DSCPT controllers are the same as those for operating condition ①.

[0105] The system output tracking of the desired command, the DSCPT controller tracking error, and other parameters under four different time-delayed DSCPT controllers are as follows: Figure 5 and Figure 6 As shown. By Figure 5 and Figure 6 It can be seen that the system reaches stability according to its respective predetermined time under the four different predetermined times, which further verifies the predetermined time performance of the DSCPT controller. The magnitude of the steady-state tracking error is also limited to 1×10⁻⁶. -4 The tracking performance of the DSCPT controller was verified in (rad).

[0106] ③ Desired command x 1d (t) = 0.2t + 5(rad), 1000 times time-varying disturbance D(t) = 150sint(N·m)

[0107] This is an extreme working condition, if the designed control method can adapt to this extreme working condition well, it can be shown that the designed control method can be widely used in various working conditions in engineering practice. Take the controller with different predetermined times for comparison:

[0108] The same parameters of the four DSCPT controllers: c1=55, c2=55, [δ]=650, γ=1, τ2=0.01, m1=1, ε=0.001, q1=1, Γ=0.5285.

[0109] The predetermined times of the four DSCPT controllers are T=1, 2, 3, 6s respectively.

[0110] The tracking error of the system output to the desired command under the action of the four different DSCPT controllers with different predetermined times is shown in Figure 7 The local amplification of the tracking error of the system output to the desired command under the action of the four different DSCPT controllers with different predetermined times is shown in Figures 8-11 From Figures 7-11 It can be seen that even in the extreme situation of 1000 times disturbance, the predetermined time performance of the DSCPT controller can still be guaranteed, and the stability of the system can also be guaranteed. After the predetermined time of the four DSCPT controllers respectively, the tracking error is less than 1×10 -3 (rad), therefore, it can be shown that the DSCPT controller has strong anti-interference ability. This enables the tank to accurately aim at the target in a high disturbance environment.

Claims

1. A scheduled time dynamic surface control method for a special vehicle horizontal system, characterized in that, The method comprises the following steps: Step 1, establishing a mathematical model of the special vehicle horizontal system; Step 2, designing a predetermined time dynamic surface controller; a composite dynamic surface error is introduced into the controller to realize the stability of the special vehicle horizontal system in any predetermined time; In step 2, the composite dynamic surface error is z1 = x1 - x 1d - μ1(t) where z1and z2are complex dynamic face errors 1 and 2, respectively, where x1is state 1, x2is state 2, x 1d is the position command that the system is expected to track, μ1(t) is a time-varying tuning function, is the filter output; In step 2, the model-based virtual control law β2 and the controller u are designed as where z1 and z2 are complex dynamic surface errors 1 and 2, respectively, is the derivative of the position command that the system is expected to track, is the derivative of the time-varying tuning function, θ1, θ2 are defined combination constants, x1 and x2 are state variables 1 and 2, respectively, c1, c2, γ are normal numbers, and δ is the upper bound of the total disturbance, is the filter output; The hyperbolic tangent term tanh (δz2 / γ) is used to ensure the continuity of the input signal of the controller, and then where z1and z2are complex dynamic face error 1 and complex dynamic face error 2, respectively, and are derivatives of z1and z2, respectively, D(t) is the total disturbance, and y2is the first order filtered error. Step 3, stability proof is performed by using Lyapunov stability theory, and the predetermined time global stability of the system is obtained.

2. The scheduled time dynamic surface control method for a special vehicle horizontal system according to claim 1, characterized in that, Step 1, the dynamic model of the special vehicle horizontal system is established, and the specific process is as follows: The electromechanical coupling dynamics equation of the special vehicle horizontal system is where q and denote the azimuth angle of the launching gyro and the elevation angle of the launching tube, respectively; is the angular velocity of the launching gyro rotation; is the angular acceleration of the launching gyro rotation; J0is the moment of inertia of the load relative to the rotation axis of the launching gyro at a certain fixed elevation angle of the launching tube; J m is the moment of inertia of the motor shaft; N is the gear reduction ratio; u is the control input voltage; R is the motor armature resistance; k t is the motor torque coefficient; k e is the motor back electromotive force coefficient; B m is the motor shaft viscous friction coefficient; B is the raceway viscous friction coefficient; d t (t) is the gear backlash nonlinear error; d r (t) is the external disturbance and unmodeled error; is the difference between the actual moment of inertia and J0.

3. The scheduled time dynamic surface control method for a special vehicle horizontal system according to claim 2, characterized in that, In step 1, the state variable x of the special vehicle horizontal system is defined as Wherein x1 is state 1, x2 is state 2, The motion equation of the special vehicle horizontal system is converted into a state equation as Wherein θ1, θ2 are defined as constant combinations and are known, D(t) is the total disturbance, and is defined as wherein d r (t) is the external disturbance and unmodeled error; is the difference between the actual moment of inertia and J0, is the angular acceleration of the rotating body, J0is the moment of inertia of the load relative to the rotating axis of the rotating body at a certain fixed launch tube pitch angle; J m is the moment of inertia of the motor shaft; N is the gear reduction ratio.

4. The scheduled time dynamic surface control method for a special vehicle horizontal system according to claim 1, characterized by, The time-varying tuning function μ1(t) satisfies the following three conditions: Condition 1, the second derivative of the time-varying tuning function is continuously bounded when t > 0 Condition 1, the second derivative of the time-varying tuning function is continuously bounded when t > 0 Condition 2, μ1(0) = 0 is always true at t ≥ T, wherein T is a predetermined time; Condition 3, μ1(0) and satisfies the condition: Wherein m1, q1 ∈ R are constants determined by the initial conditions and the expected trajectory of the system state.

5. The scheduled time dynamic surface control method for a special vehicle horizontal system according to claim 1, characterized by, In step 3, the stability proof function of the predetermined time dynamic surface controller is wherein is the derivative of Lyapunov, y2is the first order filtered error, D(t) is the total disturbance, δ is the upper bound of the total disturbance, τ2is a positive constant parameter, and Γ is a constant; Definition of vector where is the set of real numbers, the boundary set Ω is defined to prove the stability of the system signal:

6. The scheduled time dynamic surface control method of a special vehicle horizontal system according to claim 5, characterized in that, In step 3, the stability proof steps of the special vehicle horizontal system include: Prove the boundedness of all closed-loop system signals under the condition of set Ω; Proof Boundedness under the condition of the set Ω; Select parameters to make Ω true; Analyze the preset time T of the system.

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