Predetermined time dynamic surface control method for horizontal system of special vehicle

Abstract

The invention discloses a predetermined time dynamic surface control method for a special vehicle horizontal system, and the method 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 provided for solving the problems that modern combat provides higher requirements for control of a horizontal system of the special vehicle, and high precision, high aiming speed and strong disturbance resistance are covered. However, a control method adopted by a conventional special vehicle horizontal system does not have the capability of tracking a specified signal at any time, and some control methods have the problem of discontinuous control input. And meanwhile, strong disturbance resistance is low. Compared with the prior art, the control method disclosed by the invention effectively solves the problems of high precision, high aiming speed, disturbance rejection capability and 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 invention relates to the technical field of motion control, and mainly to a method of dynamic surface control with predetermined time (DSCPT) of a special vehicle level system. Background Art

[0002] With the informatization and unmanned battlefield in the future, special vehicles are required to develop towards high mobility, high precision and high stability, which puts higher requirements on the stability of the launch slewing body and rapid aiming of special vehicles during high-speed driving. The horizontal systems of modern special vehicles are divided into hydraulic and electric types. The traditional hydraulic stabilization system has outstanding disadvantages such as low efficiency, high noise and high heat generation. The electric type not only overcomes the above disadvantages, but also has low cost and high efficiency, and is the main development direction of the current horizontal stabilization system. However, due to the stronger nonlinearity and electromechanical coupling of the horizontal system of electric special vehicles. In addition, the combat environment of special vehicles on the battlefield is particularly complex, and firing first will bring significant tactical advantages and even directly affect the outcome of the battle. This puts higher requirements on the rapidity and stability of the horizontal system.

[0003] In the past few decades, researchers have made many contributions to the controller design of horizontal systems. The PID controller is the most classic controller, and its design is based on a linear system. It is one of the widely used controllers in special vehicle horizontal systems. To date, 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 actual horizontal stability systems, it is difficult for PID control to compensate for a large number of nonlinear factors. Therefore, model-based nonlinear controllers have become the research direction of special vehicle horizontal system control today. In order to solve the problem of unknown parameters in the system, nonlinear adaptive control has been widely used in special vehicle systems. 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, making the system unstable.

[0004] In order to solve the above 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 with nonlinear robust terms to deal with parameter uncertainty and unmodeled disturbances of horizontal systems, 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 disturbances, adaptive robust control can only guarantee that the tracking error is bounded. To solve this problem, robust integral feedback control of the error sign is proposed, which obtains asymptotic control effects for bidirectional stable systems with various uncertainties. However, this control strategy requires the second-order derivative of the disturbance to be bounded. In addition, in order to effectively deal with various uncertainties in the stability system of special vehicles, a state observer-based method is proposed. The adaptive control strategy combines adaptive control and adaptive control. This strategy uses the adaptive principle to deal with unknown parameters, while 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 have also been used to compensate for unknown disturbances and have been applied to other mechanical power systems. However, all of the above control methods can only ensure that the performance requirements are met when time tends to infinity. Summary of the invention

[0006] The purpose of the present invention is to provide a predetermined time dynamic surface control method for the horizontal system of a special vehicle. Based on the idea of ​​backstepping and integrating the idea of ​​dynamic surface control, the controller is designed to predefine the time when the tracking error reaches a specified range, and the controller gain contains a continuous hyperbolic tangent function to suppress the total disturbance, which effectively solves the problem of rapid aiming of the horizontal system of the special vehicle and obtains better tracking performance.

[0007] The technical solution to achieve the purpose of the present invention is: a method for controlling a predetermined time dynamic surface of a special vehicle level system, comprising the following steps:

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

[0009] Step 2, designing a predetermined time dynamic surface controller; introducing a composite dynamic surface error into the controller to achieve the stability of the special vehicle horizontal system at any predetermined time;

[0010] Step 3: Use Lyapunov stability theory to prove the stability and obtain the result that the system is globally stable within the predetermined time.

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

[0012] (1) By introducing the dynamic surface error and the time-varying coordination function, the problem that the existing control methods cannot achieve the horizontal system stability of special vehicles at any predetermined time is effectively solved.

[0013] (2) By constructing the hyperbolic tangent term, the controller input continuity and anti-interference problems are solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a schematic diagram of the principle of the dynamic surface of predetermined time (DSCPT) control method of the special vehicle level system of the present invention;

[0015] Figure 2 It is a schematic diagram of the horizontal system of special vehicles;

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

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

[0018] Figure 5 It is a diagram of the tracking process of the straight line desired instruction under the action of the four predetermined time DSCPT controllers designed by the present invention;

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

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

[0021] Figure 8 It is the tracking error diagram of 1s scheduled time;

[0022] Fig. 9 It is the tracking error diagram for the 2s scheduled time;

[0023] Fig.10 It is the tracking error graph of the 3s scheduled time;

[0024] Fig.11 It is the tracking error graph of the 6s scheduled time; DETAILED DESCRIPTION

[0025] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0026] Combination Figure 1-Figure 2 The predetermined time dynamic surface control method of the special vehicle level system of the present invention comprises the following steps:

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

[0028] Step 1.1, for the servo motor in the special vehicle horizontal system considered in the present invention, since the actual ratio of inductance to resistance is extremely small, the derivative of current with respect to time tends to zero.

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

[0030]

[0031] In formula (1), q and They represent the azimuth angle of the launching rotor and the pitch angle of the launching tube respectively; is the angular velocity of the launching rotating body; is the angular acceleration of the launch rotor; J0 is the moment of inertia of the load relative to the launch rotor axis at a fixed launch tube pitch angle; 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 viscous friction coefficient of the motor shaft; B is the viscous friction coefficient of the seat ring; d t (t) is the 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 in formula (1) is transformed 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 defined combination constants and are known; x1 and x2 are state variables 1 and 2 respectively; To define the total disturbance of the combined system, it includes backlash nonlinearity, external disturbance, unmodeled error, transmitting tube nonlinear interference, etc.

[0035] To facilitate controller design, the following assumptions are made:

[0036] Assumption 1: The system expects an angle command x 1d It is second-order continuously differentiable, and the desired angle command, the desired angular velocity command, and the desired angular acceleration command are all bounded.

[0037] Assumption 2: The total disturbance D(t) has a known upper bound δ, namely

[0038] |D(t)|≤δ (3)

[0039] Step 2, design a 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 expects to track and the command is second-order continuously differentiable. Based on the backstepping design idea, the composite dynamic surface error is introduced:

[0042]

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

[0044]

[0045] in is the filter output, β2 is the virtual control law, and 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-order derivative of the time-varying tuning function is continuous and bounded;

[0047] Condition 2, μ1(0) = 0 always holds when t ≥ T, where t is time and T is the predetermined time;

[0048] Condition 3, μ1(0) and Requirements:

[0049]

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

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

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

[0053] The tracking error of the first-order filter is defined as follows:

[0054]

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

[0056] To provide parameters for stability proof, we take the derivative of z1 and z2 in equation (4) and combine it with equation (2) to get the following expansion:

[0057]

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

[0059]

[0060] In formula (9), c1, c2, and γ are positive constants. The hyperbolic tangent term tanh(δz / γ) is used to ensure the continuity of the controller input signal. Substituting formula (9) into formula (8) yields

[0061]

[0062] Where z1 and z2 are composite dynamic surface error 1 and composite 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+γκ0. Γ and κ0 are both constants, where κ0=0.2785. Based on the Lyapunov stability proof process, we can get τ2, Γ, ε, c1 and c2 should satisfy:

[0065]

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

[0067] The Lyapunov function is defined as follows:

[0068]

[0069] Deriving equation (12) and substituting equations (5), (7) and (8) into it, we can obtain:

[0070]

[0071] In formula (13), Γ = 1 / 4 + γκ0κ0 = 0.2785, and the hyperbolic tangent term tanh(δz / γ) effectively suppresses the disturbance.

[0072] Define the vector ξ=[z1,z2,y2] T ∈R 3 , where R is a set of real numbers, and the set Ω is defined to prove the stability of the system signal:

[0073]

[0074] The proof can be completed in four steps:

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

[0076] According to assumption 1 and condition 1, we can get x 1d (t), μ1(t), It is bounded when t≥0. From the condition of equation (14), we know that z1, z2, y2 are bounded. From equation (4), we know that x1(z1, x 1d ,μ1) is bounded, so combined with formula (9), we can know Bounded. From equations (4) and (7), we can see that 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 Boundedness under the set Ω condition.

[0078] Taking the derivative of β2 in equation (9) and combining equations (2), (4), (5), and (7), we can obtain:

[0079]

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

[0081]

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

[0083] From formula (5) It can be obtained that y2(0) = 0. Substituting equations (6) and (9) into equation (4), we can obtain:

[0084]

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

[0086] The parameters are chosen so that the following inequality holds:

[0087]

[0088] From equations (12), (13), (16), and (18), we can get:

[0089]

[0090] Under the condition of set Ω, equation (19) always holds. Equation (19) shows that when V = ε 2 / 2, Therefore, V(0)=0<ε 2 / 2, when t≥0, V(t)≤ε 2 / 2 holds. All sets Ω hold. From equation (14), we can see that when t≥0, |z1(t)|≤ε holds.

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

[0092] According to condition 2, when t ≥ T, μ1(t) = 0. Combining with equation (4), when t ≥ T, |x1(t) - x 1d (t)|≤ε holds.

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

[0094] Example

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

[0096] The parameters of the special vehicle horizontal system model 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 conditions, the simulation process is divided into three parts:

[0098] ①Expected instruction x 1d(t) = sint (rad), general time-varying interference D (t) = 0.15 sint (N m)

[0099] This condition verifies the dynamic tracking performance of the Dynamic Surface Controller with Scheduled Time (DSCPT), and compares controllers with different scheduled times:

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

[0101] The preset times of the four DSCPT controllers are: T=1, 2, 3, 6s.

[0102] The tracking of the system output to the desired command and the tracking error under the four different fixed-time DSCPT controllers are as follows: Figure 3 and Figure 4 As shown. Figure 3 and Figure 4 It can be seen that under the action of the DSCPT controller, the position output of the special vehicle horizontal system has a high tracking accuracy for the command. Figure 3 and Figure 4 It can be seen that under four different scheduled times, the system reaches stability according to their respective scheduled times, which fully verifies the scheduled time performance of the DSCPT controller. The amplitude of the steady-state tracking error is strictly limited to 3×10 -4 (rad), which verifies the good tracking performance of the DSCPT controller.

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

[0104] This working condition verifies the stability performance of the DSCPT controller. The parameter settings of the four DSCPT controllers are the same as those in working condition ①.

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

[0106] ③Expected instruction x 1d (t) = 0.2t + 5 (rad), 1000 times time-varying interference D (t) = 150sint (N m)

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

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

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

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

Claims

1. A method for controlling a predetermined time dynamic surface of a special vehicle level system, characterized in that: The following steps are involved: Step 1, establishing a mathematical model of the special vehicle level system; Step 2, designing a predetermined time dynamic surface controller; introducing a composite dynamic surface error into the controller to achieve the stability of the special vehicle horizontal system at any predetermined time; Step 3: Use Lyapunov stability theory to prove the stability and obtain the result that the system is globally stable within the predetermined time.

2. The method for controlling a predetermined time dynamic surface of a special vehicle level system according to claim 1, characterized in that: The dynamic model of the special vehicle horizontal system is established as described in step 1, as follows: The electromechanical coupling dynamic equation of the special vehicle horizontal system is: In the formula, q and They represent the azimuth angle of the launching rotor and the pitch angle of the launching tube respectively; is the angular velocity of the launching rotating body; is the angular acceleration of the launch rotor; J0 is the moment of inertia of the load relative to the launch rotor axis at a fixed launch tube pitch angle; 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 viscous friction coefficient of the motor shaft; B is the viscous friction coefficient of the seat ring; d t (t) is the 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 method for controlling a predetermined time dynamic surface of a special vehicle level system according to claim 2, characterized in that: In step 1, the state variable x of the special vehicle level system is defined as: Where x1 is state 1, x2 is state 2, The motion equation of the special vehicle horizontal system machine is converted into the state equation: Where θ1 and θ2 are both known constants of defined combinations, and D(t) is the total disturbance, which is defined as: Where, 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 launch rotor, J0 is the moment of inertia of the load relative to the launch rotor axis at a fixed launch tube pitch angle; J m is the moment of inertia of the motor shaft; N is the gear reduction ratio.

4. The method for controlling a predetermined time dynamic surface of a special vehicle level system according to claim 1, characterized in that: In step 2, the composite dynamic surface error is: z1=x1-x 1d -μ1(t) Where z1 and z2 are composite dynamic surface errors 1 and 2 respectively, x1 is state 1, x2 is state 2, x 1d is the position command that the system expects to track, μ1(t) is the time-varying tuning function, is the filter output.

5. The method for controlling a predetermined time dynamic surface of a special vehicle level system according to claim 4, characterized in that: The time-varying tuning function μ1(t) satisfies the following three conditions: Condition 1, when t ≥ 0, the second-order derivative of the time-varying tuning function is continuous and bounded; Condition 2, μ1(0) = 0 always holds when t ≥ T, where T is the predetermined time; Condition 3, μ1(0) and Requirements: μ1(0)=m1=x1(0)-x 1d (0) Where m1,q1∈R are constants determined by the initial conditions and the desired trajectory of the system state.

6. The method for controlling a predetermined time dynamic surface of a special vehicle level system according to claim 1, characterized in that: In step 2, the model-based virtual control law β2 and controller u are designed as: Where z1 and z2 are composite dynamic surface errors 1 and 2 respectively, is the derivative of the position command that the system wants to track, is the derivative of the time-varying tuning function, θ1 and θ2 are both defined combined constants, x1 and x2 are state variables 1 and 2, c1, c2, and γ are positive constants, and δ is the upper bound of the total disturbance. is the filter output.

7. The method for controlling a predetermined time dynamic surface of a special vehicle level system according to claim 6, characterized in that: The hyperbolic tangent term tanh(δz / γ) is used to ensure the continuity of the controller input signal, and then: Where z1 and z2 are composite dynamic surface error 1 and composite dynamic surface error 2, respectively. and are the derivatives of z1 and z2 respectively, and D(t) is the total disturbance.

8. The method for controlling a predetermined time dynamic surface of a special vehicle level system according to claim 6, characterized in that: In step 3, the stability proof function of the predetermined time dynamic surface controller is: In the formula, is the derivative of Lyapunov, y2 is the first-order filtering error, D(t) is the total disturbance, δ is the upper bound of the total disturbance, τ2 is a positive constant parameter, Γ and κ0 are both constants; Define the vector ξ=[z1,z2,y2] T ∈R 3 , where R is a set of real numbers, and the set Ω is defined to prove the stability of the system signal:

9. The method for controlling a predetermined time dynamic surface of a special vehicle level system according to claim 7, characterized in that: In step 3, the steps for proving the stability of the special vehicle level system include: Prove the boundedness of all closed-loop system signals under the set Ω condition; prove Boundedness under the set Ω condition; Choose parameters to make Ω hold; The preset time T of the analysis system.

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