阅读说明：本技术 用于高速列车的抗饱和自适应伪pid滑模故障容错控制方法 (Anti-saturation self-adaptive pseudo PID sliding mode fault tolerance control method for high-speed train ) 是由 郭祥贵 赵君杰 方晓 李洪建 于 2019-09-19 设计创作，主要内容包括：本发明提供一种用于高速列车的抗饱和自适应伪PID滑模故障容错控制方法,能够提高高速列车跟踪期望轨迹的效果。所述方法包括：建立存在执行器故障、执行器非对称非线性饱和约束和积分二次型扰动的高速列车动态模型；给定期望轨迹的位置、速度,建立期望轨迹模型；建立执行器辅助饱和补偿系统；基于建立的高速列车动态模型、期望轨迹模型、执行器饱和补偿系统,计算轨迹跟踪误差；基于计算得到的轨迹跟踪误差,构造伪PID滑模面；基于构造的伪PID滑模面,确定自适应控制律,所述自适应控制律包括：用于实现指数稳定的标称控制律、用于抑制执行器故障和积分二次型扰动影响的补偿控制律以及自适应律。本发明涉及轨道交通控制技术领域。(The invention provides an anti-saturation self-adaptive pseudo PID sliding mode fault tolerance control method for a high-speed train, which can improve the effect of tracking an expected track of the high-speed train. The method comprises the following steps: establishing a high-speed train dynamic model with actuator faults, actuator asymmetric nonlinear saturation constraints and integral quadratic disturbance; giving the position and the speed of the expected track, and establishing an expected track model; establishing an actuator auxiliary saturation compensation system; calculating a track tracking error based on the established high-speed train dynamic model, the expected track model and the actuator saturation compensation system; constructing a pseudo PID sliding mode surface based on the calculated track tracking error; determining an adaptive control law based on the constructed pseudo PID sliding mode surface, wherein the adaptive control law comprises the following steps: a nominal control law for realizing exponential stability, a compensation control law for suppressing the influence of actuator faults and integral quadratic disturbance and an adaptive law. The invention relates to the technical field of rail transit control.)

1. An anti-saturation self-adaptive pseudo PID sliding mode fault tolerance control method for a high-speed train is characterized by comprising the following steps:

establishing a high-speed train dynamic model with actuator faults, actuator asymmetric nonlinear saturation constraints and integral quadratic disturbance;

giving the position and the speed of the expected track, and establishing an expected track model;

establishing an actuator auxiliary saturation compensation system;

calculating a track tracking error based on the established high-speed train dynamic model, the expected track model and the actuator saturation compensation system;

constructing a pseudo PID sliding mode surface based on the calculated track tracking error;

determining an adaptive control law based on the constructed pseudo PID sliding mode surface, wherein the adaptive control law comprises the following steps: a nominal control law for realizing exponential stability, a compensation control law for suppressing the influence of actuator faults and integral quadratic disturbance and an adaptive law.

2. The anti-saturation adaptive pseudo PID sliding mode fault tolerant control method for the high speed train according to claim 1, wherein the high speed train dynamic model is expressed as:

wherein x (t) and v (t) respectively represent the actual position and the actual speed of the high-speed train at the time t;

3. The anti-saturation self-adaptive pseudo PID sliding-mode fault-tolerant control method for the high-speed train according to claim 2, wherein the dynamic mathematical model when the train traction or braking force output signal has a fault is as follows:

u^F(t)＝ρ(t,t_ρ)u(t)+r(t,t_r)

where u (t) denotes the overall control law, ρ (t, t)_ρ) Is an unknown time-varying actuator fault factor, p (t, t)_ρ) Satisfies the following conditions: ρand

4. The anti-saturation adaptive pseudo PID sliding mode fault tolerant control method for the high speed train according to claim 3, wherein w is_k(t)、ξ_k(t) satisfies:

wherein, t₀Represents an initial time; psi_kFor representing disturbance input w_k(t) and disturbance output ξ_kIntegral quadratic constraint of (·).

5. The anti-saturation adaptive pseudo PID sliding mode fault tolerant control method for the high speed train according to claim 4, wherein the asymmetric nonlinear saturation constraint of the actuator is expressed as:

wherein, b_lAnd b_rRespectively representing a first saturation amplitude and a second saturation amplitude; u. of_minAnd u_maxRepresenting a first saturation clipping and a second saturation clipping, respectively; h is_r(u^F(t)) and h_l(u^F(t)) are unknown bounded nonlinear functions, all of which are used to represent the absence of actuator saturation with input u^F(t) a non-linear relationship therebetween.

6. The anti-saturation adaptive pseudo PID sliding mode fault tolerant control method for the high speed train according to claim 5, wherein the established expected track model is represented as:

wherein x is_r(t)、v_r(t) and a_r(t) respectively representing the position, velocity and acceleration of the desired trajectory at time t;

7. The anti-saturation adaptive pseudo PID sliding-mode fault tolerant control method for the high-speed train according to claim 6, wherein the established actuator assisted saturation compensation system is represented as:

wherein, c₁And c₂A constant coefficient that is positive; lambda [ alpha ]₁(t) and lambda₂(t) both represent states of the actuator assisted saturation compensation system;

8. The anti-saturation self-adaptive pseudo PID sliding mode fault tolerant control method for the high speed train according to claim 7, wherein a trajectory tracking error calculation formula is as follows:

wherein e is_x(t) and e_v(t) represents the position error and velocity error between the actual track and the expected track, x (t) and v (t) are the actual position and actual velocity of the high-speed train at time t, x_r(t) and v_r(t) position and velocity, λ, of the desired trajectory, respectively₁And (t) is the state of the actuator assisted saturation compensation system.

9. The anti-saturation self-adaptive pseudo PID sliding mode fault tolerant control method for the high speed train according to claim 8, wherein the constructed pseudo PID sliding mode surface is expressed as:

where s (t) denotes a pseudo PID sliding mode surface, and α and β both denote constant coefficients.

10. The anti-saturation adaptive pseudo-PID sliding-mode fault-tolerant control method for the high-speed train according to claim 9, wherein the adaptive control law is expressed as:

u(t)＝u_n(t)+u_c(t)

u_n(t)＝-Ks(t)

wherein u (t) represents the overall control law; u. of_n(t) represents a nominal control law for achieving exponential stability; u. of_c(t) and

wherein the content of the first and second substances,

Technical Field

The invention relates to the technical field of rail transit control, in particular to an anti-saturation self-adaptive pseudo PID sliding mode fault tolerance control method for a high-speed train.

Background

High-speed trains higher than 200km/h are widely used due to their characteristics of rapidity, comfort, convenience, safety, green traffic and economy. In order to avoid that the normal running order of the train is influenced by the late running of the train caused by human factors, the automatic driving of the high-speed train is inevitably the future development trend of a train running control system, and the core of the automatic driving is to control the train to safely, reliably, automatically and accurately track an expected track. To achieve this goal, many tracking control strategies are developed, such as adaptive sliding mode control strategies, adaptive iterative learning control strategies, adaptive inversion control strategies, and adaptive neural/fuzzy control strategies.

However, the existing adaptive sliding mode control-based strategy needs to measure the acceleration information of the expected track, while the adaptive iterative learning control strategy needs to assume that the initial speed in each iterative process is zero, and the adaptive inversion control strategy and the adaptive neural/fuzzy control strategy are complex in structure and large in calculation amount. In addition, because the high-speed train runs under the high-speed working condition for a long time, the factors such as high-temperature friction, severe vibration, high-frequency work and the like easily cause traction/braking faults or failures, thereby seriously influencing the running safety of the train. In practical application, due to the influences of air resistance, turbulence of train workshops, wind tunnel yaw angle, friction on the side of a train and the like, the running resistance of the train has the characteristics of time variation, uncertainty and the like, so that the mathematical model of the high-speed train is difficult to accurately depict, and the train is disturbed by the outside at any moment in the running process and is time-varying and unpredictable. Meanwhile, the physical structure of the actuator limits the control input, and the fixed speed limit and the temporary speed limit of the line, so that the automatic driving system of the high-speed train is a limited control system. Therefore, in order to ensure the operation safety performance of the high-speed train, a more feasible and effective control strategy needs to be proposed to solve the above problems.

Disclosure of Invention

The invention aims to solve the technical problem of providing an anti-saturation self-adaptive pseudo PID sliding mode fault tolerance control method for a high-speed train, which does not need to measure acceleration information of an expected track and can effectively solve the problem of tracking the track of the high-speed train under the conditions of actuator faults, asymmetric nonlinear saturation constraint of an actuator and integral quadratic disturbance, thereby improving the effect of tracking the expected track of the high-speed train.

In order to solve the above technical problem, an embodiment of the present invention provides an anti-saturation adaptive pseudo PID sliding mode fault tolerance control method for a high-speed train, including:

establishing a high-speed train dynamic model with actuator faults, actuator asymmetric nonlinear saturation constraints and integral quadratic disturbance;

giving the position and the speed of the expected track, and establishing an expected track model;

establishing an actuator auxiliary saturation compensation system;

calculating a track tracking error based on the established high-speed train dynamic model, the expected track model and the actuator saturation compensation system;

constructing a pseudo PID sliding mode surface based on the calculated track tracking error;

determining an adaptive control law based on the constructed pseudo PID sliding mode surface, wherein the adaptive control law comprises the following steps: a nominal control law for realizing exponential stability, a compensation control law for suppressing the influence of actuator faults and integral quadratic disturbance and an adaptive law.

Further, the high-speed train dynamic model is represented as:

wherein x (t) and v (t) respectively represent the actual position and the actual speed of the high-speed train at the time t;

and

respectively, the first derivatives of x (t) and v (t) with respect to time t; k and n respectively represent the number of disturbance input channels and the maximum number of channels; u. of^F(t) indicating a fault in the train tractive effort or braking effort output signal; sat (u)^F(t))Representing an actuator asymmetric nonlinear saturation constraint; b is_k、H_kAnd G_kBoth represent a coefficient matrix; w is a_k(t) and xi_k(t) representing the input and output of the integral quadratic perturbation, respectively; f. of_d(t, x, v) is used to describe the total resistance acting on the high speed train.

Further, the dynamic mathematical model when the train traction or braking force output signal has a fault is as follows:

u^F(t)＝ρ(t,t_ρ)u(t)+r(t,t_r)

where u (t) denotes the overall control law, ρ (t, t)_ρ) Is an unknown time-varying actuator fault factor, p (t, t)_ρ) Satisfies the following conditions:

and

fault factors rho (t, t) for unknown time-varying actuators, respectively_ρ) The upper and lower bounds of (1); r (t, t)_r) Is an unknown time varying offset actuator fault; t is t_ρAnd t_rRespectively, indicate the times at which actuator failure and bias failure occur.

Further, w_k(t)、ξ_k(t) satisfies:

wherein, t₀Represents an initial time; psi_kFor representing disturbance input w_k(t) and disturbance output ξ_kIntegral quadratic constraint of (·).

Further, the actuator asymmetric nonlinear saturation constraint is expressed as:

wherein, b_lAnd b_rRespectively representing a first saturation amplitude and a second saturation amplitude; u. of_minAnd u_maxRepresenting a first saturation clipping and a second saturation clipping, respectively; h is_r(u^F(t)) and h_l(u^F(t)) are unknown bounded nonlinear functions, all of which are used to represent the absence of actuator saturation with input u^F(t) a non-linear relationship therebetween.

Further, the established expected trajectory model is represented as:

wherein x is_r(t)、v_r(t) and a_r(t) respectively representing the position, velocity and acceleration of the desired trajectory at time t;

and

respectively represent x_r(t) and v_r(t) first derivative with respect to time t.

Further, the actuator assisted saturation compensation system is established as:

wherein, c₁And c₂A constant coefficient that is positive; lambda [ alpha ]₁(t) and lambda₂(t) both represent states of the actuator assisted saturation compensation system;

and

respectively represent lambda₁(t) and lambda₂(t) a first derivative over time t; Δ u (t) denotes a saturation input error, and Δ u (t) denotes Sat (u)^F(t))-u^F(t)。

Further, the trajectory tracking error calculation formula is:

wherein e is_x(t) and e_v(t) represents the position error and velocity error between the actual track and the expected track, x (t) and v (t) are the actual position and actual velocity of the high-speed train at time t, x_r(t) and v_r(t) position and velocity, λ, of the desired trajectory, respectively₁And (t) is the state of the actuator assisted saturation compensation system.

Further, the constructed pseudo PID sliding mode surface is expressed as:

where s (t) denotes a pseudo PID sliding mode surface, and α and β both denote constant coefficients.

Further, the adaptive control law is represented as:

u(t)＝u_n(t)+u_c(t)

u_n(t)＝-Ks(t)

wherein u (t) represents the overall control law; u. of_n(t) represents a nominal control law for achieving exponential stability; u. of_c(t) and

respectively representing for actuator failure suppression and integral twoA compensation control law and an adaptive law of the secondary disturbance influence;

to represent

The first derivative with respect to time t; k, iota and mu all represent control parameters; Ψ (t) is a polynomial

In shorthand form xi_f(t, x, v) represents constraints for constructing the controller;to adjust the law of adaptationThe parameter of the steady speed of the vehicle,

is a continuous bounded function satisfying:

wherein the content of the first and second substances,

is a normal number.

The technical scheme of the invention has the following beneficial effects:

in the scheme, a high-speed train dynamic model with actuator faults, actuator asymmetric nonlinear saturation constraints and integral quadratic disturbance is established; giving the position and the speed of the expected track, and establishing an expected track model; an actuator auxiliary saturation compensation system is established, so that the problem of asymmetric nonlinear saturation limitation of the actuator can be effectively solved; calculating a track tracking error based on the established high-speed train dynamic model, the expected track model and the actuator saturation compensation system; constructing a pseudo PID sliding mode surface based on the calculated track tracking error; based on the constructed pseudo PID sliding mode surface, an adaptive control law is determined, acceleration information of an expected track does not need to be measured, and the problem of tracking the track of the high-speed train under the condition of actuator faults, asymmetric nonlinear saturation constraint of the actuator and integral quadratic disturbance can be effectively solved based on the adaptive control law, so that the effect of tracking the expected track of the high-speed train is improved.

Drawings

Fig. 1 is a schematic flow chart of an anti-saturation adaptive pseudo PID sliding-mode fault tolerance control method for a high-speed train according to an embodiment of the present invention;

fig. 2 is a detailed control flow diagram of an anti-saturation adaptive pseudo PID sliding-mode fault tolerance control method for a high-speed train according to an embodiment of the present invention.

Detailed Description

In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.

As shown in fig. 1, an anti-saturation adaptive pseudo PID sliding-mode fault tolerance control method for a high-speed train according to an embodiment of the present invention includes:

s101, establishing a high-speed train dynamic model with actuator faults, actuator asymmetric nonlinear saturation constraints and integral quadratic disturbance;

s102, setting the position and the speed of the expected track, and establishing an expected track model;

s103, establishing an actuator auxiliary saturation compensation system;

s104, calculating a track tracking error based on the established high-speed train dynamic model, the expected track model and the actuator saturation compensation system;

s105, constructing a pseudo PID (proportion-integral-differential) sliding mode surface based on the calculated track tracking error;

s106, determining an adaptive control law based on the constructed pseudo PID sliding mode surface, wherein the adaptive control law comprises the following steps: a nominal control law for realizing exponential stability, a compensation control law for suppressing the influence of actuator faults and integral quadratic disturbance and an adaptive law.

The anti-saturation self-adaptive pseudo PID sliding mode fault tolerance control method for the high-speed train, provided by the embodiment of the invention, comprises the steps of establishing a high-speed train dynamic model with an actuator fault, an actuator asymmetric nonlinear saturation constraint and integral quadratic disturbance; giving the position and the speed of the expected track, and establishing an expected track model; an actuator auxiliary saturation compensation system is established, so that the problem of asymmetric nonlinear saturation limitation of the actuator can be effectively solved; calculating a track tracking error based on the established high-speed train dynamic model, the expected track model and the actuator saturation compensation system; constructing a pseudo PID sliding mode surface based on the calculated track tracking error; based on the constructed pseudo PID sliding mode surface, an adaptive control law is determined, acceleration information of an expected track does not need to be measured, and the problem of tracking the track of the high-speed train under the condition of actuator faults, asymmetric nonlinear saturation constraint of the actuator and integral quadratic disturbance can be effectively solved based on the adaptive control law, so that the effect of tracking the expected track of the high-speed train is improved.

In order to better understand the anti-saturation adaptive pseudo PID sliding-mode fault tolerance control method for a high-speed train provided by the embodiment of the invention, the method is described in detail, and as shown in fig. 1 and fig. 2, the method may specifically include the following steps:

s101, establishing a high-speed train dynamic model (namely, the high-speed train model in figure 2) with actuator faults, actuator asymmetric nonlinear saturation constraint and integral quadratic disturbance; the high-speed train dynamic model is expressed as:

wherein x (t) and v (t) respectively represent the actual position and the actual speed of the high-speed train at the time t;andrespectively, x (t) and v (t) versus time tThe first derivative of (a); k and n respectively represent the number of disturbance input channels and the maximum number of channels; u. of^F(t) indicating a fault in the train tractive effort or braking effort output signal; sat (u)^F(t)) represents an actuator asymmetric nonlinear saturation constraint; b is_k、H_kAnd G_kBoth represent a coefficient matrix; w is a_k(t) and xi_k(t) representing the input and output of the integral quadratic perturbation, respectively; f. of_d(t, x, v) is used to describe the total resistance acting on the high speed train.

In this example, f_d(t, x, v) is an unknown non-linear continuous function describing the total resistance acting on the high speed train, including the base resistance f_b(t, v) and additional resistance f_a(t, x) in the following specific form:

wherein m represents the total weight of the high-speed train (including passengers); a (t), b (t), c (t) and l (t) are time-varying parameters, a (t) represents the rolling mechanical resistance coefficient caused by stroke, rolling and rail resistance, b (t) represents the linear mechanical resistance coefficient caused by the friction on the rim, the impact on the rim, the rolling resistance of the wheel rail and the fluctuation effect of the rail, c (t) represents the nonlinear resistance coefficient caused by the tail resistance, the wind pressure at the head end, the turbulence in the train workshop, the wind tunnel yaw angle and the friction on the side of the train, and l (t) represents other additional resistance coefficients; θ (x) is the gradient of the actual position x.

Suppose there is a known non-negative function ξ_f(t, x, v) and an unknown non-negative constant coefficient k>0 makes the following constraint hold:

|f_d(t,x,v)|≤κξ_f(t,x,v) (3)

wherein ξ_f(t, x, v) represents constraints for constructing the controller.

In the embodiment, the dynamic mathematical model of the train in the presence of the traction or braking force output signal fault is

u^F(t)＝ρ(t,t_ρ)u(t)+r(t,t_r) (4)

WhereinU (t) denotes the overall control law, ρ (t, t)_ρ) Is an unknown time-varying actuator fault factor, p (t, t)_ρ) Satisfies the following conditions:

ρand

fault factors rho (t, t) for unknown time-varying actuators, respectively_ρ) The upper and lower bounds of (1); r (t, t)_r) Is unknown time varying offset actuator failure and assumes

Is an unknown constant; t is t_ρAnd t_rRespectively, indicate the times at which actuator failure and bias failure occur.

In this embodiment, from an actual perspective, the actuator failure includes the following situations:

in addition, w_k(t) and xi_k(t) input and output of integral quadratic perturbation, w_k(t) and xi_kThe relationship between (t) is described as follows:

wherein, t₀Represents an initial time; psi_k(. to) represents a non-linear time-varying dynamics uncertainty representing a perturbation input w_k(t) and disturbance output ξ_kIntegral quadratic constraint of (·).

If there is a time series t_a≧ 0 (where the normal number a ranges from 1 to positive infinity) and a positive constant δ_k(k ═ 1, …, n) satisfies the following formula (7):

then, equation (5) may be considered solvable.

In this example, the presence of the unknown constant δ can be further obtained from the formulas (1) and (6)_w,k>0 makes equation (8) true:

therein, ζ₁、ζ₂、δ_wAre all in a form of short-hand writing,

in this embodiment, the asymmetric nonlinear saturation constraint of the actuator caused by the actual physical limitations of the actuator is expressed as follows:

wherein, b_l<0 and b_r>0 represents a first saturation amplitude and a second saturation amplitude, respectively; u. of_min<0 and u_max>0 denotes a first saturation clip and a second saturation clip, respectively; h is_r(u^F(t)) and h_l(u^F(t)) are unknown bounded nonlinear functions, all of which are used to represent the absence of actuator saturation with input u^F(t) a non-linear relationship therebetween.

Then, the saturated input error is:

accordingly, the high-speed train dynamic model equation (1) can be rewritten as:

s102, setting the position and the speed of the expected track, and establishing an expected track model;

in this embodiment, the established expected trajectory model is represented as:

wherein x is_r(t)、v_r(t) and a_r(t) respectively representing the position, velocity and acceleration of the desired trajectory at time t;

and

respectively represent x_r(t) and v_r(t) first derivative with respect to time t.

S103, establishing an actuator auxiliary saturation compensation system;

in this embodiment, the established actuator assisted saturation compensation system is represented as:

wherein, c₁And c₂A constant coefficient that is positive; lambda [ alpha ]₁(t) and lambda₂(t) both represent states of the actuator assisted saturation compensation system;and

respectively represent lambda₁(t) and lambda₂(t) a first derivative over time t; Δ u (t) represents a saturation input error, and as an input of the actuator assisted saturation compensation system, Δ u (t) Sat (u)^F(t))-u^F(t) of (d). In this embodiment, the actuator assisted saturation compensation system equation (13) may further includeThe writing is as follows:

wherein the content of the first and second substances,

thus, the solution of λ (t) is obtained from equation (14):

due to c₁And c₂Is a positive constant coefficient, so a is a hervitz matrix. Thus, there is a constant k₀And λ₀Such that:

for any two time-varying functions a (τ) and b (τ), the following Schwartz inequality is defined

Can obtain the product

In the embodiment, the actuator auxiliary saturation compensation system can effectively solve the problem that asymmetric nonlinear saturation of the actuator is limited, and the control input u (t) is not always kept in a supersaturated state by adjusting the control input signal u (t) in advance, so that the actuator loss is greatly reduced in actual engineering, resources are saved, and the system can run more stably.

S104, calculating a track tracking error based on the established high-speed train dynamic model, the expected track model and the actuator saturation compensation system, namely: position error and velocity error between the actual trajectory and the desired trajectory;

in this embodiment, the trajectory tracking error calculation formula is:

wherein e is_x(t) and e_v(t) represents the position error and velocity error between the actual track and the expected track, x (t) and v (t) are the actual position and actual velocity of the high-speed train at time t, x_r(t) and v_r(t) position and velocity, λ, of the desired trajectory, respectively₁And (t) is the state of the actuator assisted saturation compensation system.

S105, constructing a pseudo PID sliding mode surface based on the calculated track tracking error;

in this embodiment, the constructed pseudo PID sliding mode surface is expressed as:

where s (t) represents a pseudo PID sliding mode surface, α and β are constant coefficients greater than zero.

S106, determining an adaptive control law based on the constructed pseudo PID sliding mode surface, wherein the adaptive control law comprises the following steps: nominal control law u for achieving stable exponentials_n(t) compensation control law u for suppressing actuator failure and influence of integral quadratic disturbance_c(t) and adaptation law

The specific expression is as follows:

wherein u (t) represents the overall control law; u. of_n(t) represents a nominal control law for achieving exponential stability; u. of_c(t) and

respectively show means for restrainingCompensation control law and self-adaptation law of line fault and integral quadratic disturbance influence;

to represent

The first derivative with respect to time t; k, iota and mu all represent control parameters; Ψ (t) is a polynomial

In a shorthand form of (1);

to adjust the law of adaptation

The parameter of the steady speed of the vehicle,is a continuous bounded function satisfying:

wherein the content of the first and second substances,

as unknown normal numbers.

In the embodiment, the control strategy (namely, self-adaptive control law) determined based on the sliding mode surface s (t) does not need to need the acceleration information of the strategy expected track as the existing control strategy designed based on PI, PD, PID and the terminal sliding mode surface, so that the method is more economical and has more practical application value; the control strategy is simple in structure and small in calculation amount, and compared with the existing inversion control, adaptive neural network control and fuzzy control based strategies, the control strategy has the characteristics that the calculation time is greatly reduced, and online calculation can be realized more quickly, so that the dependence on hardware is reduced.

In the embodiment, the self-adaptive control law is added in the control input, so that the problem of track tracking of the high-speed train under the faults of the actuator, the asymmetric nonlinear saturation constraint of the actuator and the integral quadratic disturbance can be effectively solved, the effect of tracking the expected track of the high-speed train is improved, and the stability of a closed-loop system in an exponential form (the stability of the index for short) is ensured.

In order to verify the effectiveness of the anti-saturation adaptive pseudo PID sliding-mode fault tolerance control method for the high-speed train provided by the embodiment of the invention, the method further comprises the following steps:

s107, analyzing the stability of the determined self-adaptive control law, wherein the specific process is as follows:

the Lyapunov (Lyapunov) function is first defined as follows:

wherein the estimation errorIs defined as

WhereinρAnd

is an unknown time-varying actuator fault factor rho (t, t) in the formula (4)_ρ) Upper and lower bounds of, and₁defined in formula (8), γ^*Will be given in formula (22).

Calculating the first derivative of the sliding mode surface s (t) with respect to time:

from the formula (3), can be obtained

Wherein the content of the first and second substances,

since Ψ (t) is not less than 0, the adaptation law in equation (17)

The expression of (A) can be known:

can be obtained from the above formula

Is solved as

Then, if

Law of adaptation

Is always non-negative and thus can be obtained

The combined formulae (17), (20) and (21) can be calculated

By the constraint in formula (8)

Can obtain the product

Will compensate the control law u_c(t) is substituted into the formula (25) to obtain:

due to the fact that

And

thereby the adaptive law in the formula (17)

Expression and

can obtain the product

Thus, the derivative of the chosen Lyapunov function in equation (19) can be calculated as:

wherein, the positive number x₁Hexix-₂The values of (A) are as follows:

right-left multiplication of pair formula (28)

Can obtain the product

For formula (29) at [0, t]Quadrature within intervalDivide, and multiply left and right

The following can be obtained:

wherein the content of the first and second substances,

the definition of the chosen Lyapunov function in equation (19) can thus be derived:

further, it is possible to obtain:

when V (0) is bounded, s (t) and

respectively exponentially stabilized in a bounded interval

Therefore, the definition of the pseudo PID sliding mode surface in the equation (16) shows that the appropriate chi region is selected₁Hexix-₂Can ensure e_x(t) and e_v(t) also bounds the index to the tunable interval. Thus proving that the closed loop system stabilizes the exponent in the adjustable interval if the initial value is bounded.

In the embodiment, the stability analysis of the Lyapunov function proves that the reliability of the provided control strategy is high, the effect of tracking the expected track of the high-speed train can be improved, and the stable and bounded index is ensured.

To sum up, the anti-saturation adaptive pseudo PID sliding-mode fault-tolerant control method for a high-speed train provided by the embodiment of the present invention provides a control strategy for solving the problem of tracking a high-speed train track under disturbance of an actuator fault, asymmetric nonlinear saturation constraint of the actuator, an unknown dynamic model and an integral quadratic form, and in an actual project, the method can realize the track tracking control of the anti-disturbance, input saturation compensation and fault tolerance of the high-speed train according to the method while combining actual parameters (for example, the actual position and the actual speed of the high-speed train), and has the following advantages:

1) a pseudo PID sliding surface is proposed, based on which the determined control strategy (i.e.: adaptive control law) does not need to measure the acceleration information of the expected track as the existing control strategy designed based on PI, PD, PID and a terminal sliding mode surface, thereby being more economical and having practical application value.

2) The actuator auxiliary saturation compensation system can effectively solve the problem that asymmetric nonlinear saturation of the actuator is limited, control input does not need to be kept in a supersaturated state all the time by adjusting a control input signal in advance, actuator loss is greatly reduced in practical engineering, resources are saved, and the system can run more stably.

3) The determined control strategy has a simple structure and small calculation amount, and compared with the existing control strategy based on inversion control, adaptive neural network control and fuzzy control, the method has the characteristics of greatly reducing the calculation time and realizing online calculation more quickly, thereby reducing the dependence on hardware.

4) A self-adaptive control law is added in the control input, so that the problem of tracking the track of the high-speed train under the conditions of actuator faults, asymmetric nonlinear saturation constraint of the actuator and integral quadratic disturbance can be effectively solved, the effect of tracking the expected track of the high-speed train is improved, and the stability of the index is ensured.

5) The proposed control strategy was demonstrated by lyapunov function stability analysis (i.e.: adaptive control law), the method can improve the effect of tracking the expected track of the high-speed train and ensure the stable and bounded index.

6) The method has universality, is suitable for most of current second-order systems, and can simultaneously solve the problems of saturated input constraint, actuator fault and integral quadratic disturbance.

It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions.

While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.