Virtual hitch train adaptive preset time smooth pursuit control method

Abstract

The application discloses a virtual coupled train self-adaptive preset time smooth tracking control method, relates to the technical field of track transportation, and is characterized in that for each train in the virtual coupled train, based on a running control model of the train, an improved barrier Lyapunov function is used to constrain the interval distance of the train, a traditional barrier Lyapunov function is used to constrain the speed of the train, an adaptive smooth tracking controller is designed for the train, and the adaptive smooth tracking controller is used to control the train, the improved barrier Lyapunov function is established by combining the traditional barrier Lyapunov function and a preset time function, the interval distance of the train is constrained, a larger constraint can be ensured for the virtual coupled train in an initial state, and a smaller constraint range can be ensured for the virtual coupled train after the virtual coupled train is established, so that the line capacity is ensured.

Description

Technical Field

[0001] This invention relates to the field of rail transit technology, and in particular to an adaptive preset-time smooth tracking control method for virtual coupled trains based on an improved obstacle Lyapunov function. Background Technology

[0002] With the accelerating pace of urbanization, rail transit, due to its advantages of low energy consumption, large capacity, and high efficiency, has become an effective way to solve surface traffic congestion and has brought convenient and fast services to passengers. However, as cities continue to expand, new problems and challenges have emerged in the operation of urban rail transit. First, the increasing passenger demand has led to a tight supply-demand relationship, with the contradiction of insufficient capacity during peak hours becoming increasingly intense. To address this issue, operating companies are constantly reducing departure intervals and increasing departure frequency; the departure intervals on many lines during peak hours are already close to the minimum value of the existing operating system. On the other hand, for sections with large passenger flows, urban rail transit operating companies need to implement regular passenger flow control measures such as passenger flow restriction to control the number of passengers entering stations, thereby alleviating passenger pressure in urban rail transit and ensuring passenger safety. However, urban rail transit passenger flow exhibits significant temporal and spatial imbalances; continuously increasing train density will result in low train occupancy rates in certain time periods or sections, leading to wasted capacity. Therefore, effectively improving capacity under existing resource conditions and achieving precise matching of passenger and train flows is one of the important directions for the development of urban rail transit. To address these issues, scientists proposed the concept of virtual coupling, which uses wireless communication technology to achieve short-distance virtual coupling between trains, replacing the traditional mechanical coupling technology. This allows trains to autonomously form platoons, thereby shortening train tracking intervals and improving the transport capacity of rail transit.

[0003] Currently, the operation control of virtual trainsets still faces the following problems: While current research has considered the constraint on the spacing between virtual trainsets using the obstacle Lyapunov function, applying this function requires ensuring that the initial spacing of the virtual trainsets falls within the range set by the function. Otherwise, the algorithm will fail, leading to uncontrollable operation of the virtual trainsets. Therefore, the traditional obstacle Lyapunov function needs improvement to ensure that the virtual trainsets have a larger constraint in the initial state and a smaller constraint range after the virtual trainsets are established, thus guaranteeing line capacity. Summary of the Invention

[0004] The purpose of this invention is to provide an adaptive preset time smooth tracking control method for virtual coupled trains. An improved obstacle Lyapunov function is established by combining the traditional obstacle Lyapunov function and the preset time function to constrain the train interval distance. This ensures that the virtual coupled train has a large constraint in the initial state and a small constraint range after the virtual coupled train is established, so as to ensure the line capacity.

[0005] To achieve the above objectives, the present invention provides the following solution.

[0006] A virtual coupled train adaptive preset time smooth tracking control method includes the following steps.

[0007] Establish an operation control model for each train in the virtual coupled train; the virtual coupled train includes multiple trains, and the coupling method between two adjacent trains adopts virtual coupling.

[0008] For each train, based on the train's operation control model, the interval distance of the train is constrained using an improved obstacle Lyapunov function, and the speed of the train is constrained using a traditional obstacle Lyapunov function. An adaptive smooth tracking controller is designed for the train, and the train is controlled using the adaptive smooth tracking controller. The improved obstacle Lyapunov function is established by combining the traditional obstacle Lyapunov function and a preset time function.

[0009] According to specific embodiments provided by the present invention, the following technical effects are disclosed.

[0010] This invention provides an adaptive preset-time smooth tracking control method for virtual coupled trains. First, an operation control model for each train in the virtual coupled train is established. For each train, based on the operation control model, an improved obstacle Lyapunov function is used to constrain the train's interval distance, and a traditional obstacle Lyapunov function is used to constrain the train's speed. An adaptive smooth tracking controller is designed for the train, and this controller is used to control the train. The improved obstacle Lyapunov function is established by combining the traditional obstacle Lyapunov function and the preset-time function. By combining the traditional obstacle Lyapunov function and the preset-time function to establish the improved obstacle Lyapunov function, the interval distance of the trains is constrained, ensuring that the virtual coupled train has a large constraint in the initial state and a smaller constraint range after the virtual coupled train is established, thus ensuring the line's transport capacity. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart of the control method provided in Embodiment 1 of the present invention.

[0013] Figure 2 This is a schematic diagram of the control method provided in Embodiment 1 of the present invention.

[0014] Figure 3 This is a comparative schematic diagram of the overall operation of the virtual coupled train provided in Embodiment 1 of the present invention; wherein, Figure 3 (a) Figure 3 (c) Figure 3 (e) and Figure 3 (g) are the distance-time diagrams between the lead train and the following train 1, the distance-time diagrams between the following train 1 and the following train 2, the distance-time diagrams between the following train 2 and the following train 3, and the acceleration-time diagrams of each train, respectively, when using a control algorithm that takes into account sensor delay and controller delay. Figure 3 (b) Figure 3 (d) Figure 3 (f) and Figure 3 (h) are the distance-time diagrams between the lead train and the following train 1, the distance-time diagrams between the following train 1 and the following train 2, the distance-time diagrams between the following train 2 and the following train 3, and the acceleration-time diagrams of each train, respectively, when using a control algorithm that does not consider sensor delay and controller delay.

[0015] Figure 4 This is a schematic diagram comparing the operation of the virtual coupled train and the changes in the constraint range when using the control algorithm that considers sensor delay and controller delay, as provided in Embodiment 1 of the present invention; wherein, Figure 4 (a) is a schematic diagram of the distance-time between the lead train and the following train 1 and a schematic diagram of the change in the constraint range of the improved obstacle Lyapunov function; Figure 4 (b) is a schematic diagram of the distance-time between the lead train and the following train 1 and a schematic diagram of the change in the constraint range of the traditional obstacle Lyapunov function; Figure 4 (c) is a schematic diagram of the distance-time between following train 1 and following train 2 and a schematic diagram of the change in the constraint range of the improved obstacle Lyapunov function; Figure 4(d) is a schematic diagram of the distance-time between following train 1 and following train 2 and a schematic diagram of the change in the constraint range of the traditional obstacle Lyapunov function; Figure 4 (e) is a schematic diagram of the distance-time between following train 2 and following train 3 and a schematic diagram of the change in the range of the improved obstacle Lyapunov function constraint; Figure 4 (f) is a schematic diagram of the distance-time between following train 2 and following train 3 and a schematic diagram of the change in the constraint range of the traditional obstacle Lyapunov function. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] The purpose of this invention is to provide an adaptive preset time smooth tracking control method for virtual coupled trains. An improved obstacle Lyapunov function is established by combining the traditional obstacle Lyapunov function and the preset time function to constrain the train interval distance. This ensures that the virtual coupled train has a large constraint in the initial state and a small constraint range after the virtual coupled train is established, so as to ensure the line capacity.

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Example 1: This example provides a virtual coupled train adaptive preset time smooth tracking control method, such as... Figure 1 and Figure 2 As shown, it includes the following steps.

[0020] S1: Establish an operation control model for each train in the virtual coupled train; the virtual coupled train includes multiple trains, and the coupling method between two adjacent trains adopts virtual coupling.

[0021] S2: For each train, based on the train's operation control model, the interval distance of the train is constrained using an improved obstacle Lyapunov function, and the speed of the train is constrained using a traditional obstacle Lyapunov function. An adaptive smooth tracking controller is designed for the train, and the train is controlled using the adaptive smooth tracking controller. The improved obstacle Lyapunov function is established by combining the traditional obstacle Lyapunov function and a preset time function.

[0022] In this embodiment, establishing the operation control model for each train in the virtual coupled train may include: performing the following steps for each train in the virtual coupled train.

[0023] (1) Establish a dynamic model of the train.

[0024] Based on the longitudinal dynamic characteristics of the train, a force analysis is performed to establish the longitudinal dynamic model of the train. The following assumptions are made first: the train model is treated as a single-mass point model; the delay time of the sensors and controllers during train operation is known; the train travels on a straight track. According to Newton's second law, the force analysis of the train yields the following dynamic model (1).

[0025]

[0026] In equation (1), x i (t) represents the position of train i at time t; v is the derivative of the position of train i at time t; i (t) represents the speed of train i at time t; F is the derivative of the velocity of train i at time t; i (t) represents the actual output control force of train i at time t; r i (v i (t) represents the basic resistance of train i at time t; w i (x i (t) represents the additional resistance of train i at time t, and has been linearized and fitted.

[0027] According to Davis's equation, the basic resistance can be expressed as equation (2).

[0028] r i (v i (t))=c1+c2v i (t)+c3(v i (t)) 2 (2).

[0029] In equation (2), c1, c2 and c3 are all unknown constants, but their upper limits are known.

[0030] Additional resistance can be further divided into the resistance shown in equation (3) below.

[0031] w i (x i (t))=w r (x i (t))+w c (x i (t))+w t (x i (t)) (3).

[0032] In equation (3), w r (x i (t) represents the ramp resistance; w c (x i (t) represents the curve resistance; w t (x i (t) represents the tunnel resistance. In this embodiment, the above three resistances are considered as functions that have already undergone linearization and fitting.

[0033] (2) Considering controller delay and sensor delay, establish the relationship between the actual output control force and the theoretical output control force of the train.

[0034] Based on the delay of the train controller, the relationship between the actual output control force of the train and the theoretical output control force of the control command input to the controller can be expressed as the following formula (4).

[0035]

[0036] In equation (4), τ is the derivative of the actual output control force of train i at time t; i The delay time of the controller for train i; sat(U i (th i U represents the saturated theoretical output control force of train i at time t, taking into account sensor delay; i (th i The theoretical output control force of train i at time t, taking into account sensor delay; h i Let be the delay time of the sensor for train i.

[0037] (3) Approximate, estimate and Laplace transform the relation to obtain the transformed relation.

[0038] This embodiment uses the Pade approximation method combined with the Laplace transform for approximation processing, and the specific process is as follows: Equation (5) and Equation (6).

[0039] For sat(U i (th i Perform a Laplace transformation to obtain the following equation (5).

[0040]

[0041] In equation (5), This indicates that a Laplace transformation is performed on sat(Ui(t-hi)); ν represents the Laplace variable; This indicates that a Laplace transform is performed on sat(Ui(t)); sat(U i (t) represents the saturation theoretical output control force of train i at time t, without considering sensor delay; U i (t) represents the theoretical output control force of train i at time t without considering sensor delay.

[0042] By performing the Pade approximation on equation (5), we obtain equation (6).

[0043]

[0044] This embodiment uses an additional variable to estimate sat(U) i (th i The calculation method is as follows (7).

[0045] x i,n+1 (t)=sat(U i (t))+sat(U i (th i )) (7).

[0046] In equation (7), x i,n+1 (t) represents the value of train i at time t used to estimate sat(U). i (th i And the estimated quantity of the design.

[0047] After performing the Laplace transformation on equation (7), and combining equations (5) and (6), we can obtain equation (8).

[0048]

[0049] In equation (8), Represents the relationship between xi,n +1 (t) is subjected to Laplace transform.

[0050] Multiply equation (8) by the denominator of equation (8) (i.e., 1+h) iv / 2), and perform an inverse Laplace transform on it to obtain the following equation (9).

[0051]

[0052] In equation (9), for sat(U i The derivative of (t)); For x i,n+1 The derivative of (t).

[0053] Rearranging equation (9), we obtain equation (10).

[0054]

[0055] In equation (10), λ i Let i be a constant corresponding to train i, which is a constant related to sensor delay, and its calculation method is as follows:

[0056] x can be calculated using (10). i,n+1 The specific value of (t).

[0057] (4) The dynamic model is adjusted using the transformed relation to obtain the train operation control model.

[0058] After the above approximation, estimation, Laplace transformation and other operations, the dynamic model of the train can be rewritten as the following equation (11). Specifically, by substituting equations (2), (4), (7) and (10) into the dynamic model of equation (1), the resulting operation control model is as follows (11).

[0059]

[0060] In equation (11), x i (t) represents the position of train i at time t; v is the derivative of the position of train i at time t; i (t) represents the speed of train i at time t; Let a be the derivative of the velocity of train i at time t; i (t) represents the acceleration of train i at time t; τ is the derivative of the acceleration of train i at time t; i The delay time of the controller for train i; sat(U i (th i The theoretical saturation output control force of train i at time t is considered when sensor delay is taken into account; U i (th i The theoretical output control force of train i at time t, taking into account sensor delay; hi r is the delay time of the sensor of train i; i (v i (t) represents the basic resistance of train i at time t; w i (x i (t) represents the additional resistance of train i at time t, which has been linearized; c2 is a constant; c3 is a constant; x is the derivative of the additional resistance of train i at time t; i,n+1 (t) represents the value of train i at time t used to estimate sat(U). i (th i The estimated quantity of the design; sat(U) i (t) represents the saturation theoretical output control force of train i at time t, without considering sensor delay; U i (t) represents the theoretical output control force of train i at time t, without considering sensor delay; For x i,n+1 The derivative of (t); λ i Let i be the constant corresponding to train i.

[0061] This embodiment adds the influence of various uncertain factors to the train's dynamics model, performing more accurate linearization analysis to establish a more precise virtual coupled train operation control model. The established virtual coupled train operation control model fully considers sensor and controller delays compared to traditional train dynamics models. Existing technologies give less consideration to sensor and controller delays. Current control algorithms often consider the impact of the train's operating environment on the algorithm, neglecting the delays in sensor acquisition of status information and traction motor reception of control commands. In contrast, the train operation control model in this embodiment fully considers the uncertain resistance caused by the external environment to the virtual coupled train, as well as the delays of the train's internal sensors and controllers.

[0062] The virtual coupled train operation control model established in this embodiment involves various uncertain influencing factors, including: sensor delay and controller delay of the train, and basic and additional resistance generated by the external environment. In order to design an adaptive smooth tracking controller for the train based on the train operation control model, this embodiment processes the unknown resistance caused by the external environment and the sensor and controller delays. The processing method includes the following steps.

[0063] (1) When designing an adaptive smooth tracking controller for a train, a radial basis function neural network is used to estimate the basic resistance and additional resistance in the operation control model.

[0064] To address the unknown resistance generated by the external environment (i.e., basic resistance and additional resistance), a radial basis function neural network (RBF neural network) is introduced. In other words, to solve the problem of external resistance with unknown nonlinear and uncertain characteristics, the RBF neural network is used to estimate these unknown nonlinear parameters.

[0065] For a continuous nonlinear function g(Z), assume Z belongs to a compact set Ω Z Then g(Z) can be estimated as follows, as shown in equation (12).

[0066]

[0067] In equation (12), W * Let S(Z) represent the ideal weights of the RBF neural network; let S(Z) represent the Gaussian kernel function; let δ(Z) represent the approximation error of the RBF neural network. In practical applications, since the approximation error δ(Z) of the RBF neural network is bounded, this embodiment assumes that this unknown but bounded approximation error is ξ.

[0068] The definition of the Gaussian kernel function is given below, as shown in equation (13).

[0069]

[0070] In equation (13), S i (Z) represents the Gaussian kernel function of the i-th kernel; η represents the center point of the Gaussian kernel function; i This represents the width of the Gaussian kernel function.

[0071] Therefore, the formula for calculating the weights of the RBF neural network can be obtained as follows (14).

[0072]

[0073] In equation (14), W represents the weight vector.

[0074] definition Let represent the largest network weight in the RBF neural network, i represent the i-th train in the virtual coupling, j represent the index of the radial basis function, and k represent the step number in the backstep control; Define It is for θ i,k The estimate, This represents the estimation error. In the subsequent controller design process, Young's inequality can be used to estimate the basic and additional resistance generated by the external environment. This will be discussed in detail in the subsequent controller design process.

[0075] (2) Sensor delay.

[0076] Since the approximation, estimation and Laplace transformation have been performed using equations (5)-(10) when establishing the operation control model, the operation control model no longer contains the sensor delay time. That is, when using the operation control model shown in equation (11) for subsequent controller design, the consideration of the delay parameter in the controller will be transformed into the consideration of the adaptive parameter of the design.

[0077] (3) Controller delay.

[0078] To address controller delay, this embodiment incorporates controller delay compensation into the backstepping control. This will be further explained in conjunction with the controller design process later.

[0079] In the existing technology, there is still no clear specification for the interval distance strategy of virtual train coupling. In current schemes, the running interval distance of virtual train coupling is often set to a constant. However, during the dynamic braking process of the trains before and after the virtual train coupling, the constant interval distance often cannot guarantee the driving safety of the virtual train coupling. Using relative braking distance as the interval strategy of the control algorithm can guarantee considerable safety. Therefore, in this embodiment, in order to ensure safety, relative braking distance is used as the interval strategy between virtual train coupling. That is, when designing the adaptive smooth tracking controller for the train, relative braking distance is used as the interval strategy. Based on this interval strategy, the control error of the virtual train coupling is defined as follows: (15).

[0080] e i (t)=x i (t)-x i-1 (t)-ψ i (t) (15).

[0081] In equation (15), e i (t) represents the distance control error between train i and the preceding train at time t; x i (t) represents the position of train i at time t; x i-1 (t) represents the position of train i-1 (which is the preceding train i) at time t; ψ i (t) represents the relative braking distance of train i at time t, and represents the spacing strategy between virtual coupled trains.

[0082]

[0083] In equation (16), χ i This is the range size coefficient corresponding to train i, which is a customizable parameter that directly determines the size coefficient of the virtual coupled train interval distance; l iThis represents the minimum safe distance for train i, a customizable parameter that indicates the minimum safe distance required to ensure the safe operation of the virtual coupled train; v i (t) represents the speed of train i at time t, indicating the actual running speed of train i; a f,i,min v is the minimum braking acceleration of train i; i-1 (t) represents the speed of train i-1 at time t; a f,i-1,max This represents the maximum braking acceleration of train i-1; Let be the activation function of train i at time t.

[0084]

[0085] Based on the above control error, the specific control objective to be achieved in the operation control of the virtual coupled train is as follows (18).

[0086]

[0087] In equation (18), the first equation represents the control target for the interval distance of the virtual coupled trains, and the second equation represents the control target for the speed of the virtual coupled trains. The interval strategy of the control algorithm is designed as a relative braking distance to ensure the safe operation of the virtual coupled trains.

[0088] Under the premise of achieving the above control objectives, the virtual coupled train operation first needs to ensure that the interval between trains is not too large to affect the actual operating efficiency and not too small to affect the actual operating safety; and the train speed also needs to be limited to meet the actual operating needs. Therefore, the following inequality (19) needs to be designed to limit the train's operating status.

[0089]

[0090] In equation (19), e i (t) represents the lower limit of the control error of the interval distance between train i and the preceding train; This is the upper limit of the control error for the distance between train i and the preceding train; v i This is the lower limit of the speed of train i, that is, the minimum speed allowed for the operation of virtual coupled trains; This represents the upper limit of train i's speed, i.e., the maximum speed allowed for virtual coupled train operation.

[0091] Since the control target is based on the relative braking distance, which changes continuously over time, the design... and e i (t) is shown in equation (20).

[0092]

[0093] To realize the state constraints between virtual coupled trains, a traditional obstacle Lyapunov function is designed as shown in equation (21).

[0094]

[0095] In equation (21), f(e i (t) represents the traditional barrier Lyapunov function that constrains the interval distance; e i (t) represents the distance control error between train i and the preceding train at time t; ζ i (t) represents the relationship between z i The added upper and lower limits (t) indirectly constrain the upper and lower limits of the spacing between virtual connections; γ i,v This represents the speed of train i within the virtual coupling after passing through a traditional obstacle using the Lyapunov function; A traditional barrier Lyapunov function for constraining velocity; for The inverse function of .

[0096] In the aforementioned traditional barrier Lyapunov function, the initial interval between trains must be located at... The algorithm can only solve the problem when the virtual trains are in a certain interval. However, in actual operation, the virtual trains may not meet the above requirements before the formation is established, which will lead to the failure of the algorithm. If the upper limit of this interval constraint is increased, it will not meet the operational requirements after the virtual train formation is established. Therefore, this embodiment introduces a preset time function to remove the above restriction. Using the preset time function, the interval constraint between virtual trains can converge from the initial value to a smaller interval constraint value required after the virtual train formation is established within a specified time.

[0097] The preset time function is defined as follows (22).

[0098]

[0099] In equation (22), φ i (t) is the preset time function of train i at time t; β i This is a user-defined parameter, meaning it's a constant whose value can be defined by the user, but it must satisfy certain conditions. T i This is a custom parameter used to determine the time it takes for the interval between virtual coupled trains to enter a pre-defined range.

[0100] The control error of the virtual coupled train operation control algorithm is redefined based on the above preset time function as shown in equation (23).

[0101] zi (t)=φ i (t)e i (t) (23).

[0102] In equation (23), z i (t) represents the distance control error between train i and the preceding train at time t, determined based on a preset time function.

[0103] Based on equation (23), the inequality shown in equation (24) can be obtained.

[0104]

[0105] Based on equation (24) above, when t = T i At this point, the spacing constraint between the virtual coupled trains will converge to the pre-set constraint range after the virtual coupling is established, which is also the constraint range of the traditional obstacle Lyapunov function. From this inequality, it can be seen that at T... i Over time, the spacing between virtual coupled trains can gradually converge from a large allowable range (i.e., constraint range) initially set to a smaller allowable range after the virtual coupled trains are established to meet operational needs.

[0106] The obstacle to improvement is the Lyapunov function as shown in equation (25).

[0107]

[0108] In equation (25), f(e) i (t) represents the barrier Lyapunov function for improvement; e i (t) represents the distance control error between train i and the preceding train at time t; ζ i (t) represents the relationship between z i (t) Added upper and lower limits; z i (t) represents the control error of the interval distance between train i and the preceding train at time t, determined based on a preset time function; φ i (t) is the preset time function of train i at time t.

[0109] Through the above design, the traditional obstacle Lyapunov function shown in Equation (21) can be used to constrain the speed of the trains in the virtual coupling, ensuring that the trains will not exceed the operating speed specified by ATS (Automatic Train Supervision). The preset time function is combined with the traditional obstacle Lyapunov function to form an improved obstacle Lyapunov function, and the improved obstacle Lyapunov function is applied to the interval distance between trains in the virtual coupling. That is, the improved obstacle Lyapunov function shown in Equation (25) is used to constrain the interval distance of the trains in the virtual coupling, so as to eliminate the requirement for the interval distance of trains in the virtual coupling before the establishment of the virtual coupling, and give the specific time when the interval distance of trains in the virtual coupling can converge to the interval distance constraint range specified after the establishment of the virtual coupling. Thus, by designing the corresponding obstacle Lyapunov function to constrain the state of the trains, the state constraint of the virtual coupling trains is completed.

[0110] In addition to constraining the speed and spacing of the trains, this embodiment also designs a saturated input function for the control force of the virtually coupled trains and performs linearization processing to ensure that the control force output by the trains in the virtual coupling has an output range, so as to form a saturated constraint of the control force. The linearization method of the saturated constraint of the control force includes the following steps.

[0111] The specific expression for the control force under saturation (i.e., the saturation theoretical output control force of train i at time t considering sensor delay) is as follows (26).

[0112]

[0113] In equation (26), U i,M =max(|U i (t)|) represents the maximum or minimum theoretical output control force that train i can output during operation. Here, it is assumed that the maximum and minimum theoretical output control forces of train i are the same.

[0114] Because equation (26) has discontinuities, it leads to sat(U i (t) is not a continuous function, therefore, when designing the controller, it needs to be approximated to make sat(U) = 0. i (t) is continuous, and the specific method is as follows (27).

[0115]

[0116] In equation (27), g(U) i (t) is sat(U i An approximate function of (t)).

[0117] Using equations (26) and (27) above, we can obtain sat(U i The function (t) is transformed into the following equation (28).

[0118]

[0119] In equation (28), ρ(U i (t) is the estimation error generated after estimating it, which has a known upper limit. To handle this estimation error, the filter shown in equation (29) is used for estimation.

[0120]

[0121] In equation (29), For estimating the sum of sat(U) with controller delay i Estimate the error present in the approximation of (t); for The derivative of .

[0122] Based on this, the constraints of the virtual coupled train operation control model include: controller saturation constraints, train speed constraints within the virtual coupled train, and interval distance constraints between trains.

[0123] Based on the train operation control model shown in Equation (11), constraints are added to the operation control model of the virtual coupled train, including: saturation constraint of control force (Equation (26)), speed constraint of trains within the virtual coupled train, and interval distance constraint between trains within the virtual coupled train. Corresponding control errors are designed according to the operating environment. Based on the study of the operating characteristics of the virtual coupled train, the above constraints during train operation are transformed into constraints on control parameters to ensure the stability and safety of train operation. This embodiment, based on the train operation control model, the processing method for each influencing factor in the operation control model, and the speed constraint, interval distance constraint, and saturation constraint of the virtual coupled train, designs an adaptive control algorithm to design the controller for the virtual coupled train, ensuring smooth tracking control of the virtual coupled train under conditions that meet operational requirements, external environmental interference, and uncertainty of internal parameters.

[0124] In this embodiment, designing an adaptive smooth tracking controller for the train may include: designing an adaptive smooth tracking controller for the train using an adaptive backstepping control method. The specific design process of using adaptive backstepping control to design the controller for the third-order dynamic model of the virtual coupled train operation includes the following steps.

[0125] (1) First, design the virtual control input for the first-order error in adaptive backstepping control.

[0126] Define the first-order virtual tracking control target as z i,1 =φ i *e i Then its derivative is as follows (30).

[0127]

[0128] Based on the aforementioned first-order virtual tracking control target and its derivative, a Lyapunov function V for the first-order error is designed. i,1 As shown in equation (31).

[0129]

[0130] By differentiating equation (31), we can obtain equation (32).

[0131]

[0132] Define a second-order virtual tracking control target z i,2 As shown in equation (33).

[0133] z i,2 =γ i,v -α i,1 (33)

[0134] In equation (33), α i,1 It is a first-order virtual control input.

[0135] Based on the above equation (33) and the mean value theorem, we can obtain the following equation (34).

[0136]

[0137] In equation (34), α i,1 +∈z i,2 ∈ is between α i,1 With z i,2 +α i,1 An unknown quantity between them.

[0138] Substituting equation (34) into equation (32) yields equation (35).

[0139]

[0140] The inequalities shown in equations (36) and (37) can be obtained using Young's inequality.

[0141]

[0142]

[0143] In the above formula, ζ i,1 For z i,1 The added upper and lower limits indirectly constrain the interval distance of virtual connections. This is a customizable variable used in Young's inequality.

[0144] Substituting the above inequality into the Lyapunov function for the first-order virtual error (i.e., equation (35)), we can obtain equation (38).

[0145]

[0146] Based on the above inequalities, a first-order virtual control input α can be designed. i,1 As shown in equation (39).

[0147]

[0148] In equation (39), k i,1 It is a user-defined variable.

[0149] (2) Then, the virtual control input is designed for the virtual tracking error of the second-order control system in the adaptive backstepping control.

[0150] For the error of the second-order control system, the Lyapunov function V is designed as shown in equation (40). i,2 .

[0151]

[0152] In equation (40), This represents the error between the estimated and actual values ​​of the squared maximum weights of the RBF neural network used in second-order backstepping control.

[0153] Differentiating equation (40) yields equation (41).

[0154]

[0155] In equation (41), These are adaptive estimation parameters used to estimate the squared maximum weights of the RBF neural network used in second-order backstepping control.

[0156] Design a third-order control system with virtual tracking error z. i,3 As shown in equation (42).

[0157]

[0158] In equation (42), α i,2 τ represents the second-order virtual control force in backstep control. iIndicates controller delay; Indicates sensor delay; By using the virtual tracking error of the third-order control system set in the third step of backstepping control, Ensure compensation for controller and sensor delays.

[0159] Substituting the virtual tracking error of the third-order control system into the Lyapunov function (i.e., equation (41)), we can obtain equation (43).

[0160]

[0161] The unknown term F in the Lyapunov function shown in equation (43) above i,2 This can be summarized as equation (44).

[0162]

[0163] By processing equation (44) using an RBF neural network, performing the first step of scaling as shown in equation (45), and further using Young's inequality, performing the second step of scaling as shown in equation (45), we can obtain equation (45).

[0164]

[0165] In equation (45), W i,2 * S represents the weight vector of the RBF neural network used in second-order backstepping control. i,2 Z represents the radial basis function vector of the RBF neural network used in second-order backstepping control. i,2 The vector containing the current state of the train under study, its preceding state, and the designed adaptive estimation parameters, which is required in second-order backstepping control, is used as the input to the RBF neural network. δ i,2 The error between the estimated and actual values ​​of the RBF neural network used in second-order backstepping control; θ i,2 p is the square of the maximum weights of the RBF neural network used in second-order backstepping control. i,2 For custom parameters; f i,2 For custom parameters; ξ i,2 This represents the upper limit of the error between the estimated value and the actual value of the RBF neural network used in second-order backstepping control.

[0166] By using equation (45), the unknown functional relationship is no longer contained in the scaling process of the Lyapunov function, thus completing the process of estimating the basic resistance and additional resistance of the train using the RBF neural network.

[0167] By processing the unknown term using equation (45), equation (43) can be transformed into equation (46).

[0168]

[0169] Based on the Lyapunov function processing described above, the second-order virtual control input α can be designed as shown in equation (47). i,2 and adaptive parameters

[0170]

[0171] In equation (47), k i,2 For custom parameters; c i,2 For custom parameters.

[0172] (3) Finally, the actual control input is designed for the virtual tracking error of the third-order control system in adaptive backstepping control.

[0173] The Lyapunov function V is designed for the error of a third-order control system as shown in equation (48). i,3 .

[0174]

[0175] In equation (48), This represents the error between the estimated and actual values ​​of the squared maximum weights of the RBF neural network used in the third-order backstepping control.

[0176] After differentiating equation (48), we can obtain equation (49).

[0177]

[0178] In equation (49), These are adaptive parameters.

[0179] Similarly, from the derivative calculation of the Lyapunov function above, we can summarize the unknown term F. i,3 As shown in equation (50) below.

[0180]

[0181] Next, the above unknown terms are scaled in two steps using the RBF neural network and Young's inequality to obtain the inequality shown in equation (51).

[0182]

[0183] In equation (51), W i,3 *S represents the weight vector of the RBF neural network used in third-order backstepping control. i,3 Z represents the radial basis function vector of the RBF neural network used in third-order backstepping control. i,3 The vector containing the current state of the train under study, its preceding state, and the designed adaptive estimation parameters, which is required in the third-order backstepping control, is used as the input to the RBF neural network. δ i，3 The error between the estimated and actual values ​​of the RBF neural network used in the third-order backstepping control; θ i,3 p is the square of the maximum weight of the RBF neural network used in the third-order backstepping control. i,3 For custom parameters; f i,3 For custom parameters; ξ i,3 This is the upper limit of the error between the estimated value and the actual value of the RBF neural network used in the third-order backstepping control. Through equation (51), the unknown functional relationship is no longer contained in the scaling process of the Lyapunov function, thus completing the process of estimating the basic resistance and additional resistance of the train using the RBF neural network.

[0184] Substituting the above inequality into the Lyapunov function (i.e., equation (49)), we can obtain the following equation (52).

[0185]

[0186] In equation (52), The parameter used in Young's inequality that can be adjusted by the user; d i,1 This is the upper limit of the additional resistance; The parameter used in Young's inequality, which can be adjusted by the user; d i,2 This is the upper limit of the derivative of the additional resistance after linearization.

[0187] Based on the above inequalities, the controller input is designed as shown in equation (53) and the adaptive parameters are designed as shown in equation (54).

[0188]

[0189]

[0190] Equation (53) is the controller designed in this embodiment. In the above equation, U i The theoretical output control force for train i; k i,3 For custom parameters; z i,3 This refers to the virtual tracking error of a third-order control system. For custom parameters; p i,3 For custom parameters; Si,3 Z represents the radial basis function vector (also known as the Gaussian kernel function output vector) of the RBF neural network used in third-order backstepping control; i,3 The vector containing the current state of the studied train, its preceding train state, and the designed adaptive estimation parameters, which is required in the third-order backstepping control, is used as the input to the RBF neural network; τ i The delay time of the controller for train i; a i f is the acceleration of train i; i,3 For custom parameters; A user-adjustable parameter used in Young's inequality; This is a user-adjustable parameter used in Young's inequality; c i,3 This is a customizable parameter.

[0191] After obtaining the controllers of each train, the upper-level ATS sends time parameters and starts detecting the train position. When the distance between the virtual coupled train and the preceding train reaches the pre-set constraint range after the virtual coupled train is established, the arrival information is sent to the upper-level ATS to facilitate further decision-making by the upper-level ATS. This allows the virtual coupled train to be controlled according to the smooth tracking control strategy required in different stations and sections under different environments.

[0192] In this embodiment, the obtained virtual control force, the adaptive laws of each neural network, and the Lyapunov functions designed for each order are substituted into the third-order Lyapunov function, that is, equations (38), (39), (43), (47), (53), and (54) are substituted into the third-order Lyapunov function to obtain the following equations (55)-(57).

[0193]

[0194]

[0195]

[0196] From the above formula, we can obtain... For a continuous nonsingular function V(t), the following inequality can be obtained, as shown in equation (58).

[0197]

[0198] The above equation demonstrates that the controller input and adaptive law designed in this embodiment can guarantee asymptotic convergence of the system, thereby ensuring the stability of the virtual coupled train operation. This proves the stability of the virtual coupled train.

[0199] Based on the above control methods, it is proven through backstepping control and Lyapunov stability theory that the virtual coupled train can maintain the overall operational stability of the virtual coupled train when the speed of the lead train changes.

[0200] This embodiment relates to a method for smooth tracking control of virtual coupled trains based on an improved obstacle Lyapunov function and adaptive backstepping control. Belonging to the field of smooth tracking control for virtual coupled trains in rail transit, the method first establishes a unit train operation control model considering sensor and controller delays. Based on the train operation control model and communication network, the desired tracking distance between trains is designed based on the concept of relative braking distance. The speed of the virtual coupled trains is constrained using a traditional obstacle Lyapunov function, and the interval distance between virtual coupled trains is constrained using an improved obstacle Lyapunov function. An adaptive smooth tracking controller is designed for the unit train by combining preset-time adaptive backstepping control theory. Multiple adaptive smooth tracking controllers are applied to each train to achieve smooth tracking control of multiple virtual coupled trains. Under the premise of ensuring safety, this method can effectively shorten the train tracking interval distance, achieving safe and efficient operation of multiple trains.

[0201] To further explain the technical solution of the present invention, the following simulation of the technical solution of this embodiment is performed using four trains as an example. The simulation process includes the following steps.

[0202] A. A simulation was conducted where four trains were virtually coupled together. Each train unit received information from the train ahead and obtained its own current status. Simulations were also performed to determine different operating speeds for the virtual coupling, and the operation of the virtually coupled trains under these different speed requirements was observed through simulation of the train controller.

[0203] A.1 Initialization and Setup: Create models and controllers for four trains: Define custom parameters for the controllers, set the starting position, speed and acceleration of each train; set the simulation time and simulation step size.

[0204] A.2 Result Analysis and Verification: Output the position and status of each train and observe the stability of the virtual coupled train operation; if the virtual coupled train operation is stable, it indicates that the system has good queue stability; if it is unstable, the system's custom parameters need to be adjusted and the simulation needs to be repeated.

[0205] B. The algorithm of the controller designed in this embodiment is compared with the traditional control algorithm that does not consider the delay of the train's sensors and controllers in the same virtual coupling operation scenario. The comparison of the virtual coupling operation results shows that the processing method for the delay of the train's sensors and controllers in the algorithm used in this embodiment is effective.

[0206] C. Adjust the time parameters in the preset time function used in this embodiment, and observe the operation of the virtual coupled train under different time parameters to determine whether the preset time function used in this embodiment can indeed ensure that the constraint range of the interval distance between virtual coupled trains can converge from a relatively large interval under the initial conditions to a relatively small interval that is allowed to change after the virtual coupled train is established within a specified time.

[0207] The above simulation algorithm can be implemented using MATLAB, or languages ​​such as Python and C++. This embodiment uses MATLAB.

[0208] In this embodiment, urban rail transit trains are taken as the research object, and a simulation experiment is conducted using subway line data as an example. In the simulation experiment, it is assumed that the virtual coupling consists of four trains: one lead train and three follower trains. Within 0-800s, the lead train runs at 20m / s; within 800-1600s, the lead train runs at 32m / s; and within 1600-2400s, the lead train runs at 12m / s. Simultaneously, the times for each follower train to enter the specified constraint range from the train in front are set to 40s, 28s, and 15s, respectively.

[0209] Figure 3 (b) Figure 3 (d) Figure 3 (f) Figure 3 (h) shows the overall operation of the virtual coupled train under the control algorithm that does not consider sensor delay and controller delay. It can be seen that the overall operation of the virtual coupled train is unstable, with large errors, and it is far from the actual tracking target. In addition, the acceleration fluctuates greatly. Figure 3 (a) Figure 3 (c) Figure 3 (e) Figure 3 (g) shows the overall operation of the virtual coupled train under the control algorithm that takes into account sensor delay and controller delay. It can be seen that the virtual coupled train operates stably and can meet the actual control requirements with small error.

[0210] Figure 4 (a) Figure 4 (c) Figure 4 (e) shows the operation of each train in the virtual coupling under the control algorithm that takes into account sensor delay and controller delay, and how the range of the improved obstacle Lyapunov function constraint changes with the speed of each train. It can be seen that the distance between each train and the train in front is always within the range of the improved obstacle Lyapunov function constraint. Figure 4 (b) Figure 4 (d) Figure 4(f) shows the operation of each train in the virtual coupling under a control algorithm that considers sensor and controller delays, and how the range of constraints imposed by the traditional obstacle Lyapunov function changes with the speed of each train. Due to the nature of the preset time function used in the improved obstacle Lyapunov, when the virtual coupling's operation time reaches the preset time, the range of constraints imposed by the improved obstacle Lyapunov function will converge to the preset range of constraints after the virtual coupling is established. This range is the same as the range of constraints imposed by the traditional obstacle Lyapunov function. It can be seen that each following train will converge to the range constrained by the traditional obstacle Lyapunov function within the preset time.

[0211] The control method provided in this embodiment is an adaptive backstepping smooth tracking control method for virtual coupled trains, based on a relative braking distance interval strategy and an improved obstacle Lyapunov function, considering the delays of train sensors and controllers. While considering the interval strategy based on relative braking distance, it fully considers the delays of sensors and controllers inside the train and the uncertain resistance caused by the external environment to the operation of the virtual coupled train, improving the transportation efficiency, stability, and robustness of the virtual coupled system. Furthermore, the use of the improved obstacle Lyapunov function allows the proposed control algorithm to be applicable to more operating scenarios of virtual coupled trains. Compared with existing technologies, the advantages of this embodiment are as follows.

[0212] (1) The virtual coupled train operation control model fully considers sensor delay and controller delay on the basis of the traditional train dynamics model, so as to fully consider the uncertain resistance caused by the external environment to the virtual coupled train and the delay of the train's internal sensors and controllers during train operation.

[0213] (2) An improved obstacle Lyapunov function is used to constrain the interval distance of virtual coupled trains. Specifically, the preset time method (i.e., preset time function) is combined with the traditional obstacle Lyapunov function to form an improved obstacle Lyapunov function. The improved obstacle Lyapunov function is then applied to the interval distance between trains in the virtual coupled trains to eliminate the requirement for the interval distance of trains in the virtual coupled trains before the establishment of the virtual coupled trains. The specific time is given for the interval distance of trains in the virtual coupled trains to converge to the interval distance constraint range specified after the establishment of the virtual coupled trains.

[0214] (3) The interval strategy of the control algorithm is designed as relative braking distance to ensure the safe operation of the virtual coupled train. The relative braking distance is used as the interval strategy instead of the fixed constant. When the virtual coupled train has an emergency failure, the safe operation of the virtual coupled train can be guaranteed.

[0215] (4) The speed of the virtual coupled train is constrained by the traditional obstacle Lyapunov function to ensure that the train does not exceed the operating speed specified by the ATS. At the same time, the control force of the virtual coupled train is designed with a saturated input function and linearized to ensure that the control force output by the train in the virtual coupled train has an output range. The constraints of the virtual coupled train operation control model in this embodiment include: saturation constraint of control force, speed constraint of train in the virtual coupled train and interval distance constraint between trains.

[0216] Based on the above advantages, this embodiment has the following technical effects.

[0217] (1) Strong anti-interference capability: It fully considers the internal sensor delay and controller delay of the train, as well as the uncertain resistance caused by the external environment to the virtual coupled train, so that the system has higher stability and reliability, thereby providing support for the virtual coupled train control strategy and technology.

[0218] (2) Improve the robustness of the control algorithm and make it easier for ATS to make decisions; For the interval distance of virtual coupled trains, an improved obstacle Lyapunov function that combines the traditional obstacle Lyapunov function with the preset time method is used to constrain it, ensuring that there is a large constraint range for the interval distance of virtual coupled trains at the beginning of the establishment of virtual coupled trains; and a small constraint range for the interval distance of virtual coupled trains after the establishment of virtual coupled trains. The above operation is used to prevent the solution error problem that may occur when using the traditional obstacle Lyapunov function, and the preset time function gives the time for the interval distance of virtual coupled trains to enter the preset constraint range after the establishment of virtual coupled trains, which is convenient for ATS to make further adjustments.

[0219] (3) Further ensure the safe operation of virtual coupled trains; on the basis of fully considering the lower limit of the interval distance required for train operation safety, the interval strategy between virtual coupled trains is calculated by relative braking distance, which can further ensure the safe operation of virtual coupled trains during dynamic braking.

[0220] (4) Achieve smooth tracking control; use relative braking distance as the interval strategy instead of using a fixed constant as the interval strategy, so as to ensure the safe operation of the virtual coupled train when an emergency failure occurs; and achieve smooth tracking control of the virtual coupled train through state constraints.

[0221] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A virtual coupled train adaptive preset time smooth pursuit control method, characterized in that, include: Establish an operation control model for each train in the virtual coupled train; the virtual coupled train includes multiple trains, and the coupling method between two adjacent trains adopts virtual coupling; For each train, based on the train's operation control model, an improved obstacle Lyapunov function is used to constrain the train's interval distance, and a traditional obstacle Lyapunov function is used to constrain the train's speed. An adaptive smooth tracking controller is designed for the train, and the adaptive smooth tracking controller is used to control the train. The improved obstacle Lyapunov function is established by combining the traditional obstacle Lyapunov function and a preset time function. The improved barrier Lyapunov function is: ； in, f ( e i ( t The Lyapunov function is a barrier to improvement. e i ( t (for trains) i exist t The distance between the vehicle and the vehicle in front is controlled to minimize error. To z i ( t Added upper and lower limits; z i ( t (This refers to a train determined based on a preset time function.) i exist t Controlling the distance between the vehicle and the vehicle in front to minimize errors; For train i exist t The preset time function for each moment; The preset time function is: ； in, It is an adjustable constant; T i It is an adjustable constant; The adaptive smooth tracking controller includes: ； in, U i For train i Theoretical output control force; k i,3 It is an adjustable constant; z i,3 This refers to the virtual tracking error of a third-order control system. These are adaptive estimation parameters used to estimate the squared maximum weights of the radial basis function neural network used in third-order backstepping control; p i,3 It is an adjustable constant; S i,3 This is the output vector of the Gaussian kernel function in the radial basis function neural network used in third-order backstepping control; Z i,3 It is a vector containing the state parameters of the current train and the preceding train in the virtual coupling, as well as the estimated parameters for unknown terms; For train i The controller's delay time; a i For train i The acceleration; f i,3 It is an adjustable constant; Adjustable parameters provided for Young's inequality; Adjustable parameters provided for Young's inequality.

2. The virtual coupled train adaptive preset time smooth tracking control method according to claim 1, characterized in that, Establish an operation control model for each train in the virtual coupled train system, specifically including: For each train in the virtual coupled train, a dynamic model of the train is established; considering controller delay and sensor delay, a relationship between the actual output control force and the theoretical output control force of the train is established; the relationship is then subjected to approximation, estimation and Laplace transformation to obtain the transformed relationship; the dynamic model is adjusted using the transformed relationship to obtain the train's operation control model.

3. The virtual coupled train adaptive preset time smooth tracking control method according to claim 1, characterized in that, The operation control model includes: ； in, x i ( t (for trains) i exist t The position at that moment; For train i exist t The derivative of the position at time; v i ( t (for trains) i exist t The speed of time; For train i exist t The derivative of the velocity at time t; a i ( t (for trains) i exist t Acceleration at any moment; For train i exist t The derivative of the acceleration at time t; For train i The controller's delay time; sat ( U i ( th i When considering sensor delay, the train... i exist t The saturation theory of time outputs control force; U i ( th i (When considering sensor delay, the train) i exist t Theoretical output control force at any given moment; h i For train i The sensor's delay time; r i ( v i ( t ()) for train i exist t The fundamental resistance of time; w i ( x i ( t ()) for train i exist t Additional resistance at any given moment; c 2 is a constant; c 3 is a constant; For train i exist t The derivative of the additional resistance at time; x i,n+1 ( t (for trains) i exist t Time is used for estimation sat ( U i ( th i And the estimated quantity of the design; sat ( U i ( t ()) For trains without considering sensor delay i exist t The saturation theory of time outputs control force; U i ( t (This refers to the train without considering sensor delay) i exist t Theoretical output control force at any given moment; for x i,n+1 ( t The derivative of ). For train i The corresponding constant.

4. The virtual coupled train adaptive preset time smooth tracking control method according to claim 1, characterized in that, When designing an adaptive smooth tracking controller for the train, using the relative braking distance as the interval strategy, the control error is: ； in, e i ( t (for trains) i exist t Controlling the distance between the vehicle and the vehicle in front to minimize errors; x i ( t (for trains) i exist t The position at that moment; x i-1 ( t (for trains) i- 1 in t The position at that moment; For train i exist t The relative braking distance at any given moment; ； in, For train i The corresponding range size coefficient; l i For train i The corresponding minimum safety distance; v i ( t (for trains) i exist t The speed of time; a f,i,min For train i The minimum braking acceleration; v i-1 ( t (for trains) i- 1 in t The speed of time; a f,i-1,max For train i- Maximum braking acceleration of 1; For train i exist t The activation function at time step.

5. The virtual coupled train adaptive preset time smooth tracking control method according to claim 1, characterized in that, When designing an adaptive smooth tracking controller for the train, a radial basis function neural network is used to estimate the basic resistance and additional resistance in the operation control model.

6. The virtual coupled train adaptive preset time smooth tracking control method according to claim 1, characterized in that, The design of an adaptive smooth tracking controller for the train specifically includes: designing an adaptive smooth tracking controller for the train using an adaptive backstepping control method.

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