CN117389158B - High-speed train tracking control method and system based on hook buffer constraint condition - Google Patents
High-speed train tracking control method and system based on hook buffer constraint condition Download PDFInfo
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Abstract
The invention discloses a high-speed train tracking control method and a system based on a hook buffer constraint condition, which relate to the technical field of train control, and the method comprises the following steps: based on the internal coupling acting force of the high-speed train, constructing a nonlinear multi-particle dynamics model; linearizing the nonlinear multi-particle dynamics model according to the displacement tracking error, the speed tracking error and the control input error to obtain a dynamics equation with coupler displacement in a high-speed train balance state; based on the failure of the high-speed train actuator, converting a dynamic equation with coupler displacement in a balanced state of the high-speed train into a train space state equation with the partial failure of the actuator; establishing an interference observer in the form of a state space; constructing an input compensation controller based on the disturbance observer; determining a composite controller according to the train space state equation, the disturbance observer and the input compensation controller; and tracking control is carried out on the high-speed train by adopting the composite controller. The invention improves the safety of train operation.
Description
Technical Field
The invention relates to the technical field of train control, in particular to a high-speed train tracking control method and system based on a hook buffer constraint condition.
Background
The high-speed motor train unit is connected through an automatic tight-lock coupler buffer device in the group-making process. The hook buffer system plays an important role in buffering and transmitting the longitudinal acting force of the train, and is a bridge for transmitting the force in the train. The influence of workshop acting force on adjacent carriages in the running process of the train is not negligible, and is important to the safety and running stability of the high-speed train. The coupler buffer system mainly comprises a coupler spring and a buffer coupler, and the magnitude of the force in the train is determined by the displacement difference and the speed difference of adjacent carriages. Excessive in-train forces can lead to fatigue failure of the coupler and even damage to cause serious derailment accidents. With the continuous increase of the running speed of the high-speed train, the risk of increasing the internal force of the train is increased, which puts higher demands on the running safety of the high-speed train. Therefore, the design of the control method of the high-speed train aiming at the displacement constraint problem of the coupler and buffer system has important practical significance.
At present, existing control methods are introduced into the constraint problem of a train coupler buffer system, such as adopting an artificial potential function to ensure that the coupler displacement is within a safe range. However, the artificial potential function can cause the problem of local minimum position oscillation and back and forth jitter, which not only can influence the comfort of riding a train, but also can cause certain mechanical damage of the coupler. Thus, ensuring that coupler displacement operates within a safe range and converges to near nominal values throughout the operation of the train remains a challenging topic.
In addition, the running environment of the high-speed train is complex and changeable, and the change of the external disturbance has burstiness and randomness, which is also an important problem to be solved by the automatic driving system of the train. However, the existing method has limited capability of processing interference, and the accuracy of interference compensation needs to be improved. And active interference suppression is not considered in the design of the controller, resulting in the controller not being able to react quickly in the case of strong interference.
Based on this, an advanced control algorithm is needed to ensure safe and stable operation of the train.
Disclosure of Invention
The invention aims to provide a high-speed train tracking control method and system based on a hook buffer constraint condition, so that the running safety of a train is improved.
In order to achieve the above object, the present invention provides the following solutions:
a high-speed train tracking control method based on a hook buffer constraint condition comprises the following steps:
based on the internal coupling acting force of the high-speed train, constructing a nonlinear multi-particle dynamics model of the high-speed train;
linearizing the nonlinear multi-particle dynamics model according to displacement tracking error, speed tracking error and control input error to obtain a dynamics equation with coupler displacement in a high-speed train balance state; the kinetic equation with coupler displacement meets the preset hook slow constraint condition;
based on the failure of the high-speed train actuator, converting a dynamic equation with coupler displacement in a balanced state of the high-speed train into a train space state equation with the partial failure of the actuator;
establishing an interference observer in the form of a state space, wherein the interference observer is used for estimating and attenuating unknown disturbance suffered by a high-speed train in the running process;
constructing an input compensation controller based on the disturbance observer;
determining a composite controller according to the train space state equation, the disturbance observer and the input compensation controller;
and tracking and controlling the high-speed train by adopting the composite controller.
The invention also discloses a high-speed train tracking control system based on the hook buffer constraint condition, which comprises the following steps:
the nonlinear multi-particle dynamics model determining module is used for constructing a nonlinear multi-particle dynamics model of the high-speed train based on the in-coupling acting force of the high-speed train;
the dynamic equation determining module is used for linearizing the nonlinear multi-particle dynamic model according to displacement tracking error, velocity tracking error and control input error to obtain a dynamic equation with coupler displacement in a high-speed train balance state; the kinetic equation with coupler displacement meets the preset hook slow constraint condition;
the train space state equation determining module is used for converting a dynamics equation with coupler displacement in a high-speed train balanced state into a train space state equation with an actuator part fault based on the high-speed train actuator fault;
the system comprises an interference observer determining module, a state space determining module and a state space determining module, wherein the interference observer determining module is used for establishing an interference observer in the form of a state space and used for estimating and attenuating unknown disturbance suffered by a high-speed train in the running process;
an input compensation controller construction module for constructing an input compensation controller based on the disturbance observer;
the composite controller determining module is used for determining a composite controller according to the train space state equation, the interference observer and the input compensation controller;
and the control module is used for tracking and controlling the high-speed train by adopting the composite controller.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the invention, the constraint of the coupler is considered, so that the displacement of the coupler always meets the safety constraint in the whole running process of the high-speed train, thereby improving the running safety of the train, compensating the influence of interference on the high-speed train through the input compensation controller, and further improving the running safety of the train.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the drawings that are needed in the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic flow chart of a high-speed train tracking control method based on a hook buffer constraint condition provided by an embodiment of the invention;
FIG. 2 is a composite control block diagram provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of a stress analysis of adjacent cars of a high-speed train according to an embodiment of the present invention;
FIG. 4 is a flowchart illustrating the selection of the compensation period value according to an embodiment of the present invention;
FIG. 5 is a graph of desired displacement and desired speed for a high speed train provided by an embodiment of the present invention;
FIG. 6 is a graph of the displacement evolution of a coupler for a portion of a high-speed train according to an embodiment of the present invention;
FIG. 7 is a graph of a partial speed tracking error of a high speed train provided by an embodiment of the present invention;
FIG. 8 is a graph of partial displacement tracking error of a high speed train provided by an embodiment of the present invention;
FIG. 9 is a graph of a portion of a control signal for a high speed train provided by an embodiment of the present invention;
FIG. 10 is a graph of a high speed train portion input compensation control signal provided by an embodiment of the present invention;
FIG. 11 is a graph of coupling force between sections of a high speed train provided by an embodiment of the present invention;
FIG. 12 is a graph of a partial estimation error of an interference observer according to an embodiment of the present invention;
FIG. 13 is a graph of partial displacement tracking of a high speed train provided by an embodiment of the present invention;
fig. 14 is a schematic structural diagram of a high-speed train tracking control system based on a hook buffer constraint condition according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a high-speed train tracking control method and system based on a hook buffer constraint condition, so that the running safety of a train is improved.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
The invention aims to provide a hybrid control strategy based on input compensation and disturbance observers for a high-speed train automatic driving system. Firstly, a multi-particle linear dynamics model with coupler displacement in a high-speed train balance state is established, then a high-speed train space state equation with an actuator part fault is established, and then an interference observer is introduced to estimate and restrain unknown complex lumped disturbance to which the train is subjected on line, so that most of disturbance to which the train is subjected is attenuated. The control method based on the interference observer is considered to have the problems that the control precision is not high, the safe operation of the coupler cannot be guaranteed, and the like, and the input compensation control signal is further designed, so that the absolute safety of the operation of the coupler of the train is guaranteed, the compensation precision of the interference is further improved, and the problem of train control in the background technology can be solved.
Example 1
As shown in fig. 1, the method for tracking and controlling the high-speed train based on the hook buffer constraint condition provided by the embodiment comprises the following steps.
Step 101: and constructing a nonlinear multi-particle dynamics model of the high-speed train based on the in-coupling acting force of the high-speed train.
Step 102: linearizing the nonlinear multi-particle dynamics model according to displacement tracking error, speed tracking error and control input error to obtain a dynamics equation with coupler displacement in a high-speed train balance state; the kinetic equation with coupler displacement meets the preset hook slow constraint condition.
Step 103: based on the failure of the high-speed train actuator, the dynamic equation with coupler displacement in the balanced state of the high-speed train is converted into the space state equation of the train with the failure of the actuator part.
Step 104: an interference observer in the form of a state space is established for estimating and attenuating unknown disturbances experienced by the high-speed train during operation.
Step 105: based on the disturbance observer, an input compensation controller is constructed.
Step 106: and determining a composite controller according to the train space state equation, the interference observer and the input compensation controller.
Step 107: and tracking and controlling the high-speed train by adopting the composite controller.
Aiming at the safety constraint of the coupler of the high-speed train and the attenuation of unknown lumped disturbance, the invention designs an input compensation control signal and an interference observer, and provides a hybrid tracking control method. In order to process unknown disturbance in the running process of the train, firstly, an interference observer is designed to process the influence of disturbance on the train. An input compensation signal was further designed considering that the disturbance observer based controller does not guarantee that the coupler meets the safety constraints and that there is no satisfactory control accuracy. Under the invention, only proper compensation period is needed to be selected, so that the absolute safety of the train coupler can be ensured, and the running safety and tracking performance of the train are improved. The overall control structure of the train is shown in fig. 2.
Step 101, taking into account coupling acting force in a train, constructing a nonlinear multi-particle dynamics model of the high-speed train, wherein the nonlinear multi-particle dynamics model is expressed as:
（1）；
wherein, among them,indicating displacement of the jth car at time t, < >>Is->Derivative of>Indicating the speed of the jth car at time t, < >>Is the mass of the 1 st carriage, +.>Indicating the speed at time t of car 1, < >>Indicating the speed at the moment t of the car 2, < >>Is->Derivative of>Control input indicating time t of car 1, < >>Indicating the displacement at the moment t of the 1 st car,/>Indicating the displacement of the car at the moment t of the 2 nd section, < + >>Unknown lumped disturbance at time t of carriage 1,/->Indicating the displacement of the ith carriage t moment, < >>Indicating the displacement at the moment t of the (i+1) th car,/->Indicating the displacement at the moment t of the i-1 th car,/->Indicating the speed at time t of the ith car, < +.>Indicating the speed at time t of the i+1 car,indicating the speed at the moment t of the i-1 car,/->Indicating the displacement of the nth car at time t +.>Indicating the displacement of the n-1 car at time t,/->Indicating the speed at time t of the nth car, < >>Acceleration at time t of nth carriage, +.>Indicating the speed at time t of the n-1 car,/->Acceleration at time t of the ith car, < +.>Control input indicating the moment t of the ith car,/-, for example>Control input indicating time t of nth car,/->、/>And->Are all Davis coefficients, < >>Is an elastic coupling coefficient->For damping coupling coefficient->Is the mass of the ith carriage, +.>Is the mass of the nth car, l is the fixed length of the car,>unknown lumped disturbance at the moment t of the ith carriage,/->The unknown lumped disturbance at the moment t of the nth carriage is n, and n is the number of carriages of the high-speed train.
The step 102 specifically includes: and defining a displacement tracking error variable, a speed tracking error variable and a control input error variable, and linearizing a train nonlinear model to obtain a dynamic equation with coupler displacement in a train balance state.
As shown in fig. 3, the coupler displacement is expressed as follows:
（2）；
wherein,for time t->Section and->Coupler displacement between coupe cars.，/>Indicating the original length of the coupler before deformation, < >>Representing a fixed length of a car.
The displacement evolution of the coupler of the high-speed train is shown in fig. 6, the track error curve of the high-speed train is shown in fig. 7, and the displacement track error is shown in fig. 8.
The stress analysis of adjacent cars of the high speed train is shown in fig. 3.
The speed of the high speed train reaches an equilibrium state with the desired speed:。
desired acceleration:。
defining a displacement error variable:。
speed error variable:。
control error variable:。
wherein,、/>and->Respectively representing the expected speeds of the 1 st, 2 nd and nth carriages at the moment t, namelyIndicating the expected speed of the ith carriage at time t，/>Is the desired speed. />、/>And->Respectively representing the expected acceleration of the 1 st, 2 nd and n th carriages at the moment t,/>Indicating the speed error of the ith carriage at time t, < >>Indicating the control error of the ith carriage at time t, < >>Indicating the desired control amount of the ith carriage at time t,/->Indicating the desired displacement +.>Indicating the total length of the train body before the ith car.
Desired displacement of high speed trainsAnd desired speed->The curve of (a) is shown in fig. 5, and the high-speed train control signal is shown in fig. 9.
The dynamic equation with coupler displacement at the high speed train equilibrium state is expressed as:
（3）；
wherein,for displacement error at time t of carriage 1, < ->Is->Derivative of>For the speed error at the moment t of the 1 st car, respectively>For the speed error at the moment t of the car 2, < >>For the displacement of the coupling between section 1 and section 2 of the car at time t, +.>Is->Derivative of>For the speed error at the moment t of the jth carriage,/->For the speed error at the moment t of the j-1 th car,/->For the displacement of the coupling between the j-1 th and the j-th carriage at time t, +.>Error is input for the control of the 1 st car t moment,/->Indicating the desired speed +.>Is->Acceleration error at time t of the articulated car, +.>Is->Displacement error of carriage t moment +.>Is->Speed error at time t of carriage section, +.>Is->Speed error at time t of carriage section, +.>Is->Speed error at time t of carriage section, +.>Is->The control input error at the moment t of the knuckle carriage,acceleration error at time t of nth carriage, < ->For error control input at time t of nth carriageDifference (S)>For the speed error at the moment t of the nth car,/->The speed error at the moment t of the (n-1) th carriage; />For time t->Section and->Coupler displacement between cars, +.>For the displacement of the coupler between the i-1 th section and the i-th carriage at the time t,is->Derivative of>The displacement of the coupler between the n-1 th section and the n th carriage at the moment t.
Constraint conditions of a dynamic equation with coupler displacement in a high-speed train balance state, namely the preset hook slow constraint conditions:
；
wherein,indicating time t->The carriage is articulated with the%>European norms of inter-carriage coupler displacement; />Indicating the maximum amplitude at which the coupler can be stretched or compressed.
Step 103, taking train actuator faults into consideration, establishes a train space state equation with actuator part faults, and the train space state equation with actuator part faults is expressed as:
（4）；
wherein,，/>is a system state variable at the time t of the high-speed train,is->Derivative of>，/>For the control input of the high-speed train t moment, < >>，/>，/>For failure matrix of actuator +.>Indicating the health factor of the actuator 1 +.>Indicating the health factor of the actuator 2 +.>Health factor representing actuator n +.>Health factor representing actuator i (i=1, 2, …, n) satisfying +.>When->Time indicates +.>The actuator of the articulated car has no fault, +.>Representing the minimum value of the health factor, A representing the system matrix, < ->Representing the input matrix, B representing the coefficient matrix of the disturbance, < ->Representing an unknown lumped disturbance of the whole high speed train at time t,。
more specifically, the method comprises the steps of,，/>。
wherein,；
；
；
。
wherein,is->Zero matrix of dimension, ">、/>、/>And->Are intermediate parameter matrices.
Step 104 designs an interference observer in a state space form, estimates and attenuates unknown complex disturbance received in the train running process on line, and improves the running stability of the train.
The disturbance observer is expressed as:
（5）；
wherein,unknown lumped disturbance for time t>Estimated value of ∈10->Is the internal state of the interference observer at the time t; />Is the gain matrix of the disturbance observer.
Defining interference observer estimation errors：/> （6）。
Wherein,and represents the estimation error of the interference observer at the time t.
Step 105 further designs an input compensation controller in an autoregressive form, considering that the accuracy of the controller based on the disturbance observer is not high and the safe operation of the coupler of the high-speed train cannot be ensured, and the specific steps include:
step 1051: and constructing a motion equation of the high-speed train under the designed disturbance observer.
Step 1052: to eliminate the strict condition of real-time performance of interference estimation errors, a small time delay is adopted to replace the real-time performance.
Step 1053: to eliminate the known condition of the estimation error a priori, a recursively formed input compensation control signal is designed.
Step 1054: and selecting a proper compensation period, ensuring the absolute safety of the coupler of the train, and finally converging the displacement of the coupler to be near a nominal value along with the increase of the running time so as to realize the safe and on-time running of the train.
The input compensation controller is expressed as:
（7）；
wherein,the input compensation control signal at the moment T is represented, k is a constant, T represents a time delay greater than zero, T 0 Indicating the start time of the high speed train system.
The input compensation control signal curve of the high-speed train is shown in FIG. 10, and the high-speed train is shown in FIG. 10、/>、/>、/>And respectively representing input compensation control signals of the carriages of section 1, section 3, section 5 and section 7 at the moment t. The coupling force curve between carriages of high-speed train is shown in FIG. 11,/->For the coupling force curve between section 1 and section 2 at time t, < >>For the coupling force curve between the 3 rd section and the 4 th section at the t moment, < >>For the coupling force curve between the 5 th section and the 6 th section of the carriage at the moment t, < >>And the coupling force curve between the 7 th section and the 8 th section of carriage at the moment t. The estimated error curve of the disturbance observer is shown in figure 12, and (2)>、/>、/>、/>And respectively representing the interference estimation errors of the carriages of section 1, section 3, section 5 and section 7 at the moment t.
The composite controller is expressed as:
（8）；
wherein,is a composite control signal at time t +.>The state feedback control is designed for keeping the system calm at the time t, and K is a gain matrix.
The high speed train displacement tracking curve is shown in fig. 13.
The specific input compensation control signal steps are as follows:
step 1: under the condition of a compound control law, namely a formula (8), the motion trail of the high-speed train system (4) meets the following conditions:
（9）；
wherein the intermediate parameter，/>Represents the start time of the high-speed train system, +.>Representation->Time points in between.
If the designed compensation control signal is able to fully compensate the effect of the remaining disturbances, then the following is true:
（10）；
in order for equation (10) to be true, the estimation error must be satisfiedReal-time, a priori known stringent conditions are difficult to achieve in a high speed train system. This stringent constraint will be removed in the next step.
To eliminate the strict condition of real-time performance of interference estimation errors, a small time delay is adopted to replace the real-time performance.
The specific steps are as follows:
step 2: dividing the time domain part of the motion track (9) of the high-speed train closed-loop system into periods ofIs shown below:
（11）；
wherein,is an arbitrary integer, +.>Is a time delay greater than zero.
Step 3: in the intervalAdopts->To compensate->In section->The influence on the high-speed train system is caused by the inside, and the following steps:
（12）；
step 4: by introducing the formula (11) into the formula (10), it is possible to obtain:
（13）；
step 5: by calculation, for anyEquation (12); can be re-expressed as:
（14）；
step 6: through an equivalent transformation, equation (14) can be rewritten as:
（15）；
step 7: order theBringing it into formula (15):
（16）；
step 8: for all ofAnd->All have
（17）；
Step 9: formula (17) can be re-expressed as
（18）；
Wherein for allAnd->All do.
As can be seen from equation (18), the input compensationContains unknown->This results in that the input compensation control cannot be directly implemented, and this problem will be solved next.
To eliminate the condition that the estimation error is known a priori, a recursively-formed input compensation control signal is designed.
Step 10: from equation (18), it can be easily obtained:
（19）；
step 11: by combining formulas (18) and (19), it is further possible to obtain:
（20）；
the design step of the input compensation ends up here.
And selecting a proper compensation period, ensuring the absolute safety of the coupler of the train, converging the displacement of the coupler to be near the nominal value finally along with the increase of the running time, realizing the safe and on-time running of the train, and selecting the compensation period, wherein the selection flow is shown in figure 4.
For the displacement constraint condition of the train coupler, assume that the high-speed train coupler satisfies at the initial moment，/>Is a reversible matrix, selecting the compensation period +.>When inequality (21) is satisfied, the coupler always operates within a safe range.
（21）；
Wherein,；/>is an unknown positive constant; />The normal number known a priori is related to the disturbance suffered by the train; />Representing a positive definite symmetry matrix; />And->Representation matrix->Maximum of (2)Singular values and minimum singular values.
It should be noted that, when step 3 is executed, since equation (12) is true, a sufficiently small compensation period is selectedWhen step 4 is executed, the formula (13) satisfies:
（22）；
this means that when a sufficiently small period is selectedWhen the train is affected by unknown disturbance, the influence of the unknown disturbance on the train can be almost completely compensated by the input compensation signal;
combining formula (13) and formula (22) can result in:
（23）；
wherein,to satisfy the Hurwitz (Hurwitz) matrix.
From equation (23) and step 1054, it can be obtained that the appropriate compensation period is selectedAnd in this way, the high-precision tracking control of the train under the safety constraint condition can be realized.
The simulation example of the present invention is as follows:
1) High speed train parameters.
Simulation experiments are carried out on a high-speed train with 8 carriages, and the mass of each carriage isThe method comprises the steps of carrying out a first treatment on the surface of the Elastic coupling coefficient->The method comprises the steps of carrying out a first treatment on the surface of the Damping coupling coefficient->The method comprises the steps of carrying out a first treatment on the surface of the Basic resistance parameter per unit->，，/>。
The unknown lumped perturbation is expressed as:
；
；
；
；
。
wherein,for slope resistance, slope angle->；/>For tunnel resistance, tunnel length->；For curve resistance, curve length->Curve center angle->；/>Representing an unknown external disturbance at time t,representation->Random numbers in between; acceleration of gravity->。/>
Assume that the coupler initial state isMeaning that there is some degree of stretching or compression of the remaining couplers except for the first coupler which is in a relaxed state. The fault parameter matrix is set as。
2) Compensation periodIs selected from the group consisting of (a).
To obtain a suitable compensation periodSo that the train coupler always works in the safety range, fig. 4 shows the compensation period by the dichotomy>Algorithm flow chart of values.
The computer CPU used in the simulation experiment is an 11th Gen Intel (R) Core (TM) i5-11400H,2.70GHz,Windows 11 operating system, and the simulation platform is Matlab2016b.
Compared with the existing control technology, the invention has the advantages that:
1. the constraint condition of the coupler is considered in the design of the controller, so that the displacement of the coupler always meets the safety constraint in the whole running process of the train. The composite control method provided by the invention can ensure that the coupler converges to the vicinity of the nominal value, and solves the problem that the train can effectively track the target curve on the premise of safe operation.
2. The existing conventional interference observer-based technology cannot fully compensate the influence of interference on the system, and even if the estimation error can be small, the small error cannot be artificially limited to the upper bound. The input compensation control law designed by the invention can almost completely compensate the influence of interference on a high-speed train system. More specifically, the compensation signal may limit the upper bound of the system state deviation caused by the estimation error, which may be arbitrarily small. And when the train is not interfered by the outside, the invented composite control method is degraded to the traditional feedback control, which is easy to realize in an actual train system.
3. The disturbances experienced by the high speed train are not necessarily of an inherited nature and period. The interference observer provided by the invention has a good estimation effect on random irregular disturbance. In addition, the interference suffered by the high-speed train in the running process is not constant and is possibly fast time-varying, the interference observer designed by the invention does not need the strict assumption that the time derivative of the interference is zero, the running scene of the train is more met, the condition of applying the interference observer is not so strict, and the application scene of the interference observer is widened.
Example 2
As shown in fig. 14, a high-speed train tracking control system based on a hook buffer constraint condition includes:
the nonlinear multi-particle dynamics model determination module 201 is configured to construct a nonlinear multi-particle dynamics model of the high-speed train based on the in-coupling acting force of the high-speed train.
The dynamic equation determining module 202 with coupler displacement is configured to linearize the nonlinear multi-particle dynamics model according to a displacement tracking error, a velocity tracking error and a control input error, so as to obtain a dynamic equation with coupler displacement in a balanced state of the high-speed train; the kinetic equation with coupler displacement meets the preset hook slow constraint condition.
The train space state equation determining module 203 is configured to convert a dynamics equation with coupler displacement in a balanced state of the high-speed train into a train space state equation with an actuator part fault based on the high-speed train actuator fault.
An disturbance observer determination module 204 is configured to establish a disturbance observer in the form of a state space that is configured to estimate and attenuate unknown disturbances experienced by the high-speed train during operation.
An input compensation controller construction module 205 is configured to construct an input compensation controller based on the disturbance observer.
A composite controller determination module 206 for determining a composite controller based on the train space state equation, the disturbance observer, and the input compensation controller.
And the control module 207 is used for carrying out tracking control on the high-speed train by adopting the composite controller.
In the present specification, each embodiment is described in a progressive manner, and each embodiment is mainly described in a different point from other embodiments, and identical and similar parts between the embodiments are all enough to refer to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, the description of which is intended only to assist in understanding the methods of the present invention and the core ideas thereof; also, it is within the scope of the present invention to be modified by those of ordinary skill in the art in light of the present teachings. In view of the foregoing, this description should not be construed as limiting the invention.
Claims (3)
1. The high-speed train tracking control method based on the hook buffer constraint condition is characterized by comprising the following steps of:
based on the internal coupling acting force of the high-speed train, constructing a nonlinear multi-particle dynamics model of the high-speed train;
linearizing the nonlinear multi-particle dynamics model according to displacement tracking error, speed tracking error and control input error to obtain a dynamics equation with coupler displacement in a high-speed train balance state; the kinetic equation with coupler displacement meets the preset hook slow constraint condition;
based on the failure of the high-speed train actuator, converting a dynamic equation with coupler displacement in a balanced state of the high-speed train into a train space state equation with the partial failure of the actuator;
establishing an interference observer in the form of a state space, wherein the interference observer is used for estimating and attenuating unknown disturbance suffered by a high-speed train in the running process;
constructing an input compensation controller based on the disturbance observer;
determining a composite controller according to the train space state equation, the disturbance observer and the input compensation controller;
tracking control is carried out on the high-speed train by adopting the composite controller;
linearizing the nonlinear multi-particle dynamics model according to displacement tracking error, speed tracking error and control input error to obtain a dynamics equation with coupler displacement in a high-speed train balance state, wherein the dynamics equation comprises the following specific steps: defining a displacement tracking error variable, a speed tracking error variable and a control input error variable, linearizing a train nonlinear model, and obtaining a dynamic equation with coupler displacement in a train balance state;
the coupler displacement is expressed as follows:
；
wherein,for time t->Section and->Coupler displacement between cars; />，Indicating the original length of the coupler before deformation, < >>Representing the fixed length of a car, < > a car>Indicating the displacement of the ith carriage t moment, < >>The displacement of the (i+1) th carriage at the moment t is represented, and l is the fixed length of the carriage;
the speed of the high speed train reaches an equilibrium state with the desired speed:；
desired acceleration:；
displacement error variable:；
speed error variable:；
control error variable:；
wherein,、/>and->Respectively representing the expected speeds of the 1 st, 2 nd and nth carriages at the moment t, namely +.>Indicating the desired speed of the ith carriage at time t,/->Is the desired speed; />、/>And->Respectively representing the expected acceleration of the 1 st, 2 nd and n th carriages at the moment t,/>Indicating the speed error of the ith carriage at time t, < >>Indicating the control error of the ith carriage at time t, < >>Indicating the desired control amount of the ith carriage at time t,/->Indicating the desired displacement +.>Representing the total length of a train body in front of an ith carriage;
the dynamic equation with coupler displacement at the high speed train equilibrium state is expressed as:
；
wherein,for displacement error at time t of carriage 1, < ->Is->Derivative of>For the speed error at the moment t of the 1 st car, respectively>For the speed error at the moment t of the car 2, < >>For the displacement of the coupling between section 1 and section 2 of the car at time t, +.>Is->Derivative of>For the speed error at the moment t of the jth carriage,/->For the speed error at the moment t of the j-1 th car,/->For the displacement of the coupling between the j-1 th and the j-th carriage at time t, +.>Error is input for the control of the 1 st car t moment,/->Indicating the desired speed +.>Is->Acceleration error at time t of the articulated car, +.>Is->Displacement error of carriage t moment +.>Is->Speed error at time t of carriage section, +.>Is->The speed error at the moment t of the articulated car,is->Speed error at time t of carriage section, +.>Is->Control input error of the carriage t moment, +.>Acceleration error at time t of nth carriage, < ->Error is input for the control of the nth car t moment,/->For the speed error at the moment t of the nth car,/->The speed error at the moment t of the (n-1) th carriage; />For time t->Section and->Coupler displacement between cars, +.>For the displacement of the coupling between section i-1 and section i carriage at time t, +.>Is thatDerivative of>The displacement of the coupler between the nth section and the nth carriage at the t moment; />And->Are all Davis coefficients, < >>Is an elastic coupling coefficient->For damping coupling coefficient->Is the mass of the 1 st carriage, +.>Is the mass of the ith carriage, +.>Is the mass of the nth carriage, +.>At the time t of the 1 st carriageUnknown lumped disturbance of->Unknown lumped disturbance at the moment t of the ith carriage,/->The unknown lumped disturbance at the moment t of the nth carriage is n, and n is the number of carriages of the high-speed train;
the preset hook slow constraint condition is as follows:
；
wherein,indicating time t->The carriage is articulated with the%>European norms of inter-carriage coupler displacement; />Representing the maximum magnitude of the coupler being stretched or compressed;
considering the failure of the train actuator, a train space state equation with the failure of the actuator part is established, and the train space state equation with the failure of the actuator part is expressed as:
；
wherein,，/>is a system state variable of the high-speed train at the moment t, < >>Is thatDerivative of>，/>For the control input of the high-speed train t moment, < >>，/>，/>For failure matrix of actuator +.>Indicating the health factor of the actuator 1 +.>Indicating the health factor of the actuator 2 +.>Health factor representing actuator n +.>Health factor representing actuator i (i=1, 2, …, n) satisfying +.>When->Time indicates +.>The actuator of the articulated car has no fault, +.>Representing the minimum value of the health factor, A representing the system matrix, < ->Representing the input matrix, B representing the coefficient matrix of the disturbance, < ->Representing unknown lumped disturbance of the whole high speed train at time t,/->；
，/>；
Wherein,；
；
；
；
wherein,is->Zero matrix of dimension, ">、/>、/>And->All are intermediate parameter matrixes;
the disturbance observer is expressed as:
；
wherein,unknown lumped disturbance for time t>Estimated value of ∈10->Is the internal state of the interference observer at the time t; />Is the gain matrix of the disturbance observer;
defining interference observer estimation errors：/>；
Wherein,representing the estimation error of the interference observer at the time t;
the input compensation controller is expressed as:
；
wherein,the input compensation control signal at the moment T is represented, k is a constant, T represents a time delay greater than zero, T 0 Indicating a start time of the high speed train system;
the composite controller is expressed as:
；
wherein,is a composite control signal at time t +.>The state feedback control is designed for keeping the system calm at the time t, and K is a gain matrix.
2. The method for tracking control of a high speed train based on the hook buffer constraint of claim 1, wherein the nonlinear multi-particle dynamics model is expressed as:
；
wherein,indicating displacement of the jth car at time t, < >>Is->Derivative of>Indicating the speed of the jth car at time t, < >>Indicating the speed at time t of car 1, < >>Indicating the speed at the moment t of the car 2, < >>Is->Derivative of>Control input indicating time t of car 1, < >>Indicating the displacement at the moment t of the 1 st car,/>Indicating the displacement of the car at the moment t of the 2 nd section, < + >>Indicating the displacement at the moment t of the i-1 th car,/->Indicating the speed at time t of the ith car, < +.>Indicating the speed at time t of the (i+1) th car,/->Indicating the speed at the moment t of the i-1 car,/->Indicating the displacement of the nth car at time t +.>Indicating the displacement of the n-1 car at time t,/->Indicating the speed at time t of the nth car, < >>Acceleration at time t of nth carriage, +.>Indicating the speed at time t of the n-1 car,/->The acceleration at the time t of the ith car is shown,control input indicating the moment t of the ith car,/-, for example>Control input indicating time t of nth car,/->Is the Davis coefficient.
3. A high-speed train tracking control system based on a hook buffer constraint condition, comprising:
the nonlinear multi-particle dynamics model determining module is used for constructing a nonlinear multi-particle dynamics model of the high-speed train based on the in-coupling acting force of the high-speed train;
the dynamic equation determining module is used for linearizing the nonlinear multi-particle dynamic model according to displacement tracking error, velocity tracking error and control input error to obtain a dynamic equation with coupler displacement in a high-speed train balance state; the kinetic equation with coupler displacement meets the preset hook slow constraint condition;
the train space state equation determining module is used for converting a dynamics equation with coupler displacement in a high-speed train balanced state into a train space state equation with an actuator part fault based on the high-speed train actuator fault;
the system comprises an interference observer determining module, a state space determining module and a state space determining module, wherein the interference observer determining module is used for establishing an interference observer in the form of a state space and used for estimating and attenuating unknown disturbance suffered by a high-speed train in the running process;
an input compensation controller construction module for constructing an input compensation controller based on the disturbance observer;
the composite controller determining module is used for determining a composite controller according to the train space state equation, the interference observer and the input compensation controller;
the control module is used for tracking and controlling the high-speed train by adopting the composite controller;
linearizing the nonlinear multi-particle dynamics model according to displacement tracking error, speed tracking error and control input error to obtain a dynamics equation with coupler displacement in a high-speed train balance state, wherein the dynamics equation comprises the following specific steps: defining a displacement tracking error variable, a speed tracking error variable and a control input error variable, linearizing a train nonlinear model, and obtaining a dynamic equation with coupler displacement in a train balance state;
the coupler displacement is expressed as follows:
；
wherein,for time t->Section and->Coupler displacement between cars; />，/>Indicating the original length of the coupler before deformation, < >>Representing the fixed length of a car, < > a car>Indicating the displacement of the ith carriage t moment, < >>The displacement of the (i+1) th carriage at the moment t is represented, and l is the fixed length of the carriage;
the speed of the high speed train reaches an equilibrium state with the desired speed:；
desired acceleration:；
displacement error variable:；
speed error variable:；
control error variable:；
wherein,、/>and->Respectively representing the expected speeds of the 1 st, 2 nd and nth carriages at the moment t, namely +.>Indicating the desired speed of the ith carriage at time t,/->Is the desired speed; />、/>And->Respectively representing the expected acceleration of the 1 st, 2 nd and n th carriages at the moment t,/>Indicating the speed error of the ith carriage at time t, < >>Indicating the control error of the ith carriage at time t, < >>Indicating the desired control amount of the ith carriage at time t,/->Indicating the desired displacement +.>Representing the total length of a train body in front of an ith carriage;
the dynamic equation with coupler displacement at the high speed train equilibrium state is expressed as:
；
wherein,for displacement error at time t of carriage 1, < ->Is->Derivative of>For the speed error at the moment t of the 1 st car, respectively>For the speed error at the moment t of the car 2, < >>For the displacement of the coupling between section 1 and section 2 of the car at time t, +.>Is->Derivative of>For the speed error at the moment t of the jth carriage,/->For the speed error at the moment t of the j-1 th car,/->For the displacement of the coupling between the j-1 th and the j-th carriage at time t, +.>Error is input for the control of the 1 st car t moment,/->Indicating the desired speed +.>Is->Acceleration error at time t of the articulated car, +.>Is->Displacement error of carriage t moment +.>Is->Speed error at time t of carriage section, +.>Is->The speed error at the moment t of the articulated car,is->Speed error at time t of carriage section, +.>Is->Control input error of the carriage t moment, +.>Acceleration error at time t of nth carriage, < ->Error is input for the control of the nth car t moment,/->For the speed error at the moment t of the nth car,/->The speed error at the moment t of the (n-1) th carriage; />For time t->Section and->Coupler displacement between cars, +.>For the displacement of the coupling between section i-1 and section i carriage at time t, +.>Is thatDerivative of>The displacement of the coupler between the nth section and the nth carriage at the t moment; />And->Are all Davis coefficients, < >>Is an elastic coupling coefficient->For damping coupling coefficient->Is the mass of the 1 st carriage, +.>Is the mass of the ith carriage, +.>Is the nth sectionThe mass of the carriage->Unknown lumped disturbance at time t of carriage 1,/->Unknown lumped disturbance at the moment t of the ith carriage,/->The unknown lumped disturbance at the moment t of the nth carriage is n, and n is the number of carriages of the high-speed train;
the preset hook slow constraint condition is as follows:
；
wherein,indicating time t->The carriage is articulated with the%>European norms of inter-carriage coupler displacement; />Representing the maximum magnitude of the coupler being stretched or compressed;
considering the failure of the train actuator, a train space state equation with the failure of the actuator part is established, and the train space state equation with the failure of the actuator part is expressed as:
；
wherein,，/>is a system state variable of the high-speed train at the moment t, < >>Is thatDerivative of>，/>For the control input of the high-speed train t moment, < >>，/>，/>For failure matrix of actuator +.>Indicating the health factor of the actuator 1 +.>Indicating the health factor of the actuator 2 +.>Health factor representing actuator n +.>Health factor representing actuator i (i=1, 2, …, n) satisfying +.>When->Time indicates +.>The actuator of the articulated car has no fault, +.>Representing the minimum value of the health factor, A representing the system matrix, < ->Representing the input matrix, B representing the coefficient matrix of the disturbance, < ->Representing unknown lumped disturbance of the whole high speed train at time t,/->；
，/>；
Wherein,；
；
；
；
wherein,is->Zero matrix of dimension, ">、/>、/>And->All are intermediate parameter matrixes;
the disturbance observer is expressed as:
；
wherein,unknown lumped disturbance for time t>Estimated value of ∈10->Is the internal state of the interference observer at the time t; />Is the gain matrix of the disturbance observer;
defining interference observer estimatesError of：/>；
Wherein,representing the estimation error of the interference observer at the time t;
the input compensation controller is expressed as:
；
wherein,the input compensation control signal at the moment T is represented, k is a constant, T represents a time delay greater than zero, T 0 Indicating a start time of the high speed train system;
the composite controller is expressed as:
；
wherein,is a composite control signal at time t +.>The state feedback control is designed for keeping the system calm at the time t, and K is a gain matrix.
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