RU2161814C1 - Device of follow-up control over longitudinal movement of motor vehicle - Google Patents

Abstract

FIELD: automatic control over longitudinal movement of motor vehicle under conditions of saturated city traffic flow. SUBSTANCE: technical objective of invention lies in reduction of follow-up errors of position thanks to formation of control over vehicle on basis of relative speed and deviation of interval between this vehicle and motor vehicle running in front of it from reference distance and on basis of evaluation of value equal to sum of acceleration of motor vehicle running in front and specific forces of resistance of vehicle to rolling and air normalized to own mass of vehicle. Device of follow-up control over longitudinal movement of motor vehicle includes meter of relative speed and interval between this vehicle and motor vehicle running in front, master unit of reference distance, former of difference of interval and reference distance, transducer of specific force generated by engine and brake systems of vehicle, control unit and unit evaluating sum of acceleration of motor vehicle running in front and specific forces of resistance of vehicle to rolling and air normalized to own mass of vehicle. EFFECT: reduction of follow-up errors. 8 dwg, 1 tbl

Description

 The invention relates to the field of traffic control of vehicles and is intended for automatic control of the longitudinal movement of the car in urban saturated traffic flow.

 The most prominent feature of modern transport is the collective nature of traffic. To a varying degree, this is characteristic of all types of transport, but it is manifested to the highest on land transport highways, where it often takes the form of a saturated flow with extreme (especially in urban conditions) values of intensity, driving dynamics and minimum distances between cars, often amounting to units of meters.

 With all the perfection of modern cars, the main element that prevents their collision is the human driver, who plays the role of the most responsible link in the vehicle monitoring system. The individuality and a certain limitation of the psychophysical qualities of a person are the reason for the incomplete adequacy of his reaction to the saturated flow state with extreme (especially in urban conditions) values of intensity, dynamism and minimal distances between cars and, as a result, even minor tracking errors lead to accidents on urban highways . In particular, the driver of a car moving in a stream is not able to register in time (at the initial stage) the changes in speed and mode of operation of the engine-brake system in front of the traveling vehicle directly by its senses, which leads to a delay in its actions [1, p. 38-43]. In this regard, it becomes an urgent problem to create a device for tracking control of the longitudinal movement of the car, which most fully compensates for the imperfection of the subjective psychophysical factor in the corresponding part, which makes it possible to reduce tracking errors and reduce the number of accidents in a saturated stream with limiting (especially in urban conditions) values of intensity, dynamism traffic and minimum distances between cars.

 A known method and device [2] for automatically controlling the speed of the car and the distance separating it from the front of the traveling car, comprising a speed controller of the vehicle at a given speed in the absence in the detection zone in front of the traveling car; interval adjuster to maintain the set distance between the vehicle and the vehicle traveling in front of the detection zone; means for establishing the beginning of a change in the path of the vehicle; a regulator for reducing the value of the set distance when switching the car to the left lane; a regulator for limiting the limiting value of the vehicle’s acceleration during the subsequent transition to the right lane when there is no vehicle in the detection zone ahead of you. In addition, the car is equipped with a means of determining the distance to the front of the traveling car.

 The main disadvantage of the device in question is the large value of position tracking errors (deviation from the set distance of the distance between the vehicle and the vehicle in front in the direction of the track during activation of the tracking mode). This is due to the fact that in the considered analog device at time intervals when the tracking mode is carried out, i.e. maintaining the specified distance between the vehicle and the vehicle in front, the most simple tracking scheme is implemented, in which the control of the vehicle's engine-brake system is formed only on the basis of data on the deviation of the distance between the vehicle and the vehicle in front of the vehicle, i.e. no more complete control of the vehicle’s engine-brake system is used, which is generated with the use of additional data, such as, for example, the vehicle’s speed relative to the front of the vehicle and the value equal to the sum of the acceleration in front of the vehicle and the specific resistance forces (normalized to the vehicle’s own mass) rolling and air of the car.

 Therefore, this analogue device for automatically controlling the vehicle speed and the distance separating it from the vehicle in front, due to large tracking errors, cannot be used for tracking control of the longitudinal movement of the car in a saturated stream with limit values of intensity, dynamics of movement and minimum distances between cars.

 There is also known a method and a follow-up control device for a car [3], comprising a distance meter that measures the distance between the car and the vehicle in front, a relative speed meter that measures the relative speed between the car and the vehicle in front, a control unit that, based on output values distance and relative speed meters controls the output power of the vehicle’s internal combustion engine when the vehicle accelerates from a standstill, taking into account relative speed and regardless of the distance so that the relative speed becomes zero if the distance measured by the meter does not reach a predetermined reference value. The engine power output is controlled based on the relative speed and distance, when the latter is at least equal to the reference (set) distance value.

 The disadvantage of such an analog device is the large position tracking errors, due to the fact that not all movement parameters are taken into account to formulate the car engine control; for example, the value equal to the sum of the acceleration in front of the traveling vehicle and the specific rolling resistance and air resistance forces of the vehicle is not taken into account, which does not allow for more complete control and reduced position tracking errors.

 Thus, this analogue device for servo control for a car, due to large position tracking errors, cannot be used for servo control of a car’s longitudinal motion in a saturated stream with limiting values of intensity, driving dynamics and minimum distances between cars.

 The known analogue device for servo control for a car [3] in its technical essence, functionality and technical result achieved is the closest to the claimed invention to a device for servo control of the longitudinal movement of a car and is considered hereinafter as a prototype device.

 The basis of the invention is the creation of a device for tracking the longitudinal control of the vehicle, which allows to reduce tracking errors in position between the vehicle and the vehicle in front, carrying out monitoring of the longitudinal movement of the vehicle based on the deviation from the reference distance of the measured distance between the vehicle and the vehicle in front , about the value of the measured relative speed between the vehicle and the vehicle in front and addition, based on data obtained evaluation (determination by means of special techniques, non-direct measurements, an approximate value of the magnitude) value equal to the sum of the acceleration of the vehicle traveling ahead and the specific forces and the rolling resistance of the vehicle air.

 The problem is solved in that in the device for monitoring the longitudinal movement of the vehicle, containing relative speed and distance meters, a reference distance adjuster, a shaper of the measured distance difference and a reference distance, a control unit, while a distance meter and a reference distance adjuster are connected to the inputs of the measured difference difference distance and reference distance, the output of which is connected to the input of the control unit, to the other input of which the meter is connected relative to speed, the output of the control unit is designed to supply a control signal to the vehicle's engine-brake system, four integrators, three difference shapers, four adders, eight amplifiers and a specific force sensor developed by the engine's engine-brake system are additionally included, while the inputs of amplifiers with odd numbers connected to the output of the first difference driver, and the inputs of the amplifiers with even numbers are connected to the output of the second difference driver, the outputs of the first and second, third and even The third, fifth and sixth, seventh and eighth amplifiers are connected in pairs to the first and second inputs of the first, second, third and fourth adders, respectively, in addition, the output of the first adder is connected to the input of the first integrator, the output of which is connected to the third input of the second adder, the output the second adder is connected to the input of the second integrator, the output of which is connected to the first input of the third difference shaper and the input of the control unit at the same time, the outputs of the third and fourth adders are connected respectively respectively, to the inputs of the third and fourth integrators, the outputs of which are respectively connected to the first inputs of the first and second difference formers, at the same time the output of the fourth integrator is connected to the third input of the third adder, the input of the specific force sensor is connected to the motor-brake system of the car, and the output of the specific power sensor is connected to the second input of the third difference shaper, the output of which is connected to the third input of the fourth adder, in addition, to the second input of the first shaper STI shaper connected to the output difference of the measured distance and the reference distance, the second input of the second difference generator connected to the output of the relative velocity meter.

In the claimed device tracking monitoring the longitudinal movement of the car, the common essential features for him and for his prototype are:
- the presence of structural elements in the form of distance and relative speed meters, a reference distance setter, a shaper of the measured distance difference and a reference distance, a control unit;
- the presence of links between the distance meter, the reference distance setter and the shaper of the difference of the measured distance and the reference distance; between a relative speed meter, a shaper of the difference in the measured distance and the reference distance and the control unit, as well as the connections between the control unit and the motor-brake system of the car itself.

A comparative analysis of the essential features of the claimed device and prototype shows that the first, unlike the prototype, has the following significant distinguishing features:
- the presence of structural elements in the form of four integrators, four adders, three difference shapers, eight amplifiers and a specific gravity sensor;
- the presence of connections between integrators, adders, difference shapers, amplifiers and the specific gravity sensor, as well as with the measured distance difference and the reference distance shaper, with a relative speed meter and a control unit, as well as specific force sensor communications with the engine-brake system of a controlled vehicle .

The set of features that ensure the achievement of a technical result:
- the presence of structural elements in the form of distance and relative speed meters, a reference distance setter, a shaper of the measured distance difference and a reference distance, four integrators, four adders, three difference shapers, eight amplifiers, a specific power sensor and a control unit;
- the presence of links between integrators, adders, difference shapers, amplifiers, a control unit, a reference distance setter and a specific gravity sensor between each other and with distance and relative speed meters, as well as a specific gravity sensor with a motor-brake system of the car.

 The technical result from the use of the claimed device tracking the longitudinal control of the vehicle is to reduce tracking errors in position that occur when tracking a vehicle ahead of a traveling vehicle.

 This set of known and distinctive essential features provides a technical result.

 It is this combination of all essential features that made it possible to create a device for tracking control of the longitudinal movement of the car.

 Based on the foregoing, we can conclude that the set of essential features of the claimed invention has a causal relationship with the achieved technical result, i.e. thanks to this combination of essential features of the invention, it has become possible to solve the problem.

 Therefore, the claimed invention is new, has an inventive step, that is, it clearly does not follow from the prior art and is suitable for industrial use.

The essence of the claimed device tracking control longitudinal movement of the car is illustrated by drawings:
FIG. 1 is a block diagram of a device for monitoring longitudinal control of a vehicle; FIG. 2 is a detailed block diagram of a device for monitoring longitudinal control of a vehicle; FIG. 3 is a functional block diagram of a device for monitoring longitudinal control of a vehicle; FIG. 4 is a diagram of the root mean square value of the tracking error on the value of the estimation time constant; FIG. 5 is a diagram of the dependence of the rms value of the tracking error on the value of the weight coefficient m, FIG. 6 is a line diagram of a level of a norm of a matrix of a functional of management quality; FIG. 7 is a timing chart of position tracking error when using the prototype and the claimed device for a situation of moderate dynamics of the flow of cars; FIG. 8 - time diagrams of the distance between the vehicle and the vehicle in front when the latter is stopped urgently (hitting an obstacle).

 The claimed device (Fig. 1) consists of a distance meter 1, a reference distance setter 2, a relative speed meter 3, a measured distance difference and a reference distance shaper 4, an estimation unit 5, a control unit 6, and a specific force sensor 7. FIG. 1 also shows the control object - the engine-brake system of the car 8.

(знак "^" над переменными служит для обозначения их оценок, т.е. приближенного значения) величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля. Блок управления 6 формирует управление W двигательно-тормозной системой автомобиля на основе данных о величине измеренной относительной скорости, отклонения измеренного расстояния от опорной дистанции, а также на основе оценки величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля. Датчик удельной силы 7 измеряет величину удельной (на единицу массы автомобиля) силы u, развиваемой двигательно-тормозной системой автомобиля.Distance meter 1 measures the distance Z _r - between the vehicle and the vehicle in front. The reference distance setter 2 sets the reference value of the distance R _о between the vehicle and the vehicle in front, which is maintained by the vehicle using the declared device for monitoring the longitudinal movement of the vehicle mounted on it. The relative speed meter 3 measures the relative speed Z _V of the vehicle relative to the front of the traveling vehicle. The shaper of the difference between the measured distance and the reference distance 4 generates at its output a value of Z _r -R _о proportional to the deviation of the measured distance Z _r from the reference distance R _about . Grade 5 forms a grade

(the “^” sign above the variables is used to indicate their estimates, that is, an approximate value) of a value equal to the sum of the acceleration ahead of the traveling vehicle and the specific forces of rolling and air resistance of the car. The control unit 6 generates control W of the vehicle's engine-brake system on the basis of data on the measured relative speed, the deviation of the measured distance from the reference distance, and also on the basis of an estimate of the value equal to the sum of the acceleration in front of the traveling vehicle and the specific rolling and air resistance forces of the vehicle. The specific gravity sensor 7 measures the value of the specific (per unit mass of the car) force u developed by the engine-brake system of the car.

величины, равной сумме ускорения ведущего автомобиля и удельных сил сопротивления качению и воздуху ведомого, управляемого автомобиля. В свою очередь формирователь разности измеренного расстояния и опорной дистанции 4 на своем выходе формирует величину Z_r-R_о, равную отклонению расстояния между автомобилем и впереди едущим транспортным средством от опорной дистанции между ними на основе данных, поступающих от измерителя расстояния 1 и задатчика опорной дистанции 2. От формирователя разности измеренного расстояния и опорной дистанции 4 и измерителя относительной скорости 3, а также от блока оценивания 5 в блок управления 6 направляются для формирования управления двигательно-тормозной системой автомобиля текущие данные о величине относительной скорости Z_V, об отклонении расстояния между автомобилем и впереди едущим транспортным средством от опорной дистанции Z_r-R_о а также об оцененной величине

Связь датчика удельной силы 7 обеспечивает поступление в блок оценивания 5 текущих данных о величине удельной силы u, развиваемой двигательно-тормозной системой автомобиля.The operation of the claimed device for controlling the longitudinal movement of the car is ensured by the relationship between the shaper of the difference between the measured distance and the reference distance 4 and the relative speed meter 3 with the evaluation unit 5, in which the evaluation is generated

a value equal to the sum of the acceleration of the driving car and the specific forces of rolling resistance and air of the driven, controlled car. In turn, the shaper of the difference in the measured distance and the reference distance 4 at its output generates a value of Z _r -R _о equal to the deviation of the distance between the vehicle and the vehicle in front from the reference distance between them based on data from the distance meter 1 and the reference distance setter 2. From the shaper of the difference of the measured distance and the reference distance 4 and the relative speed meter 3, as well as from the evaluation unit 5, the control unit 6 is sent to form a motor control flax-brake system of the car current data on the value of the relative speed Z _V , on the deviation of the distance between the vehicle and the vehicle in front from the reference distance Z _r -R _о, as well as on the estimated value

The connection of the specific gravity sensor 7 ensures the receipt of current data on the specific gravity u developed by the motor-brake system of the vehicle in the evaluation unit 5.

In expanded form (Fig. 2), the claimed device for tracking the longitudinal control of the vehicle consists of distance meters 1 and relative speed 3; reference distance setter 2; shaper of the difference between the measured distance and the reference distance 4; first 9, third 13, fifth 19, seventh 22 electric signal amplifiers with amplification factors mk _X4 , mk _X3 , mk _X1 and mk _X2 , respectively; second 11, fourth 15, sixth 20, eighth 21 electric signal amplifiers with amplification factors k _V4 , k _V3 , k _V1 and k _V2 , respectively; the first 12, second 16, third 23, fourth 26 integrators of electrical signals; first 10, second 14, third 24, fourth 25 adders and adder 29; the first 17, second 18, third 27 forwarders of the difference and the former of the difference of the measured distance and the reference distance 4; amplifiers of electrical signals 28, 30 with gains p ₁ , p ₂ , respectively; specific gravity sensor 7 developed by the engine-brake system of the car.

измеренного Z_r-R_о (от формирователя разности измеренного расстояния и опорной дистанции 4) и оцененного

(от третьего интегратора 23) отклонений расстояния от опорной дистанции, а на выходе второго формирователя разности 18 формируется разность измеренной Z_V (от измерителя скорости 3) и оцененной

(от четвертого интегратора 26) величин относительной скорости. С выхода первого 17 и второго 18 формирователей разности сигналы через первый 9, третий 13, пятый 19, седьмой 22 усилители и второй 11, четвертый 15, шестой 20, восьмой 21 усилители, соответственно, поступают на первый 10, второй 14, третий 24, четвертый 25 сумматоры, с выхода которых направляются на входы первого 12, второго 16, третьего 23, четвертого 26 интеграторов, соответственно. На выходах первого 10, второго 14, третьего 24, четвертого 25 сумматоров формируются данные о скорости изменения величины

производная от

оценки величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля), о скорости изменения величины

оценка величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля), о скорости изменения величины

оценка отклонения измеренного расстояния от опорной дистанции), о скорости изменения величины

оценка относительной скорости), соответственно. Все это позволяет на выходе второго интегратора 16 сформировать оценку

величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля, которая направляется в блок управления 6 (на сумматор 29) для формирования дополнительного слагаемого управления двигательно-тормозной системой автомобиля. Данные о величине удельной силы u, развиваемой двигательно-тормозной системой автомобиля, с помощью датчика удельной силы 7 направляются в блок оценивания 5 на второй вход третьего формирователя разности 27, на первый вход которого поступают данные об оцененной величине

равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля. Полученная на выходе третьего формирователя разности 27 разность

поступает на третий вход четвертого сумматора 25 для корректировки оцененной величины скорости изменения относительной скорости

автомобиля, которая после интегрирования в четвертом интеграторе 26 поступает одновременно на первый вход второго формирователя разности 18 и на третий вход третьего сумматора 24 для коррекции скорости изменения оценки

отклонения измеренного расстояния от опорной дистанции. При этом, если данные о расстоянии и относительной скорости между автомобилем и впереди едущим транспортным средством получаются непосредственно путем измерений указанных величин, то данные о величине, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля, вырабатываются с помощью блока оценивания 5, не требующего дополнительных измерений.The claimed device for monitoring the longitudinal movement of the car in more detail with reference to the expanded block diagram of the device for monitoring the longitudinal movement of the car (Fig. 2) works as follows: distance meters 1 and relative speed 3 measure the distance Z _r and the relative speed Z _V between the car and traveling ahead of the vehicle, and then comparing the measured distance Z _r 4 in the shaper difference with a reference value _{of the} distance r of supports produced by setter oh distance 2, the output of the difference former of the measured distance and the reference distance 4 produced electrical signals proportional to the deviation Z _r -R _a measured distance from the reference distance. Current data on the relative speed Z _V and the deviation Z _r -R _{about the} measured distance from the reference distance are sent to the evaluation unit 5 to the second inputs of the second 18 and first 17 difference shapers, respectively, and through amplifiers 30 and 28 to the adder 29 of the control unit 6 , in which the control W is formed as the sum of values proportional to the relative speed Z _V and the deviation Z _r -R _{about the} measured distance from the reference distance. At the output of the first shaper of difference 17, a difference is formed

measured Z _r -R _about (from the shaper of the difference between the measured distance and the reference distance 4) and estimated

(from the third integrator 23) deviations of the distance from the reference distance, and at the output of the second shaper of difference 18, the difference of the measured Z _V (from the speed meter 3) and the estimated

(from the fourth integrator 26) of relative velocity values. From the output of the first 17 and second 18 shapers of the difference, the signals through the first 9, third 13, fifth 19, seventh 22 amplifiers and second 11, fourth 15, sixth 20, eighth 21 amplifiers, respectively, go to the first 10, second 14, third 24, fourth 25 adders, from the output of which are directed to the inputs of the first 12, second 16, third 23, fourth 26 integrators, respectively. The outputs of the first 10, second 14, third 24, fourth 25 adders are formed data on the rate of change of magnitude

derivative of

estimates of the value equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car), the rate of change

estimation of a value equal to the sum of the acceleration ahead of the traveling vehicle and the specific forces of rolling resistance and air of the car), the rate of change

estimation of deviation of the measured distance from the reference distance), the rate of change of magnitude

relative velocity estimation), respectively. All this allows the output of the second integrator 16 to form an estimate

a value equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling and air resistance of the car, which is sent to the control unit 6 (to the adder 29) to form an additional term for controlling the engine-brake system of the car. Data on the magnitude of the specific force u developed by the engine-brake system of the car, using the specific gravity sensor 7 is sent to the evaluation unit 5 to the second input of the third difference shaper 27, the first input of which receives data on the estimated value

equal to the sum of the acceleration ahead of the traveling vehicle and the specific forces of rolling resistance and air of the car. The difference obtained at the output of the third difference shaper 27

enters the third input of the fourth adder 25 to adjust the estimated magnitude of the rate of change of relative velocity

a car, which, after integration in the fourth integrator 26, simultaneously arrives at the first input of the second difference driver 18 and at the third input of the third adder 24 to correct the rate of change in the estimate

deviations of the measured distance from the reference distance. Moreover, if data on the distance and relative speed between the vehicle and the vehicle in front is obtained directly by measuring the indicated values, then data on the value equal to the sum of the acceleration in front of the vehicle and the specific rolling and air resistance forces of the vehicle are generated using the evaluation unit 5, not requiring additional measurements.

 Thus, the claimed device performs generation of control of the engine-brake system of the car based on data on the deviation of the measured distance from the reference distance, data on measuring the relative speed and data on estimating a value equal to the sum of the acceleration in front of the traveling vehicle and the specific rolling and air resistance forces of the car.

 A functional block diagram of the claimed device for monitoring longitudinal control of a vehicle is shown in FIG. 3. The main component of the claimed device is an evaluation unit 5, which comprises an amplifier 31, a difference shaper 32, an adder 33, an integrator 34, an amplifier 35, an amplifier 36. The elements of the evaluation unit 5 shown in FIG. 3 are multi-channel. So, the amplifier 31 equivalently represents the first 9 (Fig. 2), second 11, third 13, fourth 15, fifth 19, sixth 20, seventh 22, eighth 21 amplifiers; difference shaper 32 (FIG. 3) equally represents the first 17 (FIG. 2) and second 18 difference shapers; the adder 33 (Fig. 3) equivalently represents the first 10 (Fig. 2), second 14, third 24, fourth 25 adders; the integrator 34 (Fig. 3) equivalently represents the first 12 (Fig. 2), second 16, third 23, fourth 26 integrators; the multichannel amplifier (with amplification factors equal to unity) 35 (Fig. 3) is expressed in that signals from the third 23 (Fig. 2) and fourth 26 integrators are fed to the input of the difference shaper 32 and, finally, the multichannel amplifier (with amplification factors equal to unity) 36 (Fig. 3) is expressed in the structure of the connection of the elements of the integrator 34 and the adder 33 with each other. In addition to the evaluation unit 5, the functional block diagram shows the elements 1,2, 3,4, 5, 6, 7 and 8, the purpose of which corresponds to the block diagrams (Fig. 1 and 2).

где Z_r= R₁-R₂+ε_r - измеренное расстояние; Z_V= r₂+ε_V - измеренная относительная скорость; r₁ = R₁-R₂-R_о - отклонение расстояния R₁-R₂ от опорной дистанции R_о, R₁ - положение (координата на траектории движения) впереди едущего транспортного средства; R₂ - положение (координата на траектории движения) автомобиля; R_о - опорная дистанция;

относительная скорость; ε_r и ε_V - инструментальные погрешности измерителей расстояния и относительной скорости, соответственно;

оценки величин r₁, r₂, соответственно.The functional block diagram (Fig. 3) allows you to consider the operation of the feedback elements of the claimed device tracking the longitudinal control of the vehicle. From the functional block diagram it follows that in the shaper of difference 32, the measured vector (Z _r - R _о , Z _V ) ^{T is} compared with the estimated state vector at the system output

where Z _r = R ₁ -R ₂ + ε _r is the measured distance; Z _V = r ₂ + ε _V is the measured relative velocity; r ₁ = R ₁ -R ₂ -R _o - deviation of the distance R ₁ -R ₂ from the reference distance R _o , R ₁ - position (coordinate on the trajectory of movement) in front of the traveling vehicle; R ₂ - position (coordinate on the motion path) of the car; R _about - reference distance;

relative speed; ε _r and ε _V are the instrumental errors of the distance and relative velocity meters, respectively;

estimates of r ₁ , r ₂ , respectively.

и оценку

где

оценка величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля;

скорость изменения величины

Полученная разность векторов

(разность измеренных и оцененных в блоке оценивания 5 отклонений расстояния от опорной дистанции и относительной скорости) через матрицу обратной связи K (усилитель 31) поступает для коррекции оцениваемых величин на вход сумматора 33. С выхода интегратора 34 сигнал через матриц динамики системы Ф (усилитель 36) направляется на вход сумматора 33. Матрица динамики системы Ф отражает структуру уравнений, описывающих систему "автомобиль - впереди едущее транспортное средство", что отображается в структуре соединения элементов интегратора 34 и сумматора 33 между собой. Через матрицу вектора выхода H (усилитель 35) оценка вектора состояния

поступает в виде вектора выхода

на вход формирователя разности 32 для сравнения с измерениями Z_V и Z_r-R_о.The state vector of the system r = (r ₁ , r ₂ , F, f ₁ ) ^T has its derivative

and assessment

Where

estimation of the value equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car;

rate of change

The resulting vector difference

(the difference between the deviations of the distance from the reference distance and the relative velocity measured and evaluated in the evaluation unit 5) is fed through the feedback matrix K (amplifier 31) to correct the estimated values at the input of the adder 33. From the output of the integrator 34, the signal through the dynamics matrices of system F (amplifier 36 ) is directed to the input of the adder 33. The matrix of dynamics of the system Ф reflects the structure of equations describing the system "car - driving vehicle ahead", which is displayed in the connection structure of the elements of the integrator 34 and the sum torus 33 among themselves. Through the matrix of the output vector H (amplifier 35), an estimate of the state vector

comes in the form of an output vector

to the input of the shaper difference 32 for comparison with measurements of Z _V and Z _r -R _about .

 Consider the two main modes of operation of the claimed device.

после интегрирования в интеграторе 34, и к уменьшению элементов вектора

Так как в оцененный вектор состояния

входит, кроме элементов

, еще и элемент

являющийся оценкой величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля, то уменьшается также и величина

В целом это приводит к уменьшению величины управления

(блок 6), а затем и удельной силы u, развиваемой двигательно-тормозной системой автомобиля 8, т.е. - к замедлению движения автомобиля и восстановлению расстояния Z_r, близкого к опорной дистанции R_о. В свою очередь уменьшающееся значение удельной силы u, которое поступает на вход сумматора 33, приводит к дополнительному уменьшению величины

а следовательно, к дополнительному уменьшению величины управления W, что затем приводит к дополнительному увеличению замедления автомобиля и к дополнительному восстановлению расстояния Z_r, еще более близкого к опорной дистанции R_о и т.д. В результате указанных процессов уменьшающаяся величина удельной силы u, развиваемой двигательно-тормозной системой автомобиля, приводит к замедлению его движения и восстановлению расстояния Z_r до заданной величины опорной дистанции R_о.Let the value of the element Z _r of the measurement vector Z = (Z _r , Z _V ) ^T at some point in time decrease relative to the reference distance R _о due to the deceleration of movement in front of the traveling vehicle, i.e. by reducing the relative speed Z _V ; then the decreasing negative values of the elements of the vector Δr obtained at the output of the difference shaper 32 through the amplifier 31 go to the input of the adder 33, which leads to a decrease in the elements of the vector

after integration in the integrator 34, and to reduce the elements of the vector

Since in the estimated state vector

included except items

, also an element

which is an estimate of the value equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car, the value also decreases

In general, this leads to a decrease in the amount of control

(block 6), and then the specific force u developed by the engine-brake system of the car 8, i.e. - to slow down the vehicle and restore the distance Z _r close to the reference distance R _about . In turn, the decreasing value of the specific force u, which is fed to the input of the adder 33, leads to an additional decrease in

and consequently, to an additional decrease in the control value W, which then leads to an additional increase in vehicle deceleration and to an additional restoration of the distance Z _r , even closer to the reference distance R _about , etc. As a result of these processes, a decreasing value of the specific force u developed by the motor-brake system of the car leads to a slowdown in its movement and restoration of the distance Z _r to a given value of the reference distance R _about .

 Consider the second mode of operation of the claimed device.

после интегрирования в интеграторе 34, и к увеличению элементов вектора состояния

Так как в оцененный вектор состояния

входит, кроме элементов

, еще и элемент

являющийся оценкой величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля, то увеличивается также и величина

Все это приводит к возрастанию величины управления

(блок управления 6), а затем и удельной силы u, развиваемой двигательно-тормозной системой автомобиля 8, т.е. - к ускорению движения автомобиля и восстановлению расстояния Z_r, близкого к опорной дистанции R_о. В свою очередь увеличивающееся значение силы u, которое поступает на вход сумматора 33, приводит к дополнительному возрастанию величины

а следовательно, к дополнительному возрастанию величины управления W, что затем приводит к дополнительному увеличению скорости автомобиля и к дополнительному восстановлению расстояния Z_r еще более близкого к опорной дистанции R_о и т.д. В результате указанных процессов увеличивающаяся удельная сила u, развиваемая двигательно-тормозной системой автомобиля, приводит к ускорению его движения и восстановлению расстояния Z_к до заданной величины опорной дистанции R_о.Let the value of the element Z _r of the measurement vector Z = (Z _r , Z _V ) ^T at some point in time increase relative to the reference distance R _about due to an increase in the speed of movement in front of the traveling vehicle, i.e. by increasing the relative speed Z _V ; then the increasing positive values of the elements of the vector Δr obtained at the output of the difference shaper 32 through the amplifier 31 are fed to the input of the adder 33, which leads to an increase in the elements of the vector

after integration in the integrator 34, and to increase the elements of the state vector

Since in the estimated state vector

included except items

, also an element

which is an estimate of the value equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car, the value also increases

All this leads to an increase in control

(control unit 6), and then the specific force u developed by the engine-brake system of the car 8, i.e. - to accelerate the movement of the car and restore the distance Z _r close to the reference distance R _about . In turn, the increasing value of the force u, which is input to the adder 33, leads to an additional increase in

and consequently, to an additional increase in the control value W, which then leads to an additional increase in the vehicle speed and to an additional restoration of the distance Z _r even closer to the reference distance R _о , etc. As a result of these processes, the increasing specific force u developed by the motor-brake system of the car leads to an acceleration of its movement and restoration of the distance Z _to to a given value of the reference distance R _about .

(включая компоненту

), который изменяется в соответствии с изменениями элементов вектора измерения Z = (Z_r, Z_V)^T. Выработанная в заявленном устройстве оцененная величина

наряду с Z_r и Z_V используется для формирования управления W, что обуславливает у заявленного устройства свойства следящего управления продольным движением автомобиля.Therefore, an estimated state vector is generated in the claimed device

(including component

), which changes in accordance with changes in the elements of the measurement vector Z = (Z _r , Z _V ) ^T. The estimated value generated in the claimed device

along with Z _r and Z _{V it is} used to form the control W, which determines the properties of the tracking device for the longitudinal movement of the vehicle in the claimed device.

которая обеспечивает снижение ошибок слежения.Thus, in comparison with the prototype of the claimed device contains in the control of W an additional component

which provides reduced tracking errors.

называемого вектором ошибки оценивания. Следовательно величины элементов матрицы обратной связи K влияют на точность определения оценки

по отношению к величине F. Применение порядка выбора элементов матрицы обратной связи K, приведенного в приложении 1, минимизирует ошибки слежения, реализуемые заявленным устройством следящего управления продольным движением автомобиля.The values of the parameters of the elements (Fig. 3) directly affect the values of tracking errors. So the values of the elements of the feedback matrix K (amplifier 31) determine the dynamic properties of the estimation, i.e. vector value

called the estimation error vector. Therefore, the values of the elements of the feedback matrix K affect the accuracy of determining the estimate

in relation to the value F. The application of the order of selection of the elements of the feedback matrix K, given in Appendix 1, minimizes the tracking errors implemented by the claimed tracking device for longitudinal control of the vehicle.

 For a more detailed description of the operation of the claimed device tracking the longitudinal control of the car, we turn to analytical expressions describing the processes taking place in it.

где значения индекса i относятся соответственно к впереди едущему транспортному средству (i=1) и к автомобилю (i=2),
F_i - удельная сила i-го автомобиля.The equations of the longitudinal movement of the car and the vehicle in front in terms of specific forces (accelerations) per unit mass have the form:

where the values of the index i refer respectively to the front of the traveling vehicle (i = 1) and to the car (i = 2),
F _i - specific power of the i-th car.

The ratio of the specific forces acting on the car or on the vehicle in front is written as follows [1, p. 3-11] :,
F _i = (D _i -T _i ) - (A _i + Q _i ), i = 1,2, (2)
where (D _i -T _i ) - specific (normalized to the mass of the car (i = 1) or to the mass in front of the traveling vehicle (i = 2)) force developed by its motor-brake system;
D _i - specific (normalized to the mass of the car (i = 1) or to the mass in front of the traveling vehicle (i = 2)) force developed by its propulsion system;
T _i - specific (normalized to the mass of the car (i = 1) or to the mass of the vehicle in front (i = 2)) the force developed by its braking system;
A _i - specific (normalized to the mass of the car (i = 1) or to the mass in front of the traveling vehicle (i = 2)) the force of resistance to air (force of aerodynamic resistance);
Q - specific (normalized to the mass of the car (i = 1) or to the mass in front of the traveling vehicle (i = 2)) rolling resistance force; (A _i + Q _i ) - specific (normalized to the mass of the car (i = 1) or to the mass in front of the traveling vehicle (i = 2)) rolling resistance and air.

где r₁ = R₁-R₂-R_о - компонента положения вектора состояния r,
F = F₁+(A₂ +Q₂) - величина, равная сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля; u= D₂-T₂ - удельная сила, развиваемая двигательно-тормозной системой автомобиля; причем u^- ≅ u ≅ u⁺, что отвечает физическим представлениям о конечной мощности, развиваемой двигательно-тормозной системой автомобиля,
где u^- - минимальная предельная величина удельной силы u;
u⁺ - максимальная предельная величина удельной силы u.Given that in the problem under consideration, the relative movement of the car with respect to the vehicle in front is of decisive importance, we write equation (1) in deviations from the reference distance R _о (we subtract the second from the first equation of system (1)):

where r ₁ = R ₁ -R ₂ -R _o - component of the position of the state vector r,
F = F ₁ + (A ₂ + Q ₂ ) - a value equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car; u = D ₂ -T ₂ - specific force developed by the engine-brake system of the car; moreover, u ^- ≅ u ≅ u ⁺ , which corresponds to physical ideas about the final power developed by the engine-brake system of the car,
where u ^- is the minimum limit value of the specific force u;
u ⁺ is the maximum limit value of the specific force u.

Из последнего уравнения следует, что ошибки слежения r₁ = R₁-R₂-R_о по положению тем меньше, чем меньше правая часть этого уравнения, т.е. чем ближе величина удельной силы (D₂ - T₂) к величине F₁ +(A₂ + Q₂), равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля. Это означает, что удельную силу (D₂-T₂) слезет формировать близкой по величине к F₁ + (A₂ + Q₂). Однако величина F₁ + (A₂ + Q₂) может быть непосредственно измерена, что требует применения других подходов к определению величины F₁ +(A₂ +Q₂) Для разрешения данной задачи нами применено линейное оценивание [4, стр. 11-16], [5, стр. 258-275] . Это позволяет получать текущие значения величины F₁ +(A₂ +Q₂) в виде ее оценки

на основе измерений расстояния Z_r и относительной скорости Z_V.Next, we consider equations (1 ... 3) in expanded form:

From the last equation it follows that the tracking errors r ₁ = R ₁ -R ₂ -R _о in position the smaller, the smaller the right side of this equation, i.e. the closer the specific force (D ₂ - T ₂ ) to the value of F ₁ + (A ₂ + Q ₂ ), equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car. This means that the specific force (D ₂ -T ₂ ) will peel off to form close to F ₁ + (A ₂ + Q ₂ ). However, the value of F ₁ + (A ₂ + Q ₂ ) can be directly measured, which requires the use of other approaches to determine the value of F ₁ + (A ₂ + Q ₂ ). To solve this problem, we used linear estimation [4, p. 11- 16], [5, p. 258-275]. This allows you to get the current values of the value of F ₁ + (A ₂ + Q ₂ ) in the form of its assessment

based on measurements of distance Z _r and relative speed Z _V.

The specific force u = D ₂ -T ₂ is realized as a result of the reaction of the engine-brake system to the control W, which is formed on the basis of measurements of the relative speed and deviation of the measured distance from the reference distance between the vehicle and the vehicle in front, and also on the basis of an estimate of the value equal to the sum of the acceleration ahead of the traveling vehicle and the specific forces of rolling resistance and air of the car.

Уравнения измерений соответственно имеют вид:
Z_r= R₁-R₂+ε_r, (5)
Z_V= r₂+ε_V, (6)
где Z_r и Z_V - измеренные значения расстояния между автомобилем и впереди едущим транспортным средством и относительной скорости между автомобилем и впереди едущим транспортным средством;
r₂ - точное значение относительной скорости;
ε_r и ε_V - инструментальные погрешности измерителей расстояния и относительной скорости, соответственно.The relationship between the specific force u and the control W, taking into account the characteristic delay time (τ _d ) due to the inertial reaction of the engine-brake system to the control W, is presented as follows:

The measurement equations respectively have the form:
Z _r = R ₁ -R ₂ + ε _r , (5)
Z _V = r ₂ + ε _V , (6)
where Z _r and Z _V are the measured values of the distance between the vehicle and the vehicle in front and the relative speed between the vehicle and the vehicle in front;
r ₂ is the exact value of the relative speed;
ε _r and ε _V are the instrumental errors of distance and relative velocity meters, respectively.

являющейся оценкой величины силы F, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля;
- формирования управления W как функции оцененной величины

измеренных отклонения расстояния Z_r от опорной дистанции R_о и относительной скорости Z_V.The analysis of the above equations reveals the essence of the claimed device and provides for coverage of two issues:
- definitions of strength

which is an estimate of the value of the force F equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car;
- the formation of control W as a function of the estimated value

the measured deviations of the distance Z _r from the reference distance R _about and the relative speed Z _V.

Для оценки величины F в каждой точке t₀ временного интервала слежения нами принята аппроксимация указанной функции полиномом первой степени:
F=F₀+f₁(t-t₀), F₀=const, f₁=const, t-t₀= Δt→ ε,
или

F(t₀)=F₀,

где ε - бесконечно малая величина.For comparison, we list the parameters that form the control in the prototype and the claimed device, see table. In the prototype device for forming control of the engine-brake system, only measurements of the type Z _r and Z _{V are used} , in the claimed device for forming control, in addition to measurements of the type Z _r and Z _V , an additionally estimated value is used

To estimate the value of F at each point t _{0 of} the tracking time interval, we adopted an approximation of this function by a polynomial of the first degree:
F = F ₀ + f ₁ (tt ₀ ), F ₀ = const, f ₁ = const, tt ₀ = Δt → ε,
or

F (t ₀ ) = F ₀ ,

where ε is an infinitesimal quantity.

 Next, we describe the essence of the process of estimating the magnitude of the force F, equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car.

для которого нами разработана конкретная система уравнений, реализованная в блоке оценивания 5 (фиг. 1,2,3), позволяющая получать оценку величины силы F, в следующем виде:

где

оценка вектора состояния;
Z = (Z_r, Z_V)^T - вектор измерений;
U = bu - вектор удельной силы, развиваемой двигательно-тормозной системой автомобиля;
Ф - матрица динамики системы;
K - матрица обратной связи;
H - матрица вектора выхода;
m -весовой коэффициент;

b=[0-1 0 0]^T.For this, we turn to the matrix equation that implements the linear estimation process in general form [4, p. 15), [5, p. 275], (Fig. 3):

for which we have developed a specific system of equations implemented in the evaluation unit 5 (Fig. 1, 2, 3), allowing to obtain an estimate of the magnitude of the force F, in the following form:

Where

state vector estimation;
Z = (Z _r , Z _V ) ^T is the vector of measurements;
U = bu is the vector of the specific force developed by the engine-brake system of the car;
Ф - matrix of system dynamics;
K is the feedback matrix;
H is the matrix of the output vector;
m is the weight coefficient;

b = [0-1 0 0] ^T.

 The difficulty in deciding on the choice of elements of the feedback matrix K is due to the uncertainty and dynamism of the movement of cars in urban traffic, which makes it impractical to use such a well-formalized procedure for choosing elements of the feedback matrix K, which is the Kalman filter [4, p. 28-29, p. . 86-97].

In light of this, the modal approach [5, p. 299-357] to the selection of elements of the feedback matrix K, when all the eigenvalues λ _{γ of the} operator (Ф - КН) are assumed to be equal and negative, seems to be most appropriate. λ _γ = λ ₀ , ∀γ, γ = 1,2,3,4), and the choice of a specific value of the parameter λ ₀ <0 is carried out in the process of calculating the elements of the feedback matrix K.

In connection with the above, we determine the relationship between the elements of the feedback matrix K and the parameter λ ₀ through the characteristic equation [5, p. 56-57], [6, p. 51-53] of the form:
| F-KH-Eλ | = (λ-λ ₀ ) ⁴ , (9)
where E is a 4x4 unit matrix.

где величина ошибки слежения r₁ получена численным решением системы уравнений (3,4,5,6,8,11).Taking into account that the technical result from the use of the claimed device for monitoring the longitudinal movement of the car is to reduce tracking errors by position (r ₁ ), then, when determining the optimal parameters of the claimed device, we consider the indicator characterizing the specified technical result in the form of the mean square value of the tracking error by position (the need for averaging is caused by the presence of measurement errors and the requirements for accurate determination of device parameters):

where the value of the tracking error r _{1 is} obtained by numerically solving the system of equations (3,4,5,6,8,11).

To select the value of the parameter λ ₀ and determine the elements of the feedback matrix K, we follow the order containing the following sequentially performed procedures:
1. The determination from the equations of system (8) of the dependence of the elements of the vector K _x on the value of the parameter λ ₀ under the condition m = 1 and K _V = 0 (Appendix 1).

2. The numerical solution of the system of equations (3, 4, 5, 6, 8) determines the optimal value of the parameter λ ₀ at which the rms value q of the tracking error in position (10) is minimal.

3. The determination from equations (8) of the dependence of the elements of the vector K _V on the parameter λ ₀ for an arbitrary value of the weight coefficient m and the preservation of the dynamic properties of the estimate determined by the selected value of the parameter λ ₀ and the obtained dependences of the elements of the vector K _x on the value of the parameter λ ₀ (Appendix 1 )

 4. Determination by numerical solution of the system of equations (3, 4, 5, 6, 8) of the optimal value of the weight coefficient m, at which the rms value q of the tracking error in position (10) is minimal.

 The content of these procedures is explained below.

где

амплитуда колебательной составляющей ускорения;
ω_i - круговая частота колебательного процесса.We carry out paragraph 1 of the above procedures (a detailed exposition is in Appendix 1). To perform calculations according to claim 2 of the order of the procedures, we first determine the main characteristics of the dynamics of the traffic flow. So at separate time intervals in an unsteady mode, the movement in the flow of cars is oscillatory in the longitudinal direction, in this regard, we further consider the case when the acceleration with which the car moves is described by a periodic function of the form:

Where

amplitude of the vibrational component of acceleration;
ω _i is the circular frequency of the oscillatory process.

известны, обозначим их соответственно

Зафиксировав все параметры модели заявляемого устройства и варьируя только величину параметра λ₀, выполняем по п. 2 порядка процедур многократное вычисление q (для различных значений параметра λ₀ на интервале времени [0,T] , T = 2πN/ω $\genfrac{}{}{0ex}{}{\text{*}}{\text{i}}$ . B качестве величины N принимается число, которое обеспечивает при прочих постоянных параметрах определение величины q с требуемой точностью, различия вычисляемых значений которой обусловлены случайным характером величины r₁ из-за инструментальных погрешностей измерений (5, 6). Таким образом, повторяя вычисления выражения (10), строим график функции q = q(λ₀). На указанном графике требуемое оптимальное значение λ₀ выбрано как абсцисса минимума функции q, т.е. из условия

Выполняем п. 3 порядка процедур и определяем вектор K_V. В этом случае в формировании оценки

участвуют данные обоих видов измерений: Z_r и Z_V. Однако динамические свойства оценивания остаются неизменными, так как обусловлены выбранным значением параметра λ₀ и полученными зависимостями элементов вектора K_x от величины параметра λ₀ (приложение 1).For specific car models, maximum limit values

known, we denote them accordingly

Having fixed all the parameters of the model of the claimed device and varying only the value of the parameter λ ₀ , we perform q calculation repeatedly according to clause 2 of the procedure (for different values of the parameter λ ₀ on the time interval [0, T], T = 2πN / ω $\genfrac{}{}{0ex}{}{\text{*}}{\text{i}}$ . The quantity N is taken as the number that provides, with other constant parameters, the determination of q with the required accuracy, the differences in the calculated values of which are caused by the random nature of the value of r ₁ due to instrumental measurement errors (5, 6). Thus, repeating the calculations of expression (10), we plot the function q = q (λ ₀ ). In the graph, the required optimal value λ _{0 is} selected as the abscissa of the minimum of the function q, i.e. from the condition

We perform step 3 of the order of the procedures and determine the vector K _V. In this case, in the formation of the assessment

Both types of measurements are involved: Z _r and Z _V. However, the dynamic properties of the estimation remain unchanged, as they are caused by the chosen value of the parameter λ ₀ and the obtained dependences of the elements of the vector K _x on the value of the parameter λ ₀ (Appendix 1).

We perform step 4 of the procedure. To do this, fixing all the parameters of the model of the claimed device and varying the value of the weight coefficient m, we carry out the calculations similar to paragraph 2. Repeating the calculations of expression (10) for various values of the weight coefficient m, we plot the function q = q (m). The required value of the weight coefficient m is selected on the graph as the abscissa of the minimum of the function q, i.e. from the condition m = arg min _m q (m).

 Thus, the evaluation unit 5 (Fig. 1, 2, 3) evaluates the value of F equal to the sum of the acceleration ahead of the traveling vehicle and the specific rolling resistance and air resistance of the vehicle, while the parameters of the evaluation unit of the claimed device are selected optimal.

r(0) = r₀,

Формируем управление в виде суммы трех составляющих, первые две из которых аналогичны прототипу, а третья является оценкой

величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля:

С учетом выражения (11) приводим уравнения (3,4) к виду:

r(0) = r₀,

Из этих выражений следует, что, с некоторым запаздыванием τ_d (значение τ_d для конкретных автомобилей известно исходя из инерционных свойств их двигательно-тормозных систем), величина удельной силы u стремится к значению управления

В процессе слежения величина [p₁(Z_r-R₀)+p₂Z_V]→ ε_Z, т.е. минимизируется, из этого следует, что в процессе слежения удельная сила u стремится к величине

где ε_Z - величина, размер которой определяется ошибками слежения по положению и скорости.Taking into account the foregoing, we return to equations (3.4):

r (0) = r ₀ ,

We form the control in the form of the sum of three components, the first two of which are similar to the prototype, and the third is an estimate

a value equal to the sum of the acceleration ahead of the traveling vehicle and the specific forces of rolling resistance and air of the car:

In view of expression (11), we reduce equations (3.4) to the form:

r (0) = r ₀ ,

From these expressions it follows that, with some delay τ _d (the value of τ _d for specific cars is known based on the inertial properties of their motor-brake systems), the value of the specific force u tends to the control value

In the process of tracking, the quantity [p ₁ (Z _r -R ₀ ) + p ₂ Z _V ] → ε _Z , i.e. minimized, it follows that in the process of tracking the specific force u tends to the value

where ε _Z is a quantity whose size is determined by tracking errors in position and velocity.

В устройстве-прототипе подобная компенсация не осуществляется. За счет минимизации сил в правой части уравнения (3), в заявленном устройстве реализуется достижение нового технического результата, заключающегося в снижении ошибок слежения по положению.Therefore, the specific force u close to the value of F, see the right-hand side of equation (3), compensates for the value F. Thus, the right-hand side of equation (3) is minimized by compensating for the F specific gravity u close to the estimate

In the prototype device, such compensation is not carried out. By minimizing the forces on the right side of equation (3), the claimed device achieves the achievement of a new technical result, which consists in reducing tracking errors by position.

осуществляет слежение за истинным значением величины F и что оцененная величина

близка к величине F. Это позволяет осуществлять упомянутую нами ранее минимизацию правой части уравнения (3). С этой целью записываем уравнение (7) без обратной связи:

для точного значения вектора состояния r совместно с уравнением выхода y = Hr. Тогда система уравнений относительного движения автомобилей приобретает следующий вид:

Как упоминалось ранее, нами принята аппроксимация силы F полиномом первой степени в каждой точке интервала слежения t₀, а именно: F = F₀ + f₁(t-t₀), F₀ = const, f₁ = const, t-t₀= Δt, Δt→ ε, где ε - бесконечно малый промежуток времени. Данная система уравнений (12) позволяет получить точное значение вектора состояния r = (r₁, r₂, F, f₁), если известны, т.е. точно измерены в каждый момент времени t₀ интервала слежения величины F₀ и f₁.Next, we consider in detail the process of formation of the estimation error Δr. We show that the estimated value

monitors the true value of F and that the estimated value

is close to F. This allows us to minimize the right-hand side of equation (3), which we mentioned earlier. For this purpose, we write equation (7) without feedback:

for the exact value of the state vector r together with the output equation y = Hr. Then the system of equations of relative motion of cars takes the following form:

As mentioned earlier, we adopted the approximation of the force F by a polynomial of the first degree at each point of the tracking interval t ₀ , namely: F = F ₀ + f ₁ (tt ₀ ), F ₀ = const, f ₁ = const, tt ₀ = Δt, Δt → ε, where ε is an infinitesimal period of time. This system of equations (12) allows us to obtain the exact value of the state vector r = (r ₁ , r ₂ , F, f ₁ ), if known, i.e. the values of F ₀ and f _{1 are} accurately measured at each time t _{0 of} the tracking interval.

что позволяет, используя измерения только лишь расстояния и относительной скорости: Z = (Z_r, Z_V)^T, получать оценку всех элементов вектора

в том числе и искомого

Представляем систему уравнений (7) в том виде, в котором она разработана нами для заявленного устройства (см. систему уравнений 8):

Вычитаем уравнения системы (8) из уравнений (12) и, опуская члены, содержащие случайные величины ошибок измерений как не влияющие на дальнейшие выводы, представляем результат в следующем виде:

где Δr = (Δr₁,Δr₂,ΔF,Δf₁)^T - вектор ошибки оценивания;

компонента вектора ошибки оценивания по положению;

компонента вектора ошибки оценивания относительной скорости;

компонента вектора ошибки оценивания величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля;

компонента вектора ошибки оценивания производной от величины, равной сумме ускорения впереди едущего транспортного средства и удельных сил сопротивления качению и воздуху автомобиля.To eliminate this practically impossible condition, we cover the system with feedback (see equation 7) [4, p. 15], [5, p. 275]:

which allows, using measurements of only distance and relative speed: Z = (Z _r , Z _V ) ^T , to obtain an estimate of all elements of the vector

including the desired

We represent the system of equations (7) in the form in which it was developed by us for the claimed device (see system of equations 8):

Subtract the equations of system (8) from equations (12) and, omitting the terms containing random values of measurement errors as not affecting further conclusions, we present the result in the following form:

where Δr = (Δr ₁ , Δr ₂ , ΔF, Δf ₁ ) ^T is the vector of estimation error;

component of the position estimation error vector;

component of the error estimation vector of the relative speed;

a component of the error estimation vector of a quantity equal to the sum of the acceleration ahead of the traveling vehicle and the specific rolling resistance and air resistance forces of the vehicle;

component of the error estimation vector of the derivative of a value equal to the sum of the acceleration in front of the traveling vehicle and the specific forces of rolling resistance and air of the car.

к истинному вектору r = (r₁, r₂, F, f₁), а, следовательно,

к F.System of equations (13) is an equation for the estimation error vector Δr = (Δr ₁ , Δr ₂ , ΔF, Δf ₁ ) whose value indicates how close the estimation vector is

to the true vector r = (r ₁ , r ₂ , F, f ₁ ), and therefore

to F.

где

Тогда характеристическое уравнение [5, стр. 56], [6, стр. 51- 53] для матрицы

принимает вид

которое по содержанию совпадает с характеристическим уравнением для матричного уравнения (9):

Таким образом, решения, полученные для характеристического уравнения вида |Ф-KH-Eλ| (см. уравнение 9), полностью применимы для характеристического уравнения вида |A_Δ-Eλ|.
В приложении 1 подробно рассмотрен порядок определения элементов матрицы обратной связи K, весового коэффициента m и параметра λ₀. Совпадающие характеристические уравнения |A_Δ-Eλ| и |Ф-KH-Eλ| дают одни и те же значения оптимальных величин параметра λ₀ и весового коэффициента m. Так как параметр λ₀<0, что означает асимптотическую устойчивость уравнений (13) для ошибки оценивания Δr, то с течением времени и со скоростью, определяемой величиной параметра λ₀, ошибка оценивания Δr стремится к нулю. Таким образом, из рассмотрения ошибки оценивания Δr следует, что элементы вектора

осуществляют слежение за соответствующими элементами вектора r = (к₁,к₂, F,f₁), в том числе элемент

осуществляет слежение за F.We present the system of equations of estimation errors (13) in matrix form:

Where

Then the characteristic equation [5, p. 56], [6, p. 51-53] for the matrix

takes the form

which in content coincides with the characteristic equation for the matrix equation (9):

Thus, the solutions obtained for the characteristic equation of the form | Ф-KH-Eλ | (see equation 9) are fully applicable for a characteristic equation of the form | A _Δ -Eλ |.
Appendix 1 describes in detail the procedure for determining the elements of the feedback matrix K, weight coefficient m, and parameter λ ₀ . Matching characteristic equations | A _Δ -Eλ | and | Φ-KH-Eλ | give the same values of the optimal values of the parameter λ ₀ and the weight coefficient m. Since the parameter λ ₀ <0, which means the asymptotic stability of equations (13) for the estimation error Δr, then over time and at a speed determined by the value of the parameter λ ₀ , the estimation error Δr tends to zero. Thus, from consideration of the estimation error Δr it follows that the elements of the vector

track the corresponding elements of the vector r = (k ₁ , k ₂ , F, f ₁ ), including the element

monitors F.

 All of the above is the rationale for achieving a technical result from the use of the claimed device, which consists in reducing tracking errors due to the aforementioned minimization of the right side of equation (3).

за его истинным значением r, что также приводит к увеличению ошибок оценивания, а, следовательно, и ошибок слежения. Применение оптимальной величины весового коэффициента m позволяет дополнительно уменьшить ошибку оценивания за счет оптимального соотношения влияния данных измерений расстояния Z_r и относительной скорости Z_V на формирование ошибки оценивания.The meaning of the optimality of the values of the parameter λ ₀ and the weight coefficient m is that, at the optimal values of the parameter λ ₀ and the weight coefficient m, the value of the estimation error Δr is the minimum possible. If the parameter λ ₀ and the weight coefficient m deviate from their optimal values, the estimation error Δr increases. So, as the value of parameter λ ₀ increases, the frequency bandwidth of the estimation unit expands, and accordingly, the influence of measurement errors (random variables) increases, which leads to an increase in estimation errors, and, consequently, tracking errors. With a decrease in the parameter λ ₀ , tracking errors increase due to an increase in the inertia of the estimation process and deterioration of vector tracking

beyond its true value of r, which also leads to an increase in estimation errors, and, consequently, tracking errors. The use of the optimal value of the weight coefficient m allows one to further reduce the estimation error due to the optimal ratio of the influence of the measurement data of the distance Z _r and the relative speed Z _V on the formation of the estimation error.

Consider another question related to the explanation of the operation of the claimed device, the choice of values of the sensitivity coefficients for tracking position (p ₁ ) and speed (p ₂ ).

The indicated coefficients cannot be selected solely for reasons of the required tracking sensitivity by position or speed. Depending on the values of the tracking sensitivity coefficients for the position (p ₁ ) and speed (p ₂ ), the measurement data of the distance Z _r and the relative velocity Z _V take different part in the formation of the control W (see equation 11): the weight ratio of the measurement data of the distance Z _r and relative speed Z _V predetermines various control dynamics. We have shown (Appendix 2) that there are optimal values of tracking sensitivity coefficients by position (p ₁ ) and speed (p ₂ ), at which minimization of transient processes and best control are provided.

 Currently, the claimed device is in the process of prototyping, its design characteristics are given below. The presented results of calculating the parameters and characteristics of the claimed device confirm the conclusions given in the description of its operation, the possibility of implementing the invention and achieving a technical result.

 The calculations are performed for the system of equations (3, 4, 5, 6, 8, 11), which includes the equations of motion of the car and the vehicle in front, the engine-brake system of the car, measurements, estimation and control formation.

2) u₁ ⁺ = 5,2 м/с², u₂ ⁺ = 4,55 м/с² - предельные значения удельной силы u, развиваемые двигателями впереди едущего транспортного средства и автомобиля, соответственно;
|u $\genfrac{}{}{0ex}{}{\text{-}}{\text{1}}$ | = 7,0м/c²,|u $\genfrac{}{}{0ex}{}{\text{-}}{\text{2}}$ | = 6,0м/c² - предельные значения удельной силы u, развиваемые тормозными системами впереди едущего транспортного средства и автомобиля, соответственно;
3) τ_d1≈ τ_d2= τ_d= 0,4c - постоянная времени двигательно-тормозных систем впереди едущего транспортного средства и автомобиля.The calculations were performed with respect to the Mazda RX-7 (a vehicle in front) and Mercedes SL600 [7] (a car driven by the claimed device) with the following parameter values:
1) a ₁ = 0.0287 s ^-1 , a ₂ = 0.0281 s ^-1 - specific aerodynamic drag in front of a traveling vehicle and car, respectively,

2) u ₁ ⁺ = 5.2 m / s ² , u ₂ ⁺ = 4.55 m / s ² - the ultimate values of the specific force u developed by the engines in front of the traveling vehicle and car, respectively;
| u $\genfrac{}{}{0ex}{}{\text{-}}{\text{1}}$ | = 7.0m / s ² , | u $\genfrac{}{}{0ex}{}{\text{-}}{\text{2}}$ | = 6.0m / s ² - ultimate values of specific force u developed by brake systems in front of a traveling vehicle and a car, respectively;
3) τ _d1 ≈ τ _d2 = τ _d = 0.4c is the time constant of the engine-brake systems in front of the traveling vehicle and car.

The specific rolling resistance forces are taken equal to Q ₁ = Q ₂ = 0.15 m / s ² . The root-mean-square errors of distance and velocity measurements (see equations 5, 6), described by the normal distribution law, are accepted as follows: σ _r = 0.1 m, σ _V = 0.1 m / s. The characteristic values involved in the formation of the weight matrix C (Appendix 2) are: r _1m = 0.6 m, r _2m = 0.5 m / s, u _m = 3 m / s (typical values of the parameters under consideration).

выбраны равными:

(соответствует амплитуде колебаний положения впереди едущего автомобиля, равной 4 м),
ω^* = 0,897c^-1 (соответствует периоду колебаний положения впереди едущего автомобиля, равному 7 с).Initial conditions, reference distance and parameter limits

selected equal to:

(corresponds to the amplitude of fluctuations of the position in front of the traveling car, equal to 4 m),
ω ^* = 0.897c ^-1 (corresponds to the period of fluctuations of the position in front of the traveling car, equal to 7 s).

 These parameters correspond to a fragment of a situation with moderate dynamics arising from the unsteady movement of two different cars moving one after another in an urban saturated stream: the vehicle in front drives uniformly at a speed of 30 km / h and at the same time fluctuates in position with an amplitude of 4 m, the following behind him, a car controlled by the claimed device tracking the longitudinal control of the vehicle, carries out movement, maintaining a reference distance of 7 m

 In addition, the situation with pronounced dynamics is considered when a vehicle in front makes an emergency stop (hitting an obstacle), and the next car driven by the claimed device for tracking the longitudinal movement of the car performs braking (after stopping the car, the tracking mode is turned off by the driver) .

 It is shown that the position tracking error when using the claimed device for driving a car is reduced in comparison with the case of using the prototype device for the same purpose.

(см. уравнение 11) - заявленное устройство;
- W = p₁(Z_r - R_о) + p₂Z_V - прототип.In order to compare the claimed device with the prototype, the solution of the system of equations (3, 4, 5, 6, 8, 11) was performed when forming the control in two versions:

(see equation 11) - the claimed device;
- W = p ₁ (Z _r - R _o ) + p ₂ Z _V - prototype.

The use of tracking sensitivity coefficients for the position p ₁ and speed p ₂ in the formation of control in the prototype device determines the best possible result for the prototype, since the choice of tracking sensitivity coefficients for the position p ₁ and speed p _{2 is} performed optimally (Appendix 2). All other parameters of the prototype and the claimed device are also the same. All this ensures the creation of equal conditions when comparing the claimed device with the prototype.

Numerical solutions of the system of equations (3, 4, 5, 6, 8, 11) are made using the function ode45 [8, p. 204–208], with an accuracy of ^10–6 .

Как показывают результаты вычислений, представленные на диаграмме зависимости среднеквадратичного значения ошибки слежения от величины весового коэффициента m (фиг. 5) оптимальным является значение: m= 0,2, при котором имеет место минимум величины q (см. уравнение 10), т.е. наименьшие ошибки слежения.Next, we present the results of calculating the optimal parameters of the claimed device. The dependence of the rms value of the tracking error q on the value of the estimation time constant τ ₀ (Fig. 4 in the axes (τ ₀ , q), where τ ₀ = λ $\genfrac{}{}{0ex}{}{\text{-}}{\text{0}}$ ¹ - estimation time constant) illustrates the procedure for choosing the optimal value of the estimation time constant τ ₀ (a, therefore, the optimal value of the parameter λ ₀ and column K _{x of} the feedback matrix K) for the case when m = 1 and K _V = 0 (see Appendix 1 and the order of procedures for solving equation (9)). The optimal value of the estimation time constant τ ₀ , at which a minimum of q is observed (see equation 10) (i.e., the smallest tracking errors), was 0.275 s, which corresponds to λ ₀ = -3.64 s ^-1 . For further calculations, λ ₀ = -3.64c ^{-1 was} chosen.
Further, taking into account that the value of the parameter λ _{0 is} chosen, and the elements of the vector K _{x are} determined (see Appendix 1 and the order of the procedures for solving equation (9)), we find the optimal value of the weight coefficient m, which matches the participation of measurements of distance Z _r and relative speed Z _V in the estimation of the state vector

As the results of calculations show, the diagram of the dependence of the rms value of the tracking error on the value of the weight coefficient m (Fig. 5) is optimal: m = 0.2, at which there is a minimum of q (see equation 10), i.e. . smallest tracking errors.

In both cases, when determining the optimal values of the parameter λ ₀ and the weight coefficient m, the value N = 40 was taken, which ensured an acceptable accuracy (10 ^-3 ) of calculating q.

функционала качества управления I. Значение нормы матрицы

на линиях уровня убывает по мере движения к точке оптимума 0, в которой имеет место минимум переходных процессов, т. е. наилучшее управление соответствует точке с координатами

при этом вычисленный для этой точки спектр матрицы A составляет: Λ(A) = {-0,5;-1,0±j2,915}, что свидетельствует об асимптотической устойчивости управления (матрицы A), так как все действительные части собственных чисел матрицы A имеют отрицательные значения. Исходя из изложенного, нами выбраны значения p₁=1,9 и p₂=4,2, обеспечивающие наилучшее управление.The diagram of the level lines of the matrix of the functional of control quality (Fig. 6) presents the calculation results illustrating the procedure for selecting the vector p = (p ₁ , p ₂ ), (Appendix 2). Closed curves in the stability region are the level lines of the matrix norm values

functional quality management I. The value of the norm of the matrix

on level lines decreases as it moves toward the optimum point 0, at which a minimum of transients takes place, i.e., the best control corresponds to a point with coordinates

the spectrum of the matrix A calculated for this point is: Λ (A) = {-0.5; -1.0 ± j2.915}, which indicates the asymptotic stability of the control (matrix A), since all the real parts of the eigenvalues matrices A have negative values. Based on the foregoing, we have chosen the values p ₁ = 1.9 and p ₂ = 4.2, providing the best control.

 Thus, the optimal parameters of the claimed device are uniquely determined.

 Next, we compare position tracking errors when using the prototype and the claimed device for the two most typical situations: moderate and pronounced dynamics of motion processes.

 In FIG. 7 presents time charts of tracking error by position when using the prototype and the claimed device for a situation of moderate dynamics of the flow of cars. For the prototype, the value of the amplitude of the tracking error is about 1 m, for the claimed device is about 0.6 m. This corresponds to the technical result from the use of the claimed device, which consists in reducing tracking errors in position in comparison with the prototype.

 In FIG. 8 shows time diagrams of the distance between the vehicle and the vehicle in front when the latter is stopped in an emergency (collision with an obstacle). From the diagrams it follows that the car driven by the claimed device, in comparison with the car driven by the prototype, made a complete stop at a greater distance (0.7 m) from the car that was urgently stopped in front of it, i.e. with less tracking error. This also confirms the achievement of the technical result from the use of the claimed device and in conditions of pronounced dynamics of movement.

Sources of information
1. Konoplyanko V.I. The basics of road safety. M .: DOSAAF, 1978.

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Claims (1)

 A device for monitoring the longitudinal movement of a vehicle, comprising relative speed and distance meters, a reference distance adjuster, a measured distance difference and a reference distance shaper, a control unit, and a distance meter and a reference distance adjuster are connected to the inputs of the measured distance difference and a reference distance shaper, the output of which connected to the input of the control unit, to the other input of which a relative speed meter is connected, the output of the control unit Designed for supplying a control signal to the engine-brake system of a car, characterized in that it additionally includes four integrators, three difference shapers, four adders, eight amplifiers and a specific force sensor developed by the engine-brake system of the car, while the inputs of amplifiers with odd the numbers are connected to the output of the first difference driver, and the inputs of the amplifiers with even numbers are connected to the output of the second difference driver, the outputs of the first and second, third and fourth, fifth of the second and sixth, seventh and eighth amplifiers are connected in pairs to the first and second inputs of the first, second, third and fourth adders, respectively, in addition, the output of the first adder is connected to the input of the first integrator, the output of which is connected to the third input of the second adder, the output of the second adder connected to the input of the second integrator, the output of which is connected to the first input of the third difference shaper and the input of the control unit at the same time, the outputs of the third and fourth adders are connected respectively to the inputs of the third and fourth integrators, the outputs of which are respectively connected to the first inputs of the first and second difference formers, the output of the fourth integrator is simultaneously connected to the third input of the third adder, the input of the specific gravity sensor is connected to the engine-brake system of the car, and the output of the specific gravity sensor is connected to the second input of the third difference shaper, the output of which is connected to the third input of the fourth adder, in addition, to the second input of the first difference shaper ene shaper output difference of the measured distance and the reference distance, the second input of the second difference generator connected to the output of the relative velocity meter.

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