RU2605513C1 - Method of piston in pneumatic cylinder adaptive braking creating - Google Patents

Abstract

FIELD: machine building.

SUBSTANCE: method is intended for production processes automation, particularly in automatic manipulators, as well as in other automatic devices with pneumatic cylinder. Method includes pneumatic cylinder piston braking by creation of air exhaust on output throttle adjustable by adaptive law. Exhaust control adaptive law is creating according to scheme with identifier and specified implicit reference model using ”simplified adaptability conditions” and two-phase structure. Control circuit assumes availability of information sensors on piston displacement and air pressure in pneumatic cylinder exhaust cavity and, optionally, microcontroller generation of control signals. Adjustable exhaust throttle can have any operation principle, providing adequate change in resistance to bleed air motion according to control signals.

EFFECT: smooth braking with specified parameters of pneumatic cylinder piston at end of its travel.

1 cl, 2 dwg

Description

The invention relates to the field of automation of production processes, in particular in automatic manipulators, as well as other automatic devices with a pneumatic cylinder, operating under conditions of a priori uncertainty about the current external effect on the piston of the pneumatic cylinder with a wide range of possible values and laws of change, also there is a smooth requirement with given braking parameters of the piston of the pneumatic cylinder at the end of its stroke.

Known methods of braking in a pneumatic cylinder based on the use of internal and external brake throttle devices [TM Bashta Hydraulic drive and hydropneumatic automation. - M: Engineering, 1972, p. 293, 294]. In them, the braking force is formed due to a stepwise decrease in the passage section of the bypass line at some point of the piston stroke of the pneumatic cylinder, or a smooth change in the specified section along the piston stroke. This is done using a special protrusion on the piston and an additional chamber, a switch in the bypass line, a brake valve, an exhaust throttle with a variable cross-section along the piston, etc. In this case, the braking force is determined by pre-setting the exhaust throttle and the moment of switching (the law of change) of the resistance of the exhaust throttle along the piston of the pneumatic cylinder.

Many such solutions are known, for example, patent RU 2447329 C2, 06/23/2010, IPC: F15B 15/22, F16K 31/122.

Closest to the claimed method of creating adaptive braking in the pneumatic cylinder is a method of damping the movement of the piston in the pneumatic cylinder, which involves using the control unit and the valve mechanism at first depending on the position of the piston, including at the beginning of its movement, increasing pressure in the exhaust chamber, and after a designated period of time - bleeding air from it (prototype) [patent RU 2489608 C1, 10/20/2010, IPC: F15B 11/068, F15B 15/22, F15B 15/28 F16H 61/28].

The main disadvantage of these methods of braking in the pneumatic cylinder (including the prototype) is that they are designed for a previously known value of the external impact on the piston of the pneumatic cylinder, the law of its change when moving the piston, or a rather narrow area of their possible variations. Therefore, they are not able to provide the required braking quality under conditions when the value of the external action on the piston and the nature of its change are not known in advance with a sufficiently wide range of their possible implementations. In particular, these methods do not take into account the case when the external load changes not only as the piston moves, but also changes in time.

The aim of the invention is to eliminate the disadvantage of existing methods of braking the piston in a pneumatic cylinder with adjustable exhaust in the form of ensuring a given quality of braking only with previously known values of the external impact on the piston, the law of its change when moving the piston, or a fairly narrow area of their possible implementations, as well as expanding the functional capabilities of such devices.

This goal is achieved by using the adaptive method of braking the piston in the pneumatic cylinder, which is implemented using a controlled throttle with a change in the bore, the value of which is formed depending on the position of the piston in the pneumatic cylinder and the pressure in the exhaust chamber according to a two-stage adaptive control circuit. In the first stage, the desired pressure in the exhaust chamber is calculated based on the estimates of the first current identification algorithm and the parameters of the main reference model. At the second stage, the throttle bore is formed based on the desired pressure, the second algorithm for the current identification and the parameter of the additional reference model. Moreover, in a two-stage adaptive control scheme, recurrent algorithms of current identification are used to evaluate unknown parameters of the mathematical model of piston movement in the pneumatic cylinder, and implicit reference models are used to set the required characteristics of piston braking in the pneumatic cylinder and control quality.

The essence of the invention is illustrated by the following description and the figures.

In FIG. 1 shows a diagram of a pneumatic damper with adjustable exhaust. In FIG. 2 presents the results of studies of the adaptive damper based on computer simulation.

- относительное перемещение поршня в направлении от нулевого объема выхлопной камеры,

,

; t, t₀ - текущее время и начальный его момент; V, P, ρ, m_г - объем, давление, плотность и масса газа в выхлопной камере соответственно, примем, что P(t₀)=P₀, V(t₀)=V₀, ρ(t₀)=ρ₀, m_г(t₀)=m_г0,

(

- относительное давление); заметим, что

; µ - массовая доля оставшегося газа в камере относительно начального состояния: µ(t)=m_г(t)/m_г0∈[1,0]; G - массовый расход выхлопа (будем считать истечение воздуха в выходном дросселе турбулентным); S_др - площадь проходного сечения выпускного дросселя (считаем круглой трубкой с переменным сечением, 0≤S_др≤S_{др max}, S_{др max} - максимальная площадь демпфера); P₀ - давление атмосферы; ρ₀ - плотность воздуха атмосферы; F_вн - заранее неизвестная квазистационарная внешняя сила (за время демпфирования изменяется незначительно); F_торм - тормозящая сила из-за избыточного давления в выхлопной камере: F_торм=S(P-P₀); F_тр - сила динамического трения:

, где k_тр - коэффициент вязкого трения.In FIG. 1 shows a diagram of a pneumatic damper with an adjustable exhaust with elements: 1 - attached mass; 2 - stock; 3 - cylinder; 4 - piston (piston, rod and attached mass represent the piston group - a single body); 5 - an exhaust chamber; 6 - adjustable exhaust throttle with variable flow area; 7 - an exhaust highway. In FIG. 1 for further clarification, the following notation is also introduced: m is the mass of the piston group, which is an a priori unknown quantity; S is the area of the piston; x is the displacement of the piston group, x∈ [0, x _max ], where x _max is the maximum value of x or the piston stroke;

- relative movement of the piston in the direction from the zero volume of the exhaust chamber,

,

; t, t ₀ - current time and its initial moment; V, P, ρ, m _g - volume, pressure, density and mass of gas in the exhaust chamber, respectively, we assume that P (t ₀ ) = P ₀ , V (t ₀ ) = V ₀ , ρ (t ₀ ) = ρ ₀ , m _g (t ₀ ) = m _g0 ,

(

- relative pressure); notice, that

; µ is the mass fraction of the remaining gas in the chamber relative to the initial state: µ (t) = m _g (t) / m _g0 ∈ [1,0]; G is the mass flow rate of the exhaust (we will consider the outflow of air in the output throttle turbulent); S _dr - the area of the orifice of the exhaust throttle (consider a round tube with a variable cross-section, 0≤S _dr ≤S _{dr max} , S _{dr max} - the maximum area of the damper); P ₀ - atmospheric pressure; ρ ₀ is the air density of the atmosphere; F _int - a previously unknown quasistationary external force (varies slightly during damping); F _brake - braking force due to excessive pressure in the exhaust chamber: F _brake = S (PP ₀ ); F _Tr - dynamic friction force:

where k _Tr - coefficient of viscous friction.

The method of creating adaptive braking of the piston in the pneumatic cylinder is as follows.

The quality of braking is set in the form of the parameters of the main implicit reference model: the dynamics of the braking of the piston must correspond to the dynamics of the movement of this reference model. Using two recurrent algorithms for current identification based on measuring the position of the piston and pressure in the exhaust chamber, as well as additional calculations of derivatives, unknown parameters of the mathematical model of the piston movement of the pneumatic cylinder (the first algorithm for current identification) and the control efficiency parameter (second algorithm for current identification) are estimated . Based on the estimates delivered by the first current identification algorithm and the parameters of the main reference model, the desired pressure in the exhaust chamber is formed. The control, or the size of the orifice of the throttle, is formed on the basis of the indicated desired pressure, an assessment from the second algorithm of current identification, the above variables and an additional implicit reference model that forms the requirement for the quality of achieving the desired pressure in the exhaust chamber. These calculations can be implemented in the microcontroller. A feature of constructing adaptive control is that current identification algorithms are not required to achieve accurate estimates of unknown parameters (there are only easily implemented restrictions on some estimates), and the dynamics of the piston in the pneumatic cylinder are close to the required characteristics from the first steps of forming control, regardless of the specific parameter values a pneumatic cylinder and external influences (in the field of the principal feasibility of such).

Below is the rationale for the proposed method.

In accordance with Newton’s second law, the dynamics of the movement of the piston group is determined by the balance of forces (without initial conditions):

, или

.

, or

.

,

:And through relative values

,

:

With a constant amount of gas in the working chamber (m _g = const) and without heat exchange with the environment (the braking process, as a rule, proceeds rather quickly), the thermodynamic process associated with a change in volume V corresponds to an adiabatic one, which has a dependence for air [Mordasov M.M., Trofimov A.V. Analysis and synthesis of pneumatic devices. - M.: Mechanical Engineering 1, 2005]:

For conditions of gas decrease in the exhaust chamber: part of the remaining gas as part of the total volume corresponds to an adiabatic regularity, therefore this part can be described as:

In accordance with the introduced definitions:

Hence the equation describing the dynamics of air decrease in the chamber:

In accordance with [Mordasov M.M., Trofimov A.V. Analysis and synthesis of pneumatic devices. - M.: Mechanical Engineering 1, 2005] for turbulent gas flow through the throttle, you can write:

where α _P , ϕ are coefficients depending on the design features of the inductor. Based on the law of ideal gas (we consider the pressure P not very high, R is the gas constant, T is the absolute temperature) P (t) = ρ (t) RT, hence ρ (t) = P (t) / (RT), we obtain

- априорно неизвестный коэффициент пропорциональности.Where

- a priori unknown proportionality coefficient.

Equations (1) - (4) describe the mathematical model of a pneumatic damper under the conditions under consideration.

гораздо ниже скорости изменения переменных

, µ(t). А также на основании (2), по которому

и равенств (3), (4):Further, for explanations, one more dependence is required, which is deduced from the assumption that, when the damper is operating, the rate of change of the variable

much lower than the rate of change of variables

, µ (t). And also on the basis of (2), according to which

and equalities (3), (4):

Or

Where

For the synthesis of the adaptive control law, the current identification algorithm is used, which delivers unknown parameters of equations (1) and (5), which we write in the form (without taking into account the initial conditions):

where a ₁ = -k _mp / m, a ₂ = SP ₀ / (mx _max ), a ₃ (t) = - F _int (t) / (mx _max ), a ₄ = -1.4k / (ρ ₀ Sx _max ) - unknown coefficients and functions of time.

The obtained estimates are described in the form of equalities

- вектор искомых оценок (верхний индекс «∧» обозначает оценку соответствующего параметра; «т» - транспонирование);

- вектор факторных переменных; ε₁ - невязка идентификации, дополняет равенство до точного соответствия.Where

is the vector of the desired estimates (the superscript “∧” denotes the estimate of the corresponding parameter; “t” stands for transposition);

- vector of factor variables; ε ₁ - discrepancy of identification, complements equality to exact correspondence.

A discrete algorithm of current identification (identifier) can be selected of a recursive type (described here for equation (8), for (9) it is similar and simpler):

where i = 1, 2, 3, ... - denotes the discrete time instant (t _i ) of determining the corresponding variable; Г _i - scalar or matrix gain of the identification algorithm, the choice of which designates the corresponding type of algorithm, for example [L. Lyung. System identification. Theory for the user: Per. from English / Ed. Ya.Z. Tsypkina. - M .: Nauka, 1991]:

, 0<γ<2, обычно γ=1 - со скалярным коэффициентом;

, 0 <γ <2, usually γ = 1 - with a scalar coefficient;

, Г₀=γ₀E - рекуррентный метод наименьших квадратов с фактором забывания (γ₀ - большое положительное число, Е - единичная матрица соответствующего размера, 0<<β<1 - назначаемый фактор забывания прошлых измерений).

, Г ₀ = γ ₀ E is the least square recurrence method with forgetting factor (γ ₀ is a large positive number, E is the identity matrix of the corresponding size, 0 << β <1 is the assigned forgetting factor of past measurements).

Any stable current identification algorithm (10), and these include algorithms with the indicated amplification factors, ensures, from the first steps of its operation, the convergence of the identification residual module in the region close to zero [S. Kruglov Adaptability issues of control systems with the “identifier + standard” scheme // Identification of systems and control tasks // Tp. IV international conf. SICPRO′05 (January 25-28, 2005, Moscow, IPU RAS). - M .: IPU RAS, 2005. - S. 1307-1348].

We require that the piston movement in the damper described by (1) satisfy a given stable implicit main reference model (the implicit is that this reference model exists only in the form of this equation):

- выходная координата эталона, соответствующая

; a _м1, a _м0 - назначаемые параметры эталона, обеспечивающие требуемое движение поршня демпфера в функции от времени (движение, близкое к нисходящей экспоненте).Where

- output coordinate of the reference corresponding

; a _m1 , a _m0 - assignable parameters of the standard, providing the required movement of the damper piston as a function of time (movement close to the descending exponent).

If the damper provides the desired value of the relative pressure in the form of a value

then substituting it into (8) will give:

which, due to the stability of the reference model and fast convergence to zero, provides damper behavior close to the reference one. In this case, the exact values of the estimates are not required, which corresponds to the "simplified conditions of adaptability" [Kruglov SP Adaptability issues of control systems with the “identifier + standard” scheme // Identification of systems and control tasks // Tp. IV international conf. SICPRO′05 (January 25-28, 2005, Moscow, IPU RAS). - M .: IPU RAS, 2005. - S. 1307-1348]. It is also determined there that for the stability of the closed control system under consideration there is an additional requirement:

по (14) с соответствующей перестройкой алгоритма идентификации (10) на определение лишь двух оценок:

и

.Since only the value of m is unknown here, it is not difficult to fulfill this restriction on the basis of information on the range of the value of m. An option for fulfilling condition (14) is fixing the estimate

according to (14) with the corresponding restructuring of the identification algorithm (10) to determine only two estimates:

and

.

Equations (6), (8), (10) - (14) correspond to the first stage of the adaptive control law.

по (12) используется уравнение (7) и оценка

по (9). Для этого назначается дополнительная эталонная модель:To form a condition

according to (12), equation (7) and the estimate

by (9). For this, an additional reference model is assigned:

, а выходом является

. При этом T_м назначается намного меньше времени торможения.corresponding to a stable aperiodic link with a unity gain and time constant T _m , where the input

, and the output is

. In this case, T _m is assigned much less braking time.

The law of variation of the throttle area (control) is assigned in the form

Substituting it into (9) gives

, а в соответствии с (13) -

. При этом параметры пневматического демпфера и внешняя сила заранее неизвестны. Кроме того, в силу подстройки параметров в алгоритме идентификации и, соответственно, закона управления снимаются вопросы относительно приблизительности представленных выше соотношений.Due to the stability of the additional reference model, the smallness of T _m and ε ₂ (t), the condition is very quickly reached

, and in accordance with (13) -

. In this case, the parameters of the pneumatic damper and external force are not known in advance. In addition, due to the adjustment of the parameters in the identification algorithm and, accordingly, the control law, questions regarding the approximation of the above relations are addressed.

For the stability of the control law (16), it is also required to fulfill an additional condition similar to (14):

«сверху» на основании приблизительной априорной информации о конструктивных параметрах демпфера α_P и ϕ либо на основании предварительного оценивания

.It’s easy to do by limiting the score.

“From above” on the basis of approximate a priori information on the design parameters of the damper α _P and ϕ or on the basis of preliminary assessment

.

(аналогичный (10)), (15)-(18) соответствуют второй ступени адаптивного закона управления.Equations (7), (9), an algorithm for estimating

(similar to (10)), (15) - (18) correspond to the second stage of the adaptive control law.

, S_{др max}=10^-5 м², k=2.8·10^-4 с/м, P₀=101000 Па, ρ₀=1.2 кг/м³, a _м1=-151 с^-1, a _м0=-1420 с^-2, T_м=0.01 с, γ₀=1000, β=0.99, шаг временной дискретности 0.001 с, условия (14) и (18) выполняются в виде ограничения соответствующих оценок.In FIG. Figure 2 presents the results of computer simulations of the adaptive damper with parameters (the least squares recursive method with a forgetting factor was used): m = 7.1 kg, S = 3 · 10 ^-4 m ² , x _max = 0.05 m, F _int ≈70 H (slightly varies in time), k _tr = 30 kg / s,

, S _{dr max} = 10 ^-5 m ² , k = 2.8 · 10 ^-4 s / m, P ₀ = 101000 Pa, ρ ₀ = 1.2 kg / m ³ , a _m1 = -151 s ^-1 , a _m0 = - 1420 s ^-2 , T _m = 0.01 s, γ ₀ = 1000, β = 0.99, temporal resolution step 0.001 s, conditions (14) and (18) are fulfilled as a limitation of the corresponding estimates.

, то здесь для создания нужной тормозной силы в начальный период выхлопной дроссель закрыт:

и требуемое значение S_др<0 - обеспечить нельзя. На этом этапе идет создание внутри выхлопной камеры достаточного давления. Как только это произойдет:

и S_др≥0, начинается активная фаза торможения. В этот момент времени (около 0.07 с) приравниваются значения выхода эталона и его скорости соответствующими значениями демпфера (указано стрелкой). Это вполне справедливо в силу неявности эталонной модели, дает наглядность проверки соответствия между сигналами

и

.Since braking control is only possible by bleeding air from the exhaust chamber

, then here to create the necessary braking force in the initial period, the exhaust throttle is closed:

and the required value of S _dr <0 is impossible to provide. At this stage, sufficient pressure is created inside the exhaust chamber. As soon as this happens:

and S _dr ≥0, the active phase of inhibition begins. At this point in time (about 0.07 s), the values of the standard output and its speed are equated with the corresponding damper values (indicated by the arrow). This is quite true due to the implicitness of the reference model; it gives the visibility of checking the correspondence between signals

and

.

It should be noted that due to the presented properties of the adaptive pneumatic damper, it is able to provide the functions assigned to it only within the limits of the fundamental possibility of their implementation. For example, the accuracy of data processing in a digital computer and the speed of processing a control signal determines the accuracy of control; the minimum value of the resistance of the exhaust damper (the maximum area of its passage section) determines the maximum possible braking speed, the initial volume of the exhaust chamber - the maximum braking force. These parameters specify the area of use of the adaptive pneumatic damper.

From the above it also follows that the described method of creating adaptive braking of the piston in the pneumatic cylinder also allows an initial increase in pressure in the exhaust chamber (as used in the prototype). In this case, for the presented example, there will be no (shortened) period of the initial formation of sufficient pressure in the exhaust chamber.

Claims (1)

A method of creating adaptive braking of a piston in a pneumatic cylinder, characterized in that, when bleeding air, the passage size of the adjustable throttle is formed depending on the position of the piston in the pneumatic cylinder and the pressure in the exhaust chamber according to a two-stage adaptive control scheme: at the first stage, the desired pressure in the exhaust chamber is calculated based on estimates of the unknown parameters of the mathematical model of piston motion in the pneumatic cylinder obtained on the first recurrent algorithm of current identification, and pa the main implicit reference model for setting the required piston braking performance in the pneumatic cylinder, the second stage is used to form the throttle bore size based on the desired pressure in the exhaust chamber, the throttle control efficiency obtained using the second recurrent algorithm for current identification, and the additional implicit reference parameter a model designed to set the quality of achieving the desired pressure in the exhaust chamber.

Images