CN111025906A - Underwater missile launching well lid flatness sliding mode composite control method - Google Patents

Underwater missile launching well lid flatness sliding mode composite control method Download PDF

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CN111025906A
CN111025906A CN201911313486.3A CN201911313486A CN111025906A CN 111025906 A CN111025906 A CN 111025906A CN 201911313486 A CN201911313486 A CN 201911313486A CN 111025906 A CN111025906 A CN 111025906A
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沈刚
臧万顺
陆宇
吴友生
汤裕
余文辉
芮光超
李翔
贾海杰
方磊
丁梦磊
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China University of Mining and Technology CUMT
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Abstract

The invention discloses a sliding mode composite control method for flatness of an underwater missile launching well cover. Compared with the traditional sliding mode controller, the flatness design method is embedded into the sliding mode controller, so that repeated derivation of a displacement feedback signal is avoided, the design of the controller is simplified, and the tracking precision of the system is improved.

Description

Underwater missile launching well lid flatness sliding mode composite control method
Technical Field
The invention relates to a sliding mode composite control method for flatness of a well cover launched by an underwater missile, and belongs to the technical field of automatic control.
Background
The sea-based ballistic nuclear missile is the most important secondary nuclear counterattack force in China, is usually loaded on a strategic nuclear submarine, performs strategic cruise under water all the year round, and has the advantages of strong concealment, strong survival capability and the like. From the perspective of battlefield viability and attack efficiency, the strategic nuclear submarine has greater advantages than a land-based intercontinental missile, and countries still have the most basic requirement that modern submarines are regarded as military strength of modern navy, so that the strategic nuclear submarine is highly valued by navy of countries all the time.
The underwater missile launching manhole cover opening device in the strategic nuclear submarine controls the launching manhole cover to be opened when approaching to a missile launching zero point, and controls the launching manhole cover to be closed after the missile is launched, so that the tracking precision of the underwater missile launching manhole cover opening device becomes a key link for judging whether the launching of the submarine missile is successful or not.
At present, the underwater missile launching manhole cover opening device of a submarine in China mainly adopts a hydraulic system to drive a launching manhole cover to act, and the launching manhole cover is required to be opened before missile launching and closed after missile launching, so that the launching manhole cover is required to be opened and closed stably and accurately in time.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides the sliding mode composite control method for the flatness of the launching well lid of the underwater missile, which can simplify the design of a controller and improve the tracking precision of a system, so that the opening and closing actions of the launching well lid are more stable.
In order to achieve the purpose, the underwater missile launching well lid flatness sliding mode composite control method comprises the following steps:
step 1, establishing a dynamic model of an electro-hydraulic servo system of an underwater missile launching manhole cover opening device;
step 2, establishing a state equation of the electro-hydraulic servo system according to the dynamic model in the step 1;
and 3, designing a flatness sliding mode composite controller according to a dynamic model and a state equation of the electro-hydraulic servo system.
Further, the dynamic model of the electro-hydraulic servo system of the underwater missile launching manhole cover opening device comprises a manhole cover dynamic model; the well lid dynamic model comprises a well lid and a hydraulic cylinder, one end of the hydraulic cylinder is hinged to a point C of the well lid, the other end of the hydraulic cylinder is hinged to a point A, and a rotating shaft of the well lid is hinged to a point B;
according to the kinetic model, a well lid kinetic equation in the hydraulic servo system of the underwater missile launching well lid opening device is established as follows:
Figure BDA0002323671730000021
furthermore, the dynamic model of the electro-hydraulic servo system of the underwater missile launching well lid opening device also comprises a hydraulic cylinder mathematical model, wherein the hydraulic cylinder mathematical model is a valve control hydraulic cylinder model and comprises a proportional servo valve and a double-rod hydraulic cylinder; the hydraulic cylinder flow continuity equation is as follows:
Figure BDA0002323671730000022
the balance equation of the external load force applied to the hydraulic cylinder is as follows:
Figure BDA0002323671730000023
selecting a system state variable of
Figure BDA0002323671730000024
The state equation of the hydraulic cylinder electro-hydraulic servo system can be obtained as follows:
Figure BDA0002323671730000031
y＝x1
in the formula, a1＝Ap/m，a2＝Bp/m，a3＝4βeAp/Vt，a4＝4βeCtl/Vt，a5＝4βe/Vt。
Further, in step 3, according to a dynamic model and a state equation of the hydraulic cylinder electro-hydraulic servo system, the method for designing the flatness sliding mode composite controller comprises the following steps:
1) obtaining a flatness equation by defining the control input of the hydraulic cylinder electro-hydraulic servo system and the flatness output of the hydraulic cylinder electro-hydraulic servo system;
2) redefining system state variables by defining reference signals of the hydraulic cylinder electro-hydraulic servo system to further obtain a new system state equation;
3) obtaining a system error equation by defining a system tracking error;
4) defining a sliding mode surface according to the system error equation to further obtain a system control input u;
5) introducing a system control input u
Figure BDA0002323671730000036
In the equation, the tracking error of the system approaches 0 exponentially.
Further, the flatness equation obtained by defining the control input of the hydraulic cylinder electro-hydraulic servo system and the flatness output of the hydraulic cylinder electro-hydraulic servo system is specifically as follows:
the control input of the hydraulic cylinder electro-hydraulic servo system is defined as follows: y is x1(ii) a The flatness output of the hydraulic cylinder electro-hydraulic servo system is defined as follows: u is QL, is prepared from
Figure BDA0002323671730000032
The flatness equation for x and control input u is obtained as follows:
Figure BDA0002323671730000033
by
Figure BDA0002323671730000034
The equation to x is as follows:
Figure BDA0002323671730000035
further, redefining the system state variables by defining reference signals of the hydraulic cylinder electro-hydraulic servo system to further obtain a new system state equation, which is specifically as follows:
defining a reference signal of an electro-hydraulic servo system of a hydraulic cylinder as xprRedefining the system state variables as follows:
Figure BDA0002323671730000041
therefore, according to the new system state variable, a new system state equation is obtained as follows:
Figure BDA0002323671730000042
y＝z1
wherein f is ═ a1a3z2-a1a4z3-a2z3，g＝a1a5。
Further, the system error equation is obtained by defining the system tracking error, which specifically includes:
define the system tracking error as:
Figure BDA0002323671730000043
the system error equation is further derived as follows:
Figure BDA0002323671730000044
further, according to the above system error equation, a sliding mode surface is defined, and then a system control input u is obtained, which is specifically as follows:
defining the sliding mode is as follows:
s＝k0e0+k1e1+k2e2+e3
by selecting a control parameter k0、k1、k2Let s3+k2s2+k1s+k 00 is a Helvetz matrix, and then
Figure BDA0002323671730000045
The following were used:
Figure BDA0002323671730000046
the system control input u may be expressed as:
Figure BDA0002323671730000051
in the formula, ksIs a constant greater than 0.
Further, the system control input u is introduced
Figure BDA0002323671730000052
In the equation, the tracking error of the system is exponentially close to 0, which is as follows:
introducing a System control input u
Figure BDA0002323671730000053
In the equation, we get:
Figure BDA0002323671730000054
when s is 0, the tracking error dynamics equation of the system is as follows:
Figure BDA0002323671730000055
selecting a control parameter k0、k1、k2Let s3+k2s2+k1s+k 00 being a Helvetz matrix, i.e.
Figure BDA0002323671730000056
Is a Helvelz matrix; the tracking error of the hydraulic cylinder electro-hydraulic servo system approaches to 0 according to an index s.
According to the underwater missile launching well lid flatness sliding mode composite control method, the flatness design method is embedded into the sliding mode controller, and compared with the traditional sliding mode controller, repeated derivation of state variables is avoided, so that the design of the controller is simplified, the tracking precision of a system is improved, and the accuracy of well lid launching time and the stability of opening and closing actions are improved.
Drawings
FIG. 1 is a schematic view of an underwater missile launching manhole cover according to the invention;
FIG. 2 is a schematic view of a model of a valve-controlled hydraulic cylinder according to the present invention;
FIG. 3 is a comparison graph of a tracking curve of the displacement of a hydraulic cylinder of a flatness sliding mode composite controller and a conventional sliding mode controller;
FIG. 4 is a graph comparing the tracking error curves of a flatness sliding mode composite controller and a conventional sliding mode controller.
Detailed Description
The technical solution of the present invention is explained in detail with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1 and 2, a sliding mode composite control method for flatness of a launching well lid of an underwater missile comprises the following steps:
step 1, establishing a dynamic model of an electro-hydraulic servo system of an underwater missile launching manhole cover opening device;
step 2, establishing a state equation of the electro-hydraulic servo system according to the dynamic model in the step 1;
and 3, designing a flatness sliding mode composite controller according to a dynamic model and a state equation of the electro-hydraulic servo system.
The dynamic model of the electro-hydraulic servo system of the underwater missile launching manhole cover opening device in the step 1 comprises a manhole cover dynamic model and a hydraulic cylinder mathematical model;
the well lid dynamic model comprises a well lid 1 and a hydraulic cylinder 2, one end of the hydraulic cylinder 2 is hinged to a point C of the well lid 1, the other end of the hydraulic cylinder 2 is hinged to a point A, and a rotating shaft of the well lid 1 is hinged to a point B;
according to the kinetic model, a well lid kinetic equation in the hydraulic servo system of the underwater missile launching well lid opening device is established as follows:
Figure BDA0002323671730000061
Figure BDA0002323671730000062
wherein J is the rotational inertia of the well cover and has the unit of N.m2/(m/s2) (ii) a Theta is the corner of the well cover in unit degree; theta0When the cover is closed, the included angle between the connecting line from the fixed hinge point A at the bottom of the hydraulic cylinder to the hinge point B of the rotating shaft of the well cover and the well cover is in unit degree; theta1The included angle between the axis of the hydraulic cylinder and the well cover in the closed state is unit degree; fgThe unit N is the driving force of the hydraulic cylinder to the well cover; g is the gravity of the well cover, and the unit is N; l is1The distance from a fixed hinge point A at the bottom of the hydraulic cylinder to a hinge point B of a rotating shaft of the well lid is unit m; l is2The distance from a hinge point C at the top of the hydraulic cylinder to a hinge point B of a rotating shaft of the well lid is unit m; l is3The distance from a hinge point C at the top of the hydraulic cylinder to the gravity center D of the well lid is unit m; y is the length of the hydraulic cylinderThe unit m.
The mathematical model of the hydraulic cylinder is established into a valve-controlled hydraulic cylinder model as shown in fig. 2, and comprises a proportional servo valve and a double-rod hydraulic cylinder.
The hydraulic cylinder flow continuity equation is as follows:
Figure BDA0002323671730000071
in the formula, CtlIs the total leakage coefficient of the hydraulic cylinder, VtTotal volume of cylinder inlet and return chambers, βeIs the effective bulk modulus of the hydraulic cylinder oil, ApIs the effective active area, x, of the cylinder pistonpFor displacement of the piston rod of the cylinder, p1Pressure of oil inlet of hydraulic cylinder, QLFor load flow, pLIs the load drop.
The balance equation of the external load force applied to the hydraulic cylinder is
Figure BDA0002323671730000072
In the formula, FLIs the external load force applied by the hydraulic cylinder, m is the mass of the well cover, BpThe viscous damping coefficient of the hydraulic cylinder.
Selecting a system state variable of
Figure BDA0002323671730000073
The state equation of the hydraulic cylinder electro-hydraulic servo system can be obtained as follows:
Figure BDA0002323671730000074
in the formula, a1＝Ap/m，a2＝Bp/m，a3＝4βeAp/Vt，a4＝4βeCtl/Vt，a5＝4βe/Vt。
And 3, designing a flatness sliding mode composite controller according to a dynamic model and a state equation of the hydraulic cylinder electro-hydraulic servo system as follows:
1) obtaining a flatness equation by defining the control input of the hydraulic cylinder electro-hydraulic servo system and the flatness output of the hydraulic cylinder electro-hydraulic servo system;
specifically, the control input of the hydraulic cylinder electro-hydraulic servo system is defined as follows: y is x1(ii) a The flatness output of the hydraulic cylinder electro-hydraulic servo system is defined as follows: u-QLFrom
Figure BDA0002323671730000087
The flatness equation to x and control input u is as follows:
Figure BDA0002323671730000082
equation (6) can be considered an inverse kinematics equation of the system equation of state (5) consisting of
Figure BDA0002323671730000088
The equation to x is as follows:
Figure BDA0002323671730000084
2) and redefining the system state variable by defining the reference signal of the hydraulic cylinder electro-hydraulic servo system, and further obtaining a new system state equation.
Specifically, a reference signal of an electro-hydraulic servo system of the hydraulic cylinder is defined as xprRedefining the system state variables as follows:
Figure BDA0002323671730000085
therefore, according to the new system state variable, a new system state equation is obtained as follows:
Figure BDA0002323671730000086
wherein f is ═ a1a3z2-a1a4z3-a2z3，g＝a1a5。
3) And obtaining a system error equation by defining a system tracking error.
Specifically, the system tracking error is defined as:
Figure BDA0002323671730000091
the system error equation is further derived as follows:
Figure BDA0002323671730000092
4) and defining a sliding mode surface according to the system error equation so as to obtain a system control input u.
Specifically, the definition of the sliding mode is as follows:
s＝k0e0+k1e1+k2e2+e3(11)
by selecting a control parameter k0、k1、k2Let s3+k2s2+k1s+k 00 is a Helvetz matrix, and then
Figure BDA0002323671730000093
The following were used:
Figure BDA0002323671730000094
thus, the system control input u may be expressed as:
Figure BDA0002323671730000095
in the formula, ksIs a constant greater than 0.
5) Introducing a system control input u
Figure BDA0002323671730000096
In the equation, the tracking error of the system approaches 0 exponentially.
The method comprises the following specific steps: introducing a System control input u (13)
Figure BDA0002323671730000097
In equation (12), we obtain:
Figure BDA0002323671730000098
therefore, s approaches 0 for a finite time.
When s is 0, the tracking error dynamics equation of the system is as follows:
Figure BDA0002323671730000099
selecting a control parameter k0、k1、k2Let s3+k2s2+k1s+k 00 being a Helvetz matrix, i.e.
Figure BDA0002323671730000101
Is a Helvelz matrix; therefore, the tracking error of the electro-hydraulic servo system of the hydraulic cylinder approaches 0 exponentially.
Due to the system control input u requirement in equation (13)
Figure BDA0002323671730000102
The analog quantity used by the existing control method is obtained by measuring through a displacement sensor in a hydraulic cylinder, a signal measured by the displacement sensor has measurement noise, and if the feedback signal of the displacement sensor is differentiated during design, the measurement noise of the displacement sensor is amplified, so that the tracking precision of the controller is reduced. In the present application, it is preferred that,
Figure BDA0002323671730000103
can be obtained according to the formula (7), and effectively avoids measuring the displacement sensorThe derivation of the quantity signal eliminates the influence of amplified measurement noise on the tracking precision, greatly improves the tracking precision of the system, and further improves the accuracy of the opening and closing time of the launching well lid and the stability of the opening and closing action.
According to specific embodiments, a comparison experiment is carried out on the underwater missile launching manhole cover flatness sliding mode composite control method and a conventional sliding mode control method.
The following parameters were chosen to model the system:
the mass m of the well cover is 350kg, and the effective volume elastic modulus of the oil is βe＝1x109N/m2(ii) a Leakage coefficient C of hydraulic cylindertm＝9×10-13m3Pas. pa; effective area A of hydraulic cylinder2＝1.88×10-3m2(ii) a Total volume V of hydraulic cylinder is 2.5 x 10-3m2. The gain of a conventional sliding mode controller is selected as follows: k is a radical of0＝2000、k1＝10000、k2＝1300、k s2; the gain of the flatness sliding mode controller is as follows: k is a radical of0＝4000、k1＝16000、k2＝2300、ks＝3。
The displacement of the hydraulic cylinder and the tracking error under different control methods are measured respectively, and the measurement results are shown in fig. 3 and 4. As can be seen from fig. 4, the flatness sliding mode composite controller proposed by the present invention has much higher precision than the conventional sliding mode controller.

Claims (9)

1. A sliding mode composite control method for flatness of a well cover launched by an underwater missile is characterized by comprising the following steps:
step 1, establishing a dynamic model of an electro-hydraulic servo system of an underwater missile launching manhole cover opening device;
step 2, establishing a state equation of the electro-hydraulic servo system according to the dynamic model in the step 1;
and 3, designing a flatness sliding mode composite controller according to a dynamic model and a state equation of the electro-hydraulic servo system.
2. The underwater missile launching manhole cover flatness sliding mode composite control method according to claim 1, wherein a dynamic model of an electro-hydraulic servo system of an underwater missile launching manhole cover opening device comprises a manhole cover dynamic model; the well lid dynamic model comprises a well lid (1) and a hydraulic cylinder (2), one end of the hydraulic cylinder (2) is hinged to a point C of the well lid (1), the other end of the hydraulic cylinder (2) is hinged to a point A, and a rotating shaft of the well lid (1) is hinged to a point B;
according to the kinetic model, a well lid kinetic equation in the hydraulic servo system of the underwater missile launching well lid opening device is established as follows:
Figure FDA0002323671720000011
3. the underwater missile launching well lid flatness sliding mode composite control method according to claim 2, characterized in that a dynamic model of an electro-hydraulic servo system of the underwater missile launching well lid opening device further comprises a hydraulic cylinder mathematical model, wherein the hydraulic cylinder mathematical model is a valve control hydraulic cylinder model and comprises a proportional servo valve and a double-rod hydraulic cylinder; the hydraulic cylinder flow continuity equation is as follows:
Figure FDA0002323671720000012
the balance equation of the external load force applied to the hydraulic cylinder is as follows:
Figure FDA0002323671720000013
selecting a system state variable of
Figure FDA0002323671720000014
The state equation of the hydraulic cylinder electro-hydraulic servo system can be obtained as follows:
Figure FDA0002323671720000021
y＝x1
in the formula, a1＝Ap/m，a2＝Bp/m，a3＝4βeAp/Vt，a4＝4βeCtl/Vt，a5＝4βe/Vt。
4. The underwater missile launching manhole cover flatness sliding mode composite control method according to any one of claims 1 to 3, wherein the method for designing the flatness sliding mode composite controller according to the dynamic model and the state equation of the hydraulic cylinder electro-hydraulic servo system in the step 3 is as follows:
1) obtaining a flatness equation by defining the control input of the hydraulic cylinder electro-hydraulic servo system and the flatness output of the hydraulic cylinder electro-hydraulic servo system;
2) redefining system state variables by defining reference signals of the hydraulic cylinder electro-hydraulic servo system to obtain a new system state equation;
3) obtaining a system error equation by defining a system tracking error;
4) defining a sliding mode surface according to the system error equation to further obtain a system control input u;
5) introducing a system control input u
Figure FDA0002323671720000022
In the equation, the tracking error of the system approaches 0 exponentially.
5. The underwater missile launching manhole cover flatness sliding-mode composite control method according to claim 4, wherein a flatness equation obtained by defining a hydraulic cylinder electro-hydraulic servo system control input and a hydraulic cylinder electro-hydraulic servo system flatness output is specifically as follows:
the control input of the hydraulic cylinder electro-hydraulic servo system is defined as follows: y is x1(ii) a The flatness output of the hydraulic cylinder electro-hydraulic servo system is defined as follows: u-QLThe number of atoms, denoted by y,
Figure FDA0002323671720000023
the flatness equation for x and control input u is obtained as follows:
Figure FDA0002323671720000024
the number of the groups represented by y,
Figure FDA0002323671720000031
the equation to x is as follows:
Figure FDA0002323671720000032
6. the underwater missile launching manhole cover flatness sliding-mode composite control method according to claim 5, characterized in that a new system state equation is obtained by redefining system state variables through defining reference signals of a hydraulic cylinder electro-hydraulic servo system, and the method specifically comprises the following steps:
defining a reference signal of an electro-hydraulic servo system of a hydraulic cylinder as xprRedefining the system state variables as follows:
Figure FDA0002323671720000033
therefore, according to the new system state variable, a new system state equation is obtained as follows:
Figure FDA0002323671720000034
y＝z1
wherein f is ═ a1a3z2-a1a4z3-a2z3，g＝a1a5。
7. The underwater missile launching manhole cover flatness sliding-mode composite control method according to claim 6, characterized in that a system error equation is obtained by defining a system tracking error, and specifically the following is obtained:
define the system tracking error as:
Figure FDA0002323671720000035
the systematic error equation is as follows:
Figure FDA0002323671720000036
8. the underwater missile launching manhole cover flatness sliding mode composite control method according to claim 7, characterized in that a sliding mode surface is defined according to the system error equation to obtain a system control input u, which is as follows:
defining the sliding mode is as follows:
s＝k0e0+k1e1+k2e2+e3
by selecting a control parameter k0、k1、k2Let s3+k2s2+k1s+k00 is a Helvetz matrix, and then
Figure FDA0002323671720000041
The following were used:
Figure FDA0002323671720000042
the system control input u may be expressed as:
Figure FDA0002323671720000043
in the formula, ksIs a constant greater than 0.
9. The underwater missile launching manhole cover flatness sliding-mode composite control method according to claim 8, wherein the system control input u is introduced
Figure FDA0002323671720000044
In the equation, the tracking error of the system is exponentially close to 0, which is as follows:
introducing a System control input u
Figure FDA0002323671720000045
In the equation, we get:
Figure FDA0002323671720000046
when s is 0, the tracking error dynamics equation of the system is as follows:
Figure FDA0002323671720000047
selecting a control parameter k0、k1、k2Let s3+k2s2+k1s+k00 being a Helvetz matrix, i.e.
Figure FDA0002323671720000048
Is a Helvelz matrix; the tracking error of the hydraulic cylinder electro-hydraulic servo system approaches to 0 according to an index s.
CN201911313486.3A 2019-12-18 2019-12-18 Underwater missile launching well lid flatness sliding mode composite control method Pending CN111025906A (en)

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Publication number Priority date Publication date Assignee Title
CN112987575A (en) * 2021-03-05 2021-06-18 中国矿业大学 Electro-hydraulic servo system position closed-loop tracking error limiting control method
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Application publication date: 20200417