瑞典专利SE534422C2 Ways of steering and flying missiles

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公开号:SE534422C2
申请号:SE9504545
申请日:1995-12-14
公开日:2011-08-16
发明作者:Jacques Coatantiec；Jean-Paul Labroche
申请人:Tda Armements Sas；
IPC主号:

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25 30 35 534 422 The computer 3 calculates on the basis of these two input signals a position order Ö for a rudder. This order is executed by execution means represented in this figure by an amplifier 4 and a motor 5. The reactions of the missile 6 to this order are measured by means of an instrument box comprising gyrometers 7 and accelerometers 8. The output quantity Y of the accelerometers forms the comparator 2 second input signal mentioned in the description of the function of the quantity dßg Zí at the output of the gyrometer 7 forms the second input signal of the computer 3 which was mentioned in the description of the function of this computer. this comparator.
It should be noted that the description that has just been made is intentionally simplified. It is simplified in the sense with reference to Fig. 1 and is only an example, that when talking about such a quantity as acceleration or angle of rotation, it has been implicitly assumed that these quantities have only a single component. In fact, the acceleration is about vector quantities measured by accelerometers along axes associated with the missile. In the same way, the angles of rotation are measured by gyrometers with a degree of freedom along axes that are also associated with the missile. In fact, there are therefore three inputs instead of one associated with these quantities. For the control output signals, in the same way, there are generally as many output signals as means to control, for example four if there are four rudders.
Finally, it should be pointed out that this is an example, because, as has already been pointed out, there are bodies other than rudders for maneuvering a missile. It is not excluded that several of these bodies are on the same missile at the same time. For example, for an attack missile (air-surface missile) or sea missile (surface-surface missile), which are intended to operate at low or very high altitude, one can therefore have rudders that are effective at low altitude and aimed at 10 15 20 25 30 35 534 422 drive beams that are more efficient at high altitudes. In the following, the various means for imparting a missile a transverse acceleration will be referred to as actuators.
Also in Fig. 1, the automatic steering is shown according to an idea that has long been traditional for missiles, with a steering computer and an autopilot. This method of display has been adopted for a long time because it physically corresponds to the separate units in the missile. It should be noted that physically this distinction is disappearing due to an increasing integration of the calculation functions.
The above views are intended to clarify that the invention described below is not limited to the example which will be described. The invention is applicable in control systems that are integrated or not and regardless of what means are used to generate an acceleration perpendicular to the missile axis.
When the flight tries to eliminate the roll speed, the missile is referred to as roll stabilized.
When the roll stabilization is perfectly performed, it has the great advantage that it allows a release of the equations for movement during tilting, turning and rolling, which makes it possible to achieve structures for automatic flight with the aid of three released loops.
The following does not relate to the rolling loop, since the invention only relates to the tipping and turning loops.
Fig. 2 schematically shows the preparation of control orders by means of the flight unit on the basis of the transverse accelerations Fwo and Fww which are ordered by the computer 1 (Fig. 1). This representation is like Fig. 1 shown in accordance with a Nesline structure. . for a role-stabilized missile.
Fig. 2 shows the commands in the tilting and turning channels. The acceleration commands in these two channels Two and Fwm are input into the comparators 2T and 2L which receive values for the accelerations measured on each of these channels Fwïoch Fm, by accelerometers 8T and SL. The differential accelerations at the output of the comparators are received by computers 3T and 3L for correction of tilting and turning, respectively, which likewise receive by gyrometers 7T and 7L measured rotational speeds about the tilting axis Qm and the yaw axis Rm, respectively. Depending on the measured accelerations and angular velocities, the computers 3T and 3L order quantities that define positions ömo and öwo for actuators 6lT and 6lL. The quantities Öuo and Öwo can either be quantities that directly define the position of the actuators, or quantities that are associated with this position, such as, for example, a derivative of this position with respect to time. These commands are executed by means 4T, 4L, 5T, 5L shown in this representation by means of amplifiers and motors driving the actuators 6lT and 6lL.
It is important to remember that during tipping and turning, the automatic control is performed according to the order distribution in the coordinate system connected to the missile (the accelerations and angular velocities are measured in the missile coordinate system and compared directly with the commands in this coordinate system).
In an equivalent way, it can be said that the flight coordinate system coincides with the missile coordinate system.
In the military field, inertial control of a weapon, by associating locating means, for example of the inertial type, and controls, makes it possible to deliver an explosive charge to a given geographical location defined by its coordinates.
These versatile needs of the new systems now lead to the desire to specify not only the delivery point for the charge but also the direction in the angular direction of the velocity vector for the equipment at this point. The interesting thing about this extra feature is that it provides the ability to deliver penetrating explosive charges (impact or to (angle close to angle substantially at right angles to the ground) distribute secondary weapons over a given surface the horizontal plane at the moment of launch), just mention two extreme cases. 10 15 20 25 30 35 534 422 Another important point for these future weapons is the pursuit of a minimal cost. This object can be achieved by striving to fulfill the various functions of the system using as "rustic" devices as possible. To achieve this goal, it is proposed according to the invention to simplify the control of the actuators and eliminate the position or speed sensors for the actuators.
For this reason, according to the invention, the use of operating means with only two positions, a plus position and a minus position is proposed.
Such types of actuators are known and it is known that by regular adjustment of these actuators a position corresponding to a neutral position can be achieved.
According to the invention, the use of an algorithm, which will be explained in the following, is proposed to steer and fly the missile towards its target and bring it there along a desired controlled trajectory. The most interesting thing about the method according to the invention is that the navigation law used is particularly well adapted to the flight that can be achieved with rudders with only two positions. The navigation law according to the invention results in reference values for the transverse accelerator- According to the invention, it is calculated on the basis of these references which remain constant for calculated times. values the times for adjusting the actuators to provide the calculated trajectory. Because the control law is discontinuous, the flight can also be discontinuous.
The invention thus relates to a method of steering which is applicable to a symmetrical missile, in which the yaw and tip are indicated and which is provided with operating means with two positions, a + position and a - position, wherein the holding of an operating means in one of these positions modifies the direction of the velocity vector of the missile according to a rotational angular velocity 10 15 20 25 30 35 534 422 Umax, which missile has a center of gravity and a longitudinal axis and is provided with means for determining its acceleration and its rotational speed according to the turn and tip plan, which method is intended to move the missile to a target with the coordinates xc yc zc according to a trajectory terminated tangentially to a predetermined straight fall line, which is indicated by two angles vc and wc in an earth coordinate system, wherein the displacement of the center of gravity of the missile is determined by a system of equations, the steps of characterized by a) forming a Hamiltonian equation for the system of equations which control the movement of the missile's center of gravity; b) solve the Hamilton equation in each of the missile's yaws and tipples under the condition that the target is to be reached in minimal time, this solution making it possible to determine a first constant value for the transverse acceleration to be imposed on the missile up to the time II after a time to for measuring the kinematic parameters of the missile trajectory, a second value, this time zero, for the transverse acceleration during a period between time 11 and time 12, and at again a third constant transverse acceleration between the time I2 and a time tf for falling on the target, the constant acceleration values being those which can be realized with the two-position actuator of the missile moving at the instantaneous speed of the missile; c) maneuvering the missile's actuators so that the missile performs the transverse accelerations calculated for the times to, th 12; d) periodically repeat the measurements, calculations and the resulting actuator commands.
In principle, the above-mentioned control law presupposes that you have the same load factor at the beginning and at the end of the track. This is never the case in practice and could represent a lack of robustness for the law under consideration. In order to reduce the value of the load factors to be achieved at the end of the web, a fictitious intermediate target can be used according to an embodiment variant of the method of control according to the invention. This goal is moving on a curve and coincides with the intended goal at the same time as the time remaining to reach the fictitious goal. The curve described by this fictitious target must be a curve that touches the straight reference line for missile deposition, the tangent point being located at the intended target.
In the simulations performed by the applicant, the best results have been obtained with a parabola located above the straight reference line at a vertical distance from it equal to 1/2 gtgf, where g is the gravitational acceleration and tw is the time remaining for to reach the fictitious goal.
The control law according to the invention could be used on a missile equipped with actuators whose position can be varied in a continuous manner and with an arbitrary flight law. However, as already explained above, this law is particularly well adapted to a missile that is flown by programmed change of position of a two-position actuator. This is the reason why the invention also relates to a method for flying a symmetrical missile, in which the yaw and tip plane are indicated and which is provided with operating means with two positions, a + position and a - position, and means for determining its accelerations and rotational speeds q and r according to the yaw and tilt plane, the purpose of the flight being to convert a reference value for transverse acceleration, which is a consequence of a control order, into reference values for incidence and yaw ß, at equilibrium, and for this purpose give orders for maintaining or modifying the position of the actuators, according to which way the angles of incidence and yaw at equilibrium are obtained by solving equations which take into account the reference value F for transverse acceleration and mission. 20 25 30 35 534 422 the inertia data and aerodynamic data and according to which way the positions which the actuators must occupy in order to achieve these angles of incidence and yaw is controlled by an equation system that takes into account the missile inertia and aerodynamic data and the missile actuators, the mode of flight being characterized by the steps of: - a) forming a Hamiltonian equation for the system of equations determining the position to be taken by the actuators; - b) solve the Hamilton equation thus formed with the requirement that the calculated positions for incident and yaw at equilibrium be reached in a minimum time, the solution of the Hamilton equation making it possible in two-dimensional spaces a, q for the tilt plane and B, r establish conversion curves for the gear plane; - c) place the current point of the missile with respect to the variables a, q and ß, r in each of the two-dimensional spaces a, q and ß, r respectively; - d) comparing the position of the current point with these curves, adjusting the actuator to or maintaining the position + if the current point has an ordinate iq or r which is greater than each of the points of the curves with the same abscissa a or ß; - the actuator is adjusted to or maintained in the - position if the point in question has an ordinate in q or r which is less than that of the point of the curve with the same abscissa; Periodically repeat steps a) to d).
It should be pointed out that the mode of flight is independent of the control law, even if in practice the best results are obtained with a missile that is controlled and flies according to the invention.
The methods of control and flight according to the invention will now be explained in more detail by means of the accompanying drawings, in which: Figures 1 and 2, which have already been commented on, flight control loops according to the prior art; shows 10 15 20 25 30 35 534 422 - Fig. 3 shows a control loop for a missile which utilizes the control method according to the invention; Fig. 4 is a diagram intended to show the designations used to define the equations for the motion of the missile center of gravity; Fig. 5 shows an example of a path ordered by the control method according to the invention; Fig. 6 shows an example of a conversion curve for the actuators of a missile which is flown in accordance with the method according to the invention; Fig. 7 shows a flight control loop according to the method of the invention.
Fig. 8 shows a variant of the method according to the invention which is intended to minimize the maneuvers at the end of the track.
The function of the complete system can be schematized in the form shown in Fig. 3, namely with an outer loop or control loop and an inner loop called a flight loop.
In Fig. 3, a control computer 1 receives at its input reference values for the end position and for the angle of impact for this position, as well as data originating, for example, from an inertia unit 17, which contains accelerometers and gyrometers.
Using this data, the control computer, in a manner to be explained in detail below, compiles reference values for the load factor which, if respected, enable the missile to reach its target according to a programmed final trajectory. unit 3, These reference values are entered into an airplane which receives data from the inertial unit 17. On the basis of this data and reference values for the load factor, the air unit prepares orders for switching the controls 61.
These orders affect the movement and orientation of the missile 6. These acceleration and rotation variations are detected by the accelerometers of the inertia unit 17 and the gyrometers of the inertia unit 17, and corresponding data are re-entered during the entire journey in the control computer 1 and in the flight unit 3.
It should be noted that in accordance with the mode of flight and control, it is no longer necessary to compare the position of the controls with an exact reference position, which means that the comparator 2 can be eliminated according to the state of the art.
It is possible, however, to provide for each of the two possible positions of each actuator an indicator which makes it possible to detect that the maneuver This would especially enable a degraded mode of operation in the case where at least one actuator has no longer really reached the actuator. ordered the situation. works.
The principle of governance will now be explained.
The main originality of the method according to the invention lies in the coherence between the adopted principles of control and flight.
In fact, the intentional restriction to "plus or minus" actuators imposes limits on the load factors that are easily realized with the missile.
It is known that a constant oscillation of a rudder (or any device which applies a constant torque around the center of gravity of the missile), after the response time of the missile, leads to a constant load factor. It is therefore intended that the selected rustic flight system should be well adapted to follow constant load factor reference values, at least in part, along the runway.
The following paragraphs show how the overall task for the system (imposed final position and slope) can be effectively fulfilled by meeting the load factor requirements above, whereby the system is rustic and powerful.
The first problem consists in determining a control which at the same time becomes homogeneous, a type of control which makes it possible to obtain control reference values which are simple enough to be easily realized with two-position operating means. For this purpose, an optimal control technique is used which is applied to a material point model (movement of the missile's center of gravity M).
The calculations that follow from this are thus simple (given the simplicity of the model used). To explain the calculations, we place ourselves in the plane X, Z, which here is assumed to coincide with a vertical plane of the earth.
Such a plane is shown schematically in Fig. 4.
The designations used are as follows: -V: velocity vector of the missile Y: slope of the missile velocity vector VC: reference slope of impact on the target.
The base equations for the system are as follows: å = v.cos y å = v.sin Y According to traditional notation, k and 2 denote the derivatives of the coordinates x and z with respect to time. V represents the absolute amount of the missile velocity vector V.
If one further assumes l ﬂ y: ~ «<(where F is the load factor, one has the relation Y = u.
Taking into account the limits of the position of the actuators, the load factor is assumed to be limited to a value rmaxj V rmax <rmax), which implies [UI <Umax (Umax = To simplify the explanations given here, the speed is assumed to be constant along the remaining path (in practice the calculations are performed along the path with a given frequency, which makes it possible to set the speed value again).
The goal is to achieve at tf (end time): 10 15 20 25 30 35 534 422 12 Xüf) = Xbut 2 (ff) = Zbut rüf) = re To prepare the control reference value, ie the values for the load factor in the tilting and turning plates According to the method of invention, a Hamilton equation for the system is calculated for each iteration.
The solution for the system is obtained by minimizing a magnitude J = Llfdz This means trying to minimize the "travel time" of the missile. This criterion, which is a linear function of time, makes it possible to obtain a command of the form +, 0, -, which is exactly what can be achieved directly for the intended missile. The Hamilton equation corresponding to this system is written: H = ~ 1 + Å1Vumy-Å2V ﬂ n7 + Ä3u In the Hamilton equation H, Ä1, Ä2oÜ, Ä3 are components of a vector assigned to the system.
Theoretical calculations performed by the applicant have shown that by applying the Pontryagin maximum as "travel time" and making it possible to reach the target in accordance with a key to the intended straight fall line having the reference value conclusion W "a load is obtained the optimal command, ie that which minimizes factor which is constant to a time n, zero thereafter between the time m_and a time Q, then again constant between the times Q and the end time r ﬂ The command thus obtained u has the form over '[0, fi] u = e] umu 61 = il over [q, Q] over '[q, ¶] u = O u = 52 zlmax 62: t 1 10 15 20 25 30 35 534 422 13 The signs for sh az and the values for th 12 are determined as a function of the current state of the missile x, z, Y and of the reference xc, zu yc.
In an ideal space, without gravity, the obtained web has the shape shown in Fig. 5, in the vertical plane of the web the distances are as x-coordinates and the heights as y-coordinates. - circular arc, - part of straight line (singular path), - circular arc.
The arcs of the circle correspond to constant, saturated load factors and the rectilinear part to a load factor of zero.
In practice, the control words are calculated at a given frequency (as a function of the missile's aerodynamic data of the order of 30 Hz) along axes parallel to the missile axes (two operating planes). In the case of a missile that has a large induced roll, the calculation frequency of the control words is increased to counteract this disturbance.
Appendix 1 to this application shows what has just been explained regarding the track as well as reference values u for the load factor to apply in the most general case.
It appears that the reference value for the load factor that is available at the output of a control module in the missile is particularly simple.
To ensure good control of the missile, it is sufficient to determine the times for adjustment of the rudder and the slope 3 of the rectilinear part of the trajectory.
According to the invention, ys is first calculated. 6 -2 ys = arc sm l 22 2 -arc tg ibl- Umax al * bl 1 x -r 2 _ s. with al = ° '+ 1 cm 7, - 2 cm ya V "max" max 5 b1 = Z ° z' + - f1-cos7, - 2 cozy; V "max u max 10 15 20 25 30 35 534 422 14 where xi and zi represent the instantaneous coordinates of the missile.
The detailed calculations leading to this first result are explained in Annex 2.
It can be seen that the value of 5 depends on the hypotheses assumed for Q and Q which can assume the values +1 or -1.
To obtain the correct value for ys, a coherence test is performed to verify that the result obtained is not absurd. It should first be noted that: there are two equations: s] ”max f! = 7; _ 7, 'Q thus has the sign for 72 "7 :, and (7:" 7.v) = 52 "max (ff ~ 12) 52 thus has the sign for (7c_) g) One thus begins to assume the hypothesis H1, since it is the most common, according to which 61 =], ¿'2, = 1 In this case you must a posteriori verify that 71' SïJSJ / c 'You only test this hypothesis of 7 / S ye- If this hypothesis is not verified with taking into account the final value obtained for ys, one starts again the calculation of ys assuming the hypothesis H2, according to which E1 = -1, 52: -] 10 15 20 25 30 35 534 422 15 In this case it will be necessary to a poste ~ riori verify that nrs fss ﬁ This hypothesis will be tested only if fc 5 Ü If this hypothesis is not verified taking into account the final value obtained for k with this hypothesis, one starts the calculation by assuming hypo- thesis H3 according to which 51 = 1, E2 = “'1 The hypothesis will be validated a posteriori if one obtains the connections n-rf20 7c" 7: 5o If this hypothesis is not verified one will test it last a hypothesis H4 according to which E! : _11 The hypothesis will be validated a posteriori if one obtains the connections ys-yiso yc-ysso It should be pointed out that the four considered hypotheses are exclusive, which means that if one is verified, the others can not be verified. 10 15 20 25 30 35 534 422 16 Each of these hypotheses leads to the following values for a side VS and à side 11 and 1: 2.
If H1 is validated as follows: (Ze _Zi) + cos y, - _ cos ya y = _ arg tg V "max" max S. . (acc-ng) + sm y, - _ sm 76 V "max" max T _ 7: - fi l "max r = 1 ncos + x ° _x "+ -_ sin7f -____ sí" 7 ° cozy S V S umzm ”max If H2 is validated, then: (zc-zi) _ cozy, - + cozy V u. u. y:: _ arg I.Tl3. .mBÄ (xt-xi) _ sxn y, - + sm 7G V “max" max Yi - 7 .: 11 = --_- "max 1 x - x- sin 7 , - sin yc 12: qcosys + c '- + cos 7, V 21mm "max If H3 is validated then 10 15 20 25 30 35 534 422 17 ys = - arc tg - + arc sin with al = + 5" * 7, 'sm 7c V "maa" max bl = (w "fi) + cos y, - cosyc V” max "man 71' - 75 '(1 =" max -1 x -x-'. '~. 12: ( c «) + smï, + s1nyc__2_¶§ _ / _ ¿+ 11cosy cos y, V umax umu” max s Om H4 valideras så: bl. 2 7S = -arctga - arcs1n 2 2 1 Umax dal + bl med: al : (xc - x, -) _ sm y, - _ -sm yc V ”ma” max b _ (I: ~ fi) _ com _ w ﬁ n 1 V ”max" max (ïi - 7 :) q = - - "max 1 7 + sin y (XC-rf) sin r.- Si ﬂ n) f = f C05 5 _ _ 2 C05 7, ISU max V” max u max When the calculation that makes it possible to determine the values for ys , 111 and 1: 2 is completed, you have at the output of the control computer a reference value for the load factor It is a simple, In the most general case, the load factor will be constant until the time of use for the missile. 0 15 20 25 30 35 534 422 18 11, zero until time 12 and again constant until the end time.
The reference values from this control law will be transformed in the flight unit to the reference value for incident and yaw in equilibrium.
The angle of incidence am in equilibrium, ie the angle between the projections in a vertical plane of the velocity vector of the missile and the missile axis, is the angle of incidence assumed by the missile when there is equilibrium between the torque in a vertical plane resulting from the additional force the rudder and the moment that the aerodynamic forces together exert on the missile in the absence of oscillation of the rudder.
For incidence, the equilibrium angle is determined by # Cmâ ITI r Cm ”. 75 '(cza-cma Cm)' Cma am In this formula, Cm Cma a dimensionless torque coefficient due to the incidence of the missile; Czö a dimensionless coefficient that characterizes the force due to the oscillation of the rudder surfaces; Cza is a dimensionless coefficient that characterizes the force that depends on the angle of incidence of the missile; m is the mass of the missile.
The coefficients Cmö, Cmd, Czö, Cza are aerodynamic coefficients that are characteristic of the missile (function of the Mach number).
S is the surface of the missile's main body.
In order to achieve the load factor reference (flight), it is a matter of producing this incident reference (or yaw reference), the shape of which is a consequence of windows for the current control law. 10 15 20 25 30 35 534 422 19 To establish the corresponding flight law, a linear aerodynamic model for flying the missile has been studied as an example. (described here in the tipping plane). à-q ff-: Sï (Cza.a + Cz6.å) (1) * _ .. d q '= - í-q'š'd (Cma.a + Cmfdqj-iq; CMÖ-Ö (2) In these formulas, q the tilt angle velocity of the missile is the same velocity in the yaw plane). ä is equal to 1 / 2pV2, where p is the density of the air; d is a reference length characteristic of the missile. (r is d is often equal to the caliber of the missile; B is the moment of inertia when tipping the missile.
The difference in natural dynamics between rotation of the missile shafts and rotation of the velocity vector has been exploited, allowing equation (1) to: simplify à = q This simplification neglects the rotational speed of the missile velocity vector relative to the rotational speed of the missiles connected to the missile. .
Thanks to this model, the problem of reaching the reference angle of incidence in a minimum of time has been solved.
The choice of a minimum time criterion makes it possible, by using the principle of Pontryagin minimum, to obtain oscillation reference values of the type + & Mx or which corresponds exactly to what can be achieved in -Ömax r practice with this type of missile. 10 15 20 25 30 35 534 422 20 The choice of signs for the oscillation is determined by placing the current point (a, q) (which is known by the inertial control unit) or (ß, r) in the second plane relative to a network of curves called conversion curves that depend only on the desired angle of incidence (or turning) in equilibrium and aerodynamic coefficients for the missile (follows from the solution of the optimization problem).
It can also be noted that the aerodynamic angle of incidence reflects all the forces acting on the missile, including gravity. The effect of gravity is eliminated via the flight loop.
An example of a changeover curve in the phase plane dq which corresponds to the angle of incidence is shown in Fig. 6.
If the current point ag is above the conversion curve, the fluctuation is positive. Otherwise it is negative.
The flight mode according to the invention is shown schematically in Fig. 7, which differs from Fig. 3 in that the flight unit 3 is shown in more detail. On the basis of the load factor reference determined by the control computer 1, the flight unit 3 in a first part 16 calculates the angle of incidence and the angle of rotation at equilibrium. Calculation of these angles makes it possible in a second module 15, which also receives data from the inertia control unit 17, to calculate the changeover curves of the type shown in Fig. 6. Position change reference values for the rudder arise by comparing the current position with the position on the curves .
It has been explained above that in order to reduce the load factor in the final phase of the path, a fictitious moving target is permanently aimed at a key curve to the intended, straight fall line. This variant of the control method is shown in Fig. 8.
To simplify the explanations, it has been assumed that the final path is a tangent to a straight line that is in a vertical plane. This plane is the plane of Fig. 8. The final path is a tangent to a straight line with the slope VC. The fictitious target is located on a parabola, which is located above the straight line at a vertical distance d1 from the straight line, whereby 1 tgo. cos 7G - K ﬂ ----- 2 g V ,, In this expression, K is a coefficient and Vh the horizontal velocity of the missile, tgo the remaining time to reach the fictitious target.
This variant makes it possible to practically eliminate the load factor reference values during the last 100 to 200 m to the actual target and to limit the final angles of incidence and turn.
In this way, the velocity vector is practically aligned with the missile axis.
Simulations of the control and flight algorithms according to the principles stated above have shown that very good results are obtained.
The scale of achievable final slopes goes from a few degrees to a practically vertical slope§ This applies to a missile that has a small load factor.
Incidentally, good robustness has been shown in terms of rolling: one can tolerate at least 1 t / s of induced rolling.
The application of a minimum time criterion leads to orbits that necessitate global corrections (the integral of the total load factor communicated to the missile) that are much smaller than those of traditional laws (for example, a proportional navigation law). This applies to very low switching frequencies for the rudders (<4 Hz). The event is thus energy efficient.
Finally, it appears that the effort made with regard to the flight and control algorithms in 534 422 22 in this case has very concrete repercussions on the realization and cost of the system by simplifying the flight means. 534 422 23 Appendix 1 The Hamilton equation corresponding to the control method according to the invention is written H = 1 + Å1Vcosy - Å; Vsiny + 131: 5 The principle of Pontryagin maximum gives the optimal command represented by the sign * according to the corresponding quantity. 10 ° 0mÅT3 = Olf- = + Hnmx sign (Ä3) (the corresponding path is part of an arc of a circle) .omÅ. 3 = 00ch¿'3 = 0 ,,; =: 0 (the corresponding path is a straight line). The most recent case is a special case with a singular command.
Thus, to obtain u *, Ä3 must be determined, if possible, as a function of the state to work out a robust command.
The necessary optimization conditions provide the following systems. ~ âfï H 25 Ål = t ~ âç = 0 dar ll = csre = Cl - âfl Ä2 = ~ É = Odär lz = cste = Cz (these equations make it possible- 13: MV sin y +, z2 VCOS ligt to calculate A3 ). â} 1 ___ = 0 30 åf H (tf) = O because the end time is free. 35 The Hamilton equation is thus zero along the entire trajectory. 10 15 20 25 30 534 422 24 This gives: -l + ClVcosy- C2Vsiny + l3u * = O If you examine the condition under which the singular command u * = O occurs: l3 = 0 => - 1 + C1Vcosy-C2Vsin7 = 0 u = 0 thus whereby 7: C-Éæ = 7: which gives ClVCoS7s_C-2V51n 7s = 1 one also has Ã3 = 0:> - ClVS-l ﬂ 7; '*' C2V °° 57s = 0 from which follows cozy, = VC! sin yS ~ = -VC2 A necessary condition for the singular command u * = 0 to occur is thus: y = y _, + k2n (k¿z) with cozy, = VC1 sin 7: = -VC2 If you reverse antar '/ = ï_; with cos7, * = VC1 sin 7: = -VC2 you get in; = c, V (-V.c2) + c2 1 / (Vc1) = o If further the Hamilton equation is zero along the whole path (i.e. for y = ys): I _1 + cOS2 ïs + sin2 73444 uv = o of which / luxury:: O 10 15 20 25 30 35 534 422 25 from which follows Ä; = O or z% mxÅ3 sign Og) = 0 A necessary and sufficient condition for the singular command u * = O to occur is thus ï = ïs + k2zr with cos7, = VC | meadow: -VC: Can you switch from one circular arc to another circular arc A change entails an elimination of Ä3 A30: -1 + C1V.cosy-C2Vsin7 = 0 from which 7 =) g- + k27Ä where ß is defined by the preceding relations and in these conditions Ä @ = O.
If a changeover takes place, it can only be made from an arc of a circle to a straight line with a slope of ys or from a straight line with a slope of ß to an arc of a circle.
If the original slope w_not equal to ß, the original command is non-zero. You describe an arc of a circle until you reach the slope y =%.
You then move to a straight line with a slope w (singular path). If the desired final slope yc differs from ß, another change necessarily takes place; can there be more This would mean that the missile performs a full revolution to return to a rectilinear part with the slope ys (defined on 2n when) (since one necessarily transitions from an arc of a circle to a rectilinear part with slope VS), which is absurd (loop = contrary to the minimum time).
In the general case, there are finally two conversions, whereby the sequence is: circular arc, straight line, circular arc. 10 One obtains: from where which gives from where ie 534 422 (n = am§n -_______ 51- 52) zzmax Jalz + pg 26. . 01 1) coslcosys + sxnlsxn yS = -A- / f-, b 2) sinlcosyS-f-cosisxn ys = à Û 1) cos (l - /,) = - M1- _ b 2) sm (l-ys ) = šll_ b rg (Å- “ï ﬂ z-l 'G1 y _, = l-arclg ﬁ-“ xb! -arclg - “1 10 15 20 25 30 35 534 422 27 Appendix 2 Calculation of the times ru 12 for conversion of the rudder and of the slope of the singular straight line.
This Annex shall be read as a continuation of Annex 1.
It remains to determine the conversion times and the slope of the unique course.
If one integrates the system equations with the knowledge that the command sequence is the following: o for [O, r1] z1 = s1 zzmax sl = il 0 for [11 12] u = 0 o for [r2, t_f] u = z2z1ma_, for [O , z ﬂ ï ° f '= + 51 "max which gives initial slope 741): + El Ilmax f + 7,' 171, is such that 7,: yi +51 zzma. f] of: = V.cos (a¿ um” r + y, -). V.. which gives x (¿) = x¿ + ---- [s1n (e1 umæ. t + 73-) - sxn n] 51 ”max where xi is the initial x-coordinate. ~ i: -V sin (61 umæ. t + fi) - V Which gives z = z, - + -_- [cos (e1umæl + 7, -) - cos 7,] 51 ”max where zi is the initial height for (TLTZ) oy = yx oi = Vcos7, x (I) = x (r1) + Vcos7 _, (r- q) oz '= Vsin 7,: (!) = Z (r |) -Vsin 7, (t- f1) which at t = 12 gives: 10 15 20 25 30 35 534 422 28 x (r) = x- + (Sin ïr ﬂ lï ﬁ 71) + V °° $ 7s- (f2 "'fl) 2 I 51" max ( ) _z __, _ (cozy-cozy,>) - Vsiny,. (fg_fi) Z 11 '“1 âlumax för (fzJf) °}.' = ¿2” max ï = ïs + â2 uma: <(t "f2) OI '= VCOS (}' S + EZ Umax (f-TZ »V f = + -__-_ x <> (a) zumaj 'i =" V sin (7: "i" 52 "max O" 72) ) sin (52: zum (t - 12) + ys) - sin ys], (f) =, (f,) + J- [cos (y_, + 52 uma (t - 12)) - cos ß] 52 ”max, If we write that at t = tf one should have x (f} r) = xc 3 (1f) = Zc r (ff) = rc This gives: 1) rc ~ xf : Vhfz "TÛCOSYS * 81-52 si" 73+ Ez Sin 7: ”E! sin n] max "max” NM -. E å '2) Zc "' zí = y |: ï_êg'cosïs“ (f2_fl) smïs + 2 cosïc '1 C05 fi] "max max max 3) 7 ::“ 71: 51 "max f1 + ¿2" m ﬂ of- 1-2) Use 1 and 2 to determine R on the basis of parameters that are known (initial conditions + desired target) or that can be allowed within the framework of hypotheses that will be verified a posteriori : el, el.
This gives: (ëxtfz) sin7, = - f - + -_- 'r -1 cos + (2 1) y: umax V ”max“ max 10 15 20 25 534 422 29 _. gl 2 (51 '“$ 2) _ __ sin = - (í ° --z¿ - + - cos y, - - C05 ïc ___ í cos y: (72 11) 7: V umax umax zzmax Om: (xc - x,) e;.. al - + sm y, - - sm yc V ”max mß-X 1,1 _ + 51 cos y, - - 82 cos 7 ,, V” max "mä By squaring the two equations and sum them the following relation is obtained: 2 2 f -2) (f2 ... f1) +. (i1__L. = g21 + b21 U max If M = fa21 -l-bz; and cos / I: TZ _ f ' sin Å = ---- 8l _62 -Umax if: 2_ ~ ¿> 1 or íïíl-> 1 M "max, either the hypothesis is not valid or the intended point is inaccessible (forbidden zone) because umax are insufficient.

权利要求:
Claims (8)
[1]
A method of steering applicable to a symmetrical missile, in which the yaw and tip are indicated and which are provided with actuators having two positions, a + position and a - position, the holding of an actuator in the one of these positions modifies the direction of the velocity vector of the missile according to a rotational angular velocity Umax, which missile has a center of gravity and a longitudinal axis and is provided with means for determining its acceleration and its rotational speed according to the yaw and tilt plane, which is - seen moving the missile to a target with the coordinates xc yc zc according to a trajectory ending tangentially to a predetermined straight line of fall, indicated by two angles VC and uk in an earth coordinate system, the displacement of the missile's center of gravity being determined by a system of equations, characterized by the steps of a) forming a Hamiltonian equation for the system of equations that control the displacement of the missile's center of gravity; b) solve the Hamilton equation in each of the missile's yaws and tipples under the condition that the target is reached in a minimum of time, this solution making it possible to determine a first constant value for the transverse acceleration to be applied to the missile. until the time 11 after a time two for measuring the kinematic parameters of the missile trajectory, a second value, this time zero, for the transverse acceleration during a period between time 11 and a time 12, and again a third constant transverse acceleration between time t; and a time tf for falling on the target, the constant acceleration values being those that can be realized with the two-position actuator of the missile moving at the instantaneous speed of the missile; C) operate the missile actuator so that the missile performs the transverse accelerations calculated for the times to, ru 12; d) periodically repeat the measurements, calculations and the resulting actuator commands.
[2]
2. A method of flying a symmetrical missile, in which the yaw and tip plane are indicated and which is provided with actuators having two positions, a + position and a - position, and means for determining its accelerations and rotational speeds q and r according to the yaw and tilt plane, the purpose of the flight being to convert a reference value for transverse acceleration, which is a consequence of a control order, to the reference values for incident ar and yaw B, at equilibrium, and for this purpose of ordering the maintenance or modification of the position of the actuators, according to which the angles of incidence and yaw at equilibrium are obtained by solving equations which take into account the reference value F for transverse acceleration and the missile inertial and aerodynamic data and the manner in which the positions to be taken by the actuators for attaining these angles of incidence and gear are determined by a system of equations which takes into account the inertia data and aero dynamic data and the missile actuators, wherein the mode of flight is characterized by the steps of: - a) forming a Hamiltonian equation for the system of equations which determines the position to be occupied by the actuators; - b) solve the Hamilton equation thus formed with the requirement that the calculated positions for incident and yaw at equilibrium be reached in a minimum time, the solution of the Hamilton equation making it possible in two-dimensional spaces a, q for the tilt plane and B, r establish conversion curves for the yaw plane; - c) place the current point of the missile with respect to the variables a, q and B, r in each of the two-dimensional spaces a, q and B, r respectively; 10 15 20 25 30 35 534 422 32 - d) comparing the position of the current point with these curves, the actuator being adjusted to or maintained in the position + if the current point has an ordinate iq or r which is greater than each of the point of the curves with the same abscissa a or ß; the actuator is adjusted to or maintained in the - position if the point in question has an ordinate in q or r which is less than that of the point of the curve with the same abscissa; Periodically repeat steps a) to d).
[3]
3. A method of steering and flight applicable to a symmetrical missile, in which the yaw and tip are indicated and which are provided with actuators having two positions, a + position and a - position, the holding of an actuator in one of these positions modifies the direction of the velocity vector of the missile according to a rotational angular velocity Umax, which missile has a center of gravity and a longitudinal axis and is provided with means for determining its acceleration and its rotational speed according to the yaw and tilt plane. the control is intended to move the missile to a target with the coordinates xc yc zc according to a trajectory terminating tangentially to a predetermined straight fall line, indicated by two angles W and now in a ground coordinate system, the displacement of the missile center of gravity being determined by a system of equations, the purpose of the flight being to convert a reference value for transverse acceleration, which is a consequence of a control order r, to reference values for inclinations and yaws ß, at equilibrium, and for this purpose give orders for the maintenance or modification of the position of the actuators, the angles of incidence and yaws at equilibrium being obtained by solving equations which take into account the reference value F for transverse acceleration obtained from the steering, as well as the inertial data of the missile and the aerodynamic data, the positions which the actuators must occupy in order to achieve these angles of incidence and turning are determined by an equation system 10 15 20 25 30 35 534 422 33 which takes into account the inertia and aerodynamic data of the missile and the actuators of the missile, the method being characterized by the steps of controlling: - forming a Hamiltonian equation for the system of equations which control the displacement of the center of gravity of the missile; solve the Hamilton equation in each of the missile's yaws and tipples under the condition that the target is reached in a minimum of time, this solution making it possible to determine a first constant value for the transverse acceleration to be applied to the missile up to the time rl after a time to for measuring the kinematic parameters of the missile trajectory, a second value, which this time is zero, for the transverse acceleration during a period between time 11 and a time tg, and again a third constant transverse acceleration between time 12 and a time tf for fall on the target, the constant acceleration values being those that can be realized with the missile's two-position actuator, when the missile moves at the instantaneous speed of the missile; - maneuver the missile's actuators so that the missile performs the transverse accelerations calculated for the times tm th ry - periodically repeat the measurements, calculations and the resulting actuator commands, and that in the method of flight the times for adjusting the actuators are determined as follows: - a) form a Hamiltonian equation for the system of equations which determines the position to be taken by the actuators; b) solve the Hamilton equation thus formed with the requirement that the calculated positions of incidence and yaw at equilibrium be reached in a minimum of time, the solution of the Hamilton equation making it possible in two 10 15 20 25 30 35 534 422 34 dimensional spaces a, q for the tilt plane and ß, r for the gear plane establish conversion curves; - c) place the current point of the missile with respect to the variables a, q and B, r in each of the two-dimensional spaces a, q and ß, r respectively; d) compare the position of the current point with these curves, changing the control to or maintained in the + position if the current point has an ordinate iq or r greater than the point of the curve with the same abscissa a or ß, and the control is reversed to or maintained in the --position if the current point- -ten has an ordinate iq or r that is less than that of the point of the curve with the same abscissa: Periodically repeat steps a) to d).
[4]
4. A method according to claim 2 or 3, - in order to simplify the equation system defining the rotational speed of the missile as a function of the position of the rudder, the rotational speed of the velocity vector is neglected in relation to the rotational speed of the longitudinal axis of the missile.
[5]
5. A method according to any one of claims 1 or 3, characterized in that instead of aiming at the real target with the coordinates XC Yc ZC, one aims at a moving fictitious target on a key curve to the predetermined straight line for falling on it the real goal, the fictitious goal on this curve constantly approaching the real goal and coinciding with it at the end time tf of the trajectory.
[6]
A method according to claim 5, in that the curve is a parabola, which is located n e t e c k n a t k ä n n e t e c k - n a t above the straight tangent line for precipitation.
[7]
Method according to one of Claims 1, 3, 5 or 6, characterized in that the system of equations which controls the displacements of the center of gravity of the missile is expressed in the plane of inclination by 10 '20 25 30 35 534 422 35 x' = VCOS} 'ï = Ván7 f = ”: And in the yaw plane with x '= Vcosy yH = VshxW v / = 11 / in which equations V is the absolute amount of the missile velocity vector; Y, y 'is the slope of the velocity vector and its derivatives with respect to time, respectively; w, w 'is the angle between the projection of the velocity vector and the axis Ox in the yaw plane and its derivatives with respect to time; XI Y's center of gravity in an earth coordinate system Oxyà and their derivative with respect to time, ut and ul are z and x ', y', z 'are the coordinates of the missile values to be given the projection of the missile velocity vector V' in the plane of tilt and yaw, respectively, the Hamiltonian functions having the formula HI = "I + ÄUVCOS " Ã2IVSÜ1y + lz3tlll H, = - 1 + Å1¿Vcosw +). 2, Vsín gu-.Llyzq in which expressions Ht and H1 are The Hamilton equations expressed in the tilt and gear plane, respectively; l1hÄ2hÄ3,; Å1hÄ2¿Å3, are the components of the vectors associated with the system of equations that describe the movements of the missile's center of gravity.
[8]
Method of flight according to one of Claims 2 to 4, characterized in that the system of equations which controls the movements of the missile around itself is expressed by 10 15 20 25 534 422 36 d “Sd i C a '" Sd å = LB ;-( Cma oH-lš-qj-I-íš-Cmåm å ", à-q = -š% (Czaa + Cz5 ,,. Öm) i tipplanet och d -Sd 1 -d :: = í-B _- (Cnßß + CnåI .än 'fïcfv-.fj ß + f = šâæyßß + cyâæ in the girpanet, in which equations q and r are the rotational velocities of the missile in the girder and tilt plane' ä is the aerodynamic pressure of the air ß is the inertia of the missile Cm 'and Cmß is the missile torque coefficients due to the missile's incident and yaw; Cmm and Cum are the torque coefficients due to oscillation of the tipping and gear rudders, respectively; B is the inertia of the missile; and Qm and Gu are the attenuation coefficients due to the yaw and tipping speeds, respectively. Ö is the transverse surface of the missile d is the missile diameter C28 Cyß

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同族专利:

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GB9525779D0|2009-09-09|

SE9504545A1|2011-01-16|

引用文献:

公开号 | 申请日 | 公开日 | 申请人 | 专利标题

法律状态:

优先权:

申请号 | 申请日 | 专利标题

FR9415138|1994-12-15|

FR9500585|1995-01-19|

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