CN111027206B - Self-adaptive sliding mode control method for intercepting maneuvering target with specified performance - Google Patents
Self-adaptive sliding mode control method for intercepting maneuvering target with specified performance Download PDFInfo
- Publication number
- CN111027206B CN111027206B CN201911235470.5A CN201911235470A CN111027206B CN 111027206 B CN111027206 B CN 111027206B CN 201911235470 A CN201911235470 A CN 201911235470A CN 111027206 B CN111027206 B CN 111027206B
- Authority
- CN
- China
- Prior art keywords
- guidance
- sliding mode
- target
- missile
- performance
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 42
- 238000013461 design Methods 0.000 claims abstract description 26
- 230000003044 adaptive effect Effects 0.000 claims description 20
- 230000001133 acceleration Effects 0.000 claims description 18
- 238000004088 simulation Methods 0.000 description 17
- 238000002347 injection Methods 0.000 description 4
- 239000007924 injection Substances 0.000 description 4
- 238000009795 derivation Methods 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- 230000006978 adaptation Effects 0.000 description 2
- 238000012938 design process Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000012795 verification Methods 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 239000000243 solution Substances 0.000 description 1
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
- Aiming, Guidance, Guns With A Light Source, Armor, Camouflage, And Targets (AREA)
Abstract
The invention relates to a self-adaptive sliding mode control method for intercepting maneuvering targets with specified performance, which relates to the technical field of guidance, and aims at the problems that in the prior art, in a guidance law design with sight angle constraint, the conventional guidance law can only limit the sight angle of a guidance terminal to converge to a given angle, so that the sight angle of a guidance system cannot meet the convergence speed requirement and steady-state error requirement in the whole guidance process. The performance of the guidance system can be better improved, the implementation is simple, and the guidance system can be easily applied to the control problems of other nonlinear systems.
Description
Technical Field
The invention relates to the technical field of guidance, in particular to a self-adaptive sliding mode control method for intercepting maneuvering targets with specified performance.
Background
In the missile guidance problem, the main task of the guidance law is to ensure that the missile successfully intercepts the target. The interception task of the radar stealth target and the task of the multi-missile cooperative attack target are aimed at providing higher requirements for the design of guidance laws. In the process of intercepting the stealth target by the missile, the radar reflection section of the stealth target can be identified only under a specific angle, so that the sight angle needs to be limited to a specific angle in the whole guidance process. In the multi-missile cooperative guidance process, the space configuration among missiles is limited by communication among the plurality of missiles to meet specific constraint. These all require that the state of the system converge at a specified performance during convergence. There is therefore a need to develop guidance law design issues with prescribed performance constraints. Furthermore, the prescribed performance control theory may also be used in attitude control of a spacecraft and in a robot control system.
Disclosure of Invention
The purpose of the invention is that: aiming at the problems that in the prior art, in the design of a guidance law with view angle constraint, the conventional guidance law can only limit the view angle of a guidance terminal to converge to a given angle, so that the view angle of a guidance system cannot meet the convergence speed requirement and the steady-state error requirement in the whole guidance process, the self-adaptive sliding mode control method for intercepting the maneuvering target with specified performance is provided.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the method for controlling the self-adaptive sliding mode of the interception maneuvering target with the specified performance comprises the following steps:
step one: establishing a kinetic model of a missile interception maneuvering target;
step two: for a typical nonlinear control system, combining a state tracking error e (t) of the system with a performance constraint function lambda (t) to obtain an error variable function h (t) for ensuring that the state of the system converges according to specified performance;
step three: designing a sliding mode surface of the established kinetic model of the missile interception maneuvering target;
step four: calculating the sliding mode dynamics of the sliding mode surface according to the sliding mode surface designed in the step three;
step five: utilizing the sliding mode dynamics in the step four, and ensuring that the obtained sliding mode surface and an error variable function h (t) are bounded by a Lyapunov stability theorem;
step six: and constructing a sliding mode controller according to the sliding mode surface and the error variable function h (t).
Further, the method for establishing the kinetic model of the missile interception maneuvering target comprises the following steps:
in the two-dimensional guidance system, let R denote the relative distance between the target and the missile, V m And V t Respectively representing the speeds of the missile and the target, wherein the speeds of the missile and the target are kept unchanged, and theta m And theta t Respectively representing the included angle theta between the speed of the missile and the target and the sight R L Represents the angle of view, a m Representing the normal acceleration of the missile, a t The normal acceleration of the target is represented, the missile is taken as a coordinate origin, and a two-dimensional kinetic equation of the missile target is as follows:
the guidance system is expressed as:
wherein,f is a variable containing the state of the system, d represents the external disturbance of the system, and b represents a coefficient containing the state of the system.
Further, the performance constraint function λ (t) is:
λ(t)＝(λ(0)-λ(∞))e -lt +λ(∞)
wherein l is a positive constant, lambda (0) is an initial value of a performance constraint function, let e (0) represent a state tracking error initial value in the system, lambda (0) satisfies 0 < |e (0) | < lambda (0), lambda (+++) < lambda (0), lambda (+++) > 0.
Further, the design method of the error variable function h (t) is as follows: let e (t) =x 1 -x 1d Representing tracking error, design h (t) is as follows:
further, the derivative of h (t) is
Further, the sliding mode surface design method comprises the following steps:
wherein k is 1 ,k 2 ,k 3 And ρ are both normal numbers;
the guidance law with performance index constraint suitable for intercepting maneuvering targets is designed as follows:
wherein k is 4 ,k 5 Is a normal number and satisfies k 5 ＞ρk 1 d max . Wherein d is max Is the upper bound of the target acceleration;
the guidance law with performance index constraint suitable for intercepting maneuvering targets is designed as follows:
wherein the external interference d of the system satisfies |d| to be less than or equal to d M ，d M Is an unknown normal number of times,is d M Is used for the estimation of the (c),δ＝ρk 1 is an adaptive gain coefficient。
Further, the nonlinear control system is:
wherein x is 1 、x 2 The system state is represented by u, the system input is represented by f, the variable comprising the system state is represented by d, the external disturbance of the system is represented by b, and the coefficient comprising the system state is represented by b.
The beneficial effects of the invention are as follows: the invention ensures that the sight angle of the guidance system can be converged according to a specified performance constraint function, and in the scenes of missile interception stealth targets or multi-missile cooperative guidance and the like, the sight angle of the guidance system can meet specific constraint. The performance of the guidance system can be better improved, the implementation is simple, and the guidance system can be easily applied to the control problems of other nonlinear systems.
Drawings
FIG. 1 is a desired performance index constraint;
figure 2 (a) is a comparison of constraint functions at different values of l, FIG. 2 (b) shows a difference of λ (≡infinity) a) constraint function comparison under the value;
FIG. 3 is a schematic diagram of a two-dimensional guidance system;
FIG. 4 (a) is a graph showing the relative motion trajectories of a missile and a target under three guidance laws, FIG. 4 (b) is a graph showing the change of the line of sight angle of a missile under three different guidance laws, and FIG. 4 (c) is a graph showing the guidance laws u 1 And u 0 Eye tracking error e=θ under prescribed performance function L -θ Lf FIG. 4 (d) is a graph showing the angular rate of line of sight under different guidance lawsFIG. 4 (e) is a graph showing the variation of the control amount u under three different guidance laws, and FIG. 4 (f) is a graph showing the guidance law u 1 And u 0 Respectively selecting a change chart of the sliding mode surface;
FIG. 5 (a) is a graph showing the target interception success of three guidance laws when the target maneuvers in case2, FIG. 5 (b) is a graph showing the change of the line of sight angle of the missile under three different guidance laws, and FIG. 5 (c) is a graph showing the guidance laws u 1 And u 0 Eye tracking error e=θ under prescribed performance function L -θ Lf FIG. 5 (d) is a graph showing the angular rate of line of sight under different guidance lawsFIG. 5 (e) is a graph showing the variation of the control amount u under three different guidance laws, and FIG. 5 (f) is a graph showing the guidance law u 1 And u 0 Respectively selecting a change chart of the sliding mode surface;
FIG. 6 (a) is a graph of the relative motion trajectories of a missile and a target under three guidance laws, FIG. 6 (b) is a graph of the change in the angle of view and the angular velocity of view of a missile under three different guidance laws, and FIG. 6 (c) is a graph of the guidance laws u 1 And u 0 Eye tracking error e=θ under prescribed performance function L -θ Lf FIG. 6 (d) is a graph showing the angular rate of line of sight under different guidance lawsFIG. 6 (e) is a graph showing the variation of the control amount u under three different guidance laws, and FIG. 6 (f) is a graph showing the guidance law u 2 And u 0 The change pattern of the sliding mode surface selected respectively is shown in FIG. 6 (g) as the guidance law u 2 A variation graph of the adaptive gain;
FIG. 7 (a) is a graph showing the relative motion trajectories of a missile and a target under three guidance laws, FIG. 7 (b) is a graph showing the change of the line of sight angle of a missile under three different guidance laws, and FIG. 7 (c) is a graph showing the guidance laws u 2 And u 0 Eye tracking error e=θ under prescribed performance function L -θ Lf FIG. 7 (d) is a graph showing the angular rate of line of sight under different guidance lawsFIG. 7 (e) is a graph showing the variation of the control amount u under three different guidance laws, and FIG. 7 (f) is a graph showing the guidance law u 2 And u 0 The change pattern of the sliding mode surface selected respectively is shown in FIG. 7 (g) as the guidance law u 2 A plot of the change in adaptive gain at case 2.
Detailed Description
The first embodiment is as follows: the present embodiment will be described specifically with reference to the drawings
Constraint function of desired performance index
Consider a typical nonlinear control system of the form:
wherein x is 1 、x 2 The system state is represented by u, the system input is represented by f, the variable comprising the system state is represented by d, and the external interference of the system is represented by d. In tracking control of a nonlinear system, a typical control index is: it is desirable to design control u during control such that system state x 1 Converging to x 1d ，x 2 Converging to zero. Considering the complexity of nonlinear systems, it is always desirable to be able to track the tracking error e=x of the system state during convergence before it converges to the desired state, as is the case with analytical linear systems 1 -x 1d Can meet certain index constraint. Let the desired performance index function be λ (t), i.e. the control objective is transformed into:
similarly, reference [28], designs the desired performance constraint function as follows:
λ(t)＝(λ(0)-λ(∞))e -lt +λ(∞) (3)
where l is a positive constant, λ (0) is an initial value of a performance constraint function, let e (0) represent a state tracking error initial value in the system (1), and λ (0) satisfies 0 < |e (0) | < λ (0), λ (+|) > 0.
As shown in fig. 1, a schematic diagram of a constraint function of a performance index of a desired control system is given, and in a design of the control system, the control index is desired to converge according to a prescribed constraint condition.
The following compares the performance constraint function variation under different l and λ (++) parameters:
as can be seen in fig. 2, the value of l determines the rate at which the performance constraint function converges, the greater l, the faster the rate of convergence, lambda (infinity) determines the boundary at which the performance constraint function is stable, similar to the definition of steady state error in a linear system.
In the analytical design of nonlinear systems, it is always desirable that the state of the system, such as tracking error, converges according to our desired performance index, which to some extent reflects the performance of the designed controller control process.
Similar to the idea of designing a collision avoidance function in spacecraft collision avoidance control research, for convenience of analysis, the design intermediate function is as follows:
since e (0) < lambda (0), χ 2 (0) In the definition field t= {0 < t < t=max { |e (t) | < λ (t) }, h (t) can be derived in the definition field because h (0) exists.
The derivation of h (t) can be obtained:
note 1: in order to ensure that the state in the system (1) is in the process of convergence, the system error satisfiesBecause h (0) exists, it is only necessary to ensure that the system is bounded by h (t) during convergence.
Therefore, we translate the state constraint problem in the nonlinear system tracking control problem into designing the controller so that h (t) is bounded during system state convergence.
Control object model
Consider a conventional two-dimensional in-plane guidance system model
FIG. 3 presents a schematic view of a two-dimensional guidance system. In the figure, O denotes a missile, T denotes a target, and R denotes a relative distance between the target and the missile. V (V) m And V t Representing the velocity of the missile and target, respectively, where the speed of the missile and target remain unchanged. Correspondingly, θ m And theta t Respectively representing the included angle theta between the speed of the missile and the target and the sight R L Indicating the angle of view. a, a m Representing the normal acceleration of the missile, a t Representing the normal acceleration of the target. The missile is taken as a coordinate origin, and then a two-dimensional kinetic equation of the missile target is as follows:
considering that the change of the line of sight angle in the guidance system reflects the change of the attitude angle of the missile to a certain extent, the requirement of the designed guidance law on the guidance system is reflected to a certain extent. Thus, in designing a guidance law, it is desirable that the line of sight angle of the guidance system be able to converge according to a desired performance constraint function. It is therefore an object herein to design guidance laws such that the target can be set at a desired angle θ Lf InterceptorMoving targets, and the eye-angle tracking error converges according to a specified performance index. That is, by designing a m So thatConvergence to zero, θ, within a finite time L Converging to a desired angle theta Lf And line of sight angle error theta L -θ Lf And converging according to the designated performance index.
In this section, we assume that R,θ L 、/>θ m Is accurately measured by the introducer. θ Lf Indicating the desired angle of view, x 1 ＝θ L -θ Lf Representing line of sight angle error, & lt & gt>Indicating the angular rate of line of sight. By deriving equation (7) and sorting the kinetic equations of equations (6) - (9), the guidance system in-plane considering the terminal attack angle constraint problem can be re-expressed as:
wherein,
correlation hypothesis and theory
To facilitate guidance law design, the following quotation and assumption are given:
lemma 1: for nonlinear systemsx∈R n It is assumed that there is a continuously positive function V (x) and that it is fullFoot inequality (11):
wherein μ > 0, λ > 0 and 0 < α < 1 are constants. x (t) 0 )＝x 0 Wherein t is 0 Is an initial value. The time T for the system state to reach the equilibrium point satisfies the following inequality:
that is, the system state is convergent for a finite time.
2, for the systemx∈R n . Assuming that there is a continuously positive function V (x) (definition field U.epsilon.R n ) And when τ ε (0, 1) and ζ ε R + ，/>In region U epsilon R n Above is negative and semi-positive, then there is a region U 0 ∈R n So that V (x) starts from U 0 ∈R n V (x) ≡0 can be reached in a limited time. And, if T r The time to reach V (x) ≡0 is required, then +.>Wherein V (x) 0 ) Is the initial value of V (x).
Theory 3. For nonlinear systemsx∈R n If there is a continuously differentiable function V (x), and the condition is satisfied:
(i) V (x) is a positive definite function;
(ii) There are positive real numbers c > 0 and ε E (0, 1) and 0 in the range of delta less than or equal to infinity, AndOpen neighborhood containing far pointsMake->This is true.
The system is virtually active time stable.
Suppose 1: assume a of target acceleration t Is bounded for all t.gtoreq.0 and satisfies |a t |≤d max Wherein d is max Is the upper bound for target acceleration.
Suppose 2: let it be assumed that when r=r 0 The missile with the intensity not equal to 0 can successfully intercept the target, but R 0 Belonging to the area
[R min ,R max ]＝[0.1,0.25]m。
Guidance law design
First, the definition and basic properties of some symbols are given. Let tanh (-) and dash (-) represent the hyperbolic tangent function and the hyperbolic cosine function, respectively. And some basic properties can be obtained through simple deductionThe method comprises the following steps:
tanh(x) T tanh(x)≥x T tan h (x) is 0 or more (if and only if the equation of x=0 holds) (13)
Rapid nonsingular guidance law design
The main design purpose of this section is to meet performance index constraintsOn the premise of designing a guidance law to intercept a target at a desired angle. Let e=x 1 ＝θ L -θ Lf ，/>The slide surface is designed as follows:
wherein k is 1 ,k 2 ,k 3 And ρ are both normal numbers. The sliding mode surface S is derived to obtain:
the design concept here is to satisfy the control law that ensures the function h (t) is bounded by using the bounded design of the tanh (·) function. In the case of hypothesis 1 and hypothesis 2, if the target interferes with the upper bound d max Guidance laws with performance index constraints suitable for intercepting maneuver targets are known as follows:
wherein k is 4 ,k 5 Is a normal number and satisfies k 5 ＞ρk 1 d max 。
Theorem 1: considering systems (1) - (4), suppose external interference a t Is bounded and meets |a t |＜d max . If equation (14) is chosen as the slip plane and equation (16) is chosen as the guidance law, then the following is true:
(i) The slip plane S converges to zero for a finite time.
(ii) Eye angle tracking error θ L -θ Lf The asymptotic converges to zero and the line-of-sight angular rate asymptotically converges to zero.
(iii) During the whole guidance system, the sight angle tracking error e=θ L -θ Lf Always satisfy
And (3) proving: first, an inequality (17)
The nature of the hyperbolic cosine function cosh (·) is available from assumptions 1 and (13):
the following form of lyapunov function was selected:
for V 1 Deriving along system trajectories (1) - (4), one can obtain:
substituting the formula of the controller (16) into formula (19) and combining inequality (17) can obtain:
wherein a=2k 4 ＞0，According to index 1, inequality (20) illustrates that the slip plane can converge to zero in a finite time. Thus, the proof of conclusion (i) is complete.
The movement of the system state on the slip form surface s=0 is demonstrated below.
Case 1: if it isThen e=0 can be derived from s=0, which means that the guidance system line of sight angle error e converges to zero.
Case 2: if it isThen select the lyapunov function V 2 The method comprises the following steps:
for V 2 The derivation can be obtained:
from the properties of h (t) > 0 and formula (12):
from the lyapunov stability theory, the system line-of-sight angle error asymptotically converges to zero. And the angular rate of the line of sight gradually converges to zero. The proof of conclusion (ii) is complete.
From the above demonstration, the selected sliding mode surface S converges to zero in a limited time, so the sliding mode surface S is always bounded in the convergence process, and the bounded nature of the tanh (·) function is known,is bounded, so (k) 2 h+k 3 ) e is always bounded. The following evidence is used to demonstrate that the system is always bounded at h (t) during convergence.
Assume that the system has a certain point in time t in the convergence process p The occurrence of an unbounded condition of h (t) is known from the formula (10), at this timeSo |e (t) p )|＝λ(t p ) At this time (k) 2 h+k 3 ) e is unbounded, which is the same as in the above analysis (k 2 h+k 3 ) e always contradicts, and when e (t) =0, h (t) =1, in summary, the system is always bounded during convergence. Therefore, the conclusion (iii) is proved. Thus, theorem 1 all conclusions prove complete.
And (2) injection: at the position ofIn the design process, the existence of the tanh (·) function is utilized, so that h (t) is always bounded in the system convergence process, which means that the whole system convergence process always meets the following conditions as long as |e (0) | < lambda (0)However, in the design process, if e (t) too approaches lambda (t), this will lead to a larger h (t), and the control performance of the controller will be more demanding, thus the parameter k in front of h (t) in the controller u 2 Should not be chosen too large.
And (3) injection: in theorem 1, we make the assumption of external disturbances of the system, i.e., |a t |＜d max However, in guidance system a t The information of the object contained in the system is not usually easy to measure or is measured accurately. To solve this problem, we design guidance laws in the next section by introducing adaptive control for the case where the upper bound of the system external disturbance is not known.
Fast nonsingular adaptive guidance law design
To address the situation described in the previous section where the upper interference bound is unknown outside the system, we introduce adaptive control to estimate the upper interference bound of the target. An adaptive sliding mode controller (24) is designed, wherein the external interference d of the system satisfies |d| to be less than or equal to d M ，d M Is an unknown normal number of times,is d M Estimated value of ∈10->δ＝ρk 1 Is an adaptive gain coefficient.
Theorem 2: considering systems (1) - (4), suppose external interference a t Is bounded. If equation (14) is chosen as the slip plane and equation (24) is chosen as the guidance law, then the following is true:
(i) Variable SIs bounded, adaptive parameter +.>There is an upper bound, i.e. there is a positive constant +.>Satisfy the following requirements
(ii) The sliding mode surface S converges to zero in a limited time, and the sight angle tracking error theta L -θ Lf And a small neighborhood where the angular rate of view converges asymptotically to zero;
(iii) During the whole guidance system, the sight angle tracking error e=θ L -θ Lf Always satisfy
And (3) proving: the following form of lyapunov function is selected:
for V 3 Deriving along the system trajectories (1) - (4), substituting the formulas (15) and (25) into one can obtain:
from inequality (27) the slip plane S andis bounded and thus adaptive to the parameters +.>With upper bound, i.e. positive constant +.>Satisfy->Thus, conclusion (i) demonstrates completion.
Selecting the Lyapunov function V 4 The method comprises the following steps:
for V 4 The derivation can be obtained:
wherein,due to->And->Are all bounded, so delta is bounded. V is obtainable according to the quotation 3 4 Is practically convergent for a finite time. Further available slip form surface S is practically convergent for a finite time.
Since the slip-form surface is practically convergent for a finite time, the slip-form surface converges to a region |S|+|Δ, where Δ is an unknown positive number, within a finite time. The system states e and are analyzed belowIs a variation of (c).
Since the slip plane converges to the region Δ for a limited time, it is obtained by the equation (14):
wherein |delta 1 The formula (30) can be as follows:
due to the parameter k 1 、k 2 、k 3 P and h (t) are all greater than zero,and->Same number. So (1) is->I.e. < ->When (I)>When->When (I)>Therefore we can get that the system state variable e will converge to the region +.>From the pertinence and monotonicity of the tanh (·) function, the +.>Will also converge to a small field of zero. Further, the conclusion (ii) was confirmed.
From the above, it is evident that the sliding surface S is bounded throughout the convergence process, from the bounded nature of the tanh (·) function,is bounded, so (k) 2 h+k 3 ) e is bounded. As theorem 1 proves, we can get that the system is bounded in h (t) throughout the convergence process, i.e. always satisfies +.>Conclusion (iii) evidence. So far, theorem 2 proves complete.
And (4) injection: in the convergence process of the sliding mode surface S, S does not strictly converge to zero, and then the sight angle tracking error theta of the guidance system L -θ Lf And the angular rate of view does not converge exactly to zero, but instead converges to within a neighborhood of zero. From the finite time theory, the range of this neighborhood can be determined by the system parameters we choose. In addition, since S does not converge exactly to zero, adaptive parameters may resultWith possible unlimited increases, other forms of adaptation rate or dead zone control techniques can be employed for this problem [ Li16 ]]The adaptation rate is modified as:
wherein I 1 Representing the 1-norm of the vector, gamma is a small positive constant.
And (5) injection: this may to some extent lead to buffeting due to the presence of the sign function. To mitigate the impact of this problem on closed loop systems, a continuous saturation function is used to approximate, that is to say instead of, the sign function, in the following specific form:
where σ is a small positive constant.
Fourth, simulation verification
In this section, simulation experiments were performed to verify the performance of the designed guidance laws. In order to analyze the effectiveness of the designed guidance law, we select different target maneuver modes to perform simulation experiments, and compare and analyze the simulation experiments with the previously designed guidance methods, wherein the target maneuver modes are as follows:
case 1: a, a t ＝5g m/s 2
Case 2: a, a t ＝5gcos(2t)m/s 2
To verify the performance of the designed guidance law, proportional Navigational Guidance (PNGL) was chosen for comparison with the previously designed fast non-singular terminal sliding mode guidance law (FNTMGL) [0 ]. The specific form of PNGL is as follows:
the specific form of the fast nonsingular terminal sliding mode is as follows:
r 1 ＝(2-r)η r-1 (38)
r 2 ＝(r-1)η r-2 (39)
wherein r, alpha 1 、α 2 And eta are both positive constants to be designed, 0 < r < 1.
The corresponding fntsmig format is as follows:
consider two different sets of initial scene parameters, as shown in table 1:
Table 1 Initial conditions for the missile and target.
in practice, the capacity of the kinetic actuators of the missile is limited, and therefore, given the limited maximum lateral acceleration values that can be provided, the specific form is as follows:
wherein a is Mmax =25g, that is to say that the maximum lateral acceleration that the bullet can provide is 25g, g being the gravitational acceleration (g=9.8 m/s 2 )。
Guidance law u 0 The parameters of (a) are selected as follows: alpha 1 ＝0.02，α 2 ＝0.39，r＝0.9，η＝0.25，k 1 ＝6，k 2 =2. The parameter in PNGL is n=5.
Guidance law u 1 Is verified by simulation of (a)
The first guidance law u in this context 1 The parameters were chosen as ρ=2.45, k1=0.5, k 2 ＝0.0005，k 3 ＝1，k 4 ＝0.6，k 5 =2.7, the parameters in the saturation function are chosen to be σ=0.005, the performance constraint function parameter is λ (0) =12, λ (+++) = 0.5, l=0.8.
Case1 when a t ＝5*9.8*cos(t)m/s 2 When, i.eThe target is S-shaped maneuver, the initial parameters are selected as the data in table 1, and the guidance law u 1 The simulation results of (2) are shown in fig. 4. Fig. 4 (a) shows the relative motion trajectories of the missile and the target under three guidance laws, and it can be seen from the figure that although the flight trajectories of the missile are different, the three guidance laws can successfully intercept the target, which verifies the accuracy of the designed guidance laws. The change of the angle of view of the missile under three different guidance laws is shown in FIG. 4 (b), and the guidance laws u can be seen 1 And u 0 The successful convergence of the missile's line of sight angle to the desired line of sight angle can be ensured, and the proportional guidance law cannot ensure the line of sight angle convergence because the selected proportional guidance law does not constrain the line of sight angle. The guidance law u is given in FIG. 4 (c) 1 And u 0 Eye tracking error e=θ under prescribed performance function L -θ Lf As can be seen from the graph, the guidance law u designed herein 1 On the premise of ensuring the convergence of the sight angle, the sight angle can be converged according to the expected performance index of the user, and the guidance law u 0 The convergence of the line of sight angle according to the desired performance index cannot be guaranteed, which also verifies that our designed guidance laws can cause the system state to converge according to the desired index function. FIG. 4 (d) shows the angular rate of line of sight under different guidance lawsIt can be seen that the guidance laws designed herein can well ensure convergence of the angular velocity of the line of sight. In FIG. 4 (e), the variation of the control quantity u under three different guidance laws can be seen, and the guidance laws u can be seen 0 And u 1 The normal acceleration saturation phenomenon exists in the guidance starting stage, because the selected sliding mode surface ensures rapid convergence and simultaneously tends to cause larger control quantity, and the proportional guidance generates smaller missile normal acceleration due to the selection of the effective navigation ratio. The guidance law u is given in FIG. 4 (f) 1 And u 0 The change of the sliding mode surfaces selected respectively can be seen that both sliding mode surfaces converge to zero after a certain time. This is also consistent with our theoretical analysis.
Case2, when a t ＝5*9.8m/s 2 When the initial parameters still select the data in Table 1, guidance law u 1 The simulation results of (2) are shown in fig. 5. As can be seen in fig. 5 (a), three guidance laws are successful in intercepting the target when the target is maneuvered in case 2. The change of the angle of view of the missile under three different guidance laws is shown in FIG. 5 (b), and the guidance laws u can be seen 1 And u 0 The successful convergence of the line of sight of the missile to the desired line of sight is ensured. The guidance law u is given in FIG. 5 (c) 1 And u 0 Eye tracking error e=θ under prescribed performance function L -θ Lf As can be seen from the graph, the guidance law u designed herein 1 Can make the line of sight angle converge according to the expected performance index of the user, and the guidance law u 0 The convergence of the line of sight angle according to the desired performance index cannot be guaranteed, which also verifies that our designed guidance laws can cause the system state to converge according to the desired index function. FIG. 5 (d) shows the angular rate of line of sight under different guidance lawsIs a variation of (c). In fig. 5 (e), it can be seen that the variation of the control quantity u under three different guidance laws, compared to the case of case1, can be seen that the final variation trend of the control quantity is related to the target maneuver. The guidance law u is given in FIG. 5 (f) 1 And u 0 The change of the sliding mode surfaces selected respectively can be seen that both sliding mode surfaces can ensure that the sliding mode surfaces converge to zero after a certain time.
In summary, we have demonstrated the guidance law u designed herein 1 Under the condition that the target has different maneuvering forms, the target has better guidance performance, compared with the sliding mode guidance law designed before, the guidance law u 1 The method can ensure that the tracking error of the sight angle converges according to the expected performance index in the braking and guiding process. However, the guidance law designed in this section requires that the upper bound of maneuvering information of the target is known in advance, and in consideration that parameters related to the target are not easily and accurately obtained in an actual guidance system, adaptive control is introduced in the next section, and the guidance law is constrained by design adaptive performance.
Guidance law u 2 Is verified by simulation of (a)
Similar to section 4.1, the section selects the proportional guidance law (35) and the guidance law u 0 Law u of coming and guiding 2 Comparison was performed. For the purpose of guidance law u in section 4.1 1 Is divided into simulation of simulation initial parameters to select the second set of data in table 1, guidance law u 2 Parameter selection is equal to u 1 ：ρ＝2.45，k1＝0.5，k 2 ＝0.0005，k 3 ＝1，k 4 ＝0.6，k 5 =2.7, the adaptive gain is δ=ρk 1 The parameters in the saturation function are chosen to be sigma=0.005, the performance constraint function parameter is λ (0) =12, λ (+++) = 0.5, l=0.8. PNGL and u 0 Parameters are the same as in section 4.1.
Case1 when a t ＝5*9.8*cos(t)m/s 2 When the target is S-shaped maneuver, the initial parameters are selected as the data in the table 1, and the guidance law u 2 The simulation results of (2) are shown in fig. 6. FIG. 6 (a) shows the relative motion trajectories of the missile and the target under three guidance laws, and it can be seen that the three guidance laws can intercept the target successfully, which verifies the designed guidance law u 2 Is effective in the following. FIG. 6 (b) shows the change in the angle of view and the velocity of the angle of view of the missile under three different guidance laws, respectively, from which it can be seen that the guidance laws u 1 And u 0 The successful convergence of the line of sight of the missile to the desired line of sight is ensured. The guidance law u is given in FIG. 6 (c) 1 And u 0 Eye tracking error e=θ under prescribed performance function L -θ Lf As can be seen from the graph, the designed guidance law u 2 Can also make the sight angle converge according to the expected performance index on the premise of ensuring the convergence of the sight angle, thereby guiding the law u 0 There is no guarantee that the line of sight angle converges according to the desired performance index, which also verifies the validity of the designed performance index constraint function. FIG. 6 (d) shows the angular rate of line of sight under different guidance lawsThe variation of the designed guidance law u can be seen 2 Can well ensure visionThe linear angular velocity converges and the line of sight angular velocity simulation diverges at the moment the missile encounters the target, due to the relative distance approaching zero, as is the case in fig. 6 (e) -6 (g). In FIG. 6 (e), it can be seen that the variation of the control quantity u is under three different guidance laws, the guidance law u 0 And u 2 The normal acceleration saturation phenomenon exists in the guidance starting stage, because the selected sliding mode surface ensures rapid convergence and simultaneously tends to cause larger control quantity, and the proportional guidance generates smaller missile normal acceleration due to the selection of the effective navigation ratio. The guidance law u is given in FIG. 6 (f) 2 And u 0 The variation of the slip-form surfaces selected respectively shows that both slip-form surfaces converge to a small area after a certain time. The guidance law u is given in FIG. 6 (g) 2 As can be seen, as the sliding mode surface tends to be zero, the adaptive gain value also tends to be constant.
Group data, guidance law u 2 The simulation results of (2) are shown in fig. 7. Similar to case1, fig. 7 (a) shows the relative motion trajectories of the missile and the target under three guidance laws, and it can be seen that the three guidance laws can intercept the target successfully. Fig. 7 (b) shows the change in the angle of view of the missile under three different guidance laws, respectively. The guidance law u is given in FIG. 7 (c) 2 And u 0 Eye tracking error e=θ under prescribed performance function L -θ Lf Is a change curve of (a). FIG. 7 (d) shows the angular rate of line of sight under different guidance lawsIs a variation of (c). The variation of the control quantity u under three different guidance laws can be seen in fig. 7 (e). The guidance law u is given in FIG. 7 (f) 2 And u 0 And respectively selecting the sliding mode surface changes. The guidance law u is given in FIG. 7 (g) 2 Variation of the adaptive gain at case2, it can be seen that as the slip-mode surface goes to zero, the adaptive gain value also goes to constant.
From the two simulations of FIGS. 6 and 7, it can be seen that the guidance law u designed herein 2 Compared with other forms of sliding mode guidance law or proportional guidance law, the method ensures that the sight angle converges toBased on the expected viewing angle, the viewing angle convergence process can be constrained. This facilitates analysis of the dynamic process of the guidance system. From the foregoing theoretical analysis, it can be seen that if the control system u is not limited in any way, l and λ (≡) in the performance index constraint function can be arbitrarily designed. However, in the object studied here, the normal acceleration of the missile is limited, which determines that the performance index parameter cannot be selected arbitrarily, and when the selection of i is larger, that is, the convergence speed of the system is higher, larger control u occurs, so that the performance constraint function may be invalid. In the simulation verification of the control system, guidance law u sometimes appears by changing parameters 0 Performance constraints can also be met, but this lacks theoretical support, and as the performance index constraint function changes, the controller does not always guarantee that the system tracking error meets the performance constraint. While the controller we have designed will always ensure that the controller will have the tracking error of the system meet the performance constraint function we have specified if there is no clipping, but this is not in line with the actual control system.
In order to solve the problem of performance constraint in a nonlinear system, taking an actual two-dimensional guidance system as an example, a novel sliding mode surface is designed by introducing an intermediate function, the line-of-sight angle tracking error of the guidance system and a desired performance constraint function are combined and introduced into the design of the sliding mode surface, and a guidance law meeting the desired performance constraint is designed through the limitation of the sliding mode surface. This idea is similar to the controller in the collision avoidance control of a spacecraft. The methods used herein are simpler in form and analysis of the controller and have better robustness and practicality than other documents in the direction of performance constraint studies. Finally, the effectiveness and superiority of the guidance laws designed herein were verified by comparison with the finite time sliding mode guidance laws and classical scale guidance previously designed. Furthermore, it should be emphasized that the method designed herein clips directly to the controller in the simulation in order to meet the actual system requirements. In order to make theoretical analysis and simulation more rigorous, further intensive research will be conducted in later studies on the problem of limited input performance constraints. Meanwhile, the buffeting phenomenon in the self-adaptive control is worth further research aiming at the discontinuity of the sliding die surface.
It should be noted that the detailed description is merely for explaining and describing the technical solution of the present invention, and the scope of protection of the claims should not be limited thereto. All changes which come within the meaning and range of equivalency of the claims and the specification are to be embraced within their scope.
Claims (4)
1. The self-adaptive sliding mode control method for intercepting maneuvering targets with specified performance is characterized by comprising the following steps of:
step one: establishing a kinetic model of a missile interception maneuvering target;
step two: for a typical nonlinear control system, combining a state tracking error e (t) of the system with a performance constraint function lambda (t) to obtain an error variable function h (t) for ensuring that the state of the system converges according to specified performance;
step three: designing a sliding mode surface of the established kinetic model of the missile interception maneuvering target;
step four: calculating the sliding mode dynamics of the sliding mode surface according to the sliding mode surface designed in the step three;
step five: utilizing the sliding mode dynamics in the step four, and ensuring that the obtained sliding mode surface and an error variable function h (t) are bounded by a Lyapunov stability theorem;
step six: constructing a sliding mode controller according to the sliding mode surface and an error variable function h (t);
the performance constraint function λ (t) is:
λ(t)＝(λ(0)-λ(∞))e -lt +λ(∞)
wherein l is a positive constant, lambda (0) is an initial value of a performance constraint function, let e (0) represent a state tracking error initial value in the system, lambda (0) satisfies 0 < |e (0) | < lambda (0), lambda (+++) < lambda (0), lambda (+++) > 0;
the design method of the error variable function h (t) comprises the following steps: let e (t) =x 1 -x 1d Representing tracking error, design h (t) is as follows:
the derivative of h (t) is
2. The adaptive sliding mode control method for intercepting maneuvering targets with specified performance according to claim 1, wherein the method for establishing a kinetic model of the missile intercepting maneuvering targets is as follows:
in the two-dimensional guidance system, let R denote the relative distance between the target and the missile, V m And V t Respectively representing the speeds of the missile and the target, wherein the speeds of the missile and the target are kept unchanged, and theta m And theta t Respectively representing the included angle theta between the speed of the missile and the target and the sight R L Represents the angle of view, a m Representing the normal acceleration of the missile, a t The normal acceleration of the target is represented, the missile is taken as a coordinate origin, and a two-dimensional kinetic equation of the missile target is as follows:
the guidance system is expressed as:
wherein,f is a variable containing the state of the system, d represents the external disturbance of the system, and b represents a coefficient containing the state of the system.
3. The method for controlling the self-adaptive sliding mode of the interception maneuvering target with the specified performance according to claim 2, wherein the sliding mode surface design method is as follows:
wherein k is 1 ,k 2 ,k 3 And ρ are both normal numbers;
the guidance law with performance index constraint suitable for intercepting maneuvering targets is designed as follows:
wherein k is 4 ,k 5 Is a normal number and satisfies k 5 ＞ρk 1 d max， Wherein d is max Is the upper bound of the target acceleration;
the guidance law with performance index constraint suitable for intercepting maneuvering targets is designed as follows:
δ＝ρk 1
wherein the external interference d of the system satisfies |d| to be less than or equal to d M ，d M Is an unknown normal number of times,is d M Is used for the estimation of the (c),δ＝ρk 1 is an adaptive gain coefficient.
4. The method for controlling an adaptive sliding mode of an interception maneuvering target with specified performance according to claim 1, wherein the nonlinear control system is:
wherein x is 1 、x 2 The system state is represented by u, the system input is represented by f, the variable comprising the system state is represented by d, the external disturbance of the system is represented by b, and the coefficient comprising the system state is represented by b.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911235470.5A CN111027206B (en) | 2019-12-05 | 2019-12-05 | Self-adaptive sliding mode control method for intercepting maneuvering target with specified performance |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911235470.5A CN111027206B (en) | 2019-12-05 | 2019-12-05 | Self-adaptive sliding mode control method for intercepting maneuvering target with specified performance |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111027206A CN111027206A (en) | 2020-04-17 |
| CN111027206B true CN111027206B (en) | 2024-02-09 |
Family
ID=70207680
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911235470.5A Active CN111027206B (en) | 2019-12-05 | 2019-12-05 | Self-adaptive sliding mode control method for intercepting maneuvering target with specified performance |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111027206B (en) |
Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112113466B (en) * | 2020-08-19 | 2022-07-22 | 南京理工大学 | Multi-missile cooperative guidance method with limited time convergence |
| CN112305919A (en) * | 2020-11-13 | 2021-02-02 | 西安交通大学 | Design method of fixed time sliding mode guidance law with collision angle constraint |
| CN112527011B (en) * | 2020-11-20 | 2022-07-15 | 西北工业大学 | Construction method of unified framework of guidance technology in formation collaboration |
| CN114371737A (en) * | 2022-01-17 | 2022-04-19 | 哈尔滨工业大学 | Angle-constrained intelligent ammunition optimal countermeasure collaborative guidance method |
| CN115479507B (en) * | 2022-09-14 | 2023-08-15 | 中国科学院声学研究所 | Guidance control method and system for underwater vehicle |
| CN115993073A (en) * | 2022-09-16 | 2023-04-21 | 北京理工大学 | Aircraft guidance method with falling angle constraint |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102980449A (en) * | 2012-12-25 | 2013-03-20 | 北京理工大学 | Method for controlling coordinated operation of multiple missiles |
| CN106843265A (en) * | 2016-12-30 | 2017-06-13 | 哈尔滨工业大学 | Three-dimensional many guided missile cooperative guidance method and systems of finite time convergence control |
| CN108216548A (en) * | 2016-12-15 | 2018-06-29 | 深圳光启空间技术有限公司 | A kind of control method and device for dirigible |
| CN110412874A (en) * | 2019-07-25 | 2019-11-05 | 东南大学 | Multi-missile cooperative guidance law design method for maneuvering target and time delay communication |
| CN110471275A (en) * | 2019-08-30 | 2019-11-19 | 哈尔滨工业大学 | A kind of non-singular terminal sliding formwork finite time convergence control angle restriction method of guidance |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8436283B1 (en) * | 2008-07-11 | 2013-05-07 | Davidson Technologies Inc. | System and method for guiding and controlling a missile using high order sliding mode control |
-
2019
- 2019-12-05 CN CN201911235470.5A patent/CN111027206B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102980449A (en) * | 2012-12-25 | 2013-03-20 | 北京理工大学 | Method for controlling coordinated operation of multiple missiles |
| CN108216548A (en) * | 2016-12-15 | 2018-06-29 | 深圳光启空间技术有限公司 | A kind of control method and device for dirigible |
| CN106843265A (en) * | 2016-12-30 | 2017-06-13 | 哈尔滨工业大学 | Three-dimensional many guided missile cooperative guidance method and systems of finite time convergence control |
| CN110412874A (en) * | 2019-07-25 | 2019-11-05 | 东南大学 | Multi-missile cooperative guidance law design method for maneuvering target and time delay communication |
| CN110471275A (en) * | 2019-08-30 | 2019-11-19 | 哈尔滨工业大学 | A kind of non-singular terminal sliding formwork finite time convergence control angle restriction method of guidance |
Non-Patent Citations (1)
| Title |
|---|
| 机动目标拦截含攻击角约束的新型滑模制导律;张尧;郭杰;唐胜景;商巍;张浩强;;兵工学报(08);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111027206A (en) | 2020-04-17 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111027206B (en) | Self-adaptive sliding mode control method for intercepting maneuvering target with specified performance | |
| CN106843265B (en) | Three-dimensional multi-missile cooperative guidance method and system with limited time convergence | |
| CN109557814B (en) | Finite time integral sliding mode terminal guidance law | |
| Shaferman et al. | Linear quadratic guidance laws for imposing a terminal intercept angle | |
| CN106647287B (en) | A kind of input-bound differential game guidance method based on adaptive Dynamic Programming | |
| Cho et al. | Optimal impact angle control guidance law based on linearization about collision triangle | |
| Wang et al. | New differential geometric guidance strategies for impact-time control problem | |
| Ai et al. | Field-of-view constrained two-stage guidance law design for three-dimensional salvo attack of multiple missiles via an optimal control approach | |
| CN110412874B (en) | Multi-missile cooperative guidance law design method for maneuvering target and time delay communication | |
| Xiong et al. | Hyperbolic tangent function weighted optimal intercept angle guidance law | |
| CN110187640B (en) | Multi-missile cooperative combat guidance law design method for maneuvering target and allowable communication time lag | |
| Sinha et al. | Three-dimensional guidance with terminal time constraints for wide launch envelops | |
| Liu et al. | Three-dimensional impact angle control guidance with field-of-view constraint | |
| Reisner et al. | Optimal guidance-to-collision law for an accelerating exoatmospheric interceptor missile | |
| Ji et al. | Time-varying sliding mode guidance scheme for maneuvering target interception with impact angle constraint | |
| CN110764523B (en) | Proportional-integral pre-pilot attack target method based on anti-saturation smooth transformation | |
| Hou et al. | Time-to-go estimation for terminal sliding mode based impact angle constrained guidance | |
| Kumar et al. | Minimum-effort intercept angle guidance with multiple-obstacle avoidance | |
| Li et al. | Three‐Dimensional Impact Time and Angle Control Guidance Based on MPSP | |
| Gopalan et al. | Time-optimal guidance for lateral interception of moving targets | |
| KR20160046990A (en) | Impact time control guidance method and device | |
| Zou et al. | Active defense guidance law via cooperative identification and estimation | |
| CN115033024A (en) | Multi-missile three-dimensional cooperative guidance method based on attack time and angle common constraints | |
| Chen et al. | Impact time and angle control optimal guidance with field-of-view constraint | |
| Yuru et al. | Impact time control guidance against maneuvering targets based on a nonlinear virtual relative model |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |