A method for constructing optimal sliding mode guidance law based on observer compensation

Abstract

The present invention discloses a method for constructing an optimal sliding mode guidance law based on observer compensation, which relates to the field of aircraft guidance technology. The method has strong anti-interference ability and good guidance effect, and can perform optimal guidance under angle and precision constraints for an aircraft-target relative motion model in a three-dimensional space. The technical solution of the present invention comprises the following steps: Step 1: Establishing an aircraft-target relative motion model in a three-dimensional space; Step 2: Correcting the deviation of the optimal guidance law caused by error interference through a sliding mode variable structure guidance law; Step 3: Constructing an extended state observer to observe the target maneuver and accurately compensate the guidance law.

Description

Technical Field

[0001] The present invention relates to the field of aircraft guidance technology, and in particular to a method for constructing an optimal sliding mode guidance law based on observer compensation. Background Art

[0002] When facing target strike missions in complex environments, the aircraft needs to adopt appropriate terminal guidance laws to improve guidance accuracy. According to the mission scenario and requirements, a terminal guidance law with reasonable accuracy and strong anti-interference ability is designed.

[0003] For high-speed aircraft such as reentry vehicles and boost-glide vehicles, the aircraft is usually required to be able to attack the target vertically, which is converted into a terminal guidance law design problem with angle constraints. There are many related theoretical methods at present, including proportional guidance law with offset terms, optimal guidance law, etc.

[0004] Under ideal conditions, the optimal guidance law can achieve the best hit accuracy and the optimal guidance method with the minimum energy consumption. However, there are uncertain interferences that cannot be completely eliminated in the guidance process, and the target maneuver will also affect the guidance results. The use of the optimal guidance law may produce a large guidance error. At present, the improvement method for the optimal guidance law is usually to add a sliding mode variable structure term for correction, but most theoretical methods are based on the motion of the aircraft in a two-dimensional plane and have not been extended to three-dimensional space.

[0005] Therefore, there is currently a lack of a method for optimizing the guidance law for the relative motion of three-dimensional space vehicle targets. Summary of the invention

[0006] In view of this, the present invention provides a method for constructing an optimal sliding mode guidance law based on observer compensation, which has strong anti-interference ability and good guidance effect, and can perform optimal guidance under angle and accuracy constraints for an aircraft-target relative motion model in three-dimensional space.

[0007] To achieve the above object, the technical solution of the present invention comprises the following steps:

[0008] Step 1: Establish a vehicle-target relative motion model in three-dimensional space;

[0009] Step 2: Correct the deviation of the optimal guidance law caused by error disturbance through the sliding mode variable structure guidance law;

[0010] Step 3: Construct an extended state observer to observe the target maneuvers and accurately compensate the guidance law.

[0011] As a preferred embodiment of the present invention, step 1 is specifically:

[0012] The aircraft-target relative motion model established in three-dimensional space is as follows:

[0013]

[0014] The relative motion between the aircraft and the target in three-dimensional space is decomposed into the dive plane x s Oy s and the turning plane x s Oz s Movement in two two-dimensional planes; the altitude angle of the aircraft in the dive plane is λ D ′, the reference line OT′ rotates counterclockwise to the aircraft-target line, λ D ' is negative, is D The second-order derivative of ′, is D ′ is the first-order derivative; the sight angle of the aircraft in the turning plane is λ T , is T The second-order derivative of is T The first derivative of mt is the aircraft-target distance, For R mt The first-order derivative of; v1 is the aircraft velocity vector, is the first-order derivative of v1; v2 is the velocity vector of the target, is the first-order derivative of v2; the aircraft velocity vector The component in the subduction plane is Velocity Vector The elevation angle is γ D , the azimuth is γ T ;

[0015] As a preferred embodiment of the present invention, step 2 is specifically:

[0016] Will Bring it into the aircraft-target relative motion model to get

[0017]

[0018] The guidance law instructions are derived in the dive plane and the turning plane respectively:

[0019]

[0020] in, is the control command in the dive plane, is the control command in the turning plane, ε1, ε2 are the switching term gains in the dive plane and the turning plane, k1 and k2 are the reaching law coefficients in the dive plane and the turning plane respectively; λ Topt is T The optimal trace of Dopt ′ is λ D ′ is the optimal trace.

[0021] As a preferred embodiment of the present invention, step 3 is specifically:

[0022] According to the aircraft-target relative motion model, expansion state observers in the dive plane and the turning plane are constructed respectively;

[0023] The expansion state detector of the turning plane is:

[0024]

[0025] Where e1 is the estimated error of the extended state detector of the turning plane; z 1T 、z 2T is the output of the expansion state detector of the turning plane, z 2T is the estimated value of the uncertain term, For z 1T 、z 2T The first derivative of 1T , β 2T is the gain of the expansion state detector of the turning plane; a T ,δ T is the parameter of the extended state detector of the turning plane; fun(e1,a T ,δ T ) is about e1,a T ,δ T Nonlinear function of

[0026] The expansion state detector of the subduction plane is:

[0027]

[0028] where e2 is the estimated error of the expansion state detector of the subduction plane; z 1D 、z 2D is the output of the expansion state detector of the subduction plane, z 2D is the estimated value of the uncertain term, For z 1D 、z 2D The first derivative of 1D , β 2D is the gain of the expansion state detector in the subduction plane; a D,δ D are the parameters of the expansion state detector of the subduction plane; fun(e1,a D ,δ D ) is about e1,a D ,δ D Nonlinear function of

[0029] Based on the constructed extended state observer, the guidance law is accurately compensated, and the control instruction of the optimal sliding mode guidance law based on ESO is obtained as follows:

[0030]

[0031] where e1 and e2 are the estimated errors of the expansion state observer in the dive and turn planes, respectively. 2D is the output of the expansion state observer in the subduction plane, z 2T is the output of the extended state observer in the turning plane.

[0032] Beneficial effects:

[0033] The present invention provides an optimal sliding mode guidance law based on an extended state observer for slow maneuvering targets. By establishing a relative motion model between an aircraft and a target in a three-dimensional space, an optimal sliding mode guidance law is designed based on the optimal guidance law, and an extended state observer is constructed to observe the maneuvering of the target, and the guidance law is accurately compensated. The method has strong anti-interference ability and good guidance effect, and can achieve optimal guidance under angle and accuracy constraints for maneuvering targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the spatial relationship diagram between the aircraft and the target;

[0035] Figure 2 This is the structural diagram of the optimal guidance law based on observer compensation. DETAILED DESCRIPTION

[0036] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0037] The present invention provides a method for constructing an optimal sliding mode guidance law based on an extended state observer for a slow maneuvering target, comprising the following steps:

[0038] Step 1: Establish a relative motion model between the aircraft and the target in three-dimensional space. Establish a relative motion model between the aircraft and the maneuvering target at sea. To simplify the study, the relative motion between the aircraft and the target in three-dimensional space is decomposed into the dive plane x s Oy s and the turning plane x s Oz sMotion in two two-dimensional planes. The aircraft and the target are in the dive plane x s Oy s The relative motion relationship within Figure 1 shown.

[0039] Figure 1 In, λ D ' is the height angle of the aircraft's line of sight in the dive plane, the reference line OT' rotates counterclockwise to the aircraft-target line, λ D ' is negative. Aircraft velocity vector The component in the subduction plane is The azimuth angle is γ D , in the figure γ D <0, The angle between the aircraft and the target is η D , in the figure η D > 0. The target's velocity vector Component in the subduction plane The angle with the aircraft-target line is -λ D ′, from the geometric relationship in the figure, we can see

[0040] η D =γ D -λ D ′ (1)

[0041]

[0042] Taking the derivative of both sides of the second equation in equation (2) with respect to time, we can obtain

[0043]

[0044] Rearranging the equation in (2) yields cosη D and sinη D Substituting the expression of into formula (3) we can get

[0045]

[0046] The motion of the aircraft in the dive plane during the time Δt is approximately regarded as uniform circular motion. It can be simplified to:

[0047]

[0048] Similarly, in the turning plane

[0049] η T =γ T -λ T (6)

[0050]

[0051] Assume that the angles between the aircraft velocity vector and the target velocity vector and the dive plane are both small, v T and v D can be approximated as v1, v M and v N Approximately v2, the relative motion equation between the aircraft and the target is

[0052]

[0053] The relative motion between the aircraft and the target in three-dimensional space is decomposed into the dive plane x s Oy s and the turning plane x s Oz s Movement in two two-dimensional planes; the altitude angle of the aircraft in the dive plane is λ D ′, the reference line OT′ rotates counterclockwise to the aircraft-target line, λ D ' is negative, is D The second-order derivative of ′, is D ′ is the first-order derivative; the sight angle of the aircraft in the turning plane is λ T , is T The second-order derivative of is T The first derivative of mt is the aircraft-target distance, For R mt The first-order derivative of; v1 is the aircraft velocity vector, is the first-order derivative of v1; v2 is the velocity vector of the target, is the first-order derivative of v2; the aircraft velocity vector The component in the subduction plane is Velocity Vector The elevation angle is γ D , the azimuth is γ T ;.

[0054] According to the relative position relationship between the aircraft and the target, the distance R between the aircraft and the target can be known. mt for:

[0055]

[0056] Where (X t , Y t , Z t ) is the coordinate of the target, (X m , Y m , Zm ) is the coordinate of the aircraft

[0057] Line of sight angle λ in the dive plane D 'for

[0058]

[0059] Sight height angle λ D for

[0060]

[0061] Line of sight azimuth λ T

[0062]

[0063] The above sight angle λ D ′ and the sight angle λ T Taking the derivative with respect to time t, we can get the rate of change of the sight angle as

[0064]

[0065]

[0066] Step 2: Correct the deviation of the optimal guidance law caused by error disturbance through the sliding mode variable structure guidance law.

[0067] Will Substitute this into the aircraft-target relative motion model established in step 1 to obtain

[0068]

[0069] Figure 2 The structure diagram of the optimal sliding mode guidance law based on observation period compensation. The guidance law instructions are derived in the dive plane and the turning plane respectively.

[0070] The derivation process in the subduction plane is:

[0071] Since the aircraft has a high speed in the terminal guidance stage, it is assumed that And order Available

[0072]

[0073] Use u opt and x opt To represent the control signal and optimal trajectory of the optimal guidance law,

[0074]

[0075] Let xe =xx opt ,u e =uu opt ,but

[0076]

[0077] The form of the reaching law is chosen as

[0078]

[0079] In the formula: ε——switching term gain, ε>0; k——reaching law coefficient, k>0.

[0080] Take the Lyapunov function

[0081]

[0082] Taking the derivative of the above formula, we can get

[0083]

[0084] During the flight of the aircraft, T g >0, satisfied The Lyapunov function is strictly negative definite, and the system is asymptotically stable. Using this approaching law, as the aircraft gradually approaches the target, T g and ρ gradually decrease, and the speed of approaching the sliding mode accelerates, which can ensure Will not diverge, improving the accuracy of hitting.

[0085] For S = x e Taking the derivative of both sides, we get

[0086]

[0087] but

[0088]

[0089] x e =xx opt Substituting into the above formula, we can get

[0090]

[0091] Since there is a switching function in the above formula, the function value will jump in a short time, and the control amount of the system needs a certain amount of time to reach the required amount, which will cause jitter. The saturation function sat(x) is used instead of the sign function to realize quasi-sliding mode control. The expression is as follows:

[0092]

[0093] Where δ is the boundary layer, the outside of the boundary layer is the standard sliding mode control, and the inside of the layer is the continuous state feedback control. Finally, we get

[0094]

[0095] make The same derivation method as in the dive plane can be used to obtain the guidance equation in the turning plane.

[0096]

[0097] but

[0098]

[0099] It is inferred that the control command of the optimal sliding mode guidance law is:

[0100]

[0101] Among them, ε1 and ε2 are the switching term gains in the dive plane and the turning plane, k1 and k2 are the reaching law coefficients of the dive plane and the turning plane respectively; λ Topt is T The optimal trace of Dopt ′ is λ D ′ is the optimal trace.

[0102] Step 3: Construct an extended state observer to observe the target maneuvers and accurately compensate the guidance law.

[0103] The expansion state detector of the turning plane is:

[0104]

[0105] Where e1 is the estimated error of the extended state detector of the turning plane; z 1T 、z 2T is the output of the expansion state detector of the turning plane, z 2T is the estimated value of the uncertain term, For z 1T 、z 2T The first derivative of 1T , β 2T is the gain of the expansion state detector of the turning plane; a T ,δ T is the parameter of the extended state detector of the turning plane; fun(e1,a T ,δ T ) is about e1,a T ,δ T Nonlinear function of

[0106] The expansion state detector of the subduction plane is:

[0107]

[0108] where e2 is the estimated error of the expansion state detector of the subduction plane; z 1D 、z 2D is the output of the expansion state detector of the subduction plane, z 2D is the estimated value of the uncertain term, For z 1D 、z 2D The first derivative of 1D , β 2D is the gain of the expansion state detector in the subduction plane; a D ,δ D are the parameters of the expansion state detector of the subduction plane; fun(e1,a D ,δ D ) is about e1,a D ,δ D Nonlinear function of

[0109] The nonlinear function fun(·) is defined as

[0110]

[0111]

[0112] The value of e is e1 or e2; the value of a is a D 、a T ; δ is taken as δ D , δ T .

[0113] Adjustment parameter β 1T , β 2T , β 1D , β 2D , a, δ make the observer converge, thus estimating the value of the disturbance;

[0114]

[0115] Where z1 is z 1D 、z 1T ; z2 takes the value of z 2D 、z 2T ; d(t) is an uncertain term, d(t) takes d D (t), d T (t) are the uncertainties of the dive plane and the turn plane, respectively, and satisfy L is a constant greater than 0, the control input Can measure, It is an absolutely continuous function defined in the time domain t≥0; t→T where T is the upper limit of the time domain.

[0116] Based on the constructed extended state observer, the guidance law is accurately compensated, and the control instruction of the optimal sliding mode guidance law based on ESO is obtained as follows:

[0117]

[0118] where e1 and e2 are the estimated errors of the expansion state observer in the dive and turn planes, respectively, 2D is the output of the expansion state observer in the subduction plane, z 2T is the output of the extended state observer in the turning plane.

[0119] In summary, the above are only preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for constructing an optimal sliding mode guidance law based on observer compensation, characterized in that: The steps include: Step 1: Establish a relative motion model between the aircraft and the target in three-dimensional space; specifically: The aircraft-target relative motion model established in three-dimensional space is as follows: The relative motion between the aircraft and the target in three-dimensional space is decomposed into the dive plane x s Oy s and the turning plane x s Oz s Movement in two two-dimensional planes; the altitude angle of the aircraft in the dive plane is λ D ′, is D The second-order derivative of ′, is D ′ is the first-order derivative; the sight angle of the aircraft in the turning plane is λ T , is T The second-order derivative of is T The first derivative of mt is the aircraft-target distance, For R mt The first-order derivative of; v1 is the aircraft velocity vector, is the first-order derivative of v1; v2 is the velocity vector of the target, is the first-order derivative of v2; the aircraft velocity vector The component in the subduction plane is Velocity Vector The elevation angle is γ D , the azimuth is γ T ; For γ D The first derivative of For γ T The first derivative of ; Step 2: Correct the deviation of the optimal guidance law caused by error disturbance through the sliding mode variable structure guidance law; specifically: Will Bring it into the aircraft-target relative motion model to get The guidance law instructions are derived in the dive plane and the turning plane respectively: in, is the control command in the dive plane, is the control command in the turning plane, ε1 and ε2 are the switching term gains in the diving plane and the turning plane, respectively, and k1 and k2 are the reaching law coefficients of the diving plane and the turning plane, respectively; λ Topt is T The optimal trace of Dopt ′ is λ D ′ is the optimal trace; sat() is the saturation function Step 3: Construct an extended state observer to observe the target maneuver and accurately compensate the guidance law; specifically: According to the aircraft-target relative motion model, expansion state observers in the dive plane and the turning plane are constructed respectively; The extended state observer of the turning plane is: Where e1 is the estimated error of the extended state observer in the turning plane; z 1T 、z 2T is the output of the extended state observer on the turning plane, z 2T is the estimated value of the uncertain term, For z 1T 、z 2T The first derivative of 1T , β 2T is the gain of the extended state observer in the turning plane; a T ,δ T are the parameters of the extended state observer of the turning plane; fun(e1,a T ,δ T ) is about e1,a T ,δ T Nonlinear function of The expansion state observer of the subduction plane is: where e2 is the estimated error of the expansion state observer of the subduction plane; z 1D 、z 2D is the output of the expansion state observer of the subduction plane, z 2D is the estimated value of the uncertain term, For z 1D 、z 2D The first derivative of 1D , β 2D is the gain of the expansion state observer of the subduction plane; a D ,δ D are the parameters of the expansion state observer of the subduction plane; fun(e1,a D ,δ D ) is about e1,a D ,δ D Nonlinear function of Based on the constructed extended state observer, the guidance law is accurately compensated, and the control instruction of the optimal sliding mode guidance law based on the extended state observer is obtained as follows: where e1 and e2 are the estimated errors of the expansion state observer in the dive and turn planes, respectively, 2D is the output of the expansion state observer in the subduction plane, z 2t is the output of the extended state observer in the turning plane.

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