CN116736716A - Comprehensive anti-interference smooth switching control method for transition section of tilting rotor unmanned aerial vehicle - Google Patents
Comprehensive anti-interference smooth switching control method for transition section of tilting rotor unmanned aerial vehicle Download PDFInfo
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Abstract
The invention discloses a comprehensive anti-interference smooth switching control method for a transition section of a tilting rotor unmanned aerial vehicle, which comprises the following steps: s1, a longitudinal nonlinear dynamics model of a transition section of a tilting rotor unmanned aerial vehicle is established, different operating points are selected in a tilting corridor to trim, and a switching linear system model is obtained; s2, introducing an external system to represent disturbance input generated by rotor wake; s3, designing a disturbance observer, and estimating disturbance from an external system; s4, designing a reference model, converting the longitudinal control problem of the transition section into a comprehensive anti-interference control problem of a switching linear system, and designing a comprehensive anti-interference control law; s5, designing a smooth interpolation control strategy, and inhibiting state buffeting caused by controller switching. The invention can restrain various disturbance influences of the tilting rotor unmanned aerial vehicle in the transition process, and restrain state buffeting caused by controller switching, so that the transition process of the tilting rotor unmanned aerial vehicle is more stable and safer.
Description
Technical Field
The invention relates to the technical field of flight control, in particular to a comprehensive anti-interference smooth switching control method for a transition section of a tilting rotor unmanned aerial vehicle.
Background
A tiltrotor aircraft allows it to switch between helicopter mode and fixed wing mode by mounting two rotatable nacelle at the wing tip. The tiltrotor aircraft has the advantages of the helicopter, and simultaneously can effectively solve the problems of short range, low speed, high noise and severe landing conditions of the fixed wing aircraft, and the difficulty in completing landing in complex terrains. The method has important practical significance and good development prospect for the research of the tiltrotor aircraft.
Tiltrotor aircraft possess three modes of flight in total: helicopter mode, transitional mode, and fixed wing mode. In a helicopter mode, the nacelle is in a vertical state, and at the moment, the tilting rotorcraft counteracts gravity through lift force generated by a rotor wing, so that operations such as vertical lifting and hovering can be completed; the process of switching from helicopter to fixed wing mode, or vice versa, is called transition, which is accomplished by nacelle tilting; in the fixed wing mode, the nacelle is in a horizontal state, lift force is generated by the wing to overcome gravity, and meanwhile, the rotor rotates to provide forward flying tension for the aircraft, so that high-speed flight can be realized; the tiltrotor aircraft can realize the required functions under specific conditions by switching between a helicopter mode and a fixed wing mode; for example, the helicopter is switched to a fixed wing mode for high-speed flight or to a helicopter mode for vertical take-off, landing, hovering and the like.
The advantages of the tiltrotor aircraft enable the tiltrotor aircraft to cover various flight tasks, and even further expand the flight tasks in various complex situations and terrains, and have wide development prospects. At the same time, however, due to its complex structure, related technical research presents a number of challenges, of which the most important are the modeling of the flight dynamics and the design of the control law when it is in transition mode. Firstly, the dynamic characteristics of a helicopter and a fixed wing aircraft are required to be considered simultaneously, and the tilting of a nacelle in a transition mode can cause the change of aerodynamic appearance, the strong nonlinear characteristic and the severe change of aerodynamic parameters of the nacelle, so that modeling is more difficult; secondly, during the actual nacelle tilting process, the aircraft is disturbed by a variety of disturbances including rotor wake, affecting the stability of the flight. Meanwhile, due to the complex flight control mode, the design of a proper control law for realizing stable switching between flight modes becomes a great difficulty.
Disclosure of Invention
The invention aims to: the invention aims to provide a control method for comprehensively resisting interference and smoothly switching a transition section of a tilting rotor unmanned aerial vehicle, which can realize stable transition of the transition section of the tilting rotor unmanned aerial vehicle.
The technical scheme is as follows: the invention discloses a comprehensive anti-interference smooth switching control method for a transition section of a tilting rotor unmanned aerial vehicle, which comprises the following steps of:
s1, a longitudinal nonlinear dynamics model of a transition section of a tilting rotor unmanned aerial vehicle is established, different operating points are selected in a tilting corridor to trim, and a switching linear system model is obtained;
s2, introducing an external system to represent disturbance input generated by rotor wake;
s3, designing a disturbance observer, and estimating disturbance from an external system;
s4, designing a reference model, converting the longitudinal control problem of the transition section into a comprehensive anti-interference control problem of a switching linear system, and further designing a comprehensive anti-interference control law;
s5, designing a smooth interpolation control strategy, and inhibiting state buffeting caused by controller switching.
Further, in step S1, the longitudinal nonlinear dynamics model of the transition section of the tiltrotor unmanned aerial vehicle has the following expression:
wherein [ u, w, q, θ ]] T Is four states of the system, T represents matrix transposition; u is the forward flying speed along the x coordinate axis direction of the machine body, w is the longitudinal speed along the y coordinate axis direction of the machine body, q is the pitch angle speed, and θ is the pitch angle; delta f Delta for longitudinal cyclic variation g As the total distance delta e Is the rudder deflection angle; beta M Is the tilting angle; f () is a nonlinear function satisfying the kinematic and dynamic relationships;
definition meetsA switching signal sigma (t) of the mode dependent residence time constraint is [0, +% to N= {1,2, …, N }, N is the number of subsystems for switching the linear system model; for σ (t) =i, i ε N and any t y >t x Not less than 0, satisfies:
N i (t x ,t y )≤1+T i (t x ,t y )/τ di
wherein ,Ni (t x ,t y ) Represents the total number of times to switch to the ith subsystem, T i (t x ,t y ) Indicating that the ith subsystem is at t x ,t y ) Total run time in interval, then τ di >0 is referred to as modality dependent residence time;
further, selecting n groups of operating points at the tilting corridor to trim, and obtaining an expression of an ith subsystem of the switching linear system model as follows:
wherein x (t) = [ Δu, Δw, Δq, Δθ ]] T The system is characterized in that the system comprises four state quantities, wherein Deltau is an increment of a front flying speed along the x coordinate axis direction of the machine body deviating from a state at a selected leveling point, deltaw is an increment of a longitudinal speed along the y coordinate axis direction of the machine body deviating from a state at the selected leveling point, deltaq is an increment of a pitch angle speed deviating from a state at the selected leveling point, and Deltaθ is an increment of a pitch angle deviating from a state at the selected leveling point; u (u) c (t)＝[Δδ f ,Δδ g ,Δδ e ] T Delta is the control input to the system f Delta for state at selected trim points for longitudinal cyclic variation deviations g Delta for the delta of the state at the selected trim point for collective deviations e An increment for the rudder deflection angle to deviate from the state at the selected leveling point; ρ (t) represents the disturbance input in the external system generated by the rotor wake; omega 1 (t) is a disturbance input to the tiltrotor unmanned aerial vehicle; a is that i 、B i 、H i Respectively, a constant matrix obtained by linearizing around the selected leveling points.
Further, in step S2, an external system is introduced to represent the disturbance input generated by the rotor wake, and for i e N, the specific form of the external system is:
ρ(t)＝M i φ(t)
wherein phi (t) represents the state of the external system; omega 2 (t) is a disturbance input acting on the external system, excluding the disturbance input generated by the rotor wake; c (C) i 、G i 、M i Each a constant matrix of appropriate dimensions.
Further, in step S3, the expression of the disturbance observer is as follows:
wherein ψ (t) represents the system state of the disturbance observer; and />Representing the estimates of phi (t) and rho (t), respectively; l is the disturbance observer gain;
defining disturbance observation errors as follows:
further, differential of disturbance observation error is obtainedIs represented by the expression:
further, in step S4, the expression of the reference model is as follows:
wherein ,xr (t)＝[Δu r ,Δw r ,Δq r ,Δθ r ] T To the ideal state that needs to be tracked, deltau r Delta w for the ideal forward flight velocity along the x-axis direction of the machine body to deviate from the state at the selected leveling point r Delta q for the desired longitudinal velocity in the y-axis direction of the body coordinate to deviate from the state at the selected leveling point r Delta theta for the desired pitch rate deviation from the state at the selected trim point r An increment for the ideal pitch angle to deviate from the state at the selected leveling point; r (t) is a bounded reference input of suitable dimension for generating an ideal state trajectory; a is that r 、B r Constant matrices each having appropriate dimensions;
for the ith subsystem of the switching linear system model, the control law is designed as:
wherein ,ea (t)＝x(t)-x r (t) is a state tracking error; k (K) ei (t)、K ci 、K ri Respectively a controller gain matrix to be designed;
further, a state tracking error e is obtained a Expression of differentiation of (t):
the controller expression u c (t) substitution intoIn (3), an expression of a tracking error system is obtained:
selecting K ci 、K ri Matrix, satisfy A i +B i K ci -A r＝0 and Bi K ri -B r When =0 is true, the tracking error system is simplified to:
further, an error system state e (t) = [ e ] is defined a (t),e b (t)] T Disturbance input ω (t) = [ ω ] 1 (t),ω 2 (t)] T Obtaining an expression of an error system:
wherein , and Di The respective expressions are as follows:
further, in step S5, t is used s Indicating the time t at which the s-th handover occurs s+1 Represents the s+1 thThe moment when the secondary handover occurs; introducing a transition zone [ t ] s ,t s +τ h )，τ h >0 is a constant value for σ (t s )＝i∈N，τ h Less than the corresponding residence time tau di The method comprises the steps of carrying out a first treatment on the surface of the Further, section [ t ] s ,t s+1 ) Divided into [ t ] s ,t s,0 )∪[t s,0 ,t s+1), wherein ,ts,0 ＝t s +τ h ；
Further, a smooth interpolation strategy is designed to gain K for the controller ei (t) performing a treatment to give K ei (t)＝U i (t)T i -1 (t); assuming that a coefficient matrix T exists i>0 and Ui Wherein i ε N; then for (i, j) ∈n×n, i+.j, and σ (0) =m∈n, matrix U i(t) and Ti The expression of (t) is:
wherein α (t) = (t-t) s )/τ h The method comprises the steps of carrying out a first treatment on the surface of the Each coefficient matrix T i and Ui Solving through a linear matrix inequality;
selecting a lyapunov function:
V i (e(t))＝e T (t)P i (t)e(t)
wherein ,lyapunov matrix, P representing the ith subsystem 2i Is positive definite matrix and P 1i (t)＝T i -1 (t)；
To ensure that the error system is asymptotically stable and has H ∞ Comprehensive anti-interference performance for interval t s ,t s,0 ) The following inequality needs to be satisfied:
for interval t s,0 ,t s+1 ) The following inequality needs to be satisfied:
wherein ,ηui and ηsi Respectively representing the decay rate of the Lyapunov function in the corresponding time interval; gamma ray>0 represents L of the system 2 A gain level;
further, for σ (t s )＝i，i∈N，σ(t s - ) =j, j e N and i+.j; by K ei (t)＝U i (t)T i -1 The process of (t) requires that the following linear matrix inequality be satisfied:
wherein ,
Φ Aij ＝He{A i T i +B i U i }+η si T i
and, for matrix X, he { X } = x+x T The method comprises the steps of carrying out a first treatment on the surface of the I represents an identity matrix;
then, when the switching signal sigma (t s ) Meeting the modality dependent residence time τ di >τ h Is said to be progressively stable and has an L not exceeding the formula 2 Gain of
wherein , η u ＝max i∈N (η ui )，ν＝exp{∑ i∈N (η si -η ui )τ h }；
the matrix U is further obtained by solving the above linear matrix inequality i(t) and Ti (t); according to K ei (t)＝U i (t)T i -1 (t)，A i +B i K ci ＝A r and Bi K ri ＝B r Solving to obtain a controller gain matrix K ei (t)、K ci and Kri 。
Compared with the prior art, the invention has the following remarkable effects:
1. the present invention describes the disturbance input generated by rotor wake by introducing external system, and designs disturbance observer and H at the same time ∞ The comprehensive anti-interference control scheme can inhibit the influence of various types of disturbance;
2. according to the invention, by designing a smooth interpolation control strategy, the control input can be smoother, the state jump of the system can be effectively restrained, and the transition process of the tilting rotor unmanned aerial vehicle becomes smoother and safer.
Drawings
FIG. 1 is a schematic view of a tilt corridor of a tilt rotor unmanned aerial vehicle;
FIG. 2 is a block diagram of the present invention;
figure 3 (a) is a graph of the forward flying speed response of a transition section of a tiltrotor unmanned aerial vehicle using the integrated anti-tamper control method of the present invention,
FIG. 3 (b) is an enlarged view of part of A in FIG. 3 (a);
figure 4 (a) is a graph of longitudinal speed response of a transition section of a tiltrotor unmanned aerial vehicle using the integrated anti-jamming control method of the present invention,
FIG. 4 (B) is an enlarged view of part of B in FIG. 4 (a);
figure 5 (a) is a graph of pitch angle rate response at the transition segment of a tiltrotor unmanned aerial vehicle using the integrated anti-tamper control method of the present invention,
fig. 5 (b) is a partial enlarged view of C in fig. 5 (a);
fig. 6 is a graph of pitch angle response of a transition section of a tiltrotor unmanned aerial vehicle obtained by using the integrated anti-interference control method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear, the present invention will be described in detail with reference to the accompanying drawings and specific examples. It should be understood that the detailed description is intended to illustrate the invention, and not to limit the invention. The invention is described in further detail below with reference to the drawings and the detailed description.
The rotation of the nacelle can cause the continuous change of the aerodynamic profile in the transitional process of the tiltrotor, and the strong nonlinear characteristics and the drastic aerodynamic parameter changes make it difficult for a single model to accurately describe the flight dynamics of the system; while using switched linear system modeling, this problem can be effectively solved with a multi-subsystem description of the switching system. Therefore, compared with the conventional nonlinear modeling, the method and the system can more accurately describe the flight dynamics of the transition section of the tilting rotor unmanned aerial vehicle based on the modeling of the switching linear system, and simplify the design of the controller.
The invention discloses a comprehensive anti-interference control method for a transition section of a tilting rotor unmanned aerial vehicle, which specifically comprises the following steps:
step 1, firstly, a longitudinal nonlinear dynamics model of a transition section of the tilting rotor unmanned aerial vehicle is established.
The modeling process adopts a split modeling method to model a rotor wing, a machine body and a vertical tail respectively. Further, assuming that there is no lateral movement in the process, it is reduced to a longitudinal dynamics model. Based on the euler equation of dynamics, the longitudinal nonlinear dynamics model can be expressed as:
wherein g is gravity acceleration, m g Is the aircraft mass; f (F) Xr 、F Xw 、F Xf 、F Xt Respectively representing aerodynamic forces generated by the rotor wing, the fuselage and the vertical fin in the x-axis direction; f (F) zr 、F zw 、F zf 、F zt Respectively representing aerodynamic forces generated by the rotor wing, the fuselage and the vertical tail in the z-axis direction; i y Representing moment of inertia about the y-axis; m is M r 、M w 、M f 、M t Representing aerodynamic moments generated by the rotor, wing, fuselage and vertical tail in the z-axis direction, respectively.
The established longitudinal nonlinear dynamics model can be abbreviated as:
wherein [ u, w, q, θ ]] T Is four states of the system, T represents matrix transposition; u is the forward flying speed along the x coordinate axis direction of the machine body, w is the longitudinal speed along the y coordinate axis direction of the machine body, q is the pitch angle speed, and θ is the pitch angle; delta f Delta for longitudinal cyclic variation g As the total distance delta e Is the rudder deflection angle; beta M Is the tilting angle; f () is a nonlinear function satisfying the kinematic and dynamic relationships;
defining a switching signal sigma (t) [0, ] -N= {1,2, …, N } meeting the modal dependent residence time constraint, N being the number of subsystems switching the linear system model. For σ (t) =i, i ε N and any t y >t x Not less than 0, satisfies:
N i (t x ,t y )≤1+T i (t x ,t y )/τ di (6)
wherein ,Ni (t x ,t y ) Represents the total number of times to switch to the ith subsystem, T i (t x ,t y ) Indicating that the ith subsystem is at t x ,t y ) Total run time in interval, then τ di >0 is referred to as modality dependent residence time;
further, selecting n groups of operating points at the tilting corridor to trim, and obtaining an expression of an ith subsystem of the switching linear system model as follows:
wherein x (t) = [ Δu, Δw, Δq, Δθ ]] T The system is characterized in that the system comprises four state quantities, wherein Deltau is an increment of a front flying speed along the x coordinate axis direction of the machine body deviating from a state at a selected leveling point, deltaw is an increment of a longitudinal speed along the y coordinate axis direction of the machine body deviating from a state at the selected leveling point, deltaq is an increment of a pitch angle speed deviating from a state at the selected leveling point, and Deltaθ is an increment of a pitch angle deviating from a state at the selected leveling point;u c (t)＝[Δδ f ,Δδ g ,Δδ e ] T delta is the control input to the system f Delta for state at selected trim points for longitudinal cyclic variation deviations g Delta for the delta of the state at the selected trim point for collective deviations e An increment for the rudder deflection angle to deviate from the state at the selected leveling point; ρ (t) represents the disturbance input in the external system generated by the rotor wake; omega 1 (t) is a disturbance input acting on the tiltrotor unmanned aerial vehicle, possibly wind disturbance or the like; a is that i 、B i 、H i Respectively, a constant matrix obtained by linearizing around the selected leveling points.
Step 2, introducing an external system to represent disturbance input generated by rotor wake, wherein for i epsilon N, the specific form of the external system is as follows:
ρ(t)＝M i φ(t) (9)
wherein phi (t) represents the state of the external system; omega 2 (t) is a disturbance input acting on the external system (excluding the disturbance input generated by the rotor wake); ρ (t) represents the disturbance input generated by the rotor wake; c (C) i 、G i 、M i Each a constant matrix of appropriate dimensions.
Step 3, the expression of the disturbance observer is as follows:
wherein ψ (t) represents the system state of the disturbance observer; and />Representing the estimates of phi (t) and rho (t), respectively; l is the disturbance observer gain;
defining disturbance observation errors as follows:
further, differential of disturbance observation error is obtainedIs represented by the expression:
and 4, designing a reference model, wherein the expression is as follows:
wherein ,xr (t)＝[Δu r ,Δw r ,Δq r ,Δθ r ] T To the ideal state that needs to be tracked, deltau r Delta w for the ideal forward flight velocity along the x-axis direction of the machine body to deviate from the state at the selected leveling point r Delta q for the desired longitudinal velocity in the y-axis direction of the body coordinate to deviate from the state at the selected leveling point r Delta theta for the desired pitch rate deviation from the state at the selected trim point r An increment for the ideal pitch angle to deviate from the state at the selected leveling point; r (t) is a bounded reference input of suitable dimension for generating an ideal state trajectory; a is that r 、B r Respectively is provided withA constant matrix with appropriate dimensions;
for the ith subsystem of the switching linear system model, the control law is designed as:
wherein ,ea (t)＝x(t)-x r (t) is a state tracking error; k (K) ei (t)、K ci 、K ri Respectively a controller gain matrix to be designed;
further, a state tracking error e is obtained a Expression of differentiation of (t):
the controller expression u c (t) substitution intoIn (3), an expression of a tracking error system is obtained:
selecting K ci 、K ri Matrix, satisfy A i +B i K ci -A r＝0 and Bi K ri -B r When =0 is true, the tracking error system is simplified to:
further, an error system state e (t) = [ e ] is defined a (t),e b (t)] T Disturbance input ω (t) = [ ω ] 1 (t),ω 2 (t)] T Obtaining an expression of an error system:
wherein , and Di The respective expressions are as follows:
step 5, using t s Indicating the time t at which the s-th handover occurs s+1 Indicating the time at which the (s+1) -th handover occurs; introducing a transition zone [ t ] s ,t s +τ h )，τ h >0 is a constant value for σ (t s )＝i∈N，τ h Less than the corresponding residence time tau di The method comprises the steps of carrying out a first treatment on the surface of the Further, section [ t ] s ,t s+1 ) Divided into [ t ] s ,t s,0 )∪[t s,0 ,t s+1), wherein ,ts,0 ＝t s +τ h ；
Further, a smooth interpolation strategy is designed to gain k to the controller ei (t) performing a treatment to give K ei (t)＝U i (t)T i -1 (t); assuming that a coefficient matrix T exists i>0 and Ui Wherein i ε N; then for (i, j) ∈n×n, i+.j, and σ (0) =m∈n, matrix U i(t) and Ti The expression of (t) is:
wherein α (t) = (t-t) s )/τ h The method comprises the steps of carrying out a first treatment on the surface of the Each coefficient matrix T i and Ui Solving through a subsequent linear matrix inequality;
selecting a lyapunov function:
V i (e(t))＝e T (t)P i (t)e(t) (23)
wherein ,lyapunov matrix, P representing the ith subsystem 2i Is positive definite matrix and P 1i (t)＝T i -1 (t); * Representing a matrix that can be derived from symmetry.
To ensure that the error system is asymptotically stable and has H ∞ Comprehensive anti-interference performance for interval t s ,t s,0 ) The following inequality needs to be satisfied:
for interval t s,0 ,t s+1 ) The following inequality needs to be satisfied:
wherein ,ηui and ηsi Respectively representing the decay rate of the Lyapunov function in the corresponding time interval; gamma ray>0 represents L of the system 2 A gain level;
further, for σ (t s )＝i，i∈N，σ(t s - ) =j, j e N and i+.j; by K ei (t)＝U i (t)T i -1 The process of (t) requires that the following linear matrix inequality be satisfied:
wherein ,
Φ Aij ＝He{A i T i +B i U i }+η si T i
and, for matrix X, he { X } = x+x T The method comprises the steps of carrying out a first treatment on the surface of the I represents an identity matrix;
then, when the switching signal sigma (t s ) Meeting the modality dependent residence time τ di >τ h Is said to be progressively stable and has an L not exceeding the formula 2 Gain of
wherein , η u ＝max i∈N (η ui )，v＝exp{∑ i∈N (η si -η ui )τ h }；
by solving the above linear matrix inequality, the matrix U can be further obtained i(t) and Ti (t); according to K ei (t)＝U i (t)T i -1 (t)，A i +B i K ci ＝A r and Bi K ri ＝B r Solving to obtain a controller gain matrix K ei (t)、K ci and Kri 。
In order to verify the effectiveness of the invention in the comprehensive anti-interference control of the transition section of the tilting rotor, the following simulation experiment is carried out.
In the tilting corridor shown in fig. 1, the nacelle angle is the complementary angle of the tilting angle; selecting operating points with inclination angles of 0 degrees, 12 degrees, 35 degrees, 52 degrees and 90 degrees respectively, and balancing the system; and constructs a block diagram of the control method used in this example as shown in fig. 2.
Assuming that the whole tilting process 15s ends, the switching signal σ (t) is designed to: when t e [0, 2), σ (t) =1; when t e [2, 6), σ (t) =2; when t e [6, 9), σ (t) =3; when t e [9,12 ], σ (t) =4; when t e [12,15 ], σ (t) =5.
In fig. 3 (a) -6, the comparison method represents the traditional switching control method, the smooth interpolation control strategy designed by the invention is removed, different controller gain matrixes are obtained by solving the linear inequality of the corresponding matrixes, and the rest including a reference system, a coefficient matrix and the like are consistent with the method provided by the invention; simulation is carried out to obtain comparison graphs of the state response curves of the invention and the comparison method, as shown in fig. 3 (a), fig. 4 (a), fig. 5 (a) and fig. 6.
It can be seen that in fig. 3 (a) and 3 (b), both methods have better control effect on the forward flying speed u of the transition section of the tiltrotor unmanned aerial vehicle, but the method provided by the invention can better track the ideal state track. Fig. 4 (a) and fig. 4 (b) are state response curves of a longitudinal speed w, fig. 5 (a) and fig. 5 (b) are state response curves of a pitch angle q, and fig. 6 is a state response curve of a pitch angle θ. Meanwhile, by comparing two methods in the simulation diagram, the smooth interpolation H designed by the method of the invention can be seen ∞ The control strategy can effectively inhibit state jump at the switching moment, improves the transient performance of the system and has better control effect. The simulation results fully show that the comprehensive anti-interference smooth control method of the transition section of the tilting rotor unmanned aerial vehicle can effectively solve the problem of flight mode conversion of the tilting rotor unmanned aerial vehicle.
Claims (6)
1. The comprehensive anti-interference smooth switching control method for the transition section of the tilting rotor unmanned aerial vehicle is characterized by comprising the following steps of:
s1, a longitudinal nonlinear dynamics model of a transition section of a tilting rotor unmanned aerial vehicle is established, different operating points are selected in a tilting corridor to trim, and a switching linear system model is obtained;
s2, introducing an external system to represent disturbance input generated by rotor wake;
s3, designing a disturbance observer, and estimating disturbance from an external system;
s4, designing a reference model, converting the longitudinal control problem of the transition section into a comprehensive anti-interference control problem of a switching linear system, and further designing a comprehensive anti-interference control law;
s5, designing a smooth interpolation control strategy, and inhibiting state buffeting caused by controller switching.
2. The method for controlling the integrated anti-interference smooth switching of a transition section of a tiltrotor unmanned aerial vehicle according to claim 1, wherein in step S1, a longitudinal nonlinear dynamics model of the transition section of the tiltrotor unmanned aerial vehicle is expressed as follows:
wherein [ u, w, q, θ ]] T Is four states of the system, T represents matrix transposition; u is the forward flying speed along the x coordinate axis direction of the machine body, w is the longitudinal speed along the y coordinate axis direction of the machine body, q is the pitch angle speed, and θ is the pitch angle; delta f Delta for longitudinal cyclic variation g As the total distance delta e Is the rudder deflection angle; beta M Is the tilting angle; f () is a nonlinear function satisfying the kinematic and dynamic relationships;
defining a switching signal σ (t) that satisfies a modality dependent dwell time constraint: [0, infinity) →n= {1,2, …, N }, N being the number of subsystems switching the linear system model; for σ (t) =i, i ε N and any t y ＞t x Not less than 0, satisfies:
N i (t x ，t y )≤1+T i (t x ，t y )/τ di
wherein ,Ni (t x ，t y ) Represents the total number of times to switch to the ith subsystem, T i (t x ，t y ) Indicating that the ith subsystem is at t x ，t y ) Total run time in interval, then τ di > 0 is referred to as modality dependent residence time;
further, selecting n groups of operating points at the tilting corridor to trim, and obtaining an expression of an ith subsystem of the switching linear system model as follows:
wherein x (t) = [ Δu, Δw, Δq, Δθ ]] T The system is characterized in that the system comprises four state quantities, wherein Deltau is an increment of a front flying speed along the x coordinate axis direction of the machine body deviating from a state at a selected leveling point, deltaw is an increment of a longitudinal speed along the y coordinate axis direction of the machine body deviating from a state at the selected leveling point, deltaq is an increment of a pitch angle speed deviating from a state at the selected leveling point, and Deltaθ is an increment of a pitch angle deviating from a state at the selected leveling point; u (u) c (t)＝[Δδ f ，Δδ g ，Δδ e ] T Delta is the control input to the system f Delta for state at selected trim points for longitudinal cyclic variation deviations g Delta for the delta of the state at the selected trim point for collective deviations e An increment for the rudder deflection angle to deviate from the state at the selected leveling point; ρ (t) represents an external systemA disturbance input generated by the rotor wake; omega 1 (t) is a disturbance input to the tiltrotor unmanned aerial vehicle; a is that i 、B i 、H i Respectively, a constant matrix obtained by linearizing around the selected leveling points.
3. The method for controlling the integrated anti-interference smooth switching of a transition section of a tiltrotor unmanned aerial vehicle according to claim 2, wherein in step S2, an external system is introduced to represent the disturbance input generated by the rotor wake, and for i e N, the specific form of the external system is:
ρ(t)＝M i φ(t)
wherein phi (t) represents the state of the external system; omega 2 (t) is a disturbance input acting on the external system, excluding the disturbance input generated by the rotor wake; c (C) i 、G i 、M i Each a constant matrix of appropriate dimensions.
4. The method for controlling the integrated anti-interference smooth switching of a transition section of a tiltrotor unmanned aerial vehicle according to claim 3, wherein in step S3, the expression of the disturbance observer is as follows:
wherein ψ (t) represents the system of disturbance observersA system state; and />Representing the estimates of phi (t) and rho (t), respectively; l is the disturbance observer gain;
defining disturbance observation errors as follows:
further, differential of disturbance observation error is obtainedIs represented by the expression:
5. the method for controlling the integrated anti-interference smooth switching of a transition section of a tiltrotor unmanned aerial vehicle according to claim 4, wherein in step S4, the expression of the reference model is as follows:
wherein ,xr (t)＝[Δu r ，Δw r ，Δq r ，Δθ r ] T To the ideal state that needs to be tracked, deltau r Delta w for the ideal forward flight velocity along the x-axis direction of the machine body to deviate from the state at the selected leveling point r Delta q for the desired longitudinal velocity in the y-axis direction of the body coordinate to deviate from the state at the selected leveling point r Delta theta for the desired pitch rate deviation from the state at the selected trim point r An increment for the ideal pitch angle to deviate from the state at the selected leveling point; r (t) is a bounded reference input of suitable dimension for generating an ideal state trajectory; a is that r 、B r Constant matrices each having appropriate dimensions;
for the ith subsystem of the switching linear system model, the control law is designed as:
wherein ,ea (t)＝x(t)-x r (t) is a state tracking error; k (K) ei (t)、K ci 、K ri Respectively a controller gain matrix to be designed;
further, a state tracking error e is obtained a Expression of differentiation of (t):
the controller expression u c (t) substitution intoIn (3), an expression of a tracking error system is obtained:
selecting K ci 、K ri Matrix, satisfy A i +B i K ci -A r＝0 and Bi K ri -B r When =0 is true, the tracking error system is simplified to:
further, define an error systemSystem state e (t) = [ e a (t)，e b (t)] T Disturbance input ω (t) = [ ω ] 1 (t)，ω 2 (t)] T Obtaining an expression of an error system:
wherein , and Di The respective expressions are as follows:
6. the method for integrated tamper resistant smooth transition section switching control of a tiltrotor unmanned aerial vehicle according to claim 5, wherein in step S5, t is used s Indicating the time t at which the s-th handover occurs s+1 Indicating the time at which the (s+1) -th handover occurs; introducing a transition zone [ t ] s ，t s +τ h )，τ h > 0 is a constant value for σ (t s )＝i∈N，τ h Less than the corresponding residence time tau di The method comprises the steps of carrying out a first treatment on the surface of the Further, section [ t ] s ，t s+1 ) Divided into [ t ] s ，t s，0 )∪[t s，0 ，t s+1), wherein ,ts，0 ＝t s +τ h ；
Further, a smooth interpolation strategy is designed to gain K for the controller ei (t) performing a treatment to give K ei (t)＝U i (t)T i -1 (t); assuming that a coefficient matrix T exists i＞0 and Ui Wherein i ε N; then for (i, j) ∈n×n, i+.j, and σ (0) =m∈n, matrix U i(t) and Ti The expression of (t) is:
wherein α (t) = (t-t) s )/τ h The method comprises the steps of carrying out a first treatment on the surface of the Each coefficient matrix T i and Ui Solving through a linear matrix inequality;
selecting a lyapunov function:
V i (e(t))＝e T (t)P i (t)e(t)
wherein ,lyapunov matrix, P representing the ith subsystem 2i Is positive definite matrix and P 1i (t)＝T i -1 (t)；
To ensure that the error system is asymptotically stable and has H ∞ Comprehensive anti-interference performance for interval t s ，t s，0 ) The following inequality needs to be satisfied:
for interval t s，0 ，t s+1 ) The following inequality needs to be satisfied:
wherein ,ηui and ηsi Respectively representing the decay rate of the Lyapunov function in the corresponding time interval; gamma > 0 represents L of the system 2 A gain level;
further, for σ (t s )＝i，i∈N，σ(t s - ) =j, j e N and i+.j; general purpose medicineToo K ei (t)＝U i (t)T i -1 The process of (t) requires that the following linear matrix inequality be satisfied:
wherein ,
Φ Aij ＝He{A i T i +B i U i }+η si T i
and, for matrix X, he { X } = x+x T The method comprises the steps of carrying out a first treatment on the surface of the I represents an identity matrix;
then, when the switching signal sigma (t s ) Meeting the modality dependent residence time τ di ＞τ h Is said to be progressively stable and has an L not exceeding the formula 2 Gain of
wherein , η u ＝max i∈N (η ui )，v＝exp{∑ i∈N (η si -η ui )τ h }；
the matrix U is further obtained by solving the above linear matrix inequality i(t) and Ti (t); according to K ei (t)＝U i (t)T i -1 (t)，A i +B i K ci ＝A r and Bi K ri ＝B r Solving to obtain a controller gain matrix K ei (t)、K ci and Kri 。
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