CN109062044B - Terminal iterative learning docking control method - Google Patents

Terminal iterative learning docking control method Download PDF

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CN109062044B
CN109062044B CN201810880274.2A CN201810880274A CN109062044B CN 109062044 B CN109062044 B CN 109062044B CN 201810880274 A CN201810880274 A CN 201810880274A CN 109062044 B CN109062044 B CN 109062044B
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docking
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iterative learning
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CN109062044A (en
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全权
任锦瑞
戴训华
蔡开元
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Beihang University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract

The invention provides a terminal iterative learning docking control scheme. The optimal control input is given based on a terminal iterative learning control method, and successful butt joint is realized. The method is rapid and reliable, is feedforward control with learning capability, only needs terminal information, and avoids the problems that conventional feedback control may cause control lag, over-control, high requirement on a sensor, large calculation amount, incapability of fully utilizing historical docking experience and the like. The scheme has two steps: step one, a preparation stage, namely, the off-line generation of a basis function, which comprises the generation of a reference butt joint track and the generation of a reference input; and step two, in the implementation stage, the terminal iteratively learns the design of the controller.

Description

Terminal iterative learning docking control method
Technical Field
The invention relates to a terminal iterative learning docking control method, and belongs to the technical field of flight control.
Background
In flight control, especially in multi-aircraft flight, it is often necessary to perform docking tasks between two aircraft, such as air refueling docking, unmanned aerial vehicle air docking recovery, space station docking, rotorcraft precise landing, and the like. The docking task only requires the final docking to be successful, and basically has no requirement on the docking process except safety. The docking is often accomplished with repeatability and may require multiple docks to eventually dock successfully. In practice, conventional feedback control may cause problems such as control lag, over-control, high requirements on sensors, large calculation amount, and incapability of fully utilizing historical docking experience. Therefore, a reliable docking control method based on terminal iterative learning is provided, the method is feedforward control with learning capacity, only needs terminal information, has low requirements on a sensor, and is small in calculation amount and high in reliability.
Disclosure of Invention
The invention aims to provide a reliable docking control method, which provides optimal control input through a terminal iterative learning control method to realize successful docking. The method is quick and effective, and has high reliability and safety.
The controller design of the invention adopts a terminal iterative learning control method, the basic principle of which is shown in figure 1, and each running time of the system is T ∈ [0, T]The terminal time is T, and the expected system terminal output is yd(T), the terminal output of the kth iteration system is yk(T), terminal output error
Figure BDA0001754294740000011
The terminal iterative learning controller utilizes the k-th terminal output error ek(T) obtaining a control input u for the (k + 1) th iterationk+1(t) after a plurality of iterations, finally enabling the terminal to output an error ek(T) → 0. In the butt joint control, the designed butt joint controller takes the butt joint error as input, outputs the control quantity of the next butt joint, and finally achieves the successful butt joint through a plurality of iterations.
The butt joint model adopted by the invention is as follows:
Figure BDA0001754294740000012
wherein the content of the first and second substances,
Figure BDA0001754294740000021
in order to be in the state of the system,
Figure BDA0001754294740000022
is the output of the system, and is,
Figure BDA0001754294740000023
in order to control the input of the electronic device,
Figure BDA0001754294740000024
in order to be a matrix of the system,
Figure BDA0001754294740000025
in order to input the matrix, the input matrix is,
Figure BDA0001754294740000026
is a non-linear function vector that is,
Figure BDA0001754294740000027
to be the output matrix, the output matrix is,
Figure BDA0001754294740000028
is a constant offset.
Because a typical aircraft has four control inputs and a docking mission generally requires four outputs, namely three position errors and one forward velocity error, the docking model is a four-in-four-out system. The butt joint targets are as follows: the docking position error is zero and the docking velocity error is zero or remains within a threshold. In order to solve the problems of underdrive and overdrive, the speed control target is generally achieved through saturation control or trajectory planning of the position, and a certain control input can be correspondingly abandoned, so that only a three-in three-out system needs to be considered. In the following, a three-in three-out system is considered directly, i.e. m is 3.
By using iterative learning control of the terminal to solve the docking control problem, the above model can be rewritten as the following control-oriented model
Figure BDA0001754294740000029
Wherein the content of the first and second substances,
Figure BDA00017542947400000210
for the system state of the k-th iteration,
Figure BDA00017542947400000211
the output of the system for the k-th iteration,
Figure BDA00017542947400000212
t ∈ [0, T ] as a control input for the kth iteration]Is system runtime, subscript
Figure BDA00017542947400000213
Is the initial state value x when the number of iterations, t is 0k(0) Is x0,kThe desired system terminal output is yd(T) is known. Hereinafter, for simplicity, the variables t and k will be omitted unless necessary.
For system (2), the following assumptions are made:
assume that 1: only the terminal output y (T) is measurable;
assume 2: initial state xk(0) May be reset in each iteration;
assume that 3: function phi (y)k) Satisfies the local Liphoichz condition on M, i.e. | | φ (y)k)-φ(yk-1)||≤lφ||yk-yk-1I, where lφIs a positive-liphoz constant that,
Figure BDA00017542947400000214
is an open-connection set, and the system is characterized in that,
Figure BDA00017542947400000215
representing a circle around origin 03×1A radius of.
The butt joint control targets are as follows: constructing a control input u for a kth iteration for a docking system (2)k(t)，t∈[0,T]So that
||yd(T)-yk(T) | → 0 → k → ∞ (3)
Wherein, ykAnd (T) is the terminal system output of the kth iteration.
The invention provides a terminal iterative learning docking control method, which comprises the following steps:
as shown in fig. 2, the control method specifically includes two parts:
(1) a preparation stage: a basis function is generated for a terminal iterative learning controller to be designed so that iteration can be converged quickly, and meanwhile, a docking process is controlled to avoid some dangerous conditions including overshoot and induced oscillation.
(2) The implementation stage is as follows: designing a terminal iterative learning controller to realize a butt joint control target (3);
in the docking task, the tracking aircraft is generally docked by maneuvering near the target aircraft or the target platform. In the preparation phase, there is no need to directly consider complex dockingThe model may be considered only to track the aircraft model and its reference model. By the preparation work, the basis function U can be obtainedb(t) of (d). Although the docking phase requires two iterative processes to be performed, both can be done offline prior to the docking operation. In the implementation stage, the designed terminal iterative learning controller works in a repeated learning mode, and finally, the successful butt joint is realized, so that the method is very simple and easy to use. The concrete contents of the preparation stage and the implementation stage in the control method are as follows:
the method comprises the following steps: preparatory phase-off-line generation of basis functions
A better basis function may allow the terminal iterative learning controller to converge faster. In practice, there is often a limit to the number of contacts, for example, 3-5, so a good enough basis function must be selected. While conventional basis function generation generally utilizes polynomial parameterization, the present invention employs iterative optimization to achieve better performance. As shown in fig. 3, the method specifically includes the following two steps:
(1) generation of reference docking trajectories
The reference docking trajectory refers to a reasonable flight trajectory for tracking the aircraft to complete the docking mission while avoiding some dangerous situations such as overshoot and induced oscillation. The reference docking track is obtained by adopting a terminal iterative learning method, and the method specifically comprises the following two aspects:
1) establishing a reference model
Generally, a virtual model containing three single channels and a second-order integration link on each channel is used as a reference model for tracking the aircraft
Figure BDA0001754294740000031
Wherein p isv(t)＝[xv(t)yv(t)zv(t)]TIs the reference model output, uv(t)＝[uv,x(t)uv,y(t)uv,z(t)]TIs the reference model input. The next step is to design a reference docking trajectory p for obtaining the reference docking trajectoryv,r(t) reference model input uv(t) AAnd will generally be considered specifically for the particular problem. Taking air refueling as an example, when a pilot executes an air refueling task, the general operation is to accelerate and then decelerate an oil receiver (a tracking aircraft) to realize docking, if docking fails, the pilot adjusts the acceleration-deceleration process according to the last terminal docking error, and then performs the next docking attempt. By mimicking pilot operation, reference model inputs such as those shown in FIG. 4 can be designed, with the mathematical expressions as follows:
Figure BDA0001754294740000041
wherein u isv,sIs uv(t) any element of subscript s ═ x, y, z, tstartAnd tendIs the start and end time of the docking operation, T ═ T hereend-tstart。cpeak,sIs the input peak value, tpeak,sIs from tstartThe time of the peak at the beginning. c. C1Is the slope of the rising portion of the curve in FIG. 4, c2The slope of the descending segment of the curve. Similar to pilot operation, the acceleration-deceleration process may be performed by varying the parameter t in each iterationpeak,sOr cpeak,sTo adjust. Here, t is setpeak,s/((tend-tstart) And/2) is 0.3. The next step is to optimize cpeak,sTo obtain a reference docking trajectory pv,r(t)。
2) Generating a reference docking trajectory
Terminal iterative learning control by optimization c using basis function-freepeak,sTo obtain a satisfactory reference docking trajectory pv,r(t) of (d). For the established reference model (4) with the input of the formula (5), designing a terminal iterative learning controller as
Figure BDA0001754294740000042
Wherein, cpeak,x,k+1,cpeak,y,k+1,cpeak,z,k+1Respectively as input u in the k +1 th iterationv,x(t),uv,y(t),uv,z(t) ofInput peak value, cpeak,x,k,cpeak,y,k,cpeak,z,kFor the input peak of the k-th iteration, pv(tend) As terminal output of the reference model, pd(0) Is the initial position of the target aircraft or target platform, pp(0) To track the initial position of the aircraft, a is a controller parameter. The controller (6) can obtain a satisfactory reference butt joint track p through a plurality of off-line iterationsv,r(t)。
(2) Generating a reference input
According to the obtained reference butt joint track pv,rAnd (t) obtaining a reference input by adopting an adjoint iterative learning control method, and further obtaining a basis function. The iterative learning control can realize perfect tracking of a full track, and the adjoint iterative learning control can be suitable for a minimum phase angle system (a general fixed-wing aircraft has a non-minimum phase angle characteristic). For tracking aircraft
Figure BDA0001754294740000051
Design the adjoint type iterative learning controller as
Figure BDA0001754294740000052
Wherein p isrTracking the output, x, of the aircraftrTo track the state of the aircraft, ur＝[T a e]Is the input of the system, and the system is,
Figure BDA0001754294740000053
in order to track the system matrix of the aircraft,
Figure BDA0001754294740000054
in order to input the matrix, the input matrix is,
Figure BDA0001754294740000055
to be the output matrix, the output matrix is,T,k+1,a,k+1,e,k+1is the system input for the (k + 1) th iteration,T,k,a,k,e,kis the system input for the k-th iteration,
Figure BDA0001754294740000056
is the operator corresponding to the system (7),
Figure BDA0001754294740000057
is that
Figure BDA0001754294740000058
Associated operator of αkAre controller parameters. After a plurality of off-line iterations, the actual output can perfectly track the reference docking trajectory, and at this time,T,r(t),a,r(t),e,r(t) to generate a reference trajectory pv,r(t) the corresponding system input, then the basis function is
Figure BDA0001754294740000059
To this end, the basis function Ub(t) has been obtained, i.e., the preparation work for the docking control has been completed. The implementation phase is entered next.
Step two: implementation phase-terminal iterative learning controller design
Based on the generated basis functions UbAnd (t) designing a terminal iterative learning controller. The invention provides a hybrid terminal iterative learning controller which aims to improve the performance of the controller and combine two learning objects.
Generally, only part of the initial state is controllable, and the initial state can be rewritten as
Figure BDA00017542947400000510
Wherein the content of the first and second substances,
Figure BDA00017542947400000511
represents an initial state which is not controllable and,
Figure BDA00017542947400000512
representing a controllable initial state, n1+n2N, block matrix
Figure BDA00017542947400000513
For mixing ξ and ηkSeparate, and ηkMay be used for the iterative process.
For the docking system (2), the following learning control law is designed
uk(t)＝Ub(t)qk(11)
Wherein the content of the first and second substances,
Figure BDA00017542947400000514
is a constant-value parameter vector that is,
Figure BDA00017542947400000515
is the basis function obtained in the preparation phase.
The combination of the control input and the initial state value is used as a learning object, and a learning update law is designed
Figure BDA0001754294740000061
Wherein the content of the first and second substances,
Figure BDA0001754294740000062
is a constant diagonal parameter matrix,
Figure BDA0001754294740000066
is the docking error for the k-1 iteration.
For the docking system (2), when the control law and the learning law of the terminal iterative learning are respectively designed as the equations (11) and (12) on the assumption that 1-3 are all satisfied, if the inequalities are not satisfied
α1+γ1＜1 (13)
If true, then yd(T)-yk(T) | → 0 when k → ∞, the inequality (13) is a condition derived from the compression mapping principle. Wherein
Figure BDA0001754294740000064
Here, the first and second liquid crystal display panels are,
Figure BDA0001754294740000065
as an identity matrix, β1(t) is the intermediate variable of the calculation,. tau.is the integral variable, Ub(τ) is U in the preceding textb(t), except that the integral variable is replaced in the calculation, the rest parameters are defined as before.
The invention has the advantages and beneficial effects that:
the reliable docking control method based on terminal iterative learning can successfully solve the problem of aircraft docking and increase the success rate and rapidity of docking. The method can also be applied to other occasions with repeated operation characteristics concerning the terminal, such as subway station entering control in traffic, mechanical arm movement control in industry and the like.
Drawings
Fig. 1 is a basic schematic diagram of a terminal iterative learning control method.
Fig. 2 is a schematic diagram of a terminal iterative learning docking control method.
FIG. 3 is a flow chart of the generation of an offline basis function.
FIG. 4 is a reference model input designed for airborne fueling.
Fig. 5(a), (b), (c), (d) are air-refueling reference docking trajectories.
Fig. 6 is an airborne fueling reference input.
Fig. 7 is the convergence of the air-fueling docking error.
Fig. 8 is a successful docking trajectory for airborne fueling.
The symbols in the figures are as follows:
FIG. 1: y isd(T) is the desired system terminal output, yk(T) is the system terminal output for the kth iteration, ek(T) is the terminal output error of the kth iteration, uk(t) is the control input for the kth iteration, uk+1(t) is the control input for the (k + 1) th iteration.
FIG. 2: u. ofv(t) is the reference model input, pv,r(t) is a reference docking trajectory, Ub(t) is a basis function, uk(t) is the control input for the kth iteration, ηk(t) is the controllable initial state of the kth iteration.
FIG. 3: u. ofv(t) is the reference model input, pv,r(t) is a reference docking trajectory, Ub(t) is a basis function.
FIG. 4: u. ofv,sIs the reference model input uv(t) any element of subscript s ═ x, y, z, tstartAnd tendIs the start and end time of the docking operation, cpeak,sIs the input peak value, tpeak,sIs from tstartThe time of the peak at the beginning.
FIG. 5(a), (b), (c), and (d): x is the number ofv,r，yv,r，zv,rIs the displacement of a reference track in the x, y and z directions of a coordinate system of the oiling machine, vv,x,rIs the forward speed corresponding to the reference trajectory.
FIG. 6:T,r,a,r,e,rfor generating reference track pv,rAnd (t) corresponding system input.
FIG. 7: k is the number of iterations, edockIs the docking error.
FIG. 8: and x, y and z are coordinates under the coordinates of the oiling machine.
Detailed Description
The design of the terminal iterative learning butt joint control method is carried out by taking the butt joint control of taper pipe-taper sleeve type air refueling as an example.
The simulation process is carried out on MatlabR2016b in a computer with a main frequency of 3.4GHz and a memory of 8.00GB, win7 environment.
In the docking task, the oiling machine flies forward while keeping constant-speed level, the oil receiving machine approaches the oiling machine by maneuvering and realizes docking, and then the assembly flies. The oiling machine is a KC-135 airplane, and the oil receiving machine is an F-16 airplane.
Figure BDA0001754294740000071
Outputting y ═ x for the state of the butt joint system composed of the oiling machine and the oil receiving machineeyeze]TThe distance between the oiling machine and the oil receiver in the x, y and z directions is defined as u ═ zT a e]T，T,a,eThe input is input by an oil engine accelerator, an aileron and an elevator. In the simulation, the docking speed is
Figure BDA0001754294740000072
A butt joint height of
Figure BDA0001754294740000073
tstart＝20，t end30, T10, and the initial distance between the fuel dispenser and the fuel receiver is pd(0)-pp(0)＝[6 1 -1]TThe position of the general oil receiving machine in the air refueling is controllable, so n1＝19,n 23. When the docking error is less than 0.3m, the docking can be considered to be successful.
(1) The butt joint method comprises the following specific steps:
the method comprises the following steps: preparatory phase-off-line generation of basis functions
Firstly, generating a reference docking track, designing a reference model for an oil receiving machine reference model satisfying the formula (4), inputting the reference model into the formula (5), setting the parameter of the terminal iterative learning controller (6) to be 0.5, and obtaining the satisfactory reference docking track p shown in fig. 5(a), (b), (c) and (d) after 20 times of offline iterationv,r(t)。
Aiming at the oil receiving machine system satisfying the formula (7), the adjoint iterative learning controller (8) is iterated for 20 times to obtain a reference butt joint track p capable of being generatedv,r(t) control surface inputT,r,a,r,e,rAs shown in fig. 6. Finally, a basis function matrix is obtained
Figure BDA0001754294740000081
Step two: implementation phase-terminal iterative learning controller design
Aiming at the air refueling docking model satisfying the formula (2), a control law and a learning law of terminal iterative learning are designed respectivelyTaking the controller parameter q as equations (11) and (12)1＝[1 1 1]T,L1＝diag(0.3,0.7,-1.5),L2＝diag(0.2,0.4,0.4)。
(2) Analysis of simulation results
The simulation result of the reliable docking controller in Matlab provided by the invention is as follows:
the convergence of the systematic docking error is shown by the dashed line in fig. 7, and the successful docking trajectory is shown in fig. 8. The system can realize successful docking in the second docking attempt, and the taper pipe of the oil receiver is successfully inserted into the umbrella crown of the taper sleeve discharged by the oiling machine. The designed terminal iteration controller has good convergence characteristic, and is fast and safe. To further verify the robustness of the system, consider the following system uncertainties and disturbances: the head wave interference becomes 1.2 times of the original interference; adding a crosswind disturbance; the docking height and the docking speed are changed to 1.2 times of the original ones. The convergence of the system docking error is shown as a solid line in fig. 7, the system can still realize successful docking in the second docking attempt, and the designed terminal iteration controller has strong robustness.

Claims (1)

1. A terminal iterative learning butt joint control method is provided, in the method, each time the running time of a system is T ∈ [0, T]The terminal time is T, and the expected system terminal output is yd(T), the terminal output of the kth iteration system is yk(T), terminal output error
Figure FDA0002431259480000011
The terminal iterative learning controller utilizes the k-th terminal output error ek(T) obtaining a control input u for the (k + 1) th iterationk+1(t) after a plurality of iterations, finally enabling the terminal to output an error ek(T) → 0; in the butt joint control, the designed butt joint controller takes the butt joint error as input, outputs the control quantity of the next butt joint, and finally achieves the successful butt joint through several iterations;
the docking model used was as follows:
Figure FDA0002431259480000012
wherein the content of the first and second substances,
Figure FDA0002431259480000013
in order to be in the state of the system,
Figure FDA0002431259480000014
is the output of the system, and is,
Figure FDA0002431259480000015
in order to control the input of the electronic device,
Figure FDA0002431259480000016
in order to be a matrix of the system,
Figure FDA0002431259480000017
for the input matrix, φ (·):
Figure FDA0002431259480000018
is a non-linear function vector that is,
Figure FDA0002431259480000019
to be the output matrix, the output matrix is,
Figure FDA00024312594800000110
a constant offset;
because the aircrafts all have four control inputs and four outputs, namely three position errors and one forward speed error, need to be controlled in the docking task, the docking model is a four-in four-out system; the butt joint targets are as follows: the error of the docking position is zero, and the error of the docking speed is zero or kept within a threshold value; in order to solve the problems of underactuation and overdrive, the speed control target can be achieved through saturation control or trajectory planning of positions, and a certain control input is correspondingly abandoned, so that only a three-in three-out system needs to be considered; in the following, consider directly a three-in-three-out system, i.e. m-3;
the problem of butt joint control is solved by adopting terminal iterative learning control, and the above model is rewritten into the following control-oriented model
Figure FDA00024312594800000111
Wherein the content of the first and second substances,
Figure FDA00024312594800000112
for the system state of the k-th iteration,
Figure FDA00024312594800000113
the output of the system for the k-th iteration,
Figure FDA00024312594800000114
control input for the kth iteration T ∈ [0, T]Is system runtime, subscript
Figure FDA00024312594800000115
Is the initial state value x when the number of iterations, t is 0k(0) Is x0,kThe desired system terminal output is yd(T) is known; for simplicity, the variables t and k will be omitted;
for equation (2), the following assumptions are made:
assume that 1: only the terminal output y (T) is measurable;
assume 2: initial state xk(0) Reset in each iteration;
assume that 3: function phi (y)k) Satisfies the local Liphoichz condition on M, i.e. | | φ (y)k)-φ(yk-1)||≤lφ||yk-yk-1I, where lφIs a positive-liphoz constant that,
Figure FDA0002431259480000021
is an open-connection set, and the system is characterized in that,
Figure FDA0002431259480000022
representing a circle around origin 03×1A neighborhood of radius of;
the butt joint control targets are as follows: constructing a control input u for the kth iteration for dock (2)k(t)，t∈[0,T]So that
||yd(T)-yk(T) | → 0 → k → ∞ (3)
Wherein, yk(T) is the terminal system output of the kth iteration;
the method is characterized in that: the control method specifically comprises two parts:
(1) a preparation stage: generating a basis function for a terminal iterative learning controller to be designed to enable iteration to be rapidly converged, and simultaneously controlling a butt joint process to avoid the dangerous condition of overshoot and induced oscillation;
(2) the implementation stage is as follows: designing a terminal iterative learning controller to realize a butt joint control target (3);
in the docking task, the tracking aircraft approaches to the target aircraft or the target platform through maneuvering to realize docking; in the preparation stage, a complex docking model does not need to be directly considered, and only a tracking aircraft model and a reference model thereof are considered; by preparation work, the basis function U is obtainedb(t); although the docking phase requires the execution of two iterative processes, they are all done offline prior to the docking operation; in the implementation stage, the designed terminal iterative learning controller works in a repeated learning mode and finally realizes successful docking, and the specific contents of the preparation stage and the implementation stage in the control method are as follows:
the method comprises the following steps: preparatory phase-off-line generation of basis functions
Obtaining a basis function by adopting an iterative optimization method, which specifically comprises the following two steps:
(1) generation of reference docking trajectories
The reference docking track refers to a reasonable flight track for tracking the aircraft to complete the docking task, meanwhile, dangerous conditions are avoided, and the reference docking track is obtained by adopting a terminal iterative learning method, and the method specifically comprises the following two aspects:
1) establishing a reference model
A virtual model containing three single channels and a second-order integral link on each channel is used as a reference model for tracking the aircraft
Figure FDA0002431259480000031
Wherein p isv(t)＝[xv(t) yv(t) zv(t)]TIs the reference model output, uv(t)＝[uv,x(t) uv,y(t) uv,z(t)]TIs a reference model input; the next step is to design a reference docking trajectory p for obtaining the reference docking trajectoryv,r(t) reference model input uv(t), designing a reference model input, and mathematically expressing the following:
Figure FDA0002431259480000032
wherein u isv,sIs uv(t) any element of subscript s ═ x, y, z, tstartAnd tendIs the start and end time of the docking operation, T ═ T hereend-tstart；cpeak,sIs the input peak value, tpeak,sIs from tstartThe time of the peak at the beginning; c. C1Is the slope of the rising segment of the curve, c2The slope of the descending segment of the curve; the acceleration-deceleration process is performed by varying the parameter t in each iterationpeak,sOr cpeak,sTo adjust; here, t is setpeak,s/((tend-tstart) (2) ═ 0.3; the next step is to optimize cpeak,sTo obtain a reference docking trajectory pv,r(t)；
2) Generating a reference docking trajectory
Terminal iterative learning control by optimization c using basis function-freepeak,sTo obtain a reference docking trajectory pv,r(t); for the established reference model formula (4) with the input of formula (5), designing the terminal iterative learning controller as
Figure FDA0002431259480000041
Wherein, cpeak,x,k+1,cpeak,y,k+1,cpeakz,,k+1Respectively as input u in the k +1 th iterationv,x(t),uv,y(t),uv,z(t) input peak value, cpeak,x,k,cpeak,y,k,cpeak,z,kFor the input peak of the k-th iteration, pv(tend) As terminal output of the reference model, pd(0) Is the initial position of the target aircraft or target platform, pp(0) To track the initial position of the aircraft, a is a controller parameter; the controller (6) obtains a reference butt joint track p through a plurality of off-line iterationsv,r(t)；
(2) Generating a reference input
According to the obtained reference butt joint track pv,r(t) obtaining a reference input by adopting an adjoint iterative learning control method, and further obtaining a basis function; the iterative learning control realizes perfect tracking of a full track, and the adjoint iterative learning control can be suitable for a minimum phase angle system; for tracking aircraft
Figure FDA0002431259480000042
Design the adjoint type iterative learning controller as
Figure FDA0002431259480000043
Wherein p isrTracking the output, x, of the aircraftrTo track the state of the aircraft, ur＝[T a e]Is the input of the system, and the system is,
Figure FDA0002431259480000044
in order to track the system matrix of the aircraft,
Figure FDA0002431259480000045
in order to input the matrix, the input matrix is,
Figure FDA0002431259480000046
to be the output matrix, the output matrix is,T,k+1,a,k+1,e,k+1is the system input for the (k + 1) th iteration,T,k,a,k,e,kis the system input for the k-th iteration,
Figure FDA0002431259480000047
is an operator corresponding to the formula (7),
Figure FDA0002431259480000048
is that
Figure FDA0002431259480000049
Associated operator of αkIs a controller parameter; after a plurality of off-line iterations, the actual output can perfectly track the reference docking trajectory, and at this time,T,r(t),a,r(t),e,r(t) to generate a reference trajectory pv,r(t) the corresponding system input, then the basis function is
Figure FDA0002431259480000051
To this end, the basis function Ub(t) has been obtained, i.e. the preparation of the docking control has been completed; then entering into the implementation stage;
step two: implementation phase-terminal iterative learning controller design
Based on the generated basis functions Ub(t) designing a terminal iterative learning controller; the traditional terminal iterative learning controller takes a control input or an initial state value as a learning object, and a hybrid terminal iterative learning controller is arranged below the traditional terminal iterative learning controller;
only part of the initial state is controllable, and according to the state controllability, the initial state is rewritten into
Figure FDA00024312594800000510
Wherein the content of the first and second substances,
Figure FDA0002431259480000052
represents an initial state which is not controllable and,
Figure FDA0002431259480000053
representing a controllable initial state, n1+n2N, block matrix
Figure FDA0002431259480000054
For mixing ξ and ηkSeparate, and ηkFor an iterative process;
for the butt joint type (2), the following learning control law is designed
uk(t)＝Ub(t)qk(11)
Wherein the content of the first and second substances,
Figure FDA0002431259480000055
is a constant-value parameter vector that is,
Figure FDA0002431259480000056
is the basis function obtained in the preparation phase;
the combination of the control input and the initial state value is used as a learning object, and a learning update law is designed
Figure FDA0002431259480000057
Wherein the content of the first and second substances,
Figure FDA0002431259480000058
is a constant diagonal parameter matrix,
Figure FDA0002431259480000059
is the docking error for the k-1 iteration;
for the butt-joint equation (2), when the terminal iterative learning control law and the learning update law are respectively designed as equations (11) and (12) on the assumption that 1-3 are all satisfied, if the inequalities are not satisfied
α1+γ1＜1 (13)
If true, then yd(T)-yk(T) | → 0 when k → ∞, the inequality (13) is a condition derived from the compression mapping principle; wherein
Figure FDA0002431259480000061
Here, the first and second liquid crystal display panels are,
Figure FDA0002431259480000062
as an identity matrix, β1(t) is the intermediate variable of the calculation,. tau.is the integral variable, Ub(τ) is U in the preceding textb(t), only the integral variable is replaced in the calculation.
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