CN115686034A - Unmanned underwater vehicle track tracking control method considering failure of speed sensor - Google Patents
Unmanned underwater vehicle track tracking control method considering failure of speed sensor Download PDFInfo
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Abstract
The invention provides a track tracking control method of an unmanned underwater vehicle considering failure of a speed sensor, which comprises the following steps: establishing a navigation mathematical model, and setting an expected track mathematical model; designing a speed observer based on a position signal, and designing a longitudinal moment and transverse moment disturbance observer on the basis of the speed observer; designing virtual control laws of longitudinal speed and transverse speed, introducing an instruction filter to constrain the amplitude and speed of the virtual control laws, and solving the problem of increased computational complexity caused by high-order derivation of the virtual control laws; designing a trajectory tracking sliding mode controller based on the virtual control law and the output of the instruction filter, and compensating the disturbance of longitudinal torque and transverse torque based on the estimation value of the disturbance observer; the technical scheme of the invention solves the problems that the performance failure of the speed sensor of the unmanned underwater vehicle after underwater operation is not considered in the prior art, and the tracking failure of the controller is caused because the torque output of the controller exceeds the maximum output of the propeller of the unmanned underwater vehicle.
Description
Technical Field
The invention relates to the technical field of track tracking control of unmanned underwater vehicles, in particular to a track tracking control method of an unmanned underwater vehicle considering failure of a speed sensor.
Background
In recent years, the motion control of an under-actuated unmanned underwater vehicle has become a research hotspot of ocean engineering, and the unmanned underwater vehicle plays an important role in oceanographic observation, submarine resource exploration, hydrological measurement and mapping, submarine rescue and the like, and has wide application prospect. With the improvement of the automation degree, the unmanned submersible vehicle is deployed and recovered by using the unmanned boat without depending on manpower, so that a new research hotspot is formed. In order to complete automatic deployment and recovery of the unmanned underwater vehicle, the unmanned underwater vehicle must realize track tracking, particularly high-precision water surface track tracking. Therefore, research on trajectory tracking during deployment and recovery of unmanned underwater vehicles becomes more and more important. However, currently, the research on trajectory tracking of the unmanned underwater vehicle on the water surface is relatively lacking, and in the prior art, the trajectory tracking of the unmanned underwater vehicle in the automatic deployment and recovery process has the defects that the influence caused by wind, wave and flow in the navigation process or the interference caused by unmodeled parts outside the system cannot be accurately estimated, the interference is not compensated, the accuracy of a speed sensor of the unmanned underwater vehicle after completing underwater operation is greatly influenced or even fails, the expected output of a controller is not limited according to the dynamic performance of the unmanned underwater vehicle, and the like. These disadvantages are more evident especially in environments where sea surface wave disturbances are complex and uncertain.
The existing research on the water surface track tracking method in the laying and recovery process of the unmanned underwater vehicle mainly has the following defects:
1) The accuracy of the speed sensor of the unmanned underwater vehicle is greatly influenced or even fails after the unmanned underwater vehicle finishes underwater operation. The track Tracking Control methods designed by the backstepping Sliding Mode, such as the papers of track Tracking Control of an under-utilized UUV Using a Novel Nonlinear Integral Tracking Mode Surface, and dynamic Tracking Mode Control of the track Tracking of under-utilized underwater vehicles, do not consider that the influence of the sensor precision after the underwater operation of the unmanned underwater vehicle can cause the Control precision to be reduced or even fail. The traditional track tracking control method designed for the unmanned ship on the water surface does not consider the influence of the precision of the speed sensor on track tracking, for example, the limitation on the virtual control law is considered in the article of 'under-actuated ship track tracking instruction filtering sliding mode robust control', but the influence caused by the failure of the speed sensor is not considered.
2) The traditional track tracking control method designed for the unmanned ship on the water surface does not consider the dynamic performance of the unmanned underwater vehicle, does not limit the expected output of the controller, and does not solve the problem of increased computational complexity caused by calculating a high-order derivative by a virtual control law. For example, the control method proposed in article "under-actuated ship adaptive dynamic surface output feedback trajectory tracking control with nonlinear observer" does not impose limitation on the desired output of the controller, and does not avoid the problem of increased computational complexity caused by high-order derivation of the virtual control law in the process of calculating the control law. Similarly, the control method proposed in patent No. CN113835338A, CN110134012a and the like is also not applicable to the water surface trajectory tracking control of the unmanned underwater vehicle because the desired output is not limited.
3) The influence caused by wind, wave and flow or the interference generated by unmodeled parts outside the system is not observed in the sailing process, and the interference is not compensated. For example, the control method proposed in the article "underwater robot position tracking control based on command filtering" does not observe and compensate for various disturbances of the system.
Disclosure of Invention
In order to solve the problems of track tracking control in the process of laying and recovering the unmanned underwater vehicle in the prior art, the invention considers the track tracking problem of the unmanned underwater vehicle under the condition that the unmanned underwater vehicle cannot measure a speed vector, simultaneously considers the interference generated by the internal part, the external part and the unmodeled part of the system, limits the output of the controller by restricting the virtual control law in order to prevent the expected output of the controller from exceeding the upper limit of the thrust of the unmanned underwater vehicle driver, and provides a corresponding control method.
In order to achieve the purpose, the invention is realized by the following technical scheme:
the track tracking control method of the unmanned underwater vehicle considering the failure of the speed sensor is characterized by comprising the following steps of:
s1, establishing a water surface navigation mathematical model of the unmanned underwater vehicle, and setting an expected track mathematical model.
S2, designing a speed vector observer based on the position signal, designing a disturbance observer in the longitudinal moment and transverse moment directions on the basis, and verifying the validity of the disturbance observer through Lyapunov theorem.
And S3, designing a virtual control law of longitudinal speed and transverse speed based on the real-time position error, introducing an instruction filter to constrain the amplitude and the speed of the virtual control law on the basis of the virtual control law, solving the problem that the calculation complexity is increased due to the fact that high-order derivation needs to be carried out on the virtual control law when the actual control law is solved, and verifying the effectiveness of the virtual control law through the Lyapunov theorem.
And S4, designing a track tracking sliding mode controller of the unmanned underwater vehicle based on the virtual control law and the output value of the instruction filter, compensating the disturbance of the longitudinal moment and the transverse moment based on the system disturbance estimation value observed by the disturbance observer, and verifying the effectiveness of the track tracking sliding mode controller through Lyapunov theorem.
And S5, verifying the effectiveness of the proposed method through simulation.
Further, the step S1 specifically includes:
defining a northeast coordinate system OXYZ and an attached coordinate system O respectively B X B Y B Z B And two coordinate systems, wherein a northeast coordinate system XOY is set as an inertial coordinate system, an arbitrary point O on the earth is taken as an origin of the coordinate system, OX points to the true north, OY points to the true east, and OZ is vertical to the plane where OX and OY are located and faces downwards. Will attach body coordinate system O B X B Y B Z B As an inertial coordinate system, assuming that the unmanned underwater vehicle body is symmetrical left and right, the central point is taken as the origin O of the inertial coordinate system B ，O B X B The axis points along the hullDirection of boat bow, O B Y B Directed vertically to starboard, O B Z B Perpendicular to the hull and down. And performing dynamic modeling on the unmanned underwater vehicle in the water surface navigation process to obtain a six-degree-of-freedom model comprising surging (surge), swaying (sway), heaving (heave), rolling (roll), pitching (pitch) and yawing (yaw). Neglecting the hydrodynamic resistance term higher than the second order and the motions of heave, pitch and roll, and establishing a kinematic and dynamic model as follows:
in the formula, eta = [ x, y, psi =] T X, y represents the unmanned vehicle motion position vector, psi ∈ [0,2 pi]Representing a heading angle, J (ψ) is a conversion matrix of a northeast coordinate system and an attached body coordinate system, v = [ u, v, r] T The velocity vector of the motion of the unmanned underwater vehicle in the attached coordinate system is represented, and u, v and r respectively represent surging, swaying and yawing velocities.
Representing an inertia matrix containing additional mass, C (v) representing a diagonally symmetric matrix,
denotes a damping matrix, τ = [ ] u ,τ v ,τ r ] T Representing moment control input vector, τ u 、τ v 、τ r Respectively representing the control forces of surge, sway and yaw, tau d ＝[τ du ,τ dv ,τ dr ] T System disturbance torque vector, τ du 、τ dv 、τ dr Representing the disturbance moments in the surge, sway, and yaw directions, respectively.
Further, the step S2 specifically includes:
firstly, designing a speed vector observer based on a position signal, eliminating a C (v) v term with a speed vector v in a model because the speed vector v cannot be measured, and introducing a variable matrix P (eta, v):
P(η,v)＝H(η)v (2)
in the formula, H (eta) 3×3 Is a mapping matrix of velocity vectors v to P (η, v).
The derivation of equation (2) yields:
to eliminate the term with velocity vector v in equation (3), the variable Y is introduced:
to make Y =0 and thereby eliminate the term containing the velocity vector v in equation (3), let:
thus, there are:
P＝Y-H(η)M -1 DH -1 (η)P+H(η)M -1 (τ+τ d ) (6)
and then designing a speed observer as follows:
in the formula (I), the compound is shown in the specification,
is the observed value of eta, P of the observer, K 1 、K 2 A matrix is designed for the gain of the signal,
is the observation error of the observer.
To prove the effectiveness of the designed speed vector observer, the observation error of the observer is defined as:
in the formula (I), the compound is shown in the specification,
in order to observe the error of the observer,
is the position error of the observer observations.
Defining the Lyapunov function:
in the formula, x 1 、x 2 The matrix is designed for positive definite. The derivation is carried out on the formula (9) and is obtained from the formula (8):
and order:
x 1 J(ψ)H -1 (η)＝x 2 K 2 (11)
then there are:
as defined by Lyapunov's theorem, the observer shown in equation (7) converges asymptotically.
On the basis of designing a speed observer, designing a disturbance observer for an unknown disturbance part, and carrying out online estimation on disturbance in the surge and heading directions according to the formula (6):
in the formula (I), the compound is shown in the specification,
for a disturbance observer, carrying out unknown disturbance tau on unmodeled parts and inside and outside of the system d Observed value of, K 0 ∈R 3×3 Is a design matrix composed of positive definite parameters.
In the actual situation where the temperature is too high,
failure to pass the observed value
Directly obtaining, and thus introducing, auxiliary variables
And then designing a disturbance observer as follows:
in the formula, unknown disturbance tau is generated for the disturbance observer to the unmodeled part and the inside and outside of the system d Observed value of, K 0 ∈R 3×3 Is a design matrix composed of positive definite parameters.
To prove the effectiveness of the designed moment disturbance observer, a Lyapunov function is defined:
in the formula (I), the compound is shown in the specification,
τ d is the true value of the disturbance of the system,
an error is estimated for the parameter data.
The derivation of equation (15) can be:
from this, the observation error of the disturbance observer expressed by the equation (14) can be known
Converging progressively to zero in a finite time.
Further, the step S3 specifically includes:
and designing a virtual control law of longitudinal speed and transverse speed based on the real-time position error. First, the error between the actual position and the desired trajectory position is defined as:
in the formula, x d As the abscissa, y, of the desired trajectory d Is the ordinate of the desired trajectory, x is the abscissa of the actual tracking position, and y is the ordinate of the actual tracking position.
And (3) solving a first derivative of the formula (17), and combining the unmanned submersible vehicle kinematics and the dynamic model formula (1) to obtain:
in order to make the position tracking error converge to zero, a vertical virtual control law a is designed ud And a horizontal virtual rate a vd Comprises the following steps:
in the formula (I), the compound is shown in the specification,
wherein k > 0,c > 0 is a design constant.
To prevent the output of the virtual control from exceeding the maximum value of the torque which can be provided by the propeller of the unmanned underwater vehicle and solve the problem that the output of the virtual control exceeds the maximum value of the torque which can be provided by the propeller of the unmanned underwater vehicleIn the process of solving the actual control law, the high-order derivation of the virtual control law is required to generate the problem of increased calculation complexity, the speed and the amplitude of the virtual control law are limited by using an instruction filter, and the longitudinal virtual control law a is required to be solved ud And a horizontal virtual rate a vd As input to the command filter, the output of the command filter
And
and the method is used for solving the actual control law.
Definition of instruction filter:
in order to solve the problem of complexity expansion of differentiation which is possibly generated by derivation of the virtual control law when the actual control law is obtained, reduce the workload of reverse calculation and prevent the control law from being invalid due to input saturation, the amplitude and the speed of the virtual control law are limited; the instruction filter can also handle constraints of intermediate state variables, as compared to a first order filter. Therefore, the command filter is introduced to process the virtual control law.
The state space expression for the instruction filter is defined as:
in the formula, x id As input to the filter, z 1 For the output of this filter, ζ and ω are the damping and bandwidth, respectively, of the instruction filter. When the effect of amplitude and velocity is not taken into account, x id And z 1 The linear relationship between them is:
when inputting x id When bounded, then z is output 1 、
Is also bounded, and in the case where ω is large, | z 1 -x id I tends to zero.
To prove the effectiveness of the virtual control law, a Lyapunov function is defined:
derived from formula (19):
substituting equation (22) into equation (18) has:
when (u-a) ud ) And (v-a) vd ) Towards 0:
the derivation of equation (22) in combination with equation (25) yields:
from this, it can be seen that the virtual control law shown in equation (19) can control the position error x e 、y e Asymptotically converging to zero. The virtual control law may also be considered a speed expectation for the unmanned vehicle to reach the target position.
Further, the step S4 specifically includes:
designing a longitudinal thrust control law and a transverse thrust control law; firstly, designing a longitudinal thrust control law, and setting an error u between a longitudinal speed and an expected longitudinal speed e Comprises the following steps:
in the formula (I), the compound is shown in the specification,
for the observation of the longitudinal velocity u by the velocity observer, a ud Is a virtual control law of longitudinal speed.
Designing integral slip-form surface s for longitudinal speed error 1 ：
In the formula, mu 1 > 0 is a constant.
In order to further obtain the longitudinal thrust control law, the derivation is carried out on the formula (28) and the formula (1) is combined to obtain:
in the formula (I), the compound is shown in the specification,
is an estimate of the observer's velocity vector u, v, r, τ u Is the actual control law of the longitudinal thrust,
for virtual control law a ud Output value, m, through instruction filter 11 、m 22 、d 11 The coefficients in the inertia matrix M and the damping matrix D of the additional mass in equation (1) are shown, respectively.
Further, the longitudinal thrust control law τ is obtained from the equations (29) and (14) u Comprises the following steps:
in the formula, λ 1 ＞0；
Is the observed compensation value of the interference observer to the longitudinal disturbance in the equation (7).
Law of longitudinal thrust control designed to demonstrate u Defining the Lyapunov function:
the derivation is obtained by the derivation of equation (31) and the substitution of equations (29) and (30):
since when t → ∞ is reached,
therefore, the following are provided:
thus signal s 1 The agreement is eventually bounded.
Secondly, designing a transverse thrust control law, and setting the error between the transverse speed and the expected transverse speed as follows:
because the power system of the unmanned underwater vehicle is an under-actuated system and has no thrust output in the transverse direction, the steering torque tau is required r The following linear sliding mode surfaces are designed:
in the formula, mu 2 > 0 is a constant.
To further determine the lateral thrust control law, equation (35) is derived with respect to time:
in the formula (I), the compound is shown in the specification,
for virtual control law a vd A first derivative output value that passes through the instruction filter,
for virtual control law a vd The second derivative output value of the instruction filter. Also, in combination with formula (1):
in the formula, τ r Is the actual control law of the transverse direction moment. Combining formula (37) with formula (1), formula (36) can be expressed as:
from formula (38) in combination with formula (14):
in the formula, λ 2 ＞0；
And (4) compensating the observed lateral disturbance value for the disturbance observer.
To demonstrate the designed transverse direction moment control law tau r Defining the Lyapunov function:
the derivation of equation (40) and the substitution of equations (38) and (39) yields:
since when t → ∞ is reached,
therefore, there are:
thus signal s 2 The agreement is eventually bounded.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention fully considers the problems that in the recovery process of the unmanned underwater vehicle after the underwater task is finished, the speed sensor is possibly influenced by pressure and a humid environment to cause the reduction of observation precision, and the reduction of control precision of a control law is caused, even the control law is invalid, and specially designs the speed observer based on the position vector. The control effect is not influenced by pressure intensity and a moist environment.
2. The influence of internal and external disturbance of the system and part of disturbance which is not modeled on the system on the laying and recovery process of the unmanned underwater vehicle is fully considered, a disturbance observer of longitudinal moment and transverse moment is designed based on a speed observer model, and the control law is compensated based on the observation value of the disturbance observer in actual control.
3. In consideration of the performance of the unmanned underwater vehicle driver, the expected output of the control law is limited by the command filter, compared with the prior art, the control law designed by the invention takes longer time for tracking the expected track, but the control law is advantageous in that the control law is prevented from failing because the output torque exceeds the maximum output performance of the driver.
Drawings
In order to more clearly illustrate the technical solutions of the prior art and the embodiments of the present invention, the drawings used in the description of the prior art and the embodiments will be briefly introduced below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a system block diagram of the present invention;
FIG. 2 is a schematic diagram of kinematics and dynamics modeling of the unmanned underwater vehicle in the invention;
FIG. 3 is a schematic diagram of the trajectory tracking effect of the present invention;
FIG. 4 is a graph comparing the expected longitudinal position response to the actual longitudinal position response of the present invention;
FIG. 5 is a graph comparing the expected longitudinal position response to the actual longitudinal position response of the present invention;
FIG. 6 is a comparison of the observed value of longitudinal velocity and the actual value of longitudinal velocity by the observer according to the present invention;
FIG. 7 is a comparison of the observed value of the lateral velocity and the actual value of the lateral velocity by the observer of the present invention;
FIG. 8 is a comparison graph of the observed value of the heading angular velocity and the actual value of the heading angular velocity by the observer according to the present invention;
FIG. 9 is a graph of the variation of the vertical virtual control law according to the present invention;
FIG. 10 is a graph of the variation of the horizontal virtual control law of the present invention;
FIG. 11 is a graph of the change in longitudinal speed control law input according to the present invention;
FIG. 12 is a lateral velocity control law input profile according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the present invention provides a track following control method for an unmanned underwater vehicle considering the failure of a speed sensor, comprising the following steps:
s1, establishing a water surface navigation mathematical model of the unmanned underwater vehicle, and setting an expected track mathematical model.
S2, designing a speed vector observer based on the position signal, designing a disturbance observer in the longitudinal moment and transverse moment directions on the basis, and verifying the validity of the disturbance observer through Lyapunov theorem.
And S3, designing a virtual control law of longitudinal speed and transverse speed based on the real-time position error, introducing an instruction filter to constrain the amplitude and the speed of the virtual control law on the basis of the virtual control law, solving the problem that the calculation complexity is increased due to the fact that high-order derivation needs to be carried out on the virtual control law when the actual control law is solved, and verifying the effectiveness of the virtual control law through the Lyapunov theorem.
And S4, designing a track tracking sliding mode controller of the unmanned underwater vehicle based on the virtual control law and the output value of the instruction filter, compensating the disturbance of the longitudinal moment and the transverse moment based on the system disturbance estimation value observed by the disturbance observer, and verifying the effectiveness of the track tracking sliding mode controller through Lyapunov theorem.
And S5, verifying the effectiveness of the proposed method through simulation.
The step S1 specifically includes:
respectively defining a northeast coordinate system OXYZ and an attached coordinate system O B X B Y B Z B And two coordinate systems, wherein a northeast coordinate system XOY is set as an inertial coordinate system, an arbitrary point O on the earth is taken as an origin of the coordinate system, OX points to the true north, OY points to the true east, and OZ is vertical to the plane where OX and OY are located and faces downwards. Will enclose body coordinate system O B X B Y B Z B As an inertial coordinate system, assuming that the unmanned underwater vehicle body is symmetrical left and right, the central point is taken as the origin O of the inertial coordinate system B ，O B X B The shaft points to the boat bow direction along the boat body, O B Y B Directed vertically to starboard, O B Z B Perpendicular to the hull and down. The dynamics modeling is carried out on the unmanned underwater vehicle in the water surface navigation process, and a six-degree-of-freedom model comprising surging (surge), swaying (sway), heaving (heave), rolling (roll), pitching (pitch) and yawing (yaw) is obtained and is shown in fig. 2. Neglecting hydrodynamic resistance terms higher than the second order and heave (yaw), pitch (pitch) and roll (roll) motions, and establishing a kinematic and dynamic model as follows:
in the formula, eta = [ x, y, psi =] T X, y represents the unmanned vehicle motion position vector, psi ∈ [0,2 pi]Representing the heading angle, J (ψ) is a conversion matrix of the northeast coordinate system and the satellite coordinate system, v = [ u, v, r] T The velocity vector of the motion of the unmanned underwater vehicle in the attached coordinate system is represented, and u, v and r respectively represent surging, swaying and yawing velocities.
Representing an inertial matrix containing additional masses, C (v) representing a diagonally symmetric matrix,
represents a damping matrix, τ = [ τ ] u ,τ v ,τ r ] T Representing moment control input vector, τ u 、τ v 、τ r Respectively representing the control forces of surge, sway and yaw, tau d ＝[τ du ,τ dv ,τ dr ] T System disturbance torque vector, τ du 、τ dv 、τ dr Representing the disturbance moments in the surging, swaying, and yawing directions, respectively.
The step S2 specifically includes:
firstly, designing a speed vector observer based on a position signal, eliminating a C (v) v term with a speed vector v in a model because the speed vector v cannot be measured, and introducing a variable matrix P (eta, v):
P(η,v)＝H(η)v (2)
in the formula, H (eta) 3×3 Is a mapping matrix of velocity vectors v to P (η, v).
The derivation of equation (2) yields:
to eliminate the term with velocity vector v in equation (3), the variable Y is introduced:
to make Y =0 and thereby eliminate the term containing the velocity vector v in equation (3), let:
thus, there are:
P＝Y-H(η)M -1 DH -1 (η)P+H(η)M -1 (τ+τ d ) (6)
and then designing a speed observer as follows:
in the formula (I), the compound is shown in the specification,
is the observed value of eta, P of the observer, K 1 、K 2 A matrix is designed for the gain of the signal,
is the observation error of the observer.
To prove the effectiveness of the designed speed vector observer, the observation error of the observer is defined as:
in the formula (I), the compound is shown in the specification,
in order to observe the error of the observer,
is the position error of the observer observations.
Defining the Lyapunov function:
in the formula, x 1 、x 2 The matrix is designed for positive definite. The derivation is carried out on the formula (9) and is obtained from the formula (8):
and let:
x 1 J(ψ)H -1 (η)＝x 2 K 2 (11)
then there are:
as defined by Lyapunov's theorem, the observer shown in equation (7) converges asymptotically.
On the basis of designing a speed observer, designing a disturbance observer for an unknown disturbance part, and carrying out online estimation on disturbance in the surge and heading directions according to the formula (6):
in the formula (I), the compound is shown in the specification,
for a disturbance observer, carrying out unknown disturbance tau on unmodeled parts and inside and outside of the system d Observed value of, K 0 ∈R 3×3 Is a design matrix composed of positive definite parameters.
In the actual situation where the temperature is too high,
failure to pass the observed value
Directly obtained, thus introducing auxiliary variables
And then designing a disturbance observer as follows:
in the formula, unknown disturbance tau is generated for the disturbance observer to the unmodeled part and the inside and outside of the system d Observed value of, K 0 ∈R 3×3 Is a design matrix composed of positive definite parameters.
To prove the effectiveness of the designed moment disturbance observer, a Lyapunov function is defined:
in the formula (I), the compound is shown in the specification,
τ d is the true value of the disturbance of the system,
an error is estimated for the parameter data.
The derivation of equation (15) can be:
from this, the observation error of the disturbance observer expressed by the equation (14) can be known
Converging progressively to zero in a finite time.
The step S3 specifically includes:
and designing a virtual control law of longitudinal speed and transverse speed based on the real-time position error. First, the error between the actual position and the desired trajectory position is defined as:
in the formula, x d As the abscissa, y, of the desired trajectory d X is the abscissa of the actual tracking position, and y is the ordinate of the actual tracking position.
And (3) solving a first derivative of the formula (17), and combining the unmanned submersible vehicle kinematics and the dynamic model formula (1) to obtain:
in order to make the position tracking error converge to zero, a vertical virtual control law a is designed ud And a horizontal virtual rate a vd Comprises the following steps:
in the formula (I), the compound is shown in the specification,
whereinK > 0,c > 0 is a design constant.
In order to prevent the output of virtual control from exceeding the maximum value of the moment provided by the propeller of the unmanned underwater vehicle and solve the problem that the high-order derivation of the virtual control law is required in the process of solving the actual control law so as to increase the calculation complexity, an instruction filter is used for limiting the speed and the amplitude of the virtual control law, and a longitudinal virtual control law a is required to be limited ud And a horizontal virtual rate a vd As input to the command filter, the output of the command filter
And
and the method is used for solving the actual control law.
Definition of instruction filter:
in order to solve the problem of complexity expansion of differentiation which is possibly generated by derivation of the virtual control law when the actual control law is obtained, reduce the workload of reverse calculation and prevent the problem of control law failure caused by input saturation, the amplitude and the speed of the virtual control law are limited; the instruction filter can also handle constraints of intermediate state variables, as compared to a first order filter. Therefore, the command filter is introduced to process the virtual control law.
The state space expression for the instruction filter is defined as:
in the formula, x id Is the input of the filter, z 1 For the output of this filter, ζ and ω are the damping and bandwidth, respectively, of the instruction filter. When the effect of amplitude and velocity is not taken into account, x id And z 1 The linear relationship between them is:
when inputting x id When bounded, then z is output 1 、
Is also bounded, and in the case where ω is large, | z 1 -x id I tends to zero.
To prove the effectiveness of the virtual control law, a Lyapunov function is defined:
obtained by the formula (19):
substituting equation (22) into equation (18) has:
when (u-a) ud ) And (v-a) vd ) When the ratio is close to 0:
the derivation of equation (22) in combination with equation (25) yields:
from this, it can be seen that the virtual control law shown in equation (19) can control the position error x e 、y e Asymptotically converging to zero. The virtual control law may also be considered a speed expectation for the unmanned vehicle to reach the target position.
The step S4 specifically includes:
design longitudinal thrust controlLaw and lateral thrust control law; firstly, designing a longitudinal thrust control law, and setting an error u between a longitudinal speed and an expected longitudinal speed e Comprises the following steps:
in the formula (I), the compound is shown in the specification,
for the observation of the longitudinal velocity u by the velocity observer, a ud Is a virtual control law of longitudinal speed.
Designing integral slip-form surface s for longitudinal speed error 1 ：
In the formula, mu 1 > 0 is a constant.
In order to further obtain the longitudinal thrust control law, the derivation is carried out on the formula (28) and the formula (1) is combined to obtain:
in the formula (I), the compound is shown in the specification,
is an estimate of the observer's velocity vector u, v, r, τ u Is the actual control law of the longitudinal thrust,
for the virtual control law a ud Output value, m, through instruction filter 11 、m 22 、d 11 The coefficients in the inertia matrix M and the damping matrix D of the additional mass in equation (1) are shown, respectively.
Further, the longitudinal thrust control law τ is obtained from the equations (29) and (14) u Comprises the following steps:
in the formula, λ 1 ＞0；
Is the observed compensation value of the interference observer to the longitudinal disturbance in the formula (7).
Designed to demonstrate longitudinal thrust control law τ u Defining the Lyapunov function:
the derivation of equation (31) and the substitution of equations (29) and (30) yields:
since when t → ∞ is reached,
therefore, the following are provided:
thus signal s 1 The agreement is eventually bounded.
Secondly, designing a transverse thrust control law, and setting the error between the transverse speed and the expected transverse speed as follows:
because the power system of the unmanned underwater vehicle is an under-actuated system and has no thrust output in the transverse direction, the steering torque tau is required r The following linear sliding mode surfaces are designed:
in the formula, mu 2 0 is a constant.
To further determine the lateral thrust control law, equation (35) is derived over time:
in the formula (I), the compound is shown in the specification,
for virtual control law a vd A first derivative output value that passes through the instruction filter,
for virtual control law a vd The second derivative output value of the instruction filter. Also, in combination with formula (1):
in the formula, τ r Is the actual control law of the transverse direction moment. Combining formula (37) with formula (1), formula (36) can be expressed as:
from formula (38) in combination with formula (14):
in the formula of lambda 2 ＞0；
Compensating values for the observation of lateral disturbances by a disturbance observer。
To demonstrate the designed transverse direction moment control law tau r Defining the Lyapunov function:
the derivation of equation (40) and the substitution of equations (38) and (39) yields:
since when t → ∞ is satisfied,
therefore, there are:
thus signal s 2 The agreement is eventually bounded.
In the step S5, simulation verification is performed on the trajectory tracking control in the unmanned underwater vehicle deployment and recovery process, and the validity of the verification method specifically includes:
the reference trajectory is defined as follows:
setting longitudinal and transverse unmodeled parts and external disturbance tau in the system du And τ dr Comprises the following steps:
setting the kinetic equation M, C and D matrix of the unmanned underwater vehicle as follows:
simulation related parameter mu 1 ＝1，μ 2 ＝0.02，λ 1 ＝1，λ 2 ＝1，ζ 1 ＝0.9，ζ 2 ＝0.9，ω 1 ＝20rad/s，ω 2 =20rad/s, design matrix K 0 、K 1 、K 2 Setting as follows:
K 0 ＝[2,0,2] T ,
unmanned underwater vehicle initial position [ x (0), y (0), psi (0)] T ＝[0m,0m,0.5rad] T Initial state [ u (0), v (0), r (0)] T ＝[3m/s,0m/s,0rad/s] T 。
The result of the expected track tracking path and the actual track tracking path pair shown in fig. 3 shows that the control method provided by the invention can well enable the unmanned underwater vehicle to run on the expected path, and keep a stable state all the time, and has good performance.
The unmanned underwater vehicle position tracking variation curves are shown in fig. 4-5, and at 83s, the longitudinal position tracks the upper expected path, and at 189s, the transverse position tracks the upper expected path.
The observed values of the observer on the states of the unmanned underwater vehicle are shown in fig. 6-8, which shows that the velocity vector can be observed quickly and accurately.
The outputs of the horizontal and vertical virtual control laws are shown in fig. 9-10, and the outputs of the vertical and horizontal actual control laws are shown in fig. 11-12, so that it can be seen that the control law curve is smooth and has good robustness.
As can be seen from the variation curves of the vertical and horizontal actual control laws shown in fig. 9-10, there is a strong chattering phenomenon in the interval of 80s-120s, and it can be seen from the combination of equations (30) and (39) and fig. 9-10 that the chattering phenomenon is caused by the strong chattering in the interval of 80s-120s in the virtual control law. The derivation process of the virtual control law combining the formula (17) and the formula (19) can be seen that the essence of the virtual control law is that the unmanned underwater vehicle essentially represents the slave unmanned underwater vehicleThe expected values of the longitudinal speed and the lateral speed in the process from the current actual position to the desired position, and therefore the virtual control law is highly correlated with the current longitudinal and lateral actual positions and the desired longitudinal and lateral positions, in other words, the essential cause of the jitter of the virtual control law is the error value between the actual position and the desired track position shown in equation (17). It can be seen from the relationship between the longitudinal position and the transverse position shown in fig. 4-5 that at the 80 th s, the actual longitudinal position coincides with the desired longitudinal position, but the system is not completely stable at this time, because the actual transverse position does not coincide with the desired transverse position, during which the transverse actual control law is always active, and the magnitude of the transverse velocity is continuously adjusted, but since the unmanned vehicle is an under-actuated system, the longitudinal velocity is affected by the transverse velocity component, and then the longitudinal thrust control law must be affected by the component from the transverse velocity, and the longitudinal thrust control law is designed based on the integral surface of the velocity difference, so that the longitudinal thrust control law switches back and forth near the sliding surface to keep stable, resulting in the buffeting of the output of the longitudinal control law shown in fig. 11. As can be seen in connection with fig. 4 and 6, the longitudinal thrust control law, by switching back and forth near the sliding mode face, ensures that the longitudinal actual position tracks the upper longitudinal desired position exactly from 83 seconds and is not deflected by the influence of the transverse thrust. Similarly, for the lateral thrust control law, before the 80s moment, because the longitudinal speed is not constrained, the lateral thrust control law can freely control and adjust the lateral speed of the unmanned underwater vehicle, so that the lateral actual position of the unmanned underwater vehicle tracks the expected actual position, but after the 80s moment, because the longitudinal speed is constrained by the longitudinal thrust control law and the unmanned underwater vehicle is an under-actuated system, the change of the lateral speed is necessarily influenced by the longitudinal speed component, which partially influences the interference in the switching process of the longitudinal control law near the sliding mode surface, because after the 80s moment, the longitudinal thrust control law ensures the longitudinal tracking effect in the form of buffeting, which partially influences the lateral speed in the form of buffeting, and in the 80s-120s process, the lateral thrust control law is the same as in the process of confirming that the actual lateral position reaches the expected lateral positionWhen the actual transverse position is tracked in the process of the expected transverse position, the output of the transverse thrust control law is gradually reduced, the influence on the longitudinal speed is also reduced, and therefore the buffeting of the transverse thrust control law and the buffeting of the longitudinal thrust control law are synchronously gradually reduced until y in the formula (17) e =0, v in formula (34) e =0, and further s in formula (35) 2 And =0, the buffeting in the transverse control law when the whole system reaches a stable state completely disappears.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (1)
1. An unmanned underwater vehicle track tracking control method considering speed sensor failure is characterized by comprising the following steps:
s1, establishing a water surface navigation mathematical model of the unmanned underwater vehicle, and setting an expected track mathematical model;
s2, designing a speed vector observer based on the position signal, designing a disturbance observer in the longitudinal moment and transverse moment directions on the basis, and verifying the validity of the disturbance observer through Lyapunov theorem;
s3, designing a virtual control law of longitudinal speed and transverse speed based on the real-time position error, introducing an instruction filter to constrain the amplitude and speed of the virtual control law on the basis of the virtual control law, solving the problem that the high-order derivation needs to be carried out on the virtual control law when the actual control law is solved to increase the computational complexity, and verifying the effectiveness of the virtual control law through Lyapunov theorem;
s4, designing a track tracking sliding mode controller of the unmanned underwater vehicle based on the virtual control law and the output value of the instruction filter, compensating disturbance of longitudinal moment and transverse moment based on a system disturbance estimation value observed by a disturbance observer, and verifying effectiveness of the track tracking sliding mode controller through Lyapunov theorem;
s5, verifying the effectiveness of the proposed method through simulation;
in S1, establishing a kinematics and dynamics model comprises the following steps:
in the formula, eta = [ x, y, psi =] T X, y represents the unmanned vehicle motion position vector, psi ∈ [0,2 pi]Representing the heading angle, J (ψ) is a conversion matrix of the northeast coordinate system and the satellite coordinate system, v = [ u, v, r] T Representing the motion velocity vector of the unmanned underwater vehicle in an attached coordinate system, wherein u, v and r respectively represent surging, swaying and yawing velocities;
representing an inertial matrix containing additional masses, C (v) representing a diagonally symmetric matrix,
denotes a damping matrix, τ = [ ] u ,τ v ,τ r ] T Representing moment control input vector, τ u 、τ v 、τ r Respectively representing the control forces of surge, sway and yaw, tau d ＝[τ du ,τ dv ,τ dr ] T System disturbance torque vector, τ du 、τ dv 、τ dr Respectively representing disturbance moments in the surge, sway and bow directions;
in S2, a velocity vector observer based on a position signal is designed first, and since the velocity vector v is not measurable, the C (v) v term with the velocity vector v in the model is eliminated, and a variable matrix P (η, v) is introduced:
P(η,v)＝H(η)v (2)
in the formula, H (eta) 3×3 Is a mapping matrix of velocity vectors v to P (eta, v);
the derivation of equation (2) yields:
to eliminate the term with velocity vector v in equation (3), the variable Y is introduced:
thus, there are:
P＝Y-H(η)M -1 DH -1 (η)P+H(η)M -1 (τ+τ d ) (5)
and then designing a speed observer as follows:
in the formula (I), the compound is shown in the specification,
is the observed value of eta, P of the observer, K 1 、K 2 A matrix is designed for the gain of the signal,
is the observation error of the observer;
on the basis of designing a speed observer, designing a disturbance observer for an unknown disturbance part, and carrying out online estimation on disturbance in the surge and heading directions according to the formula (5):
in the formula (I), the compound is shown in the specification,
for a disturbance observer, carrying out unknown disturbance tau on unmodeled parts and inside and outside of the system d Observed value of, K 0 ∈R 3×3 A design matrix consisting of positive definite parameters;
in the actual situation where the temperature is too high,
failure to pass the observed value
Directly obtained, thus introducing auxiliary variables
And then designing a disturbance observer as follows:
in the formula (I), the compound is shown in the specification,
for a disturbance observer, carrying out unknown disturbance tau on unmodeled parts and inside and outside of the system d Observed value of, K 0 ∈R 3×3 A design matrix consisting of positive definite parameters;
in the S3, a virtual control law of longitudinal speed and transverse speed is designed based on the real-time position error; first, the error between the actual position and the desired trajectory position is defined as:
in the formula, x d As the abscissa, y, of the desired trajectory d Is the ordinate of the expected track, x is the abscissa of the actual tracking position, and y is the ordinate of the actual tracking position;
and (3) obtaining a derivative of the formula (9) by combining the unmanned submersible vehicle kinematics and the dynamic model formula (1):
in order to make the position tracking error converge to zero, a vertical virtual control law a is designed ud And a horizontal virtual rate a vd Comprises the following steps:
in the formula (I), the compound is shown in the specification,
wherein k is more than 0,c is more than 0 and is a design constant;
in order to prevent the output of virtual control from exceeding the maximum value of the moment provided by the propeller of the unmanned underwater vehicle and solve the problem that the high-order derivation of the virtual control law is required in the process of solving the actual control law so as to increase the calculation complexity, an instruction filter is used for limiting the speed and the amplitude of the virtual control law, and a longitudinal virtual control law a is required to be limited ud And a horizontal virtual rate a vd As input to the command filter, the output of the command filter
And
the method is used for solving the actual control law;
in S4, a longitudinal thrust control law and a transverse thrust control law are designed; firstly, designing a longitudinal thrust control law, and setting an error u between a longitudinal speed and an expected longitudinal speed e Comprises the following steps:
in the formula (I), the compound is shown in the specification,
for the observation of the longitudinal velocity u by the velocity observer, a ud A virtual control law for longitudinal velocity;
designing integral slip-form surface s for longitudinal speed error 1 ：
In the formula, mu 1 0 is a constant;
in order to further obtain the longitudinal thrust control law, the derivation is carried out on the formula (13) and the formula (1) is combined to obtain:
in the formula (I), the compound is shown in the specification,
is an estimate of the observer's velocity vector u, v, r, τ u Is the actual control law of the longitudinal thrust,
for virtual control law a ud Output value, m, through instruction filter 11 、m 22 、d 11 Coefficients in an inertia matrix M and a damping matrix D of the additional mass in the formula (1) respectively;
further, the longitudinal thrust control law τ is obtained from the equations (14) and (8) u Comprises the following steps:
in the formula, λ 1 ＞0；
Is an observed compensation value of the interference observer in the formula (8) to longitudinal disturbance;
secondly, designing a transverse thrust control law, and setting an error v between the transverse speed and the expected transverse speed e Comprises the following steps:
in the formula (I), the compound is shown in the specification,
for the observation of the lateral velocity v by the velocity observer, a vd A virtual control law for lateral velocity;
because the power system of the unmanned underwater vehicle is an under-actuated system and has no thrust output in the transverse direction, the steering torque tau is required r Design the following linear sliding form surface s 2 ：
In the formula, mu 2 > 0 is a constant;
to further determine the lateral thrust control law, equation (17) is derived with respect to time:
in the formula (I), the compound is shown in the specification,
for virtual control law a vd A first derivative output value that passes through the instruction filter,
for virtual control law a vd Passing through a second derivative output value of the instruction filter; also, in combination with formula (1):
in the formula (I), the compound is shown in the specification,
is an estimate of the observer's velocity u, v, r, τ r Is the actual control law of the moment in the transverse direction, m 11 、m 22 、m 33 、d 22 、d 33 Coefficients in an inertia matrix M and a damping matrix D of the additional mass in the formula (1) respectively; combining formula (19) with formula (1), formula (18) can be represented as:
law of transverse thrust control τ obtained by combining equation (20) with equation (8) r Comprises the following steps:
in the formula, λ 2 ＞0；
Is the observed compensation value of the interference observer to the lateral disturbance in the formula (8).
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