CN113835338B - Finite time tracking control method and device for under-actuated unmanned ship with integral sliding mode - Google Patents
Finite time tracking control method and device for under-actuated unmanned ship with integral sliding mode Download PDFInfo
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Abstract
An under-actuated unmanned ship finite time tracking control method and device based on an integral sliding mode belong to the technical field of unmanned ship track tracking control. The traditional back-step design of the existing under-actuated unmanned ship is too complex, and the traditional PID control is difficult to effectively control ship tracking. The tracking control method comprises the steps of establishing a high-order under-actuated unmanned ship dynamics model obtained based on unmanned ship model conversion; according to the high-order under-actuated unmanned ship dynamics model, a finite time integral sliding mode controller is designed; and designing a finite time tracking controller and a self-adaptive law to eliminate external interference uncertainty according to the high-order under-actuated unmanned ship dynamics model and the finite time integral sliding mode controller. Compared with the prior art, the method has the beneficial effects that the back-step design is avoided, and the calculated amount is effectively reduced; the designed integral sliding mode controller still has good tracking precision and quick response capability under the conditions of external interference and the like.
Description
Technical Field
The invention relates to a finite time control method of an under-actuated unmanned ship, and belongs to the technical field of unmanned ship track tracking control.
Background
Along with the development of society, the exploration requirement of human beings on sea is continuously improved, the operation requirement of complex dangerous sea areas is faced, the tracking control algorithm of the under-actuated unmanned ship becomes the main research direction of the academic world, and compared with the full-actuated unmanned ship, the under-actuated system has the outstanding advantages of high speed, high adaptability and low cost, so that the research on the tracking control problem of the unmanned ship has extremely high practical significance.
However, the model uncertainty problem and external disturbances associated with increasingly complex operating environments make the controller design of an under-actuated system a difficult task. Because the key to the completion rate of an under-actuated unmanned boat mission is the high accuracy and fast response characteristics of its control system, the design of high performance under-actuated tracking controllers still faces many challenges. On the one hand, obvious nonlinearities exist in the kinematics and dynamics models of the under-actuated unmanned ship, so that the traditional linear control algorithm cannot effectively solve the problem of stabilizing control, and the traditional backstepping design is too complex. On the other hand, because the ship is in a complex marine environment, the ship is time-varying and is not known to be interfered by the outside during movement, and an accurate mathematical model is difficult to obtain, so that the traditional PID control is difficult to effectively control the ship tracking. Therefore, in order to ensure that the under-actuated unmanned ship still has good tracking precision and quick response capability under the conditions of uncertain model, external interference and the like, the track tracking control algorithm is particularly important.
Disclosure of Invention
The invention aims to solve the problems that the traditional back-step design steps in the kinematics and dynamics model of the under-actuated unmanned ship are too complex and the traditional PID control is difficult to effectively control ship tracking.
The method for controlling the finite time tracking of the underactuated unmanned ship based on the integral sliding mode comprises the following steps:
(1) Establishing a high-order under-actuated unmanned ship dynamics model obtained based on unmanned ship model conversion;
(2) According to the high-order under-actuated unmanned ship dynamics model, a finite time integral sliding mode controller is designed;
(3) And designing a finite time tracking controller and a self-adaptive law to eliminate external interference uncertainty according to the high-order under-actuated unmanned ship dynamics model and the finite time integral sliding mode controller.
Further, the finite time tracking control method of the under-actuated unmanned aerial vehicle based on the integral sliding mode is characterized in that the establishing of the high-order under-actuated unmanned aerial vehicle dynamics model based on model conversion is as follows:
，
wherein,；/>representing the position of the unmanned ship under the geocentric coordinate system,/->Representing yaw angle;，/>representing the relevant linear velocity in the body coordinate system, is->Represents angular velocity; />Is the inertial matrix of the system; />Representing a kinetic characteristic function>Representing a kinetic characteristic function; />For control input +.>Is an environmental disturbance.
Further, the error vector equation of the high-order under-actuated unmanned ship dynamics model is as follows:
，
wherein,representing errors, which are specifically defined as +.>，/>Representing an error variable; />Representing the third derivative of the error; />Representing a kinetic characteristic matrix of the transformation model; />A model force coefficient matrix representing the transformation model; />A control input representing a transformation model, which is defined as +.>，/>Representing the thrust rate of change; />Representing a control torque input; />Represents the external disturbance of the transformation model, which is defined as +.>Wherein->Representing the rate of change of the component of the external disturbance in the heave degrees of freedom, +.>An external disturbance moment expressed in the degree of freedom of bow and satisfying，/>，/>。
Further, the error variable in the error vector equation of the high-order under-actuated unmanned ship dynamics model is defined as:
，
wherein,representing a reference desired trajectory of the under-actuated unmanned boat.
Further, the finite time integral sliding mode controller designed according to the high-order under-actuated unmanned ship dynamics model is:
wherein,control parameters which are positive and satisfy +.>，/>An upper bound value representing an interference norm; />A transpose representing the transformation model properties; />、/>、/>All represent control parameters; />Representing the error; />Representing the error first derivative; />Representing the second derivative of the error; />、/>、/>All representing control parameters.
Further, the integral sliding mode in the limited time integral sliding mode controller is as follows
，
Wherein the method comprises the steps of，/>，/>，/>Control parameters for the design, and control parameters +.>Satisfy->。
Further, the designing a finite time tracking controller and designing an adaptive law to eliminate external interference uncertainty according to the high-order under-actuated unmanned ship dynamics model and the finite time integral sliding mode controller comprises the following steps:
the finite time tracking controller is:
the self-adaptive law is as follows:
wherein the method comprises the steps of,/>,/>,/>Is positive control parameter, < >>Representation of transformationAn inverse matrix of model dynamics; />Representing an estimate of the external disturbance, +.>Representing the sliding mode variable.
The invention provides a finite time tracking control device of an underactuated unmanned ship based on an integral sliding mode, which comprises the following components: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including instructions for performing a data-driven based unmanned aerial vehicle sensor fault detection method as set forth in any of the preceding claims.
The invention provides a computer device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the finite time tracking control method of the under-actuated unmanned aerial vehicle based on the integral sliding mode.
The present invention provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of a method as any one of the above.
The invention has the beneficial effects that:
the invention solves the problems that the traditional back-step design steps in the kinematics and dynamics model of the under-actuated unmanned ship are too complex and the traditional PID control is difficult to effectively control ship tracking.
The invention replaces a great number of complex steps of back-step design by mathematical operation, thereby saving time cost; the finite time tracking controller of the underactuated unmanned ship based on the integral sliding mode is designed, and the tracking response time of the ship is shorter and more accurate.
According to the invention, the ship tracking is accurately controlled by designing the finite time integral sliding mode controller and the self-adaptive rate, and the existing ship tracking technology generally can only respond within 20 seconds to track the ship; the invention can respond within 10 seconds, and realizes the tracking of the ship.
The invention shortens the response time by one time, and can more accurately acquire the real-time state of the ship.
The method and the device are suitable for the technical field of track tracking control.
Drawings
FIG. 1 is a flow chart of an integral sliding mode finite time control method;
FIG. 2 is a trace plot of an under-actuated unmanned boat;
FIG. 3 is an under-actuated unmanned boat control input diagram;
FIG. 4 is a graph of the tracking error time response of an under-actuated unmanned boat, with the left graph being the tracking error time response of the x-axis moment and the right graph being the tracking error time response of the y-axis moment;
FIG. 5 is a graph of yaw rate response;
fig. 6 is an adaptive estimation graph.
Detailed Description
Embodiment one, this embodiment will be described with reference to fig. 1, 2 and 3. The finite time tracking control method of the under-actuated unmanned ship based on the integral sliding mode of the embodiment comprises the following steps:
(1) Establishing a high-order under-actuated unmanned ship dynamics model obtained based on unmanned ship model conversion;
(2) According to the high-order under-actuated unmanned ship dynamics model, a finite time integral sliding mode controller is designed;
(3) According to the high-order under-actuated unmanned ship dynamics model and the limited time integral sliding mode controller, designing a limited time tracking controller and a self-adaptive law to eliminate external interference uncertainty;
the finite time tracking control method of the under-actuated unmanned aerial vehicle based on the integral sliding mode is characterized in that the establishment of a high-order under-actuated unmanned aerial vehicle dynamics model based on model conversion is as follows:
，
wherein,；/>representing the position of the unmanned ship under the geocentric coordinate system,/->Representing yaw angle;，/>representing the relative linear velocity in the satellite coordinate system,/->Represents angular velocity; />For controlling force input, ++>Is an external environmental disturbance. />Is a rotation matrix between the geocentric coordinate system and the satellite coordinate system. />Is the inertial matrix of the system; />And->And respectively representing a Coriolis force matrix and a hydrodynamic coefficient matrix of the unmanned ship. The definition of each matrix is as follows:
wherein,the weight force is added to the sum of the weight of the unmanned ship and the weight of each unmanned ship. />Is a coefficient of the coriolis force matrix, +.>Is the hydrodynamic coefficient.
The kinetic model was developed as follows:
the error vector equation of the high-order under-actuated unmanned ship dynamics model comprises the following error variables:
，
wherein,representing a reference desired trajectory of the under-actuated unmanned boat.
The tracking problem studied can be converted to stabilize the tracking error at the equilibrium point, so deriving the tracking error equation can be:
by definition，/>The state space equation is obtained as follows:
wherein the method comprises the steps of，/>；
Taking the singular problem into consideration, deriving the tracking error again:
by definitionThe following equation is obtained:
by defining the following auxiliary variables:
finally, a tracking error vector equation after model conversion is obtained as follows:
wherein,representing errors, which are specifically defined as +.>，/>A control input representing a transformation model, which is defined as +.>，/>Representing the thrust rate of change; />Representing a control torque input; />Represents the external disturbance of the transformation model, which is defined as +.>And satisfy->，/>，/>；
。
The finite time integral sliding mode controller designed according to the high-order under-actuated unmanned ship dynamics model comprises:
for convenience of subsequent deduction, the definition is as follows:
introduction of the quotation 1 the following formula:
,/>
wherein,,/>by means of the quotients it can be demonstrated that the Lyapunov function is +.>Can satisfy the stability therein, wherein->。
The introduction theorem 2 is of the formula:
if the system meets the above formula, the system can be stabilized in a limited time.
The integral sliding mode in the limited time integral sliding mode controller is
，
Wherein the method comprises the steps of，/>，/>，/>Control parameters for the design, and control parameters +.>Satisfy->。
The designed finite time integral sliding mode controller is as follows:
，
wherein,control parameters which are positive and satisfy +.>，/>An upper bound value representing an interference norm; />A transpose representing the transformation model properties; />、/>、/>And +.>、/>、/>All represent control parameters; />Representing the error; />Representing the error first derivative; />Representing the second derivative of the error.
Selecting a Lyapunov function:
，
taking into account that，/>The derivative of the Lyapunov function satisfies the lemen 1, thus yielding +.>The finite time converges to +.>。
The substitution returns to the slip form surface as follows:
。
according to the high-order under-actuated unmanned ship dynamics model and the limited time integral sliding mode controller, designing a limited time tracking controller and a self-adaptive law to eliminate external interference uncertainty, comprising:
the finite time tracking controller is
，
The self-adaptive law is
，
Wherein the method comprises the steps of,/>,/>,/>Is positive control parameter, < >>An inverse matrix representing the dynamics of the transformation model; />Representing an estimate of the external disturbance, +.>Representing the sliding mode variable.
Estimating error termsHas the following definitions:
；
in order to verify the stability and robustness of the integral sliding mode control of the unmanned ship, a Lyapunov function is selected:
；
deriving the above results in Lyapunov function satisfying positive and negative derivatives, i.e. provingAnd->Has consistent stability.
Upper limit value for external interferenceThere are the following definitions:
，
；
selecting a Lyapunov function:
；
it is finally demonstrated by the quotients 1 that the integrated sliding surface S with the adaptive law will converge to 0 in a finite time.
The performance of the finite time integral sliding mode controller is demonstrated and verified through a simulation example. Model parameters for the unmanned boat are shown in table 1:
TABLE 1
The initial state of the unmanned boat is set as follows:
，/>，/>，/>，，/>。
the desired trajectory instructions are as follows:
。
wherein,is time. The time-varying external interference is set as follows:
the parameters of the finite time integral sliding mode controller are shown in table 2:
TABLE 2
4-6, FIG. 4 is a tracking error time response diagram of the under-actuated unmanned ship, the left diagram is a tracking error time response diagram of the x-axis moment, and the right diagram is a tracking error time response diagram of the y-axis moment; as can be seen from fig. 4, the tracking error quickly converges to the zero point, the tracking convergence time of the present invention is about 10 seconds, and the convergence time of the prior art is about 20 seconds.
FIG. 5 is a graph of the yaw rate response, showing the convergence of the underactuated unmanned boat of the present invention over a finite period of time. Fig. 6 is a self-adaptive estimation diagram, and it can be seen that the self-adaptive value of the present invention is small, and external interference can be well eliminated.
In a second embodiment, the finite time tracking control device of an underactuated unmanned ship based on an integral sliding mode according to the second embodiment includes: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including instructions for performing a method of finite time tracking control of an under-actuated unmanned aerial vehicle based on an integral sliding mode as in any of the above embodiments.
The third embodiment is a computer device according to the present embodiment, wherein: the method comprises a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the finite time tracking control method of the underactuated unmanned ship based on the integral sliding mode.
A computer readable storage medium according to a fourth embodiment is characterized in that a computer program is stored on the computer readable storage medium, and the computer program is executed by a processor to perform the steps of the method for controlling finite time tracking of an underactuated unmanned ship based on an integral sliding mode according to any one of the above embodiments.
The foregoing examples are merely specific embodiments of the present application, and are not intended to limit the scope of the present application, but the present application is not limited thereto, and those skilled in the art will appreciate that while the foregoing examples are described in detail, the present application is not limited thereto. Any person skilled in the art may modify or easily conceive of the technical solution described in the foregoing embodiments, or make equivalent substitutions for some of the technical features within the technical scope of the disclosure of the present application; such modifications, changes or substitutions do not depart from the spirit and scope of the corresponding technical solutions. Are intended to be encompassed within the scope of this application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (8)
1. The finite time tracking control method of the underactuated unmanned ship based on the integral sliding mode is characterized by comprising the following steps of:
(1) Establishing a high-order under-actuated unmanned ship dynamics model obtained based on unmanned ship model conversion;
(2) According to the high-order under-actuated unmanned ship dynamics model, a finite time integral sliding mode controller is designed;
(3) According to the high-order under-actuated unmanned ship dynamics model and the limited time integral sliding mode controller, designing a limited time tracking controller and a self-adaptive law to eliminate external interference uncertainty;
the designed finite time integral sliding mode controller is as follows:
wherein,control parameters which are positive and satisfy +.>，/>An upper bound value representing an interference norm; />A transpose representing the transformation model properties; />、/>、/>And +.>、/>、/>All represent control parameters; />Representing the error; />Representing the error first derivative; />Representing the second derivative of the error;
the integral sliding mode in the limited time integral sliding mode controller is
，
Wherein the method comprises the steps of，/>，/>，/>Control parameters for the design, and control parameters +.>Satisfy->，/>Indicating error, & lt>Representing a kinetic characteristic matrix of the transformation model; />A model force coefficient matrix representing the transformation model; />An inverse matrix representing the dynamics of the transformation model; />Representing the sliding mode variable.
2. The finite time tracking control method of the underactuated unmanned aerial vehicle based on the integral sliding mode according to claim 1, wherein the establishing of the high-order underactuated unmanned aerial vehicle dynamics model based on model conversion is as follows:
wherein,；/>representing the position of the unmanned ship under the geocentric coordinate system,/->Representing yaw angle;，/>representing the relevant linear velocity in the body coordinate system, is->Represents angular velocity; />Is the inertial matrix of the system; />Representation ofKinetic characterization function->Representing a kinetic characteristic function; />For control input +.>Is an environmental disturbance;is a rotation matrix between the geocentric coordinate system and the satellite coordinate system.
3. The finite time tracking control method of the under-actuated unmanned aerial vehicle based on the integral sliding mode according to claim 2, wherein an error vector equation of the high-order under-actuated unmanned aerial vehicle dynamics model is as follows:
，
wherein,representing errors, which are specifically defined as +.>，/>Representing an error variable; />Representing the third derivative of the error; />A control input representing a transformation model, which is defined as +.>，/>Representing the thrust rate of change; />Representing a control torque input; />Represents the external disturbance of the transformation model, which is defined as +.>Wherein->Representing the rate of change of the component of the external disturbance in the heave degrees of freedom, +.>An external disturbance moment expressed in the degree of freedom of yaw and satisfying +.>，/>，/>。
4. The finite time tracking control method of the under-actuated unmanned aerial vehicle based on the integral sliding mode according to claim 3, wherein the error variable in the error vector equation of the high-order under-actuated unmanned aerial vehicle dynamics model is:
，
wherein,representing a reference desired trajectory of the under-actuated unmanned boat.
5. The method for controlling finite time tracking of an underactuated unmanned ship based on an integral sliding mode according to claim 1, wherein the designing a finite time tracking controller and designing an adaptive law to eliminate external interference uncertainty according to the high-order underactuated unmanned ship dynamics model and the finite time integral sliding mode controller comprises:
the finite time tracking controller is:
the self-adaptive law is as follows:
，
wherein,, />, />, />is a positive control parameter; />Representing an estimate of the external disturbance.
6. An under-actuated unmanned aerial vehicle's finite time tracking control device based on integral sliding mode includes: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the programs including instructions for performing a method of finite time tracking control of an under-actuated unmanned aerial vehicle based on an integral sliding mode as claimed in any of claims 1 to 5.
7. A computer device, characterized by: comprising a memory and a processor, the memory having stored therein a computer program, which when run by the processor performs a method of finite time tracking control of an under-actuated unmanned aerial vehicle based on an integral sliding mode as claimed in any one of claims 1 to 5.
8. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a computer program which, when executed by a processor, performs the steps of a method for finite time tracking control of an under-actuated unmanned ship based on an integral sliding mode as claimed in any one of claims 1 to 5.
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