CN106444794B - A kind of printenv drive lacking UUV vertical plane path trace sliding-mode control - Google Patents
A kind of printenv drive lacking UUV vertical plane path trace sliding-mode control Download PDFInfo
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Abstract
The present invention is to provide a kind of printenv drive lacking UUV vertical plane path trace sliding-mode controls.One, it initializes；Two, the current state of UUV is obtained；Three, drive lacking UUV level error equation is established, position deviation x is obtainede,zeAnd course deviation value θe；Four, using sliding-mode control, in the case where unknown parameters, speed of a ship or plane Sliding Mode Adaptive Control rule, position sliding formwork control ratio and Angle of Trim Sliding Mode Adaptive Control rule are separately designed, by thrust Xprop, expectation the speed of a ship or planeAnd torque MpropControl, make eu→0,xe→0,θe→0；Five, it is directed to boundary-layer design Fuzzy Control Law；K=k+1 is enabled, step 2 is jumped back to, carries out the update of control law and adaptive law next time.The present invention can be achieved to only rely on vertical plane kinetic model and design to make system quelling controller, for with probabilistic hydrodynamic parameter design adaptive law, and then control system is made to get rid of the dependence to parameter, system obtains robustness, improves the uncertain influence to sliding formwork control approach procedure.
Description
Technical Field
The invention relates to a UUV path tracking control method, in particular to a UUV path tracking control method for an expected path in a vertical plane.
Background
Path tracking control of an Unmanned Underwater Vehicle (UUV) is an important technical basis for realizing various purposes of the UUV. The method has important significance for UUV control theory and engineering application by deeply researching the problems existing in UUV path tracking.
At present, in the aspect of under-actuated UUV path tracking control, a mainstream idea is to establish a kinematic error equation based on a Serret-Frenet coordinate system and then combine the kinematic error equation, a kinetic equation and various control methods to realize control. Common control algorithms include a back-stepping method, model prediction control, sliding mode variable structure control and the like. The backstepping method has obvious advantages for stabilizing a complex strong nonlinear and high-coupling system. However, the problems of poor resistance to uncertainty and external interference, expansion of derivatives due to multiple derivatives, and the presence of singular values are restricting the application of this method. The model predictive control has the capability of real-time correction on parameter error rolling in the model and has good robustness. However, the algorithm is mainly used for linear systems, and challenges of nonlinear processing, real-time performance improvement and the like still exist for complex nonlinear systems like UUVs. The sliding mode variable structure control is a control algorithm with strong robustness and strong anti-interference capability, and the buffeting problem can be weakened by using a proper function to carry out switching control, designing a parameter self-adaptation law and the like.
Path tracking studies of under-actuated UUVs in the vertical plane direction are still rare, and most focus on path tracking in the horizontal plane. The motion of the under-actuated UUV in the vertical plane mostly controls only the depth. GV Lakhekar and VDS autonomous model published in 2013 in "IEEE International Conference on Fuzzy Systems" at a Novel adaptive Fuzzy sliding mode controller for depth control of undersewater vehicles "proposed a linear adaptive Fuzzy sliding mode controller for the depth control of UUV.
Disclosure of Invention
The invention aims to provide a parameter-free under-actuated UUV vertical surface path tracking sliding mode control method which can improve the navigational speed tracking precision and reduce the calculated amount.
The purpose of the invention is realized as follows:
step one, initialization:
adaptive parameters for uncertain parameters of UUVAssigning initial values and determining the ideal speed u for the path tracking processdDefining the updating times t as 0, i as 1-8;
step two, acquiring the current state of the UUV:
obtaining the current time state through a sensor of the UUV: u and w are respectively longitudinal and vertical velocities, r is a longitudinal inclination velocity, x and z are respectively a longitudinal coordinate and a vertical coordinate of the gravity center of the UUV under a fixed coordinate system { I }, theta is a longitudinal inclination angle, and a longitudinal velocity error e is determinedu＝u-ud；
Step three, establishing an under-actuated UUV horizontal plane error equation based on a Serret-Frenet coordinate system to obtain the longitudinal position deviation x of the center of gravity of the UUV under the coordinate { I }eAnd a vertical deviation zeAnd course deviation value thetae；
Respectively designing a speed sliding mode adaptive control law, a position sliding mode control law and a pitch angle sliding mode adaptive control law by using a sliding mode control method under the condition of unknown parameters, and carrying out thrust XpropDesired speed of flightAnd a torque MpropControl of e isu→0,xe→0,θe→0；
Step five, aiming at the boundary layer thickness k of the sliding mode controlleriRespectively designing fuzzy control laws when i is 1-3;
and (5) making t be t +1, jumping back to the step two, updating the next control law and the self-adaptive law, and realizing accurate control on path tracking of the UUV vertical plane.
The method mainly focuses on vertical plane path tracking control of the underactuated UUV with uncertain parameters. The method can realize the controller which is stabilized by only depending on the design of the vertical plane dynamic model, designs the self-adaptive law for the hydrodynamic parameters with uncertainty, further enables the control system to get rid of the dependence on the parameters, obtains the robustness of the system, improves the influence of the uncertainty on the sliding mode control approach process, and is suitable for various under-actuated UUV.
The invention designs an under-actuated UUV path tracking control system based on a self-adaptive sliding mode by utilizing a decoupling thought. Firstly, the invention deduces an under-actuated UUV vertical plane dynamic model with ocean current interference and an error model of vertical plane position and attitude. Secondly, the invention provides a novel sliding mode approach rate, the feasibility of the approach rate is proved, and a vertical plane under-actuated UUV path tracking controller is designed by utilizing the approach rate. Furthermore, by utilizing the Lyapunov stability theory, an adaptive law is designed for uncertain parameters in the navigational speed tracking and pitch angle tracking control rate of the UUV, so that the UUV path tracking system gets rid of the dependence on the parameters, and the UUV obtains the robustness to the uncertain parameters. And finally, based on the characteristic that the boundary layer thickness has great influence on UUV (unmanned Underwater vehicle) speed tracking, a boundary layer thickness adaptive law of T-S fuzzy control is designed by utilizing simulation experience so as to improve speed tracking accuracy and reduce calculated amount.
Drawings
FIG. 1 is a vertical plane modeling diagram of a UUV;
FIG. 2 is a coordinate system for tracking an under-actuated UUV vertical path;
FIG. 3 is a control flow diagram of the present invention;
fig. 4 is a simulation diagram of under-actuated UUV vertical position tracking.
Detailed Description
The invention is described in more detail below by way of example with reference to the accompanying drawings.
The first embodiment is as follows: a parameter-free under-actuated UUV vertical surface path tracking sliding mode control method comprises the following steps:
the invention aims to provide a parameter-free under-actuated UUV vertical surface path tracking sliding mode control method which can improve the navigational speed tracking precision and reduce the calculated amount.
The purpose of the invention is realized as follows:
step one, initialization:
adaptive parameters for uncertain parameters of UUVAssigning initial values and determining the ideal speed u for the path tracking processdDefining the updating times t as 0, i as 1-8;
step two, acquiring the current state of the UUV:
obtaining the current time state through a sensor of the UUV: u and w are respectively longitudinal and vertical velocities, r is a longitudinal inclination velocity, x and z are respectively a longitudinal coordinate and a vertical coordinate of the gravity center of the UUV under a fixed coordinate system { I }, theta is a longitudinal inclination angle, and a longitudinal velocity error e is determinedu＝u-ud；
Step three, establishing an under-actuated UUV horizontal plane error equation based on a Serret-Frenet coordinate system to obtain the longitudinal position deviation x of the center of gravity of the UUV under the coordinate { I }eAnd a vertical deviation zeAnd course deviation value thetae；
Respectively designing a speed sliding mode adaptive control law, a position sliding mode control law and a pitch angle sliding mode adaptive control law by using a sliding mode control method under the condition of unknown parameters, and carrying out thrust XpropDesired speed of flightAnd a torque MpropControl of e isu→0,xe→0,θe→0；
Step five, aiming at the boundary layer thickness k of the sliding mode controlleriRespectively designing fuzzy control laws when i is 1-3;
and (5) making t be t +1, jumping back to the step two, updating the next control law and the self-adaptive law, and realizing accurate control on path tracking of the UUV vertical plane.
The second embodiment is as follows:
on the basis of the first specific embodiment, the horizontal plane error equation of the under-actuated UUV is established based on the Serret-Frenet coordinate system in the third step of the first specific embodiment to obtain the position deviation xe,zeAnd course deviation value thetaeThe specific process is as follows:
for the motion of the UUV in the vertical plane, only a three-degree-of-freedom model is needed to be established, and the variables to be considered are as follows: the position quantity x, z, the pitch angle θ, and the longitudinal velocity u, the lateral velocity w, and the pitch angle angular velocity q. The available equations for the kinematics of the UUV vertical plane are:
the gravity center of the UUV is at the original point of { B }, the gravity and the buoyancy are equal, the UUV structure is symmetrical left and right, the UUV structure is considered to be symmetrical up and down approximately, and the UUV vertical plane kinetic equation can be obtained through a series of simplifications as follows:
in the above formula, the first and second carbon atoms are,d1＝-Xu-Xu|u||u|,d2＝-Zw-Zw|w||w|,d3＝-Mq-Mq|q||q|，the projection of the distance from the floating center to the gravity center of the UUV on the vertical direction of the UUV is represented by W, wherein X is the gravity of the UUV(),Z(),M()Is a hydrodynamic coefficient, Xprop＝Cnn | n | is propeller thrust of UUV, CnIs a coefficient measured by experiment, N is the rotating speed of the propeller, NpropThe heading moment of the UUV.
The UUV moving in the vertical plane cannot consider the interference generated by the transverse ocean current, and the ocean current flow velocity under { I } can be expressed as:
VI＝[uI,0,wI]T (3)
then the ocean current flow rate at { B } can be expressed as:
wherein:
the two ends of the formula (4) are subjected to derivation and are arranged as follows:
can be solved to obtain:
the horizontal plane dynamical model with ocean current disturbances can be expressed as:
furthermore, given a desired path in the { I } coordinate system:
where μ - - - -the arc length of the desired path, xd,zd-coordinates of the vertical plane expected path under { I }.
Because the coordinate value of the distance from the origin O of the coordinate system { B } to the origin D of { SF } (i.e., the expected point of UUV) under { I } is the position error of UUV, based on the velocity relationship of UUV with respect to the expected point D, the following velocity relationship can be easily established:
in the above formula, kvCurvature of the desired path of the vertical plane
xe,zePosition error of UUV in vertical plane
Substituting the first two formulas of formula (1) into formula (10), and considering thatThen the error equation for the vertical plane UUV path tracing can be written as:
wherein, thetae＝θ+α-θdIndicating a pitch error.
The third concrete implementation mode: in the case where the parameters are unknown by using the sliding mode control method according to the fourth embodiment on the basis of the first or second embodimentUnder the condition, respectively designing a speed sliding mode self-adaptive control law, a position sliding mode control law and a pitch angle sliding mode self-adaptive control law, and carrying out thrust XpropDesired speed of flightAnd a torque MpropControl of e isu→0,xe→0,θeThe specific process for → 0 is as follows:
using a novel slip form approach rate
Where s represents a sliding mode surface function, k>In equation (12), when the state point is far from the sliding mode surface, the exponential approaching term plays a main role to make the state point approach the sliding mode surface quickly, and when the state point reaches the vicinity of the sliding mode surface, -k | s | Y |αThe sgns term plays a major role in improving the control quality by reducing the switching gain appropriately.
By combining a novel approach rate (12), firstly, a sliding mode control law of a navigational speed tracking subsystem and a position tracking subsystem is designed for the UUV. Selecting sliding mode surface function s for tracking navigational speed1ver＝u-udSliding mode surface function s of position tracking2ver＝xe-0, combined with the first pattern in the kinetic model (8) with ocean current disturbances and the first pattern in the error model (11), can be easily designed:
selecting a sliding mode surface function for a heading angle tracking control subsystemc is greater than 0, and by combining the third formula in the formula (8) and the third formula in the formula (11), the heading phase angle tracking control law is as follows:
k1＞0,k2>0 and k3>0 is the switching gain, ε1＞0,ε2>0 and ε3Coefficient of >0 exponential approximation term, 0 < α1＜1,0＜α2< 1 and 0 < α3< 1 is a design parameter.
And verification proves that the three designed tracking control rules can be stable. Considering the influence of parameter uncertainty existing in the UUV mathematical model (the influence of ocean current interference is added into the model), for the speed and pitch angle tracking control subsystem designed based on the first-order and second-order mathematical models, the sliding mode approaching process of the system is also influenced by the uncertain interference. For this reason, it is necessary to design adaptation laws for the relevant uncertain parameters.
In the following, an adaptive law is designed for uncertain parameters in the pitch angle control law. Rewriting a third formula in a kinetic model (8) with ocean current disturbances:
wherein:
the control law (14) can be rewritten as:
let uncertain parameter b in (15) and (17)1,b2,b3And b4Are respectively estimated asAndsimultaneous definition ofAndthen it can be obtained:
to bow phase angle sliding mode surface functionDerivation is provided byCombination (18):
selecting a Lyapunov function:
taking the derivative of both ends of (20), and substituting (19) into:
according to the last step of equation (21), an uncertainty is selectedThe adaptation law of (1) is as follows:
wherein the constant ρ1＞0,ρ2＞0,ρ3＞0,ρ4Is greater than 0. By substituting the formula (22) into the formula (21), a compound having the formulaWith equal sign only at s3verTaken at 0, so the UUV pitch tracking error is Lyapunov-mean stable, then s3verIs bounded, control input MpropBound, and stable design of the adaptive law for uncertain parameters in the pitch angle control law.
According to the design idea of the pitch angle, the uncertain parameter self-adaptation law of UUV navigational speed tracking control is easily obtained. The first formula in formula (8) was chosen as follows:
wherein:
then it is uncertainItem(s)The adaptation law of (a) can be expressed as:
likewise, the speed tracking subsystem and the position tracking subsystem of the UUV in vertical motion may prove stable.
Therefore, the UUV vertical plane path tracking adaptive sliding mode control system designed by the invention can be expressed as follows:
the fourth concrete implementation mode: on the basis of any one of the above specific embodiments, a specific process of designing a fuzzy control law for a boundary layer of a sliding mode controller in step five of the present embodiment is as follows:
first, the symbolic function in the first equation in equation (26) needs to be replaced by Sigmoid function:
wherein,λ1the boundary layer thickness parameter is indicated.
And designing a front part and a back part of the T-S fuzzy control based on experience so as to improve the UUV speed tracking precision.
From experience, the boundary layer thicknessDegree phi and parameter lambda in formula (27)1The relationship of (c) can be written as: phi 1/lambda1. Thus, a smaller boundary layer thickness φ will correspond to a larger λ1The value will correspond to a smaller lambda otherwise1The value is obtained. Boundary layer thickness phi and navigational speed tracking steady-state error uessCan be expressed as:
φ＝kess|uess| (28)
wherein the proportionality coefficient kessIs greater than 0. UUV speed tracking error ueWill converge to u quickly under the action of the control law (27)essTherefore, the formula (28) can be considered as:
φ≈kess|ue| (29)
due to the relation shown in (29), UUV speed tracking error | ueI is used as input of the fuzzy controller, and the boundary layer thickness phi is used as output. The expert experience for the T-S fuzzy model building can be summarized as follows: when ueWhen | is larger, selecting phi to be larger to reduce buffeting; when ueWhen | is smaller, select a larger one to improve the tracking accuracy.
Considering that the UUV operating speed used in the present invention generally does not exceed 4 knots (about 2m/s), then | ueThe discourse domain of | is [0,2 |)]Since the static error of the cruise tracking is approximately stabilized at (cruise (section) × 0.1) m/s, | u can be used as a criterion for dividing the fuzzy seteThe universe of discourse of | is divided into three fuzzy sets of Z (zero), S (small) and B (large), as shown in figure 1.
l1,l2Should be selected to meet the completeness requirement. Based on the relation (29), the back-piece of the T-S fuzzy rule can be established, then the fuzzy rule can be written as:
wherein, DeltaiWhere i is 1,2, and 3 each represent a modeThe collection of mashes Z, S, B. Coefficient of proportionality kiessI is 1,2 and 3, which is determined by UUV speed value simulation experience. The parameter identification process of the front piece and the back piece is omitted in the design process, the calculated amount is small, and the real-time performance is good.
The following simulation experiments were performed in combination with the verification examples, and the experimental results are shown in fig. 4:
selecting path y as 15sin (0.15x) as initial variable of desired path, UUVInitial value b of adaptive parameter1＝b2＝b3＝b4＝b5＝b6＝b7＝b80; figure 4 illustrates the effect of under-actuated UUV on vertical plane path tracking under Adaptive Sliding Mode Control (ASMC).
Experiments prove that the self-adaptive sliding mode fuzzy controller provided by the invention has better control performance. In practical application, accurate path tracking is realized by a self-adaptive method without obtaining specific hydrodynamic parameters of the under-actuated UUV. Meanwhile, the control requirements can be further met by adjusting the control parameters.
Claims (1)
1. A parameter-free under-actuated UUV vertical surface path tracking sliding mode control method is characterized by comprising the following steps:
step one, initialization:
adaptive parameters for uncertain parameters of UUVAssigning initial values and determining the ideal speed u for the path tracking processdDefining the updating times t as 0, i as 1-8;
step two, acquiring the current state of the UUV:
obtaining the current time state through a sensor of the UUV: u and w are respectively longitudinal and vertical velocities, r is a longitudinal inclination velocity, x and z are respectively a longitudinal coordinate and a vertical coordinate of the gravity center of the UUV under a fixed coordinate system { I }, theta is a longitudinal inclination angle, and a longitudinal velocity error e is determinedu＝u-ud；
Step three, establishing an under-actuated UUV horizontal plane error equation based on a Serret-Frenet coordinate system to obtain the longitudinal position deviation x of the center of gravity of the UUV under the coordinate { I }eVertical deviation zeAnd course deviation value thetae；
Respectively designing a speed sliding mode adaptive control law, a position sliding mode control law and a pitch angle sliding mode adaptive control law by using a sliding mode control method under the condition of unknown parameters, and carrying out thrust XpropDesired speed of flightAnd a torque MpropControl of e isu→0,xe→0,θe→0；
Step five, aiming at the boundary layer thickness k of the sliding mode controlleriRespectively designing fuzzy control laws when i is 1-3;
making k equal to k +1, jumping back to the second step, updating the next control law and the self-adaptive law, and realizing accurate control on path tracking of the UUV vertical plane;
the third step specifically comprises:
for the motion of the UUV in the vertical plane, only a three-degree-of-freedom model needs to be established, and the kinematic equation of the UUV vertical plane is as follows:
the gravity center of the UUV is arranged at the original point of { B }, the gravity and the buoyancy are equal, the UUV structure is symmetrical left and right, the UUV structure is considered to be symmetrical up and down approximately, and the dynamic equation of the UUV vertical plane is simplified as follows:
in the above formula, the first and second carbon atoms are,d1＝-Xu-Xu|u||u|,d2＝-Zw-Zw|w||w|,d3＝-Mq-Mq|q||q|，the projection of the distance from the floating center to the gravity center of the UUV on the vertical direction of the UUV is represented by W, wherein X is the gravity of the UUV(),Z(),M()Is a hydrodynamic coefficient, Xprop＝Cnn | n | is propeller thrust of UUV, CnIs a coefficient measured by experiment, N is the rotating speed of the propeller, NpropThe bow turning moment of the UUV is taken as the bow turning moment of the UUV;
the ocean current flow rate at { I } is expressed as:
VI＝[uI,0,wI]T (3)
the ocean current flow rate at { B } is expressed as:
wherein:
the horizontal plane dynamics model with ocean current disturbances is then expressed as:
given a desired path in the { I } coordinate system:
where μ - - - -the arc length of the desired path, xd,zd-coordinates of the vertical plane expected path under { I };
kvcurvature of the desired path of the vertical plane
xe,zePosition error of UUV in vertical plane
The error equation for vertical plane UUV path tracking is:
wherein, thetae＝θ+α-θdRepresenting a pitch error;
the concrete process of the step four comprises:
the approach rate of the slip form is as follows:
wherein s represents a sliding mode surface function, k is a switching gain, epsilon is an exponential approximation term coefficient, and the coefficient is a design parameter, wherein the coefficient is more than 0 and more than α and less than 1;
firstly, designing sliding mode control laws of a navigational speed tracking subsystem and a position tracking subsystem for a UUV, and selecting a sliding mode surface function s for navigational speed tracking1ver＝u-udSliding mode surface function s of position tracking2ver＝xe-0, then:
selecting a sliding mode surface function for a heading angle tracking control subsystemThe heading phase angle tracking control law is as follows:
k1＞0,k2>0 and k3>0 is the switching gain, ε1＞0,ε2>0 and ε3>0 is a coefficient that counts the approximation term,
0＜α1＜1,0＜α2< 1 and 0 < α3< 1 is a design parameter;
in the formulas (14) and (15), a large number of uncertain parameters are provided, an adaptive law is designed for the uncertain parameters, and the expected path is tracked under the condition that parameters such as water power and the like are unknown;
firstly, designing an adaptive law for uncertain parameters in a pitch angle control law, and rewriting the control law (15) into the following steps:
wherein,
let uncertain parameter b in (16)1,b2,b3And b4Are respectively estimated asAndsimultaneous definition ofAndthen, the following steps are obtained:
to bow phase angle sliding mode surface functionDerivation is provided byCombining formula (17) to obtain:
selecting a Lyapunov function:
obtain uncertaintyThe adaptation law of (1) is as follows:
wherein the constant ρ1＞0,ρ2＞0,ρ3＞0,ρ4＞0；
Similarly, the uncertain parameter self-adaption law for UUV navigational speed tracking control is designed as follows:
wherein:
uncertainty termThe adaptation law of (a) is expressed as:
therefore, the UUV vertical plane path tracking adaptive sliding mode control system is expressed as follows:
the concrete process of the step five comprises:
firstly, a Sigmoid function is used for replacing a sign function in a designed adaptive sliding mode control function:
wherein,λ1representing a boundary layer thickness parameter;
boundary layer thickness phi and navigational speed tracking steady-state error uessCan be expressed as:
φ＝kess|uess| (24)
wherein, the ratioCoefficient kessUUV speed tracking error u >0eWill converge to u quickly under the action of the control law (22)essTherefore, formula (24) is considered to be:
φ≈kess|ue| (25)
the fuzzy rule is written as:
wherein, DeltaiI is 1,2,3 respectively representing the fuzzy set Z, S, B; coefficient of proportionality kiessI is 1,2 and 3, which is determined by the UUV actual speed value.
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