CN106406095B - The asymmetric limited full driving surface vessel Trajectory Tracking Control method of input and output - Google Patents
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Abstract
The present invention relates to a kind of asymmetric limited full driving surface vessel Trajectory Tracking Control methods of input and output, first carry out error calculation by given track expectation pursuit gain；Then kinematics control in track is carried out according to track kinematical equation and virtual controlling rule is calculated；The indeterminate in surface vessel model is approached using neural network, Design assistant control system solves the problems, such as damp constraint, then obtains control amount based on surface vessel kinetics equation；This control amount is finally used for surface vessel model.In practical application, the quantity of states such as track, the speed of surface vessel are obtained by sensor measurement, and the executing agencies such as steering engine and propeller will be transmitted to by the control amount that this method is calculated, can be realized the anti-indeterminate of surface vessel, disturbance rejection, the asymmetric saturation problem of anti-executing agency Trajectory Tracking Control function.
Description
Technical Field
The invention provides a track tracking control method for a full-drive surface ship with asymmetrically limited input and output, provides a new control method for tracking an expected track, which inhibits the influence of external disturbance, for a full-drive unmanned surface ship with asymmetrically limited input and output, and belongs to the technical field of automatic control.
Background
In recent years, there have been increasing studies on motion control of unmanned surface vessels. The track tracking control is taken as a typical motion control, and has great significance for the work in the aspects of navigation, intelligent survey, intelligent detection and the like. Therefore, a controller with high-performance track tracking capability needs to be designed for the unmanned surface vessel, so that the accurate reference track or virtual object of the surface vessel is realized. However, in practical systems, input saturation problems can occur, which can lead to performance degradation, lead-lag, negative pulse signal generation, and even system instability. Meanwhile, the propeller of the surface ship can only output positive power, or when the effectiveness of the actuator is partially lost, the asymmetric input saturation condition can occur. In addition, when a surface vessel travels in a narrow river, the course of the vessel is strictly limited by the two banks of the river, and therefore, the problem of limited output needs to be considered. The limits of the system output are also asymmetric when the flight path is not in the middle of the river.
Therefore, the invention discloses a full-drive surface ship track tracking control method with asymmetric input and output limitation, which is a surface ship track tracking control theory which is pointed and solves the problem that the input and output are limited by asymmetry by taking the problems as entry points. A bounded Lyapunov function, a hyperbolic tangent function and a Nussbaum function are introduced to solve the problem of time-varying asymmetric input and output limitation; estimating bounded uncertainty terms and external disturbances by using an adaptive algorithm; meanwhile, the instruction filter is used for avoiding complex derivation operation. The method solves the problem of limited input and output asymmetry, ensures the gradual stability of the system, can realize reliable track tracking, and provides an efficient and feasible design means for the track tracking control engineering of the surface ship.
Disclosure of Invention
(1) The purpose is as follows: the invention aims to provide a full-drive surface ship trajectory tracking control method with asymmetric input and output limitation, and a control engineer can combine actual parameters and simultaneously realize trajectory tracking control of the surface ship with asymmetric limitation on uncertainty resistance, disturbance resistance and input and output resistance.
(2) The technical scheme is as follows: the invention relates to a full-drive surface ship track tracking control method with asymmetric limited input and output, which mainly comprises the following steps: firstly, error calculation is carried out according to a given expected tracking value of the track; then, carrying out trajectory kinematics control calculation according to a trajectory kinematics equation to obtain a virtual control law; an auxiliary control system is designed to solve the problem of actuator saturation by approaching an uncertain item in a surface ship model through a neural network, and then a control quantity is obtained based on a surface ship dynamic equation; finally, the control quantity is used for the surface ship model. In practical application, the state quantities such as the track, the speed and the like of the water surface ship are measured by a sensor, and the control quantity obtained by calculation by the method is transmitted to actuating mechanisms such as a steering engine, a propeller and the like, so that the track tracking control function of resisting uncertainty, disturbance and asymmetric saturation of the actuating mechanisms of the water surface ship can be realized.
The invention discloses a full-drive surface ship track tracking control method with asymmetric limited input and output, which comprises the following specific steps of:
step one given a desired tracking trajectory: given a desired planar position (x)d,yd) (ii) a Given a desired yaw angle ψdThe expected tracking track is shown as ηd＝[xd,yd,ψd]T。
Step two, calculating a track tracking error: calculating an error z between the actual trajectory and the desired trajectory1＝η-ηd。
Step three, processing the input saturated part: introducing smooth piecewise functionThe approximation describes the actuator model.
Step four virtual control quantity α10Calculating the virtual control amount α required to eliminate the error between the desired trajectory and the actual trajectory10。
Step five virtual control quantity α20Calculating a virtual control amount α required to eliminate an error between a desired speed and an actual speed20。
Designing a system control law: the control amount phi required to eliminate the error between the desired output and the actual output of the actuator is calculated.
Wherein the given desired tracking trajectory in step one comprises ηd＝[xd,yd,ψd]TThe three components mean: (x)d,yd) Indicating the desired plane position, ψdIndicating a desired yaw angle.
Wherein, the method for calculating the track tracking error in the step two comprises the following steps:
z1＝η-ηd
η is the actual track of the water surface ship under the inertial coordinate system, η ═ x, y, ψ]TWhere (x, y) denotes the position of the surface vessel and ψ denotes the yaw angle.
Wherein, in step three, the input saturated part is processed, and the calculation method is as follows:
according to fig. 1, the inertial and body coordinate systems shown in the figure are first established. Thereby obtaining the three-degree-of-freedom nonlinear motion equation of the surface ship:
wherein η ═ x, y, ψ]TFor the actual trajectory of the ship in the inertial frame, (x, y) indicates the position of the surface ship and ψ indicates the yaw angle. U, v, r]TThe speed vector of the ship in the body coordinate system is shown, u, v and r are decomposition quantities of the speed vector along the body coordinate system and respectively represent the advancing speed, the transverse speed and the yaw rate. R (psi) is a rotation matrix satisfying R-1(ψ)＝RT(ψ)：
M is a non-singular, symmetric positive definite inertial matrix. C (upsilon) is a centripetal matrix and D (upsilon) is a damping matrix. The three are respectively expressed as follows:
b(t)＝[b1(t) b2(t) b3(t)]Tfor uncertainty terms, including unmodeledUncertainty terms, and unknown time-varying interference quantities.The output of the saturation actuator and the input of the system. The relationship of the actuator input and output can be expressed as:
wherein,the control quantity under the condition of actuator saturation is not considered, and the control quantity can be regarded as the input of the saturated actuator.Andare each tauiThe upper and lower limits of (2). However, the relationship between the input and the output is not smooth, and the design using the inverse step method is not possible. Thus defining a smooth piecewise functionTo approximately represent the actuator input-output relationship.
The equation of motion of the surface vessel can be rewritten as
Wherein, is a bounded vector of functions that is,c is more than 0, phi is a control law which needs to be designed later.
Wherein the virtual control quantity α is calculated as described in step four10The calculation method is as follows:
1) calculating the error of the actual trajectory from the given desired trajectory: z is a radical of1＝η-ηd。
2) Given the asymmetric output limit: k is a radical ofc(t) is the lower limit of the system output, kd(t) is the upper limit of the system output, the difference between the upper and lower limits of the output and the given expected track
kαi＝ηdi-kci，kbi＝kdi-ηdi,(i＝1,2,3)。
3) Calculating z1Derivative of (a):
4) design virtual control α10：
Wherein k is1＝diag(k11,k12,k13) Is a positive definite symmetric matrix; k is a radical ofα1More than 0, p is more than or equal to 0 and is a positive integer,
Q＝diag(Q1,Q2,Q3) And is and
e1to assist the state of the system, is shown as
Wherein,is a very small constant, ke1＞1，γ1＞0，
Δα1＝α1-α10By a differential tracking filter as shown in fig. 2, can be obtained from αi0(i-1, 2) to yield αiAnd its derivative value
Thereby avoiding complex derivation operations.
Wherein the virtual control amount α is calculated as described in step five20The calculation method is as follows:
1) calculating the error of the actual speed from the desired speed: z is a radical of2＝v-α1。
2) Calculating z2Derivative of (a):
3) design virtual control α20：
Wherein k isα2＞0，e2And e1Similarly, a state variable of the auxiliary system is shown as
Wherein,is a very small constant, ke2＞1，γ2＞0，
Δα2＝α2-α20。
4) And (3) self-adaptation law design: law of design adaptationThe uncertainty term in the model and the external disturbance are approximately estimated by an adaptive algorithm,
wherein gamma isf,γσ＞0，ρ∈R+。
Wherein, in the system control law design in the step six, the design method is as follows:
1) calculating the error of the actual output of the actuator from the expected output:
2) calculating z3Derivative of (a):wherein Θ is diag (θ)1,θ2,θ3)，Since time-varying theta brings great difficulty to design and analysis, a Nussbaum function array N ═ diag (N) is introduced1(χ1),N2(χ2),N3(χ3))，
3) Design control amount phi:
wherein k is3＝diag(k31,k32,k33) And is a positive definite symmetric matrix.
(3) The advantages and effects are as follows:
compared with the prior art, the water surface ship track tracking control method with the asymmetrically saturated actuator has the advantages that:
1) the method avoids model linearization, can be directly applied to a nonlinear model, has concise and efficient steps, and can ensure the gradual stability of a system;
2) the method can effectively solve the problem of asymmetric saturation of the actuator, and greatly improves the adverse effect on the system stability and the performances in all aspects caused by the asymmetric saturation of the actuator;
3) the method can ensure that the water surface ship reliably tracks the reference track when advancing in a narrow river channel by carrying out asymmetric limitation on the output;
4) the self-adaptive algorithm is adopted to well inhibit the influence of model uncertainty and external disturbance on the system;
5) the algorithm of the method is simple in structure, high in response speed and easy to implement in engineering.
In the application process, a control engineer can give any expected track and corresponding input and output limits of the surface ship according to actual requirements, and directly transmit the control quantity obtained by calculation of the method to an execution mechanism to realize the function of track tracking control.
Drawings
Fig. 1 is a model diagram of a surface vessel according to the present invention.
Fig. 2 is a block diagram of the filter of the present invention.
The symbols are as follows:
ηd ηd＝[xd,yd,ψd]Tto expect a surface ship travel trajectory, wherein (x)d,yd) Indicating the desired plane position, ψdIndicating the yaw angle.
η η＝[x,y,ψ]TIs the actual track of the surface ship;
υ υ＝[u,v,r]Tthe velocity vector of the surface ship, u, v and r are respectively the decomposition quantity of the velocity vector along a ship body coordinate system;
α10 α10is a designed virtual control quantity;
α20 α20is a designed virtual control quantity;
α1 α1the desired speed of the surface vessel can be represented by α10Obtaining the result through a filter;
α2 α2for the desired output of the actuator, α20Obtaining the result through a filter;
z1 z1error between the desired trajectory and the actual trajectory;
z2 z2is the error between the desired speed and the actual speed;
z3 z3is the error between the desired speed and the actual speed;
b b(t)＝[b1(t)b2(t)b3(t)]Tthe uncertainty term comprises unmodeled power and unknown time-varying interference;
the input quantity of the system under the saturation of the actuator is not considered;
is the output of the saturation actuator and the system input;
is a smooth piecewise function for approximately representing the actuator saturation model;
is a bounded function;
b B are model uncertainties b andthe sum of (1);
kc(t) kc(t) is the minimum output limit of the system;
kd(t) kd(t) is the maximum output limit of the system;
phi is a system control quantity;
a minimum value defined for the system input;
a maximum value defined for the system input;
e1,e2 e1,e2state variables of the auxiliary system;
is an estimate of the uncertainty term;
Detailed Description
The technical scheme of the invention is further explained in the following by combining the attached drawings.
The invention discloses a full-drive surface ship track tracking control method with asymmetric limited input and output, which comprises the following specific steps of: the method comprises the following steps: given an expected tracking value
1) As shown in fig. 1, an inertial coordinate system is established with a fixed point as an origin, the x-axis pointing to the north and the y-axis pointing to the east; and establishing a body coordinate system by taking the geometric center of the structure in the surface ship model as an origin, pointing the x axis to the head of the ship and the y axis to be perpendicular to the x axis.
2) Given the desired trajectory of ηd＝[xd,yd,ψd]TThe three components mean: (x)d,yd) Indicating the desired plane position, ψdIndicating the yaw angle.
Step two: calculating the tracking error z1
z1＝η-ηd
Step three: processing input saturated portions
According to fig. 1, the inertial and body coordinate systems shown in the figure are first established. Thereby obtaining the three-degree-of-freedom nonlinear motion equation of the surface ship:
wherein η ═ x, y, ψ]TFor the actual trajectory of the ship in the inertial frame, (x, y) indicates the position of the surface ship and ψ indicates the yaw angle. U, v, r]TThe speed vector of the ship in the body coordinate system is shown, u, v and r are decomposition quantities of the speed vector along the body coordinate system and respectively represent the advancing speed, the transverse speed and the yaw rate. R (psi) is a rotation matrix satisfying R-1(ψ)＝RT(ψ)：
M is a non-singular, symmetric positive definite inertial matrix. C (upsilon) is a centripetal matrix and D (upsilon) is a damping matrix. The three are respectively expressed as follows:
b(t)＝[b1(t)b2(t)b3(t)]Tand the uncertainty term comprises an unmodeled uncertainty term and an unknown time-varying interference quantity.The output of the saturation actuator and the input of the system. The relationship of the actuator input and output can be expressed as:
wherein,the control quantity under the condition of actuator saturation is not considered, and the control quantity can be regarded as the input of the saturated actuator.Andis divided into
Is other thaniThe upper and lower limits of (2). However, the relationship between the input and the output is not smooth, and the design using the inverse step method is not possible. Thus determining
Defining a smooth piecewise functionTo approximately represent the actuator input-output relationship.
The equation of motion of the surface vessel can be rewritten as
Wherein, is a bounded vector of functions that is,c is more than 0, phi is a control law which needs to be designed later.
Step four, calculating the virtual control quantity α10
1) Calculating the error of the actual trajectory from the given desired trajectory: z is a radical of1＝η-ηd。
2) Given the asymmetric output limit: k is a radical ofc(t) is the lower limit of the system output，kd(t) is the upper limit of the system output, the difference between the upper and lower limits of the output and the given expected track
kαi＝ηdi-kci，kbi＝kdi-ηdi,(i＝1,2,3)。
3) Calculating z1Derivative of (a):
4) design virtual control α10：
Wherein k is1＝diag(k11,k12,k13) Is a positive definite symmetric matrix; k is a radical ofα1More than 0, p is more than or equal to 0 and is a positive integer,
Q＝diag(Q1,Q2,Q3) And is and
e1to assist the state of the system, is shown as
Wherein,is a very small constant, ke1＞1，γ1＞0，
Δα1＝α1-α10By a differential tracking filter as shown in fig. 2, can be obtained from αi0(i-1, 2) to yield αiAnd its derivative value
Thereby avoiding complex derivation operations.
Step five, calculating the virtual control quantity α20
1) Calculating the error of the actual speed from the desired speed: z is a radical of2＝v-α1。
2) Calculating z2Derivative of (a):
3) design virtual control α20：
Wherein k isα2＞0，e2And e1Similarly, a state variable of the auxiliary system is shown as
Wherein k is a very small constante2＞1，γ2＞0，
Δα2＝α2-α20。
4) And (3) self-adaptation law design: law of design adaptationThe uncertainty term in the model and the external disturbance are approximately estimated by an adaptive algorithm,
wherein gamma isf,γσ＞0，ρ∈R+。
Step six: control law of design system
1) Calculating the error of the actual output of the actuator from the expected output:
2) calculating z3Derivative of (a):wherein Θ is diag (θ)1,θ2,θ3)，Since time-varying theta brings great difficulty to design and analysis, a Nussbaum function array N ═ diag (N) is introduced1(χ1),N2(χ2),N3(χ3))，
3) Design control amount phi:
wherein k is3＝diag(k31,k32,k33) And is a positive definite symmetric matrix.
Claims (5)
1. A full-drive surface ship track tracking control method with asymmetric input and output limitation is characterized by comprising the following steps: the method comprises the following specific steps:
step one given a desired tracking trajectory: given a desired planar position (x)d,yd) (ii) a Given a desired yaw angle ψdThe expected tracking track is shown as ηd＝[xd,yd,ψd]T；
Step two, calculating a track tracking error: calculating an error z between the actual trajectory and the desired trajectory1＝η-ηd；
Step three, processing the input saturated part: introducing smooth piecewise functionApproximately describing the actuator model;
step four virtual control quantity α10Calculating the virtual control amount α required to eliminate the error between the desired trajectory and the actual trajectory10；
Step five virtual control quantity α20Calculating a virtual control amount α required to eliminate an error between a desired speed and an actual speed20；
Designing a system control law: calculating a control quantity phi required for eliminating an error between the expected output and the actual output of the actuator;
wherein, the input saturated part is processed in the third step, and the calculation method is as follows:
firstly, establishing an inertial coordinate system and a body coordinate system; thereby obtaining the three-degree-of-freedom nonlinear motion equation of the surface ship:
wherein η ═ x, y, ψ]TThe actual trajectory of the ship under the inertial coordinate system, (x, y) represents the position of the surface ship, and psi represents the yaw angle; u, v, r]TThe speed vector of the ship under the body coordinate system is shown, u, v and r are decomposition quantities of the speed vector along the body coordinate system and respectively represent the advancing speed, the transverse speed and the yaw rate; r (psi) is a rotation matrix satisfying R-1(ψ)＝RT(ψ)：
M is a nonsingular, symmetrical positive definite inertial matrix; c (upsilon) is a centripetal matrix, and D (upsilon) is a damping matrix; the three are respectively expressed as follows:
b(t)＝[b1(t) b2(t) b3(t)]Tthe uncertainty items comprise unmodeled uncertainty items and unknown time-varying interference quantity;the output of the saturation actuator and the input of the system; the relationship of the actuator input and output can be expressed as:
wherein,the control quantity under the saturation of the actuator is not considered, and the control quantity can be regarded as the input of the saturated actuator;andare each tauiThe upper and lower limits of (d); however, at this time, the relation curve of input and output is not smooth, and the design cannot be carried out by using a reverse step method; thus defining a smooth piecewise functionTo approximately represent the actuator input-output relationship;
the equation of motion of the surface vessel can be rewritten as
Wherein, is a bounded vector of functions that is,c is more than 0, phi is a control law which needs to be designed later.
2. The input-output asymmetric limited full-drive surface ship trajectory tracking control method according to claim 1, characterized by comprising the following steps: the method for calculating the track tracking error in the second step is as follows:
z1＝η-ηd
η is the actual track of the water surface ship under the inertial coordinate system, η ═ x, y, ψ]TWhere (x, y) denotes the position of the surface vessel and ψ denotes the yaw angle.
3. The method for tracking and controlling the trajectory of the full-drive surface ship with the asymmetrically limited input and output according to claim 1, wherein the step four is to calculate the virtual control quantity α10The calculation method is as follows:
1) calculating the error of the actual trajectory from the given desired trajectory: z is a radical of1＝η-ηd；
2) Given the asymmetric output limit: k is a radical ofc(t) is the lower limit of the system output, kd(t) is the upper limit of the system output, the difference between the upper and lower limits of the output and the given expected track
kαi＝ηdi-kci，kbi＝kdi-ηdi,(i＝1,2,3)；
3) Calculating z1Derivative of (a):
4) design virtual control α10：
Wherein k is1＝diag(k11,k12,k13) Is a positive definite symmetric matrix; k is a radical ofα1More than 0, p is more than or equal to 0 and is a positive integer,
Q＝diag(Q1,Q2,Q3) And is and
e1to assist the state of the system, is shown as
Wherein,is a very small constant, ke1＞1，γ1＞0，Δα1＝α1-α10By means of a differential tracking filter, can be represented by αi0(i-1, 2) to yield αiAnd its derivative value
4. The input-output asymmetric limitation full-drive surface ship trajectory tracking control method according to claim 1, characterized in that the virtual control quantity α is calculated in the step five20The calculation method is as follows:
1) calculating the error of the actual speed from the desired speed: z is a radical of2＝v-α1；
2) Calculating z2Derivative of (a):
3) design virtual control α20：
Wherein k isα2＞0，e2And e1Similarly, a state variable of the auxiliary system is shown as
Wherein,is a very small constantNumber, ke2＞1，γ2＞0，Δα2＝α2-α20；
4) And (3) self-adaptation law design: law of design adaptationThe uncertainty term in the model and the external disturbance are approximately estimated by an adaptive algorithm,
wherein gamma isf,γσ＞0，ρ∈R+。
5. The input-output asymmetric limited full-drive surface ship trajectory tracking control method according to claim 1, characterized by comprising the following steps: and sixthly, designing a system control law, wherein the design method comprises the following steps:
1) calculating the error of the actual output of the actuator from the expected output:
2) calculating z3Derivative of (a):wherein Θ is diag (θ)1,θ2,θ3)，Since time-varying theta brings great difficulty to design and analysis, a Nussbaum function array N ═ diag (N) is introduced1(χ1),N2(χ2),N3(χ3))，
3) Design control amount phi:
wherein k is3＝diag(k31,k32,k33) And is a positive definite symmetric matrix.
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| CN114661056B (en) * | 2022-05-19 | 2022-12-27 | 浙江大学湖州研究院 | Differential water surface unmanned ship trajectory tracking method considering propeller servo control |
| CN115328126B (en) * | 2022-08-08 | 2023-11-24 | 大连海事大学 | Unmanned ship self-adaptive sliding mode track tracking control method and control system thereof |
| CN116577997B (en) * | 2023-07-06 | 2023-10-03 | 西北工业大学 | Omnidirectional trolley parameter identification method based on concurrent learning |
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