CN112947375B - Composite self-adaptive fault-tolerant controller design method considering unknown dead zone - Google Patents
Composite self-adaptive fault-tolerant controller design method considering unknown dead zone Download PDFInfo
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Abstract
The invention discloses a design method of a composite self-adaptive fault-tolerant controller considering an unknown dead zone, which comprises the following steps: building a ship model; establishing a dead zone model according to the dead zone nonlinear characteristics of the ship actuator, and establishing a fault model by combining the fault type of the ship actuator; estimating a speed variable of the ship based on the robust neural network; calculating dead zone parameters of the dead zone model and fault parameters of the actuator according to errors between the actual speed and the estimated speed of the ship; constructing a dead zone inverse model according to the dead zone parameters to compensate the dead zone model; compensating the fault model according to the fault parameters; calculating a dead zone model and a control law after fault model compensation; and adjusting a control input vector of the ship actuator according to the control law to control the ship to perform dynamic positioning. The invention can keep the normal running of the dynamic positioning task under the condition that the propeller with an unknown dead zone has an unknown fault.
Description
Technical Field
The invention relates to the field of ship control engineering and ship automation equipment, in particular to a design method of a composite self-adaptive fault-tolerant controller considering an unknown dead zone.
Background
Dynamic positioning (Dynamic Positioning, DP) technology has been widely used in marine engineering, and is an important technology for realizing the positioning of a ship on water berth and a platform. The dynamic positioning system can calculate the deviation between the current attitude of the ship and the expected attitude by measuring the current attitude of the ship, so as to calculate the thrust and the direction required for reaching the expected attitude, and send a control command to an actuator, and the ship is kept at the expected position and heading through the thrust generated by the actuator.
Because power positioning ships are often applied to precise offshore operation tasks such as oil and gas drilling, underwater cable and pipeline laying, dredging and the like, in recent years, domestic and foreign students have made a great deal of research work on the control performance of power positioning ships. Most of the problems to be solved are focused on optimizing and innovating control algorithms to improve positioning accuracy based on the premise that the actuator is in good condition and no dead zone input exists. However, there is no mention in the current research effort as to how to solve the dead zone nonlinearity and actuator failure problems.
Based on the analysis, the existing dynamic positioning control algorithm mainly has the following two defects:
firstly, most control algorithms ignore dead zone nonlinearity of an actuator, which is an inherent physical characteristic of the actuator, and the existence of the dead zone nonlinearity may cause the adjustment quality of a ship control system to be reduced, so that the positioning accuracy is reduced.
Secondly, in ocean engineering practice, due to severe ocean environment and corrosion and erosion of seawater, equipment such as ship actuators and sensors are easy to age and damage, efficiency loss and offset faults of the ship actuators are easy to occur, and therefore the positioning accuracy of the dynamic positioning ship is reduced, the control performance is reduced, and even the dynamic positioning ship is out of control.
Disclosure of Invention
The invention provides a design method of a composite self-adaptive fault-tolerant controller considering an unknown dead zone, which aims to overcome the technical problems.
The invention relates to a design method of a composite self-adaptive fault-tolerant controller considering an unknown dead zone, which comprises the following steps:
building a ship model;
establishing a dead zone model according to the dead zone nonlinear characteristic of the ship actuator; establishing a fault model according to the dead zone model and combining the fault type of the ship actuator; adding the fault model to the ship model to obtain a ship model with actuator faults and dead zone inputs;
estimating a speed variable of the ship based on the robust neural network;
designing a dynamic positioning ship controller according to the ship model with the actuator fault and dead zone input, a posture vector in the ship model and the speed variable;
calculating dead zone parameters of the dead zone model according to errors between the actual speed and the estimated speed of the ship; constructing a dead zone inverse model according to the dead zone parameters to compensate the dead zone model;
calculating fault parameters according to errors between the actual speed and the estimated speed of the ship; compensating the fault model according to the fault parameters;
calculating the control law of the dead zone model and the fault model after compensation; and adjusting a control input vector of the ship actuator according to the control law so as to control the ship to execute dynamic positioning.
Further, the building of the ship model includes:
establishing a three-degree-of-freedom mathematical model of the dynamic positioning ship as (1);
in the method, in the process of the invention,representing the attitude vector of the ship,/->Representing a speed variable; r (ψ) is the conversion matrix and there is R -1 (ψ)＝R T (ψ) and ||r (ψ) |=1; m is an inertial matrix, D l Represents a linear damping matrix, D n (v) A nonlinear damping term; />Representing a disturbance vector;
τ＝T(β)κ(n)u p (2)
in the method, in the process of the invention,representing a control input vector, ">Q is the number of equivalent thrusters, which is a configuration matrix depending on the actuator position; beta is the azimuth of the azimuth thruster, +.>Representing a matrix of force coefficients dependent on the rotational speed of the propeller, u p ＝[|p 1 |p 1 ,|p 2 |p 2 ,…,|p q |p q ] T Wherein p is i ∈[-1,1]I=1, 2, … q is the actual controllable input pitch ratio of the actuator.
Further, the dead zone model is built according to the dead zone nonlinear characteristics of the ship actuator; according to the dead zone model, and combining the fault type of the ship actuator, establishing a fault model, which comprises the following steps:
the dead zone model is represented by formula (3):
the fault model is represented by formula (4):
in the method, in the process of the invention,representing a driving efficiency matrix and having 0.ltoreq.k pi ≤1,i＝1,2,…q，/>Is a bias fault vector, ">Representing actuator dead zone output vector, u p An output vector representing the actuator; for dead zone models, s r ,s l Represent the slope and satisfy s r ＞0,s l ＞0，|s r |≠|s l |，b r ,b l Represents the turning point and satisfies b l ≤0,b r ≥0,|b l |≠|b r |。
Further, three assumptions are set before the fault model is built, including:
assume one: the inertial matrix M is positive and reversible;
suppose two: for the environmental disturbance vector to satisfyWherein->Is an unknown constant vector;
assume three: dead zone parameter satisfies s r ≥s r0 ,s l ≥s l0 Wherein s is r0 ,s l0 Is two smaller normal quantities;
the fault model exhibits four operating states of the actuator based on the three assumptions, including:
mode one: when k is pi =1 andindicating that the executor is operating normally;
mode two: when 0 < k pi < 1 andrepresenting an actuator portion efficiency loss fault;
mode three: when k is pi =1 andrepresenting an actuator bias fault;
mode four: when k is pi =0, at this timeIndicating a total efficiency loss failure of the actuator.
Further, the estimating the speed variable of the ship based on the robust neural network comprises:
equation (5) is derived based on young's inequality:
in the formula, v e ＝β v -v is the velocity error dynamics, beta v Is the output vector of the filter, gamma z ＝diag{γ zu ,γ zv ,γ zr And is the design parameter matrix, z is the prediction error,S v (v)＝diag{S v (v),S v (v),S v (v) RBF matrix in the form of Gaussian function, A v ＝[A u ,A v ,A r ] T Is a neural network weight matrix and has b v ＝||A v || F ，b v ω v ＝A v v e ；/>φ v (v)＝1+||S v (v)||||β v ||，k vn Representing a matrix of design parameters>Is a robust neural damping term;
virtual control law alpha up Represented by formula (6);
wherein k is v Representing a positive design parameter matrix;
constructing an estimation model of formula (7) to estimate the speed variable;
where ζ is the designed parameter matrix.
Further, the designing a dynamic positioning ship controller according to the ship model with actuator failure and dead zone input, a posture vector in the ship model, and the speed variable, comprises:
definition eta d For a normally expected pose, the error vector η e ＝η d - η; based on formula (1), η e The derivative of (2) is represented by formula (8);
virtual control law alpha according to equation (9) v Is designed as follows:
α v ＝R -1 (ψ)k η η e (9)
wherein k is η Is a design parameter in the form of a diagonal matrix;
a first order filter of formula (10) is introduced:
wherein t is v ＝diag{t u ,t v ,t r Is a time constant matrix, beta v Is the output vector of the filter; the input error of the filter is defined as q v ＝[q u ,q v ,q r ] T ＝α v -β v Obtaining the formula (11):
wherein B is v (·)＝[B u (·),B v (·),B r (·)] T Vectors representing constant functions in which all elements are bounded, i.e.Wherein->Are all unknown normal numbers;
combining formula (9) and formula (10) yields:
further, the calculating the dead zone parameter of the dead zone model according to the error between the actual speed and the estimated speed of the ship comprises:
calculating an error z between the actual speed and the estimated speed of the ship by the formula (13);
adaptive parameters by equation (14)Estimating unknown dead zone parameters;
in the method, in the process of the invention,is positive definite matrix, T i (. Cndot.) is the ith column, (-) of the configuration matrix of actuator positions>The expression of (2) has been given in the formula (20), γ z ＝diag{γ zu ,γ zv ,γ zr Is a design parameter matrix Γ λi ,Γ θi ,/>σ λi ,σ θi Is a design parameter;
the dead zone model compensation is carried out by constructing a dead zone inverse model according to the dead zone parameters, and the method comprises the following steps:
the dead zone inverse model is expressed as:
wherein phi is 1 (·),Φ 2 (. Cndot.) is a smooth continuous function, expressed as:
wherein a is 0 Is a design parameter;
the dead zone model is expressed as:
will v pi Designed by the formula (18) -formula (20), whereinIs->Is a function of the estimated value of (2);
input ω of the ith actuator pi Can be expressed as:
based on the formulas (17) and (18), the compensation error is expressed as:
in the method, in the process of the invention,δ i the upper bound of (c) can be derived as:
wherein, when t is more than or equal to 0,is bounded and is associated with +.> Gradually converging to 0.
Further, the compensating the fault model according to the fault parameters includes:
by adaptive parameters in equations (24) and (25)And->To compensate for actuator gain and actuator failure;
further, the control law after the dead zone model and the fault model are compensated is calculated; adjusting a control input vector of a marine vessel actuator according to the control law, comprising:
the control law after the dead zone model and the fault model compensation is expressed as follows by the formula (26):
the control input vector p of the marine vessel actuator is expressed by equation (27):
in the method, in the process of the invention,T * representing the pseudo-inverse of T i (. Cndot.) represents the ith column, (. Cndot.) of matrix T (. Cndot.)>Epsilon is a constant and satisfies epsilon > 0.
The invention solves the problems of reduced regulation quality, poor system stability, reduced positioning accuracy and the like of the ship control system caused by inherent dead zone nonlinearity of the dynamic positioning ship actuator by utilizing the dead zone constraint compensation strategy, and can greatly improve the control performance of the system. The invention solves the problem of unknown faults of the actuator in the marine vessel dynamic positioning operation process, and can realize the continuous maintenance of the normal running of the dynamic positioning task under the condition that the actuator has unknown faults.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to the drawings without inventive effort to a person skilled in the art.
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of a power positioning marine propulsion arrangement in accordance with the present invention;
FIG. 3 is a schematic diagram of dead zone nonlinear compensation in the present invention;
FIG. 4 is a diagram of the dynamic positioning control logic of the ship in the present invention;
FIG. 5 is a view of a two-dimensional wind field and corresponding wind-generated wave surface under 6-level sea conditions in a simulation test of the present invention;
FIG. 6 is a comparative view of motion trajectories of vessels in a simulation test of the present invention;
FIG. 7 is a comparative view of ship attitude variables in a simulation test of the present invention;
FIG. 8 is a comparison of control inputs from a ship in a simulation test of the present invention;
FIG. 9 is a graph of dead zone parameter estimation of an actuator in a simulation test of the present invention;
FIG. 10 is a diagram of the motion profile of a vessel under actuator failure in a simulation test of the present invention;
FIG. 11 is a graph of actual control inputs under actuator failure in a simulation test of the present invention;
FIG. 12 adaptive parameters in simulation experiments of the present inventionAnd->A graph is input.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1 and 4, the present embodiment provides a method for designing a composite adaptive fault-tolerant controller in consideration of an unknown dead zone, including:
101. building a ship model;
specifically, according to navigability and a manipulation theory, a three-degree-of-freedom mathematical model of the dynamic positioning ship is established as formula (1);
in the method, in the process of the invention,representing the attitude vector of the ship,/->Representing a speed variable; r (ψ) is the conversion matrix and there is R -1 (ψ)＝R T (ψ) and|R (ψ) |=1; m is an inertial matrix, D l Represents a linear damping matrix, D n (v) A nonlinear damping term; />Representing a disturbance vector;
τ＝T(β)κ(n)u p (2)
in the method, in the process of the invention,representing a control input vector, ">Q is the number of equivalent thrusters, which is a configuration matrix depending on the actuator position; as shown in FIG. 2, the position distribution of the actuator is shown in FIG. 2, where β is the azimuth of the azimuth thruster, +.>Representing a matrix of force coefficients dependent on the rotational speed of the propeller, u p ＝[|p 1 |p 1 ,|p 2 |p 2 ,…,|p q |p q ] T Wherein p is i ∈[-1,1]I=1, 2, … q is the actual controllable input pitch ratio of the actuator.
102. Establishing a dead zone model according to the dead zone nonlinear characteristic of the ship actuator; establishing a fault model according to the dead zone model and combining the fault type of the ship actuator; adding the fault model into a ship model to obtain the ship model with actuator faults and dead zone inputs;
specifically, in actual engineering, the propeller may suffer from bias faults and efficiency loss faults as well as dead zone nonlinearities inherent in the actuator. Therefore, we build an actuator fault model and a dead zone model.
The dead zone model is represented by equation (3):
the fault model is represented by equation (4):
in the method, in the process of the invention,representing a driving efficiency matrix and having 0.ltoreq.k pi ≤1,i＝1,2,…q，/>Is a bias fault vector, ">Representing actuator dead zone output vector, u p An output vector representing the actuator; for dead zone models, s r ,s l Represent the slope and satisfy s r ＞0,s l ＞0，|s r |≠|s l |，b r ,b l Represents the turning point and satisfies b l ≤0,b r ≥0,|b l |≠|b r | a. The invention relates to a method for producing a fibre-reinforced plastic composite. The dead zone pattern is shown in fig. 3. In fig. 3, (a) is a dead zone nonlinearity, and (b) is a smooth dead zone inverse model.
Three assumptions are set before the fault model is built, including:
assume one: the inertial matrix M is positive and reversible;
suppose two: for the environmental disturbance vector to satisfyWherein->Is an unknown constant vector;
assume three: dead zone parameter satisfies s r ≥s r0 ,s l ≥s l0 Wherein s is r0 ,s l0 Is two smaller normal quantities;
the fault model exhibits four operating states of the actuator based on the three assumptions, including:
mode one: when k is pi =1 andindicating that the executor is operating normally;
mode two: when 0 < k pi < 1 andrepresenting an actuator portion efficiency loss fault;
mode three: when k is pi =1 andrepresenting an actuator bias fault;
mode four: when k is pi =0, at this timeIndicating a total efficiency loss failure of the actuator.
103. Estimating a speed variable of the ship based on the robust neural network;
specifically, formula (5) is derived based on the young's inequality:
in the formula, v e ＝β v -v is the velocity error dynamics, beta v Is the output vector of the filter, gamma z ＝diag{γ zu ,γ zv ,γ zr And is the design parameter matrix, z is the prediction error,S v (v)＝diag{S v (v),S v (v),S v (v) RBF matrix in the form of Gaussian function, A v ＝[A u ,A v ,A r ] T Is a neural network weight matrix and has b v ＝||A v || F ，φ v (v)＝1+||S v (v)||||β v ||，k vn Representing a matrix of design parameters>Is a robust neural damping term;
virtual control law alpha up Represented by formula (6);
wherein k is v Representing a positive design parameter matrix;
constructing an estimation model of formula (7) to estimate the speed variable;
where ζ is the designed parameter matrix.
104. Designing a dynamic positioning ship controller according to a ship model with actuator faults and dead zone inputs, and attitude vectors and speed variables in the ship model;
specifically, define η d For a normally expected pose, the error vector η e ＝η d - η; based on formula (1), η e The derivative of (2) is represented by formula (8);
virtual control law alpha according to equation (9) v Is designed as follows:
α v ＝R -1 (ψ)k η η e (9)
wherein k is η Is a design parameter in the form of a diagonal matrix;
a first order filter of formula (10) is introduced:
wherein t is v ＝diag{t u ,t v ,t r Is a time constant matrix, beta v Is the output vector of the filter; the input error of the filter is defined as q v ＝[q u ,q v ,q r ] T ＝α v -β v Obtaining the formula (11):
wherein B is v (·)＝[B u (·),B v (·),B r (·)] T Vectors representing constant functions in which all elements are bounded, i.e.Wherein->Are all unknown normal numbers;
combining formula (9) and formula (10) yields:
105. calculating dead zone parameters of the dead zone model according to errors between the actual speed and the estimated speed of the ship; constructing a dead zone inverse model according to the dead zone parameters to compensate the dead zone model;
specifically, an error z between the actual speed and the estimated speed of the ship is calculated by the formula (13);
adaptive parameters by equation (14)Estimating unknown dead zone parameters;
in the method, in the process of the invention,is positive definite matrix, T i (. Cndot.) is the ith column, (-) of the configuration matrix of actuator positions>The expression of (2) has been given in the formula (20), γ z ＝diag{γ zu ,γ zv ,γ zr Is a design parameter matrix Γ λi ,Γ θi ,/>σ λi ,σ θi Is a design parameter;
the dead zone inverse model is expressed as:
wherein phi is 1 (·),Φ 2 (. Cndot.) is a smooth continuous function, expressed as:
wherein a is 0 Is a design parameter;
the dead zone model is expressed as:
will v pi Designed by the formula (18) -formula (20), whereinIs->Is a function of the estimated value of (2);
input ω of the ith actuator pi Can be expressed as:
based on the formulas (17) and (18), the compensation error is expressed as:
in the method, in the process of the invention,δ i the upper bound of (c) can be derived as:
wherein, when t is more than or equal to 0,is bounded and is associated with +.> Gradually converging to 0.
106. Calculating fault parameters according to errors between the actual speed and the estimated speed of the ship; compensating the fault model according to the fault parameters;
specifically, defineThere is->Wherein iota= [1, …,1] T . Thus, we can get;
by the adaptive parameters in equations (25) and (26)And->To compensate for actuator gain and actuator failure;
107. calculating a dead zone model and a control law after fault model compensation; and adjusting a control input vector of the ship actuator according to the control law to control the ship to perform dynamic positioning.
Specifically, the control law after dead zone model and fault model compensation is expressed by equation (27):
the control input vector p of the marine vessel actuator is expressed by equation (28):
in the method, in the process of the invention,T * representing the pseudo-inverse of T i (. Cndot.) represents the ith column, (. Cndot.) of matrix T (. Cndot.)>Epsilon is a constant and satisfies epsilon > 0.
The simulation test is specifically as follows:
to verify the effectiveness of the control algorithm proposed by the present invention, we selected a length of 76.2m and a mass of 4.591 ×10 6 The ship of kg is the controlled object, and the ship is provided with a full-rotation propeller, three tunnel propellers and two main propellers.
For environmental disturbance, a physics-based mathematical model (i.e., JONSWAP wave spectrum and NORSOK wind spectrum) is used to simulate sea wind and irregular wind waves. As shown in FIG. 5, the wind speed was 16.3m/s and the wind direction was 90deg. The expected attitude of the experimental vessel is eta d ＝[10m,10m,120deg] T The initial state is [ x, y, ψ, u, v, r]| t＝0 ＝[0m,0m,135deg,0m/s,0m/s,0deg/s]. In order to verify the effectiveness of the dead zone compensation mechanism provided by the invention, the algorithm provided by the invention is compared with the algorithm which takes dead zone input into consideration in the prior art. As shown in fig. 6 and 7, although both control algorithms can be maintained near the desired position, the control algorithm proposed by the present invention has higher accuracy and stability. As shown in fig. 8, compared toThe algorithm in the prior art has the advantages that the control input curve of the algorithm is more stable and smooth, so that the algorithm has higher positioning precision and energy efficiency. Fig. 9 shows an estimated variation of the actuator dead zone parameter.
In order to further verify the effectiveness of the fault compensation strategy of the algorithm provided by the invention, a fault experiment is carried out. In the experiment, the initial attitude of the experimental ship is eta= [0m,6m,136deg] T When t is E [0,500 ]]When the expected posture is eta d1 ＝[10m,24m,120deg] T The method comprises the steps of carrying out a first treatment on the surface of the When t is E (500, 1000]When the posture eta is desired d2 ＝[16m,0m,140deg] T The method comprises the steps of carrying out a first treatment on the surface of the When t is E (1000, 1500]When the posture eta is desired d3 ＝[8m,-40m,160deg] T . Furthermore, at 800s, we chose No.5 actuator to suffer from bias failure; at 1300s, the No.3 and No.1 actuators suffered from partial efficiency loss faults and bias faults. Fig. 10 shows the motion profile of the vessel in case of an actuator failure. As shown in fig. 11, when the actuator fails, the vessel performing the positioning task may briefly deviate from the desired position, and the controller returns the vessel to the desired attitude by adjusting the control input of the actuator. Furthermore, it can be seen from fig. 11 that the azimuth angle of the full-circle propeller jumps, which is normal. Because the azimuth angle of the full-rotation propeller takes the value range (-180 deg,180 deg)]In engineering practice, the value range is (0, 360 deg)]Therefore, the switching operation is required in engineering practice. Fig. 12 shows a curve of the adaptive parameter for compensating the failure of the actuator, and as can be seen from fig. 12, when the actuator fails, the adaptive parameter also changes correspondingly to compensate the failure of the actuator.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention.
Claims (9)
1. The design method of the composite adaptive fault-tolerant controller taking the unknown dead zone into consideration is characterized by comprising the following steps of:
building a ship model;
establishing a dead zone model according to the dead zone nonlinear characteristic of the ship actuator; establishing a fault model according to the dead zone model and combining the fault type of the ship actuator; adding the fault model to the ship model to obtain a ship model with actuator faults and dead zone inputs;
estimating a speed variable of the ship based on the robust neural network;
designing a dynamic positioning ship controller according to the ship model with the actuator fault and dead zone input, a posture vector in the ship model and the speed variable;
calculating dead zone parameters of the dead zone model according to errors between the actual speed and the estimated speed of the ship; constructing a dead zone inverse model according to the dead zone parameters to compensate the dead zone model;
calculating fault parameters according to errors between the actual speed and the estimated speed of the ship; compensating the fault model according to the fault parameters;
calculating the control law of the dead zone model and the fault model after compensation; and adjusting a control input vector of the ship actuator according to the control law so as to control the ship to execute dynamic positioning.
2. The method for designing a composite adaptive fault-tolerant controller taking into account unknown dead zones according to claim 1, wherein the building a ship model comprises:
establishing a three-degree-of-freedom mathematical model of the dynamic positioning ship as (1);
in the method, in the process of the invention,representing the attitude vector of the ship,/->Representing a speed variable; r (ψ) is the conversion matrix and there is R -1 (ψ)＝R T (ψ) and ||r (ψ) |=1; m is an inertial matrix, D l Represents a linear damping matrix, D n (v) A nonlinear damping term; />Representing a disturbance vector;
τ＝T(β)κ(n)u p (2)
in the method, in the process of the invention,representing a control input vector, ">Q is the number of equivalent thrusters, which is a configuration matrix depending on the actuator position; beta is the azimuth of the azimuth thruster, +.>Representing a matrix of force coefficients dependent on the rotational speed of the propeller, u p ＝[|p 1 |p 1 ,|p 2 |p 2 ,…,|p q |p q ] T Wherein p is i ∈[-1,1]I=1, 2, … q is the actual controllable input pitch ratio of the actuator.
3. The method for designing the composite adaptive fault-tolerant controller taking into account the unknown dead zone according to claim 2, wherein the dead zone model is built according to the dead zone nonlinear characteristics of the ship actuator; according to the dead zone model, and combining the fault type of the ship actuator, establishing a fault model, which comprises the following steps:
the dead zone model is represented by formula (3):
the fault model is represented by formula (4):
in the method, in the process of the invention,representing a driving efficiency matrix and having 0.ltoreq.k pi ≤1,i＝1,2,…q，Is a bias fault vector, ">Representing actuator dead zone output vector, u p An output vector representing the actuator; for dead zone models, s r ,s l Represent the slope and satisfy s r ＞0,s l ＞0，|s r |≠|s l |，b r ,b l Represents the turning point and satisfies b l ≤0,b r ≥0,|b l |≠|b r |。
4. A method of designing a composite adaptive fault tolerant controller taking into account unknown dead zones as claimed in claim 3, wherein setting three hypotheses prior to building the fault model comprises:
assume one: the inertial matrix M is positive and reversible;
suppose two: for the environmental disturbance vector to satisfyWherein->Is an unknown constant vector;
assume three: dead zone parameter satisfies s r ≥s r0 ,s l ≥s l0 Wherein s is r0 ,s l0 Is two smaller normal quantities;
the fault model exhibits four operating states of the actuator based on the three assumptions, including:
mode one: when k is pi =1 andindicating that the executor is operating normally;
mode two: when 0 < k pi < 1 andrepresenting an actuator portion efficiency loss fault;
mode three: when k is pi =1 andrepresenting an actuator bias fault;
mode four: when k is pi =0, at this timeIndicating a total efficiency loss failure of the actuator.
5. The method for designing a composite adaptive fault-tolerant controller taking into account unknown dead zones according to claim 4, wherein the estimating the speed variable of the vessel based on the robust neural network comprises:
equation (5) is derived based on young's inequality:
in the formula, v e ＝β v -v is the velocity error dynamics, beta v Is the output vector of the filter, gamma z ＝diag{γ zu ,γ zv ,γ zr And is the design parameter matrix, z is the prediction error,S v (v)＝diag{S v (v),S v (v),S v (v) RBF matrix in the form of Gaussian function, A v ＝[A u ,A v ,A r ] T Is a neural network weight matrix and has b v ＝||A v || F ，/>b v ω v ＝A v v e ；/>φ v (v)＝1+||S v (v)||||β v ||，k vn A matrix of design parameters is represented,is a robust neural damping term;
virtual control law alpha up Represented by formula (6);
wherein k is v Representing a positive design parameter matrix;
constructing an estimation model of formula (7) to estimate the speed variable;
where ζ is the designed parameter matrix.
6. The method of designing a composite adaptive fault tolerant controller taking into account unknown dead band of claim 5, wherein said designing a dynamic positioning marine controller based on said marine model with actuator fault and dead band inputs, attitude vectors in the marine model, and said speed variables comprises:
definition eta d For a normally expected pose, the error vector η e ＝η d - η; based on formula (1), η e The derivative of (2) is represented by formula (8);
virtual control law alpha according to equation (9) v Is designed as follows:
α v ＝R -1 (ψ)k η η e (9)
wherein k is η Is a design parameter in the form of a diagonal matrix;
a first order filter of formula (10) is introduced:
wherein t is v ＝diag{t u ,t v ,t r Is a time constant matrix, beta v Is the output vector of the filter; the input error of the filter is defined as q v ＝[q u ,q v ,q r ] T ＝α v -β v Obtaining the formula (11):
wherein B is v (·)＝[B u (·),B v (·),B r (·)] T Vectors representing constant functions in which all elements are bounded, i.e.Wherein->Are all unknown normal numbers;
combining formula (9) and formula (10) yields:
7. the method of designing a composite adaptive fault-tolerant controller taking into account unknown dead zones according to claim 6, wherein said calculating dead zone parameters of the dead zone model from the error between the actual speed and the estimated speed of the vessel comprises:
calculating an error z between the actual speed and the estimated speed of the ship by the formula (13);
adaptive parameters by equation (14)Estimating unknown dead zone parameters;
in the method, in the process of the invention,is positive definite matrix, T i (. Cndot.) is the ith column, (-) of the configuration matrix of actuator positions>The expression of (2) has been given in the formula (20), γ z ＝diag{γ zu ,γ zv ,γ zr Is a design parameter matrix Γ λi ,Γ θi ,/>σ λi ,σ θi Is a design parameter;
the dead zone model compensation is carried out by constructing a dead zone inverse model according to the dead zone parameters, and the method comprises the following steps:
the dead zone inverse model is expressed as:
wherein phi is 1 (·),Φ 2 (. Cndot.) is a smooth continuous function, expressed as:
wherein a is 0 Is a design parameter;
the dead zone model is expressed as:
will v pi Designed by the formula (18) -formula (20), whereinIs->Is a function of the estimated value of (2);
input ω of the ith actuator pi Can be expressed as:
based on the formulas (17) and (18), the compensation error is expressed as:
in the method, in the process of the invention,δ i the upper bound of (c) can be derived as:
wherein, when t is more than or equal to 0,is bounded and is associated with +.>a 0 →0，/>Gradually converging to 0.
8. The method of designing a composite adaptive fault tolerant controller taking into account unknown dead-bands of claim 7, wherein said compensating the fault model based on the fault parameters comprises:
by adaptive parameters in equations (24) and (25)And->To compensate for actuator gain and actuator failure;
9. the method for designing a composite adaptive fault-tolerant controller taking into account unknown dead zones according to claim 8, wherein said calculating said dead zone model and said fault model compensated control law; adjusting a control input vector of a marine vessel actuator according to the control law, comprising:
the control law after the dead zone model and the fault model compensation is expressed as follows by the formula (26):
the control input vector p of the marine vessel actuator is expressed by equation (27):
in the method, in the process of the invention,T * representing the pseudo-inverse of T i (. Cndot.) represents the ith column, (. Cndot.) of matrix T (. Cndot.)>Epsilon is a constant and satisfies epsilon > 0.
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