CN118244770B - Repeated learning composite disturbance-resistant error-tolerant control method for unmanned ship - Google Patents
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Abstract
The invention belongs to the technical field of unmanned ship control, and discloses a repeated learning composite disturbance-rejection error-tolerant control method for an unmanned ship. The method comprises the following steps: setting up an unmanned ship dynamic positioning test simulation system, and setting up a corresponding mathematical model according to the dynamics characteristics of the unmanned ship; constructing a proper disturbance observer and a fault estimator, estimating faults of the unmanned ship power positioning system, and estimating the disturbance and the faults; and finally, designing a repeated learning composite disturbance rejection error-tolerant controller for the unmanned ship dynamic positioning system based on the periodicity of the ideal system, and completing the composite disturbance rejection error-tolerant control of the unmanned ship dynamic positioning system under the action of the controller. The method can ensure that the system can safely and stably operate when the speed information of the unmanned ship power positioning system is unavailable due to noise pollution and disturbance and actuator faults exist at the same time.
Description
Technical Field
The invention belongs to the technical field of unmanned ship control, and relates to a repeated learning composite disturbance-resistant error-tolerant control method for an unmanned ship.
Background
The Unmanned ship (Unmanned MARINE VEHICLES, UMVS) is used as an Unmanned platform capable of remotely controlling or autonomously controlling navigation, has the characteristics of low cost, good flexibility, high concealment and the like, is used for marine operation tasks, has the capability of executing tasks in all weather, and can particularly replace human beings to execute dangerous and time-consuming operation tasks. With the progress and innovation of the related technology, the application prospect of the unmanned ship is wider and wider, and in the civil aspect, the unmanned ship can be used for marine environment monitoring, resource exploration, marine rescue and the like. In the military aspect, unmanned ships carry different weapon systems and can be used for marine reconnaissance, monitoring, replenishment, attack, ship reversing and the like. Therefore, the problem of motion control of unmanned boats is receiving extensive attention from academia and industry.
Marine dynamic positioning (Dynamic Positioning, DP) technology allows accurate control of unmanned boats at fixed locations, heading or predetermined paths. However, UMVs is susceptible to strong external disturbances caused by ocean currents, waves and wind due to the complex marine environment. The problem of DP tamper resistance is thus a critical issue for unmanned boats to control accurately. The distinction between anti-interference capability and anti-interference control methods can be divided into two types: disturbance rejection and disturbance cancellation. Disturbance rejection is the reduction of the effect of disturbance on system performance by parameter optimization or robust control. Disturbance elimination is to accurately compensate for disturbance by designing a disturbance observer. Clearly, the disturbance cancellation has better control performance than disturbance suppression. In the current research on DP anti-interference, researchers develop various DP control methods based on disturbance observers. For example, based on velocity information, a slowly varying disturbance due to second order wave drift, ocean currents, wind and non-simulated dynamics is designed for a disturbance observer. However, the speed information is not measurable in the actual environment due to noise pollution, and in order to avoid the lack of speed information, it is proposed that the state observer is based on a disturbance observer, and the fast estimation performance of the disturbance observer may not be guaranteed due to neglecting the preconditions satisfied by the gain of the disturbance observer. How to estimate such low frequency disturbances quickly and accurately in case the speed information is not available, no effective solution exists at present.
On the other hand, in a severe marine environment, a propeller-type propeller as a main actuator is liable to malfunction UMVs when performing tasks. Thus, actuator failure is also a major factor threatening DP motion control. To eliminate the impact of faults on the system, a common strategy is fault compensation or passive fault tolerance. Fault compensation is favored over passive fault tolerance because it can accurately counteract faults. For example, researchers design fault state observers to estimate actuator failure coefficients, or a finite time estimator under input constraints, to estimate additive hybrid fault terms (faults, disturbances, and uncertainties). Researchers have also developed learning fault estimators for switching unmanned boats. However, most fault estimation results for UMVs require corresponding matching conditions and ignore measurement noise. The unavailability of the speed information results in failure to meet the match condition. Furthermore, no effective solution to the co-design problem of fault estimation and disturbance estimation of UMVs lacking speed information has been presented.
When using the estimates of faults and disturbances in the design of the DP tracking controller, it was found that the tracking control result of UMVs takes the periodic signal as the desired target, but does not take advantage of the repeatability of the periodic signal. Since the operation result of the previous cycle is learned to guide the next cycle, the repeated learning controller is a more suitable tracking controller in the face of a periodically desired target.
However, conventional proportional-derivative (Proportional Derivative, PD) type learning controllers rely on measurement output, which is ineffective due to the presence of measurement noise and the unavailability of velocity information. Therefore, designing a proportional-derivative type repeating learning composite disturbance rejection error controller with measured noise and unmeasured speed information UMVs is a challenge, and no corresponding repeating learning controller design method exists at present.
Disclosure of Invention
The invention aims to provide a repeated learning composite disturbance-resistant fault-tolerant control method for an unmanned ship, which is used for ensuring that the unmanned ship power positioning system can safely and stably operate when the speed information of the unmanned ship power positioning system is unavailable due to noise pollution on the output of the unmanned ship power positioning system and disturbance and actuator faults exist at the same time.
In order to achieve the above purpose, the invention adopts the following technical scheme:
The repeated learning composite disturbance-resistant error-tolerant control method for the unmanned ship comprises the following steps of:
Step 1, building an unmanned ship dynamic positioning test simulation system, and building a corresponding mathematical model according to the dynamics characteristics of the unmanned ship;
Step 2, designing a disturbance observer and a fault estimator for the unmanned ship dynamic positioning system, and realizing accurate estimation of disturbance and fault through the disturbance observer and the fault estimator;
And step 3, designing a repeated learning composite disturbance rejection error-tolerant controller for the unmanned ship dynamic positioning system with unavailable speed information, and obtaining the disturbance observer gain, repeated learning control gain and feedback control gain under the condition that the safe and stable operation condition of the system is met.
In addition, on the basis of the repeated learning composite disturbance-resistant fault-tolerant control method of the unmanned ship, the invention also provides a repeated learning composite disturbance-resistant fault-tolerant control system of the unmanned ship corresponding to the repeated learning composite disturbance-resistant fault-tolerant control method, which adopts the following technical scheme:
the repeated learning composite disturbance-resistant error-tolerant control system of the unmanned ship comprises the following modules:
the model building module is used for building an unmanned ship dynamic positioning test simulation system and building a corresponding mathematical model according to the dynamic characteristics of the unmanned ship;
The disturbance observer and fault estimator design module is used for designing a disturbance observer and a fault estimator for the unmanned ship dynamic positioning system, and realizing accurate estimation of disturbance and fault through the disturbance observer and the fault estimator;
and the controller construction and gain solving module is used for designing a repeated learning composite disturbance rejection error-tolerant controller for the unmanned ship dynamic positioning system with unavailable speed information, and obtaining the disturbance observer gain, repeated learning control gain and feedback control gain under the condition that the safe and stable operation condition of the system is met.
The invention has the following advantages:
As described above, the invention provides a repeated learning composite disturbance rejection error tolerant control method of unmanned ships under the conditions of uncontrollable speed information, executor faults and multiple disturbances, and provides a fast converging fault-disturbance comprehensive estimator based on an intermediate estimator and a virtual disturbance observer in the design process.
Drawings
FIG. 1 is a block flow diagram of a method for repeated learning composite disturbance rejection error tolerant control of an unmanned ship in an embodiment of the invention.
FIG. 2 is a control block diagram of a composite disturbance-tolerant controller based on repeated learning provided by the invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawings and detailed description:
Example 1
As shown in fig. 1, the embodiment describes a method for controlling repeated learning composite disturbance rejection of an unmanned ship, which includes the following steps:
Step 1, a power positioning test simulation system of the unmanned ship is built in advance, a corresponding power positioning mathematical model is built according to the dynamics characteristics of the unmanned ship, and faults and disturbance of an actuator are represented into the built mathematical model, so that a foundation is provided for subsequent analysis. The state equation of the unmanned ship dynamic positioning system is described as follows:
(1)
Vector quantity The definition is as follows:，、 And Respectively representing the longitudinal moving speed, the swinging speed and the yaw angular speed of the fixed body frame, the superscript T represents the transposition of corresponding vectors,Is shown in the firstTime of day.
Vector quantityThe definition is as follows:，、 And Respectively representing the abscissa, the ordinate and the yaw angle of the position with the earth as a reference system,Representation ofIs a first derivative of (a).
Rotation matrixThe definition is as follows:
。
Vector quantity Representing vectorsIs the first derivative of (a); the invertible matrix is represented by a matrix of invertible elements, Representing the damping matrix of the device,Representing a mooring force matrix; representing a fault-containing propulsion force, which is described in the form:
(2)
Wherein the method comprises the steps of Representing the control inputs of the system,Representing an additive actuator failure; composite disturbanceThe description is as follows:
(3)
(4)
Wherein the method comprises the steps of Is a slowly varying disturbance caused by second order waves, ocean currents, wind and non-modeling dynamics,Is thatIs used as a first derivative of (a),Representing an unknown disturbance; Representing a bias time constant matrix, the superscript-1 representing the inverse of the matrix; representing the magnitude bounded noise vector, Representing a diagonal matrix.
Due to the presence of noise, the speed UMVs is in most cases not measurable, i.eIs not available.
The unmanned ship dynamic positioning system is positioned inLinearizing the system while defining a state vectorThe UMVs system, which is not speed measurable, is described as:
(5)
Wherein the method comprises the steps of ，，D is a constant matrix; And Respectively representing an identity matrix and a 0 matrix with proper dimensions; And Representing measurement output and measurement noise, respectively.
Assume that、、Derivative of faultIs a bounded function and satisfies:
，，，；
wherein, 、、、Is a known constant.
And 2, designing a disturbance observer and a fault estimator for the unmanned ship dynamic positioning system, and realizing accurate estimation of disturbance and fault through the disturbance observer and the fault estimator.
Assuming that the states are all measurable, the disturbance observer is constructed as follows:
(6)
Wherein the method comprises the steps of Representation ofIs used for the estimation of the (c),Is an auxiliary state vector that is used to determine the state of the object,Is thatIs used as a first derivative of (a),Is the disturbance observer gain, matrixIs defined as。
Due to the failure to obtainThe above disturbance observer is ineffective, so the following virtual disturbance observer is designed:
(7)
wherein, Representation ofIs determined by the virtual estimate of (a). Further, the observed error is defined as:
；
an observed error system of the form:
(8)
Wherein the method comprises the steps of Indicating the error of the observation and,Representing the first derivative of the observed error.
This means that whenIs a Hertz matrix, virtual estimateCan perfectly track。
To achieve fault estimation, the following intermediate vectors are designed：
(9)
Wherein the method comprises the steps ofIs an adjustable variable of the design and derives the following equation:
(10)
Combining equations (7) - (10) to obtain a comprehensive fault disturbance estimator of the form:
(11)
Wherein the method comprises the steps of 、、、、AndRespectively are、、、、AndIs used for the estimation of (a),Representing observer gain;、、 Respectively is 、、Is a first derivative of (a).
The disturbance and fault estimators are designed separately, whereas the fault and disturbance are coupled on the same measurement channel, so that it is difficult to distinguish between the disturbance and the fault, but the sum of the disturbance and fault estimators is estimated accurately. The two information are different in nature but similar, so the fault and disturbance sums are accurately estimated.
Defining corresponding error vectors respectively:，，，， And 。
The derived error system is thus as follows:
(12)
Wherein the auxiliary matrix 、AndRespectively defined as，AndGiven disturbance observer gainSo that the auxiliary matrixIs a Hulvitz matrix; furthermore matrixThe design is as follows:
；
Wherein the method comprises the steps of Is a scalar, and the matrix is unknownSatisfy the following requirementsIs a helvetz matrix.
Further, a Lyapunov function of the form is constructed for the error system shown in equation (12) as follows:
(13)
Wherein the energy storage function 、、、Respectively defined as:
，， And 。
And matrix、、AndAre positive definite matrices.
Further, deriving the constructed lyapunov function over time, deriving:
(14)
wherein the function is Expressed as: Wherein Representing the matrix.
Diagonal matrix，Is a diagonal matrix symbol.
According to，AndIt can be deduced that:
(15)
Wherein the method comprises the steps of In order to assist in the matrix,Is a scalar. Auxiliary vectorAndRespectively defined as:
And ；
Auxiliary matrixThe definition is as follows:
。
Wherein:
；
；
；
。
Auxiliary matrix The definition is as follows:
。
Further, to ensure estimation errors 、AndThe agreement is eventually bounded, requiring satisfaction:
(16)
and the corresponding observer gain is obtained as: 。
And step 3, designing a repeated learning composite disturbance rejection error-tolerant controller for the unmanned ship dynamic positioning system with unavailable speed information, and obtaining the disturbance observer gain, repeated learning control gain and feedback control gain under the condition that the safe and stable operation condition of the system is met.
The method comprises the steps of designing and repeatedly learning a composite disturbance-rejection error-tolerant controller by utilizing periodic information, and describing an ideal model of the unmanned ship as follows:
(17)
Wherein the method comprises the steps of 、AndRespectively representing the ideal state, ideal input and ideal output of the unmanned ship dynamic positioning system; Representation of Is the first derivative of (a); since the state trace of an ideal system has periodicity, namely:
(18)
Wherein the method comprises the steps of Representing a period length.
In order to counteract the effects of faults and disturbances, the observer-based repetitive learning composite immunity fault-tolerant controller is designed to:
(19)
wherein, The control law of repeated learning is indicated,Which represents the feedback controller and which is configured to control,Representing an anti-disturbance fault-tolerant controller,The repeated learning control rate of the previous cycle is indicated,Representing the system estimation error of the previous period,Indicating that the last period of system output has occurred,Representing the system estimate output of the last cycle,Is a subscript of the number of the symbol,；、AndIs to repeatedly learn the control gain matrix,Is a matrix of feedback control gains that are,Is thatIs a first derivative of (a).
Further, the error of the observer state from the ideal state of the system is expressed as:
(20)
wherein error vectors are input The definition is as follows:， Representing ideal input, auxiliary error vector The definition is as follows: Weighting matrix The definition is as follows:。
the control input of the ideal unmanned ship dynamic positioning system also has periodicity, namely: 。
thus inputting error vector The rewrites to the following form:
(21)
Wherein the method comprises the steps of Representing the input error of the previous cycle.
Defining a gain matrixThe method comprises the following steps: gain matrix The method comprises the following steps:。
thus deriving an error input vector The method comprises the following steps:
(22)
Thus obtaining an input error vector The method meets the following conditions:
(23)
Wherein the method comprises the steps of Satisfy the following requirements。
Time ofExpressed in periodic form as:， denoted as the first A period of time approaching infinityWhile; The relationship of the resulting input iteration input error to the initial input error is therefore expressed as:
(24)
Wherein the method comprises the steps of Representing the systematic input error for the k-1 th cycle,Representing the systematic input error for the k-2 th cycle,Representing the initial system input error of the system.
Indicating that whenIn the time-course of which the first and second contact surfaces,Converging to 0.
Further, constructing a Lyapunov function for the repeated learning composite anti-disturbance fault-tolerant controller:
(25)
deriving the lyapunov function in equation (25), deriving:
。
Known from the inequality condition:
(26)
(27)
wherein, AndIs scalar and the feedback control gain is; Thus, there are:
(28)
Wherein the method comprises the steps of 。
Finally, the stability conditions of the unmanned ship dynamic positioning system are as follows:
(29)
(30)
Obtaining a repeated learning control gain matrix ，MatrixIs defined as. The observer gain, the feedback control gain and the repeated learning control gain of the system are obtained, so that the system can still have better control tracking performance when disturbance and actuator faults exist. The fault and disturbance of the unmanned ship power positioning system are accurately estimated through the design estimator, the influence of speed information deficiency is effectively overcome, a PD-type repeated learning controller is designed for the system on the basis, the composite disturbance-resistant error-tolerant control of the unmanned ship power positioning system is realized, and the gain of a disturbance observer and a controller which enable the unmanned ship power positioning system to be finally bounded is provided.
FIG. 2 shows a control block diagram of a re-learning composite anti-disturbance fault tolerant controller in accordance with the present invention. Wherein the sensor of fig. 2 is used to measure the actual output of the system and to convert the output signal to a desired signal via the sensor for subsequent analysis. The observer and the estimator are used for comparing signals measured by the sensor to obtain the sum of disturbance and fault signals, and the magnitude of the disturbance and fault signals is accurately estimated through the estimator. The memory is used for recording the value of the observer and simultaneously recording the output value of the last period of operation, and data support is provided for repeated learning of the system. The controller is used for outputting control signals of the system, and mainly comprises feedback control and repeated learning control.
The method of the invention well ensures that the unmanned ship power positioning system can safely and stably operate when the speed information of the unmanned ship power positioning system is unavailable due to noise pollution on the output of the unmanned ship power positioning system and disturbance and actuator faults exist at the same time.
Example 2
Embodiment 2 describes a repeated learning composite disturbance-resistant fault-tolerant control system for an unmanned ship, which is based on the same inventive concept as the repeated learning composite disturbance-resistant fault-tolerant control method for an unmanned ship described in embodiment 1.
The repeated learning composite disturbance-rejection error-tolerant control system of the unmanned ship in the embodiment comprises the following modules:
the model building module is used for building an unmanned ship dynamic positioning test simulation system and building a corresponding mathematical model according to the dynamic characteristics of the unmanned ship;
The disturbance observer and fault estimator design module is used for designing a disturbance observer and a fault estimator for the unmanned ship dynamic positioning system, and realizing accurate estimation of disturbance and fault through the disturbance observer and the fault estimator;
and the controller construction and gain solving module is used for designing a repeated learning composite disturbance rejection error-tolerant controller for the unmanned ship dynamic positioning system with unavailable speed information, and obtaining the disturbance observer gain, repeated learning control gain and feedback control gain under the condition that the safe and stable operation condition of the system is met.
It should be noted that, in the repeated learning composite disturbance rejection error tolerant control system of the unmanned ship described in embodiment 2, the implementation process of the functions and actions of each functional module is specifically described in the implementation process of the corresponding steps in the method in embodiment 1, and will not be described herein.
Example 3
Embodiment 3 describes a computer device including a memory and one or more processors. Executable code is stored in the memory. The steps for implementing the repeated learning composite disturbance rejection error tolerant control method of unmanned boat in embodiment 1 described above when the processor executes the executable code.
In this embodiment, the computer device is any device or apparatus having data processing capability, which is not described herein.
Example 4
Embodiment 4 describes a computer-readable storage medium having stored thereon a program which, when executed by a processor, is configured to implement the steps of the repetitive learning composite tamper error control method of the unmanned ship of embodiment 1 described above.
The computer readable storage medium may be any internal storage unit of a device or apparatus having data processing capability, such as a hard disk or a memory, or may be any external storage device of a device having data processing capability, such as a plug-in hard disk, a smart memory card (SMART MEDIA CARD, SMC), an SD card, a flash memory card (FLASH CARD), or the like, provided on the device.
The foregoing description is, of course, merely illustrative of preferred embodiments of the present invention, and it should be understood that the present invention is not limited to the above-described embodiments, but is intended to cover all modifications, equivalents and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.
Claims (1)
1. The repeated learning composite disturbance-resistant error-tolerant control method for the unmanned ship is characterized by comprising the following steps of:
Step1, building an unmanned ship dynamic positioning test simulation system, and building a corresponding mathematical model according to the dynamics characteristics of the unmanned ship;
step 2, designing a disturbance observer and a fault estimator for the unmanned ship dynamic positioning system, and realizing accurate estimation of disturbance and fault through the disturbance observer and the fault estimator;
Step 3, designing a repeated learning composite disturbance rejection error-tolerant controller for the unmanned ship dynamic positioning system with unavailable speed information, and obtaining the disturbance observer gain, repeated learning control gain and feedback control gain under the condition that the safe and stable operation condition of the system is met;
In the step 1, the state equation of the unmanned ship dynamic positioning system is described as follows:
vector κ (t) is defined as: v x(t)、vy (T) and r (T) respectively represent the longitudinal movement speed, the swinging speed and the yaw rate of the fixed body frame, the superscript T represents the transposition of the corresponding vectors, and T represents the moment T;
The vector phi (t) is defined as: e x(t)、Ey (t) and τ (t) represent the position abscissa, ordinate and yaw angle respectively with respect to the earth, Representing the first derivative of phi (t);
Rotation matrix The definition is as follows:
Vector quantity Representing the first derivative of vector κ (t); m represents a reversible matrix, W represents a damping matrix, and Z represents a mooring force matrix; u f (t) represents a fault-containing propulsion, which is described as follows:
uf(t)＝u(t)+f(t) (2)
where u (t) represents a system control input and f (t) represents an additive actuator fault; the composite disturbance d (t) is described as:
d(t)＝rs(t)+rd(t) (3)
Where r s (t) is a slowly varying disturbance caused by second order waves, ocean currents, wind and non-modeling dynamics, Is the first derivative of r s (t), r d (t) represents an unknown disturbance; t represents a bias time constant matrix, and the superscript-1 represents the inverse of the matrix; η (t) represents the magnitude bounded noise vector and n represents the diagonal matrix;
Linearizing the unmanned aerial vehicle dynamic positioning system at τ (t) =0 while defining a state vector The UMVs system, which is not speed measurable, is described as:
Wherein the method comprises the steps of D is a constant matrix; i and 0 respectively represent an identity matrix and a0 matrix of suitable dimensions; y (t) and r y (t) represent measurement output and measurement noise, respectively;
in the step2, assuming that the states are all measurable, the disturbance observer is constructed as follows:
Wherein the method comprises the steps of An estimated value representing r s (t), h (t) is the auxiliary state vector,Is the first derivative of h (t), L is the disturbance observer gain, and matrix E is defined as
Since κ (t) cannot be obtained, a virtual disturbance observer as shown in equation (7) is designed:
wherein, A virtual estimate representing r s (t); further, the observed error is defined as:
an observed error system of the form:
Wherein the method comprises the steps of Indicating the error of the observation and,A first derivative representing an observed error;
In step 2, in order to realize fault estimation, the following intermediate vector μ (t) is designed:
μ(t)＝f(t)-Fx(t) (9)
where F is an adjustable variable of the design, and derives the following equation:
Combining equations (7) - (10) to obtain a comprehensive fault disturbance estimator of the form:
Wherein the method comprises the steps of AndEstimates of x (t), y (t), r s (t), h (t), μ (t), and f (t), respectively, G represents observer gain; Respectively is Is the first derivative of (a);
In the step 2, corresponding error vectors are defined respectively: And
The error system for deriving the unmanned boat is thus as follows:
Wherein the auxiliary matrix AndRespectively defined asAndGiven the disturbance observer gain L, the auxiliary matrix is madeIs a Hulvitz matrix; the matrix F is furthermore designed in the form:
where i > 0 is a scalar and the matrix is unknown Satisfy the following requirementsIs a Hulvitz matrix;
the lyapunov function is constructed for the error system shown in equation (12) as follows:
V(t)＝V1(t)+V2(t)+V3(t)+V4(t) (13)
Wherein the energy storage function V 1(t)、V2(t)、V3(t)、V4 (t) is defined as:
And
And matrices P, Q, R and Y are both positive definite matrices; deriving the constructed Lyapunov function over time, deriving:
The function He (X) is expressed as: he (X) =x T +x, where X represents a matrix;
Diagonal matrix Diag { } is a diagonal matrix symbol;
According to AndIt can be deduced that:
Wherein the method comprises the steps of As auxiliary matrix, α and γ are scalar quantities; the auxiliary vectors X (t) and v (t) are defined as: And The auxiliary matrix xi 11 is defined as:
Wherein:
the auxiliary matrix xi 12 is defined as:
To ensure that the estimation errors e f(t)、es (t) and e x (t) agree to be eventually bounded, it is necessary to satisfy:
and the corresponding observer gain is obtained as:
in the step 3, firstly, an ideal model of the unmanned ship is described as follows:
Wherein x d(t)、ud (t) and y d (t) represent the ideal state, ideal input and ideal output, respectively, of the unmanned boat dynamic positioning system; Representing the first derivative of x d (t); since the state trace of an ideal system has periodicity, namely:
xd(t+T)＝xd(t) (18)
wherein T represents a cycle length;
in order to counteract the effects of faults and disturbances, the observer-based repetitive learning composite immunity fault-tolerant controller is designed to:
wherein u r (T) represents a repeated learning control law, u c (T) represents a feedback controller, u fs (T) represents an immunity error-tolerant controller, u r (T-T) represents a previous period repeated learning control rate, Representing the last periodic system estimation error, y (T-T) representing the last periodic system output,Representing the system estimate output of the last cycle,Is a subscript of the number of the symbol,R d、Rp and R y are repeated learning control gain matrices, K c is a feedback control gain matrix,Is thatIs the first derivative of (a);
the error of the observer state from the ideal state of the system is expressed as:
wherein error vectors are input The definition is as follows: u d (t) represents the ideal input, and the auxiliary error vector ε (t) is defined as: The weighting matrix W is defined as:
The control input of the ideal unmanned ship dynamic positioning system also has periodicity, namely: u d(t)＝ud (T-T);
thus inputting error vector The rewrites to the following form:
Wherein the method comprises the steps of An input error representing a previous cycle;
The gain matrix R p is And matrix R y is
Thus deriving an error input vectorThe method comprises the following steps:
Thus obtaining an input error vector The method meets the following conditions:
Wherein psi satisfies II+R d B II is less than or equal to psi; the time t is expressed in a periodic form as: t=t 0 +kt, k being denoted as kth period, k→infinity when time goes to infinity, t 0 e [0, t);
The relationship of the resulting input iteration input error to the initial input error is therefore expressed as:
Wherein the method comprises the steps of Representing the systematic input error for the k-1 th cycle,Representing the systematic input error for the k-2 th cycle,Representing an initial system input error of the system; when the psi is less than 1, the process,Converging to 0;
in the step 3, a lyapunov function is constructed for repeatedly learning the composite disturbance-resistant fault-tolerant controller:
deriving the lyapunov function in equation (25), deriving:
Known from the inequality condition:
wherein δ 1 and δ 2 are scalar quantities and the feedback control gain is Thus, there are:
Wherein the method comprises the steps of
Under the condition that disturbance and actuator faults exist simultaneously, the designed repeated learning composite disturbance-resistant fault-tolerant controller is utilized to ensure safe and stable operation of the unmanned ship power positioning system, and the stability conditions of the unmanned ship power positioning system are as follows:
||I+RdB|| <1 (29)
The feedback control gain and the repeated learning control gain matrix are respectively: And The matrix W is defined as:
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