A fault-tolerant motion control method for catamaran under single rudder and single propeller damage

Abstract

The application discloses a kind of single rudder single propeller damage under twin-hull ship fault-tolerant motion control method, belong to warship motion control field.The method of the application includes: according to the speed prediction sequence solved by speed controller, obtain the turning moment sequence generated due to the rotation of propeller;For the input-output relationship in the prediction time domain solved by the heading model;Calculate the constraint and coefficient matrix required for quadratic programming;Solve quadratic programming, and take the first item of result as control output.The application is suitable for single rudder single propeller damage under twin-hull ship fault-tolerant motion control, which is beneficial to increase the reliability of twin-hull ship under the condition of actuator damage, so that the twin-hull ship can also be stable and safe navigation under fault condition.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ship motion control, and more particularly to a catamaran fault-tolerant motion control method under single rudder and single propeller damage. BACKGROUND

[0002] With the continuous development of unmanned autonomous and artificial intelligence technology, various unmanned combat system platforms such as unmanned aerial vehicles, unmanned ships, and unmanned underwater vehicles are playing an increasingly important role in sea battlefield cooperation and have become an effective means to gain sea warfare advantage.

[0003] A catamaran refers to a ship connected by a reinforced frame on the upper part of two separate underwater hulls, having two rudders and two propellers, and is widely used in the field of ship research. Fault-tolerant control refers to the stable operation of a control system when an actuator or component fails, and meets certain performance indicators. The complex and variable environment of the sea battlefield and the coupling between the two hulls bring uncertainty to the navigation of the catamaran, so it is necessary to study the motion control method of the catamaran under typical actuator failures. A typical actuator failure is single rudder and single propeller damage, that is, the rudder on one side is stuck and the propeller on that side also stops rotating.

[0004] Ship speed and heading control is of great significance for modern ship navigation, and good speed and heading control is the basis for safe and stable operation of ships. The speed and heading control of modern ships can be achieved by designing separate or coupled speed controllers and heading controllers. Predictive control, as a control algorithm born from engineering practice, is widely used in engineering control field and has the advantage of handling explicit constraints. The model predictive control-based controller can be designed to control the speed and heading of the ship. SUMMARY

[0005] Therefore, the present application provides a catamaran fault-tolerant control method and system under single rudder and single propeller damage, aiming to increase the reliability of the catamaran under actuator damage and enable the catamaran to operate stably and safely under fault conditions.

[0006] To achieve the above-mentioned purpose, the technical solution of the present application includes the following steps:

[0007] S1: Measure the state of the catamaran through a sensor and estimate the disturbance.

[0008] S2: Construct a heading and speed control augmented state model of the catamaran under single rudder and single propeller damage, substitute the speed control augmented state model into the model predictive control algorithm, and obtain a speed predictive controller.

[0009] S3: Solve the speed prediction sequence according to the said speed prediction controller, and then deduce the turning moment sequence due to the rotation of the propeller, and take the turning moment sequence as the explicit correction of the moment generated by the propeller into the course control model.

[0010] S4: Based on the said course control model, solve the input and output relationship in the entire prediction time domain.

[0011] S5: Write the course control problem as a quadratic programming problem with constraints and objective functions, calculate the constraints and coefficient matrix required by the quadratic programming; solve the quadratic programming, and take the first item of the result as the control output.

[0012] Further, the augmented state model of the course and speed control of the catamaran under the condition of single rudder and single propeller damage is constructed, specifically:

[0013] The augmented state space equation of the course and speed control of the ship of the catamaran is

[0014]

[0015]

[0016]

[0017] Wherein, u(k), u(k+1) are the forward speeds at k time and k+1 time respectively, v(k), v(k+1) are the transverse drift speeds at k time and k+1 time respectively, r(k), r(k+1) are the turning bow angle speeds at k time and k+1 time respectively, ψ(k), ψ(k+1) are the course angles at k time and k+1 time respectively, n(k) is the propeller speed at k time, δ(k), δ(k+1) are the propeller rudder angles at k time and k+1 time respectively, G u is the state matrix of the speed state space equation, H u is the input matrix of the speed state space equation, G ψ is the state matrix of the course state space equation, H ψ is the input matrix of the course state space equation; k is the discrete time, Δn(k) is the change amount of n(k); I is the unit matrix.

[0018] The augmented state model of the course and speed control of the catamaran under the condition of single rudder and single propeller damage is:

[0019]

[0020] Wherein n(k) is the speed of the single-sided propeller at k time, δ(k) is the rudder angle of the single-sided rudder at k time, H ψn2n(k) is the torque generated by the different rotating speed of the two propellers, F is the torque generated by the rudder jamming, which is a constant not changing with time; Δδ(k) is the change of δ(k); H ψδ is the coefficient matrix of Δδ(k).

[0021] Further, in S3, the speed prediction sequence is solved according to the ship speed prediction controller, and then the steering torque sequence generated by the propeller rotation is derived, specifically as follows:

[0022] S301) The input and output relationship in the entire prediction time domain is solved through the ship speed state space model;

[0023] S302) The ship speed control problem is written as a quadratic programming problem format with constraints and objective functions, and the constraint and coefficient matrix A and b required for quadratic programming are calculated;

[0024] S303) The quadratic programming is solved to obtain the prediction speed sequence and then the steering torque sequence generated by the propeller rotation is derived c u is the control time domain of the speed controller, is the control amount at the 0th to c u time respectively.

[0025] Further, S4: the input and output relationship in the entire prediction time domain is solved based on the ship heading control model;

[0026] For the heading model, the input and output relationship in the prediction time domain is

[0027]

[0028] where y1~y p are the outputs at the 1st to pth time respectively, p is the range of the prediction time domain, x0is the input in the prediction time domain, Δδ0~Δδ c-1 are the rudder angle change amounts at the 0th to c-1th time respectively, G P , E P and H P are the coefficient matrices of the input and output relationship in the entire prediction time domain, C is the control coefficient matrix, G ψ is a function of the forward speed u, I is the unit matrix;

[0029]

[0030] N is a compensation term, N includes an explicit compensation term and an implicit compensation term, is the explicit compensation term, is the steering torque generated by the propeller respectively Explicit compensation. This is an implicit compensation term, which includes the torque generated by the faulty servo and external disturbances. e0 is the sum of the torque of the faulty servo and external disturbances at a given moment.

[0031] The coefficient matrix G, representing the relationship between input and output over the entire prediction time domain, is obtained using the above formula. P E P With H P .

[0032] Furthermore, in S5, the heading control problem is written as a quadratic programming problem with constraints and an objective function. The constraints and coefficient matrices required for the quadratic programming are calculated as follows:

[0033] The heading control problem can be written as a quadratic programming problem with constraints and an objective function.

[0034]

[0035]

[0036] Where: J is the objective function, Δu P is the rudder angle increment output vector, const is a constant term, lb and ub are used to limit the execution range of the actuator, and dlb and dub are used to limit the rate of change of the actuator; and calculate the constraint and coefficient matrices A and b required for quadratic programming;

[0037] A = H P T H P b = (ref - G) P x0-E P e0) T H P

[0038] Where H P G P E P Ref is the input-output relationship matrix obtained in step S4 for the entire prediction time domain, where ref is the optimized reference trajectory and x0 is the input in the prediction time domain.

[0039] Beneficial effects:

[0040] (1) The single rudder single propeller damage under the catamaran speed and heading fault-tolerant control method and system provided by the application rewrites the speed and heading state space equation for the special case of single rudder single propeller failure, and designs a speed prediction controller and a heading prediction controller based on model prediction control, and performs explicit correction of the yawing moment generated by the single-sided intact propeller and implicit correction of the moment generated by the fault rudder and external disturbance in the heading control, so that the catamaran can also operate stably and safely under fault conditions, and the reliability of the catamaran under the failure of the actuator is increased.

[0041] (2) In the single rudder single propeller damage under the catamaran speed and heading fault-tolerant control method and system provided by the application, the constraints of rudder angle and rudder speed are considered when designing the controller, thereby improving the stability of the heading control. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is the algorithm flowchart of the embodiment of the application. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical scheme and advantages of the application clearer, the application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and not to limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0044] The embodiment of the application provides a single rudder single propeller damage under the catamaran speed and heading fault-tolerant control method, which comprises the following steps:

[0045] S1. Measure the state of the controlled object by a sensor and estimate the disturbance.

[0046] S2: Build a heading speed control augmented state model of the catamaran under the condition of single rudder single propeller damage, substitute the speed control augmented state model into the model prediction control algorithm, and obtain a speed prediction controller;

[0047] When one side of the rudder is stuck and the propeller on that side is also stopped, the propeller on the other side will also add an additional turning moment while applying a forward thrust to the ship, causing the ship to continuously yaw to one side without rudder. In order to balance this turning moment, the rudder needs to maintain a certain angle. The method inputs the control sequence of the speed controller into the heading controller in advance, thereby feeding forward compensation to the turning moment generated by the propeller, and a single rudder single propeller damage under the ship fault-tolerant motion controller is designed.

[0048] The linear discrete state space model of the ship speed and heading can be simplified as:

[0049]

[0050] where u is the forward velocity, v is the cross drift velocity, r is the yaw rate, ψ is the heading angle, n and δ are the input variables, representing the propeller speed and rudder angle respectively. u ψ are the state matrices of the velocity and heading state space equations, H u and H ψ are the input matrices of the two equations. ψ is a function of the forward velocity u. In the case of small nonlinearity of the ship or low precision requirement of the model, G ψ can be approximated as a constant matrix to simplify the controller design process.

[0051] Referring to the above equations, the augmented model of the ship in the case of single rudder and single propeller damage can be written as follows:

[0052]

[0053] where n(k) is the single-side propeller speed and δ(k) is the rudder angle of the side. In the heading state equation, H ψn2 n(k) is the torque generated by the difference in the speed of the two sides of the propeller (i.e., one side rotates and the other side does not), and F is the torque generated by the rudder jam, which is a constant that does not change with time.

[0054] At this time, both the propeller speed and the rudder angle affect the output of the heading model, while the speed model is mainly related to the propeller speed and has less coupling with the rudder angle. An ideal controller design goal is to let the propeller mainly control the speed and let the rudder angle control the heading. Therefore, the speed controller is designed first, and then the control sequence of the speed controller is input to the heading controller for compensation, so as to achieve the design effect of controller decoupling.

[0055] First, the linear predictive controller design method is used to design the speed controller.

[0056] For the augmented linear state space model

[0057]

[0058] where G, H, and C are the coefficient matrices of the new state space equation. Given the system state x(k) at time k, the predicted value of the state quantity at future time k+n can be obtained from the prediction model:

[0059]

[0060] where p is the prediction time domain, c is the control time domain, G n is the nth power of G, and e(k+n-1) is e k+n-1 ​Disturbances in the prediction horizon are generally considered constant and equal to the current disturbance, i.e. e0 = e1 =... = e p The current disturbance can be obtained by subtracting the predicted state from the model in the last control period from the actual state measured at the current time, i.e. e0 = x(k) - x predict (k|k-1). Based on the above assumption, the input and output y P output sequence can be written as

[0061] y P = G P x0 + H P Δu P + E P e0

[0062] where x0 is the initial state of the system, C, G are coefficient matrices, G i is the i-th power of G,

[0063] The observation H P matrix c+1 to p rows, which correspond to the influence of the controller on the system after the control horizon to the end of the prediction horizon, can be seen that the H P matrix considers that in the control horizon, the controller will adjust in real time; from the control horizon to the end of the prediction horizon, the controller keeps the output of the last step of the control horizon unchanged, i.e. Δu(k+c+1) = Δu(k+c+2) =... = Δu(k+p) = 0.

[0064] Linear predictive control obtains the final control sequence by solving a quadratic programming problem, and the objective is to minimize the deviation of the system state from the reference trajectory in the prediction horizon as much as possible. The objective function can be written as:

[0065] J = (ref - y P ) T P(ref - y P ) + Δu P T QΔu P

[0066]

[0067] Where ref is a p x 1 vector, called the reference trajectory. The present invention directly uses the set value as the reference trajectory, i.e. ref i = set. The first term (ref - y P ) T P(ref - y P) for measuring the deviation of the reference trajectory from the system state, the second term is a soft constraint for damping the controller oscillation. P is a p x p matrix and Q is a c x c matrix, both of which are weight matrices, generally diagonal matrices (the weight values on the diagonal of the matrix are generally given directly, generally given from large to small according to the priority of the problem considered). dlb and dub are c x 1 vectors for limiting the rate of change of the actuator. lb and ub are used to limit the execution range of the actuator. In order to be able to use the solver to perform quadratic programming operation, it is necessary to write the execution range constraint as a constraint on Δu P :

[0068] lb' ≤ A ∑ Δu P ≤ ub'

[0069] wherein

[0070]

[0071] u0 is the value of the input quantity at the current time. In addition, in order to facilitate quadratic programming solution, it is also necessary to expand the objective function

[0072]

[0073] wherein

[0074] A = H P T H P , b = (ref - G P x0 - E P e0) T H P

[0075] In the formula, Const is a constant term generated after expansion, which has no effect on the calculation of quadratic programming, and can be ignored in actual calculation.

[0076] For the control sequence obtained by quadratic programming, the predictive control takes the first set of control quantities as the output of the controller. In each control period, the controller will solve the quadratic programming problem described above once and update the control sequence, realizing the rolling optimization of the controller. As for the design of the predictive controller of ship motion, the model is written in the augmented form:

[0077]

[0078]

[0079]

[0080] Substitute the augmented form of the speed model and the heading model into the model predictive control algorithm respectively, and the design of the speed controller and the heading controller can be completed.

[0081] The control sequence derived by the speed controller is denoted as where c u is the control horizon of the speed controller. Then for the course model, the relationship between the input and the output in the prediction horizon can be written as

[0082]

[0083] c is the control horizon where

[0084]

[0085]

[0086]

[0087] N contains two parts, one is the explicit correction for the moment generated by the propeller, and the other is the implicit correction for other errors. e0 is the implicit correction part, which is used to correct the implicit error, including the moment generated by the fault rudder, external disturbance and other errors.

[0088] Substitute the course control state space equation into the predictive control framework, and the design of the course controller of the catamaran under the condition of single propeller and single rudder damage can be completed. Compared with the ordinary course controller, this method makes an additional compensation for the yawing moment generated by the propeller. This compensation is a kind of feedforward compensation, which can quickly suppress the influence of the propeller yawing moment on the course.

[0089] Firstly, the speed controller is solved based on model predictive control, and the propeller sequence used for speed control is obtained, and then the compensation term of the course controller is obtained. Then G P , E P and H P are obtained. Finally, the course control output can be obtained by substituting into the linear predictive control framework.

[0090] Based on the above principle, step S2 specifically includes the following steps:

[0091] S2.1 The augmented state space equation of the ship course and speed control is

[0092]

[0093]

[0094]

[0095] where u is the forward speed, v is the lateral drift speed, r is the yaw angle speed, ψ is the course angle, n and δ are the input quantities, representing the propeller speed and rudder angle respectively; k and k+1 in the brackets represent the discrete time; Gu G ψ The state matrices H are the velocity and heading state space equations, respectively. u With H ψ This is the input matrix for the two equations.

[0096] S2.2 The augmented state-space equations for ship heading and speed control under single rudder and single propeller failure conditions are rewritten as follows:

[0097]

[0098] Where n(k) is the rotational speed of the propeller on one side, and δ(k) is the rudder angle of the servo motor on that side. H ψn2 n(k) is the torque generated by the different rotational speeds of the two propellers, F is the torque generated by the servo motor jamming, and H ψδ Let be the coefficient matrix of Δδ(k).

[0099] S3. Design of a speed controller based on linear predictive control. Based on the speed prediction sequence obtained from the speed controller, the sequence of steering torque generated by propeller rotation is derived. The steering torque sequence is substituted into the global linear model of heading as an explicit correction of the steering torque generated by the propeller.

[0100] S301: By using the speed state-space model, the input-output relationship within the entire prediction time domain can be solved, which can be written as:

[0101] y P =G P x0+H P Δu P +E P e0

[0102] Where yP is the output vector from time k+1 to time k+p. Δu P This is a sequence of velocity changes from time k+1 to time k+p; I is the identity matrix, G is the coefficient matrix in the augmented linear space state model, and C is the control coefficient matrix in the augmented linear space state model. H is the control coefficient matrix in the augmented linear space state model.

[0103] Observe H P Rows c+1 to p of the matrix correspond to the controller's impact on the system from the control time domain to the prediction time domain. It can be seen that H... P The matrix assumes that the controller will adjust in real time within the control time domain; after the control time domain and until the end of the prediction time domain, the controller keeps the output of the last step of the control time domain unchanged, that is, Δu(k+c+1)=Δu(k+c+2)=…=Δu(k+p)=0.

[0104] S302: Write the speed control problem as a quadratic programming problem with constraints and objective function

[0105] J = (ref - y P ) T P(ref - y P ) + Au P T QAu P

[0106]

[0107] Where ref = set, the reference trajectory. The first term (ref - y P ) T P(ref - y P ) in the objective function J is used to measure the deviation of the reference trajectory from the system state, and the second term is a soft constraint used to suppress the controller oscillation. P, Q are weight matrices, dlb and dub are used to limit the actuator change rate. lb and ub are used to limit the actuator execution range. The execution range constraint is written as a constraint on Au P : lb' ≤ A Σ Au P ≤ ub'

[0108] Where u0 is the value of the input at the current time. In addition, in order to facilitate quadratic programming solution, the objective function is expanded

[0109]

[0110] A = H P T H P , b = (ref - G P x0 - E P e0) T H P

[0111] Where Const is the constant term generated after expansion, which has no effect on the calculation of quadratic programming, and can be ignored in actual calculation. And calculate the constraint and coefficient matrix A and b.

[0112] S303: Solve the above quadratic programming to obtain the predicted speed sequence According to the relationship between the input and output in the control time domain of the speed linear predictive controller

[0113] y P = G P x0 + H P Au P + EP e0

[0114] And from the predicted velocity sequence The sequence of steering torques generated by propeller rotation is introduced.

[0115] S4: Based on the heading control model, the input and output relationship in the entire prediction time domain is obtained by solving;

[0116] For the global linear model of the heading, solve for the coefficient matrix G that represents the relationship between input and output throughout the entire prediction time domain. P E P With H P The compensation term here includes implicit compensation for other errors. It also includes explicit compensation for the steering torque generated by the propeller.

[0117] Step S4 specifically includes:

[0118] For the heading model, the relationship between input and output in the prediction time domain can be written as:

[0119]

[0120] in

[0121]

[0122]

[0123] Where y1~y p These represent the outputs at times 1 to p, where p is the range of the prediction time domain, x0 is the input within the prediction time domain, and Δδ0 to Δδ c-1 These represent the changes in rudder angle from time 0 to time c-1, respectively, G P E P With H P This is the coefficient matrix representing the input-output relationship over the entire prediction time domain. C is the control coefficient matrix in the augmented linear space state model, G ψ Let u be a function of forward velocity. I is the identity matrix;

[0124]

[0125] N represents the compensation term, which includes explicit and implicit compensation terms. This is an explicit compensation item. These are the steering torques generated on the propeller. Explicit compensation, is the sum of the fault rudder torque and external disturbance at a time.

[0126] Solve the coefficient matrix G of the input and output relationship in the whole prediction time domain according to the above formula P , E P and H P .

[0127] S5: write the course control problem into the format of a quadratic programming problem with constraints and objective function, calculate the constraint and coefficient matrix A and b required by the quadratic programming;

[0128]

[0129]

[0130] Wherein: J is the objective function, Δu P is the rudder angle increment output vector, const is a constant term, lb and ub are used to limit the execution range of the actuator, dlb and dub are used to limit the change rate of the actuator; and calculate the constraint and coefficient matrix A and b required by the quadratic programming;

[0131] A = H P T H P , b = (ref - G P x0 - E P e0) T H P

[0132] Wherein H P , G P , E P are the input and output relationship matrices in the whole prediction time domain obtained in step S4, e0 is, ref is the optimization reference trajectory, and x0 is the input in the prediction time domain.

[0133] S6: solve the quadratic programming, and take the first item of the result as the control amount output.

[0134] Solve the above quadratic programming to obtain a predicted course sequence Take the first item ψ0 of the predicted course sequence as the control amount output.

[0135] Correspondingly, the ship course interval control system used in the embodiment of the application to realize a twin-hull ship fault-tolerant motion control method under the condition of single-rudder and single-propeller damage comprises

[0136] A speed linear prediction controller module is used to control the ship speed, and a predicted speed sequence generated based on model prediction control is used to further derive a turning torque sequence generated due to the rotation of the propeller which is an explicit correction to the moment generated by the propeller, is put into the heading model expression as an explicit correction to the moment generated by the propeller;

[0137] heading linear prediction controller module, for controlling the heading of the ship, deducing the relationship between the input and output in the prediction horizon based on the heading global linear model, and calculating the constraint and coefficient matrix A and b required by the quadratic programming, solving the quadratic programming problem and taking the first term of the result as the control output;

[0138] speed global linear model module, for describing the speed control model of the catamaran under the condition of single rudder and single propeller damage;

[0139] heading global linear model module, for describing the heading control model of the catamaran under the condition of single rudder and single propeller damage;

[0140] Rolling optimization module, for taking the first term in the sequence output by the speed prediction controller and the heading prediction controller as the control output, to complete the rolling optimization of control;

[0141] Software and hardware constraint module: for limiting the execution range and change rate of the actuator, as a constraint of the quadratic programming, that is, lb≤u P ≤ub, dlb≤Δu P ≤dub;

[0142] Feedback correction module: for deviation processing in the heading controller design and reflecting in the next control cycle, completing the further stable control of the heading by explicit correction to the moment generated by the propeller and implicit correction to other errors;

[0143] Quadratic programming module, constructing a cost function containing the optimization reference trajectory ref, the rudder angle increment output vector Δu P and the multi-step prediction state variable y P , combining the rudder angle constraint condition and the rudder speed constraint condition, solving the quadratic programming under the constraint condition, so as to obtain the rudder angle increment output vector Δu P under the constraint of the rudder angle and the rudder speed.

[0144] Figure 1 is the heading and speed prediction control flow chart of the catamaran under the condition of single rudder and single propeller damage.

[0145] In summary, the above is only a preferred embodiment of the present application, and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A fault-tolerant motion control method for a catamaran under single rudder and single propeller failure, characterized in that, The method comprises the following steps: S1: measuring the catamaran state through a sensor, and estimating disturbance; S2: constructing a heading and speed control augmented state model of the catamaran under the condition of single rudder and single propeller damage, substituting the speed control augmented state model into a model predictive control algorithm to obtain a speed predictive controller; S3: solving a speed prediction sequence according to the speed predictive controller, and further deriving a turning torque sequence generated due to propeller rotation, and substituting the turning torque sequence as an explicit correction of the torque generated by the propeller into a heading control model; S4: based on the heading control model, solving the input and output relationship in the entire prediction time domain; S5: writing the heading control problem as a quadratic programming problem with constraints and objective functions, calculating the constraint and coefficient matrix required by the quadratic programming, solving the quadratic programming, and taking the first item of the result as the control output.

2. The fault-tolerant motion control method of a catamaran under rudder and propeller failure according to claim 1, wherein, The heading and speed control augmented state model of the catamaran under the condition of single rudder and single propeller damage is constructed as follows: The ship heading and speed control augmented state space equation of the catamaran is constructed as follows Wherein, u(k), u(k+1) are forward speeds at k time and k+1 time respectively, v(k), v(k+1) are cross drift speeds at k time and k+1 time respectively, r(k), r(k+1) are turning bow angular velocities at k time and k+1 time respectively, ψ(k), ψ(k+1) are heading angles at k time and k+1 time respectively, n(k) is the propeller rotating speed at k time, δ(k), δ(k+1) are propeller rudder angles at k time and k+1 time respectively, G u is the state matrix of the velocity state space equation, H u is the input matrix of the velocity state space equation, G ψ is the state matrix of the heading state space equation, H ψ is the input matrix of the heading state space equation; k is the discrete time, Δn(k) is the n(k) change amount; I is the unit matrix; The heading and speed control augmented state model of the catamaran under the condition of single rudder and single propeller damage is as follows: where n(k) is the speed of the single propeller at time k, δ(k) is the rudder angle of the single rudder at time k, H ψn2 n(k) is the torque generated by the difference between the speeds of the two propellers, F is the torque generated by the rudder jam, which is a constant that does not change with time; Δδ(k) is the change in δ(k); H ψδ is the coefficient matrix of Δδ(k).

3. The fault-tolerant motion control method of a catamaran under rudder and propeller failure according to claim 1, wherein, In S3, according to the speed predictive controller, the speed prediction sequence is solved, and further the turning torque sequence generated due to propeller rotation is derived, specifically as follows: S301) solving the input and output relationship in the entire prediction time domain through the speed state space model; S302) writing the speed control problem as a quadratic programming problem with constraints and objective functions, and calculating the constraint and coefficient matrix A and b required by the quadratic programming; S303) Solve the quadratic programming problem to obtain the predicted velocity sequence, and then deduce the steering torque sequence caused by the propeller rotation. c u For the control time domain of the speed controller, They are respectively from the 0th to the cth u The amount of control at any given moment.

4. The fault-tolerant motion control method for a catamaran with a single rudder and a single propeller under damage according to any one of claims 1 to 3, characterized in that, In S4, based on the heading control model, the input and output relationship in the entire prediction time domain is solved; For the heading model, the relationship between the input and output in the prediction time domain is where y1~y p are outputs at the 1st~p-th time, respectively, p is a range of a prediction time domain, x0is an input within the prediction time domain, Δδ0~Δδ c-1 are rudder angle change amounts at the 0th~c-1th time, respectively, G P , E P , and H P are coefficient matrices of input and output relationships within the entire prediction time domain, C is a control coefficient matrix, G ψ is a function with respect to a forward speed u, I is an identity matrix; N is a compensation term, N includes explicit compensation term and implicit compensation term, is an explicit compensation term, respectively are explicit compensations of the turning moment generated by the propeller, is an implicit compensation term, which contains the moment generated by the fault rudder and external disturbance, e0 is the sum of the moment generated by the fault rudder and external disturbance at a moment.​ Solving the coefficient matrix G for the input-output relationship over the entire prediction horizon according to the above equation P , E P and H P .

5. The fault-tolerant motion control method for a catamaran with a single rudder and a single propeller under damage according to any one of claims 1 to 3, characterized in that, In S5, the heading control problem is written as a quadratic programming problem with constraints and objective functions, and the constraint and coefficient matrix required by the quadratic programming is calculated, specifically as follows: The heading control problem is written as a quadratic programming problem with constraints and objective functions where: J is the objective function, Δu P is the rudder angle increment output vector, const is the constant term, lb and ub are used to limit the execution range of the actuator, dlb and dub are used to limit the change rate of the actuator; and the constraints and coefficient matrices A and b required for quadratic programming are calculated; A = H P T H P b = (ref - G P x0 - E P e0) T H P where H P , G P , E P are the input-output relationship matrices over the entire prediction horizon solved in step S4, ref is the optimal reference trajectory, and x0 is the input over the prediction horizon.

Images