CN118331315A - System and method for controlling fault-tolerant output constraint of submarine with preset tracking precision - Google Patents
System and method for controlling fault-tolerant output constraint of submarine with preset tracking precision Download PDFInfo
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Abstract
The invention discloses a fault-tolerant output constraint control system and a fault-tolerant output constraint control method for a submarine with preset tracking precision, wherein the control system comprises expected track input and a closed-loop system of the submarine, and the closed-loop system of the submarine comprises a feedback controller and a model of the submarine; the expected motion track is input into the expected motion track of the underwater vehicle, the expected motion track of the underwater vehicle is subtracted by the closed loop system of the underwater vehicle according to the actual motion track of the underwater vehicle, the position error of the underwater vehicle is obtained, the position error is input into the system through the feedback controller, and the system is input into a model acting on the underwater vehicle, so that the actual motion track of the underwater vehicle is obtained. The invention gets rid of the dependence on links such as identification, approximation, estimation, observation, derivation and the like, further simplifies the structure of the controller, can preset the overshoot, convergence time/speed and steady state value of the position tracking error of the submarine, and ensures that the control signal is continuous and free from the phenomenon of rapid increase.
Description
Technical Field
The invention relates to a fault-tolerant control system and a fault-tolerant control method, in particular to a fault-tolerant output constraint control system and a fault-tolerant output constraint control method for a submarine with preset tracking precision.
Background
Ocean is vital to life on earth and is an integral part of climate regulation, maintenance of ecosystem and support of biodiversity. As a major channel of global trade, the ocean promotes the level of productivity development, export and innovation in developed countries, while promoting economic growth and the level of living in developing countries. In addition, the ocean world provides important energy sources for humans, whether by utilizing ocean waves and offshore wind energy, to mine subsea oil and gas deposits, or to produce fish. In view of the extreme conditions of the environment, further marine exploration is expected to elucidate fundamental problems concerning life origin, which cannot be accomplished without naval vessel tools.
To date, most vessels used to acquire scientific data fall within a more traditional class of vehicles, such as propeller driven unmanned aerial vehicles, submarines, or wheeled rovers. Applications such as marine forecasting, deep sea exploration and underwater inspection of oil and gas pipelines are typical examples of underwater vessels that are required to operate under various constraints and with a high degree of autonomy. In particular, submarines have a number of successful records in a variety of offshore operations, featuring constrained high-dimensional nonlinear dynamics, particularly in the case of under-driven systems, which can create significant complexity due to model uncertainty and various operational constraints.
As a typical marine control problem, completing trajectory tracking of a submarine remains to be solved. Trajectory tracking means that the submarine follows a space-time trajectory with strict time requirements, which is of great significance for marine applications such as navigation safety, emission reduction and energy conservation. In contrast to path tracking, trajectory tracking requires not only steering control laws but also dedicated speed control laws. There are a number of unresolved problems in the trajectory tracking control of underactuated submarines to date.
Disclosure of Invention
In order to solve the problems that the convergence rate of tracking errors and the size of a residual error set depend on unknown model parameters, interference boundaries, a neural network, a fuzzy logic system or a self-adaptive technology and cannot fully compensate a nonlinear function of the system, algorithm calculation burden is brought, and the like, the invention provides a fault-tolerant output constraint control system and a fault-tolerant output constraint control method of a submarine with preset tracking precision. The invention gets rid of the dependence on links such as identification, approximation, estimation, observation, derivation and the like, further simplifies the structure of the controller, can preset the overshoot, convergence time/speed and steady state value of the position tracking error of the submarine, and ensures that the control signal is continuous and free from the phenomenon of rapid increase.
The invention aims at realizing the following technical scheme:
The utility model provides a preset tracking accuracy's submarine fault-tolerant output constraint control system, includes desired track input P d, submarine's closed loop system, wherein:
The closed loop system of the submarine comprises a feedback controller C and a model P of the submarine;
The expected track input P d inputs an expected motion track x d、yd、zd of the submarine;
The method comprises the steps that a closed loop system of the underwater vehicle subtracts an expected motion track x d of the underwater vehicle according to an actual motion track x of the underwater vehicle to obtain a position error e x of the underwater vehicle, the closed loop system of the underwater vehicle subtracts the expected motion track y d of the underwater vehicle according to an actual motion track y of the underwater vehicle to obtain a position error e y of the underwater vehicle, and the closed loop system of the underwater vehicle subtracts the expected motion track z d of the underwater vehicle according to an actual motion track z of the underwater vehicle to obtain a position error e z of the underwater vehicle;
the position error e x、ey、ez is subjected to feedback controller C to obtain system input tau u、τr、τω;
The system input tau u、τr、τω acts on the model P of the submarine to obtain the actual motion trail x, y and z of the submarine.
A method for performing fault-tolerant output constraint control of a submarine by using the fault-tolerant output constraint control system of the submarine comprises the following steps:
step (1) uses a nonlinear output feedback system of the form:
Wherein (x, y, z) and ψ represent the position and yaw angle, respectively, of the submarine in the inertial system; η= [ u, v, ω, r ] T, u, v, ω, r represent heave, heave and yaw speeds of the submarine respectively; τ u、τr and τ ω represent system inputs, respectively; f u(η)、fv(η)、fω (η) and f r (η) represent nonlinear functions; d u(t)、dv(t)、dω (t) and d r (t) represent bounded environmental disturbances caused by sea wind and waves; g u、gω and g r represent unknown positive constants related to the submarine mass;
Step (2) uses an actuator of the form:
τi＝ρi(t)αi(t)+σi(t)，i＝u，r，ω
Wherein α i (t) is a command control signal to be designed; ρ i (t) and σ i (t) represent multiplication and addition actuator faults, respectively;
The control target of the fault-tolerant output constraint control system of the submarine is that the system outputs x (t), y (t) and z (t) track the expected motion track x d(t)、yd(t)、zd (t), and the position error is described as:
ex(t)＝x(t)-xd(t)
ey(t)＝y(t)-yd(t)
ez(t)＝z(t)-zd(t)
the position error on the XY plane is described as:
z1＝||col(ex,ey)||
step (4) constructing a tracking error boundary and an asymmetric time-varying constraint function
Step (41) of designing a tracking error boundary:
p(t)＝γ1Φ(t)+γ2
Wherein t r > 0 represents a design parameter;
Step (42) designing an asymmetric time-varying constraint function:
kz(t)＝(ka(t)-zd(t))q(t)
wherein k a (t), And q (t) represents a design function, q (t) = (1-q ∞)e-μt+q∞;
step (5) feedback controller design
Step (51) designs the auxiliary variables z 2 and ζ for e x、ey and ψ:
Step (52) designing an adjustment function And adjusts the error variable e z and the system state z 3 by using an adjusting function:
wherein t s > 0 represents a design parameter;
Step (53) converts the auxiliary variable and the adjusted error in the following manner:
Where k i denotes the controller parameters and satisfying the conditions k i＞0;z4 (t) and z 5 (t) are velocity tracking errors, z 6 (t) is an adjusted velocity tracking error, z 4(t)＝u-ud,z5(t)＝r-rd,
Step (54) is based on a back-stepping design process, and the following controllers are designed:
ud(t)＝-c1sξβ1
rd(t)＝-c2sξβ2
wd(t)＝-c3β3
αi(t)＝-cmβj i＝u,ω,r,j＝4,5,6
Wherein c m, m=1, 2, …,6 represent controller parameters, and satisfying c m＞0;sξ＝sgn(ξ);ud(t)、rd (t) and w d (t) represents a virtual control rate;
Step (6) fault-tolerant output constraint control of the submarine
Step (61), the upper computer inputs a desired motion track x d(t)、yd(t)、zd (t) to the submarine driver;
And (62) feeding back position information to a feedback controller after a position sensor on the submarine detects the position change of the submarine, performing closed-loop operation after the feedback controller receives the signal and feeding the operation result to a driver, and controlling the output force and the direction of each motor by the output current of the driver so as to track the expected motion trail.
Compared with the prior art, the invention has the following advantages:
1. Aiming at the problem of position tracking control of the submarine craft with strong nonlinear characteristics and time-varying characteristics, the invention designs an output feedback controller with simple structure from the perspective of a nonlinear output feedback system. Namely: the structure of the controller is simplified by adjusting and transforming auxiliary variables and error signals; the continuous control signal without the phenomenon of rapid increase is ensured by presetting the overshoot of the position tracking error of the submarine, the convergence time/speed, the asymmetric time-varying constraint and the steady state value.
2. The present invention achieves convergence of errors to a predetermined set within a fixed period of time by combining a new boundary function with a constraint processing strategy.
3. The present invention does not require calculation of virtual control signal derivatives nor relies on information related to vehicle dynamics parameters, interference boundaries or fault characteristics, and does not use auxiliary techniques such as adaptation techniques, neural networks, observers or filters, thereby simplifying controller design.
4. The invention uses error correction technology to eliminate the limitation that the controller parameter needs to be selected in a complicated and fussy recursion way in the design process of the high-order system.
5. The controller designed by the invention can effectively realize the position tracking control of the submarine, and can be used for tracking the track of the submarine influenced by model uncertainty, environmental interference and potential actuator faults.
Drawings
FIG. 1 is a schematic diagram of a position tracking control system for a submarine according to the invention;
FIG. 2 is a position tracking diagram, left of the controller designed in the present invention, right of the self-adaptive fast nonsingular integral T-terminal sliding mode controller (AFNITSMC);
FIG. 3 is a position tracking error plot, left for a controller designed in the present invention, right for an adaptive fast nonsingular integral T-terminal sliding mode based controller (AFNITSMC);
FIG. 4 is a graph of velocity tracking error, left for a controller designed in accordance with the present invention, right for an adaptive fast nonsingular integral T-terminal sliding mode based controller (AFNITSMC);
fig. 5 is a graph of propeller output thrust, left for the controller designed in the present invention, and right for the adaptive fast nonsingular integral T-terminal sliding mode based controller (AFNITSMC).
FIG. 6 is a graph of tracking error for a controller incorporating upper and lower bounds in accordance with the present invention.
Detailed Description
The following description of the present invention is provided with reference to the accompanying drawings, but is not limited to the following description, and any modifications or equivalent substitutions of the present invention should be included in the scope of the present invention without departing from the spirit and scope of the present invention.
The invention provides a fault-tolerant output constraint control system of a submarine, which is preset with tracking precision, as shown in fig. 1, wherein the fault-tolerant output constraint control system of the submarine comprises an expected track input P d and a closed loop system of the submarine, and the fault-tolerant output constraint control system comprises the following components:
The closed loop system of the submarine comprises a feedback controller C and a model P of the submarine;
The expected track input P d inputs an expected motion track x d、yd、zd of the submarine;
The method comprises the steps that a closed loop system of the underwater vehicle subtracts an expected motion track x d of the underwater vehicle according to an actual motion track x of the underwater vehicle to obtain a position error e x of the underwater vehicle, the closed loop system of the underwater vehicle subtracts the expected motion track y d of the underwater vehicle according to an actual motion track y of the underwater vehicle to obtain a position error e y of the underwater vehicle, and the closed loop system of the underwater vehicle subtracts the expected motion track z d of the underwater vehicle according to an actual motion track z of the underwater vehicle to obtain a position error e z of the underwater vehicle;
the position error e x、ey、ez is subjected to feedback controller C to obtain system input tau u、τr、τω;
The system input tau u、τr、τω acts on the model P of the submarine to obtain the actual motion trail x, y and z of the submarine.
A method for performing fault-tolerant output constraint control of a submarine by using the fault-tolerant output constraint control system of the submarine comprises the following steps:
step (1) uses a nonlinear output feedback system of the form:
Wherein (x, y, z) and ψ represent the position and yaw angle, respectively, of the submarine in the inertial system; η= [ u, v, ω, r ] T, u, v, ω, r represent heave, heave and yaw speeds of the submarine respectively; τ u、τr and τ ω represent system inputs including thrust and torque produced by the propeller in the heave, heave and yaw directions, respectively; f u(η)、fv(η)、fω (η) and f r (η) represent nonlinear functions; d u(t)、dv(t)、dω (t) and d r (t) represent bounded environmental disturbances caused by sea wind and waves; g u、gω and g r represent unknown positive constants related to the mass of the submarine.
Step (2) uses an actuator of the form:
τi＝ρi(t)αi(t)+σi(t)，i＝u，r，ω
Wherein α i (t) is a command control signal to be designed; ρ i (t) and σ i (t) represent multiplication and addition actuator faults, respectively.
The control target of the fault-tolerant output constraint control system of the submarine is that the system outputs x (t), y (t) and z (t) track the expected motion track x d(t)、yd(t)、zd (t), and the position error is described as:
ex(t)＝x(t)-xd(t)
ey(t)＝y(t)-yd(t)
ez(t)＝z(t)-zd(t)
the position error on the XY plane is described as:
z1＝||col(ex,ey)||
step (4) constructing a tracking error boundary and an asymmetric time-varying constraint function
Step (41) of designing a tracking error boundary:
p(t)＝γ1Φ(t)+γ2
Wherein t r > 0 represents a design parameter.
Step (42) designing an asymmetric time-varying constraint function:
kz(t)＝(ka(t)-zd(t))q(t)
wherein k a (t), And q (t) represents a design function, q (t) = (1-q ∞)e-μt+q∞.
Step (5) feedback controller design
Step (51) designs the auxiliary variables z 2 and ζ for e x、ey and ψ:
Step (52) designing an adjustment function And adjusts the error variable e z and the system state z 3 by using an adjusting function:
Wherein t s > 0 represents a design parameter.
Step (53) converts the auxiliary variable and the modified error in the following manner:
Wherein k i represents the controller parameters, and satisfying the conditions k i＞0;z4 (t) and z 5 (t) is the velocity error, z 6 (t) is the adjusted velocity tracking error:
z4(t)＝u-ud
z5(t)＝r-rd
step (54) is based on a back-stepping design process, and the following controllers are designed:
ud(t)＝-c1sξβ1
rd(t)＝-c2sξβ2
wd(t)＝-c3β3
αi(t)＝-cmβj i＝u，ω，r，j＝4，5，6
Where c m, m=1, 2,..6 represents controller parameters, and satisfying c m＞0;sξ＝sgn(ξ);ud(t)、rd (t) and w d (t) represents virtual control rate.
Step (6) fault-tolerant output constraint control of the submarine
Step (61), the upper computer inputs a desired motion track x d(t)、yd(t)、zd (t) to the submarine driver;
And (62) feeding back position information to a feedback controller after a position sensor on the submarine detects the position change of the submarine, performing closed-loop operation after the feedback controller receives the signal and feeding the operation result to a driver, and controlling the output force and the direction of each motor by the output current of the driver so as to track the expected motion trail.
Examples:
Step (1) uses the following form of the submarine dynamics and kinematics equations:
Wherein the method comprises the steps of ,m11＝21.5,m22＝26.5,m33＝26.5,m44＝8,Xu＝-70,Xu|u|＝-100,Yv＝-100,Yv|v|＝-200,W＝176.6,B＝181.2,Zω＝-100,Zω|ω|＝-200,Nr＝-50,Nr|r|＝-100.
Step (2) uses an actuator of the form:
τi＝ρi(t)αi(t)+σi(t)，i＝u，r，ω
Where α i (t), i=u, r, ω is the command control signal to be designed; ρ i (t) and σ i (t), i=u, r, ω represent multiplication and addition actuator faults, respectively.
In this embodiment:
step (3) the system control target tracks the desired motion trajectory x d(t)、yd(t)、zd (t) for the system outputs x (t), y (t), z (t), the tracking error is described as:
ex(t)＝x(t)-xd(t)
ey(t)＝y(t)-yd(t)
ez(t)＝z(t)-zd(t)
further, the position error on the XY plane is described as:
z1＝||col(ex,ey)||
In this embodiment, x d(t)＝sin(0.2t),yd(t)＝cos(0.2t),zd (t) =0.1t+1.5.
Step (4) constructing a tracking error boundary and an asymmetric time-varying constraint function
Step (41) of designing a tracking error boundary:
p(t)＝γ1Φ(t)+γ2
Where γ 1＝0.96、γ2＝0.04、tr =8.
Step (42) designing an asymmetric time-varying constraint function:
kz(t)＝(kaz(t)-zd(t))q(t)
in this embodiment, k a (t) =0.5+0.1t, q(t)＝(1-0.02)e-0.1t+0.02。
Step (5) controller design
Step (51) designs the auxiliary variables z 2 and ζ for e x、ey and ψ:
Step (52) designing an adjustment function And adjusts the error variable e z and the system state z 3 by using an adjusting function:
Where t s = 10.
Step (53) converts the auxiliary variable and the modified error in the following manner:
Where k 2＝0.002,k4＝0.008,k5＝0.014,k6＝0.02;z4 (t) and z 5 (t) are velocity errors.
z4(t)＝u(t)-ud(t)
z5(t)＝r(t)-rd(t)
Step (54) is based on a back-stepping design process, and the following controllers are designed:
ud(t)＝-c1sξβ1
rd(t)＝-c2sξβ2
wd(t)＝-c3β3
αi(t)＝-cjβj i＝u，ω，r，j＝4，5，6
wherein ,c1＝2.5,c2＝3,c3＝1,c4＝70,c5＝140,c6＝50;sξ＝sgn(ξ);ud(t)、rd(t) and w d (t) represent virtual control rates.
Step (6) uses the existing self-adaptive fast nonsingular integral T-terminal sliding mode controller to carry out comparison experiments, and the controller is required to operate under the same condition. The controller parameters are q1＝5,q2＝3,γ1＝13,γ2＝3,K1＝diag(0.2,0.2,1,1),K2＝diag(0.001,0.005,0.01,0.01),K3＝diag(1.2,1.2,1.2),K4＝diag(1,1,1).
As can be seen from FIG. 2, the controller designed by the present invention and the existing AFNITSMC can realize the tracking control of the submarine. The two controllers behave differently at the initial stage, and the tracking speed of the controller designed by the invention from the initial state to the designated reference output is greater than AFNITSMC. In addition, after the executor fails, the controller designed by the invention still accurately and continuously tracks the reference output; AFNITSMC the tracking error is obviously increased, and the tracking error is regulated to be within a specified limit about 30s after the fault occurs.
As can be seen from fig. 3, after the actuator fails, under the same condition, the position tracking error of the controller designed by the invention does not generate obvious jitter, the tracking error of AFNITSMC is obviously increased, and the tracking error is adjusted to be within the specified limit about 30s after the failure occurs.
As can be seen from fig. 4, the controller designed by the invention ensures that the speed of the submarine is continuous and has no abrupt change when the position tracking of the submarine is realized.
As can be seen from fig. 5, the thrust of the three propellers of the controller designed by the invention is always within the saturation limit of the propellers, and reasonable control force is generated after the failure of the actuator, while the thrust of the three propellers of AFNITSMC exceeds the saturation limit in the initial stage, and part of propellers break through the saturation limit at the moment of non-smooth transition.
As can be seen from fig. 6, the tracking errors of the controller designed by the invention are all kept within the preset limit, so that the output tracking errors of the submarine can be converged to the preset set in a fixed time period.
As can be seen from the results shown in fig. 2-6, compared with the existing method, the method not only can ensure the control precision, but also can realize that the output tracking error of the underwater vehicle converges to a preset set within a fixed time period, and the thrust of all the propellers does not exceed the saturation limit.
Claims (3)
1. The fault-tolerant output constraint control system of the submarine is characterized by comprising an expected track input P d and a closed-loop system of the submarine, wherein the expected track input P d is preset, and the control system comprises the following components:
The closed loop system of the submarine comprises a feedback controller C and a model P of the submarine;
The expected track input p d inputs an expected motion track x d、yd、zd of the submarine;
The method comprises the steps that a closed loop system of the underwater vehicle subtracts an expected motion track x d of the underwater vehicle according to an actual motion track x of the underwater vehicle to obtain a position error e x of the underwater vehicle, the closed loop system of the underwater vehicle subtracts the expected motion track y d of the underwater vehicle according to an actual motion track y of the underwater vehicle to obtain a position error e y of the underwater vehicle, and the closed loop system of the underwater vehicle subtracts the expected motion track z d of the underwater vehicle according to an actual motion track z of the underwater vehicle to obtain a position error e z of the underwater vehicle;
the position error e x、ey、ez is subjected to feedback controller C to obtain system input tau u、τr、τω;
The system input tau u、τr、τω acts on the model P of the submarine to obtain the actual motion trail x, y and z of the submarine.
2. The method for performing fault-tolerant output constraint control of the submarine with preset tracking precision by using the control system is characterized by comprising the following steps of:
step (1) uses a nonlinear output feedback system of the form:
wherein (x, y, z) and ψ represent the position and yaw angle, respectively, of the submarine in the inertial system; η= [ u, v, ω, r ] T, u, v, ω, r represent heave, heave and yaw speeds of the submarine respectively; τ u、τr and τ ω represent system inputs, respectively; f u(η)、fv(η)、fω (η) and f r (η) represent nonlinear functions; d u(t)、dv(t)、dω (t) and d r (t) represent bounded environmental disturbances caused by sea wind and waves; g u、gω and g r represent unknown positive constants related to the submarine mass;
Step (2) uses an actuator of the form:
τi＝ρi(t)αi(t)+σi(t)，i＝u,r,ω
Wherein α i (t) is a command control signal to be designed; ρ i (t) and σ i (t) represent multiplication and addition actuator faults, respectively;
The control target of the fault-tolerant output constraint control system of the submarine is that the system outputs x (t), y (t) and z (t) track the expected motion track x d(t)、yd(t)、zd (t), and the position error is described as:
ex(t)＝x(t)-xd(t)
ey(t)＝y(t)-yd(t)
ez(t)＝z(t)-zd(t)
the position error on the XY plane is described as:
z1＝||col(ex,ey)||
step (4) constructing a tracking error boundary and an asymmetric time-varying constraint function
Step (41) of designing a tracking error boundary:
p(t)＝γ1Φ(t)+γ2
wherein t r >0 represents a design parameter;
Step (42) designing an asymmetric time-varying constraint function:
wherein k a (t), And q (t) represents a design function, q (t) = (1-q ∞)e-μt+q∞;
step (5) feedback controller design
Step (51) designs the auxiliary variables z 2 and ζ for e x、ey and ψ:
Step (52) designing an adjustment function And adjusts the error variable e z and the system state z 3 by using an adjusting function:
Wherein t s >0 represents a design parameter;
Step (53) converts the auxiliary variable and the adjusted error in the following manner:
wherein k i represents a controller parameter, and satisfying the conditions k i>0;z4 (t) and z 5 (t) is a velocity tracking error, and z 6 (t) is an adjusted velocity tracking error;
step (54) is based on a back-stepping design process, and the following controllers are designed:
ud(t)＝-c1sξβ1
rd(t)＝-c2sξβ2
wd(t)＝-c3β3
αi(t)＝-cmβj i＝u,ω,r,j＝4,5,6
Wherein c m, m=1, 2, …,6 represent controller parameters, and satisfying c m>0;sξ＝sgn(ξ);ud(t)、rd (t) and w d (t) represents a virtual control rate;
Step (6) fault-tolerant output constraint control of the submarine
Step (61), the upper computer inputs a desired motion track x d(t)、yd(t)、zd (t) to the submarine driver;
And (62) feeding back position information to a feedback controller after a position sensor on the submarine detects the position change of the submarine, performing closed-loop operation after the feedback controller receives the signal and feeding the operation result to a driver, and controlling the output force and the direction of each motor by the output current of the driver so as to track the expected motion trail.
3. The method for fault-tolerant output constraint control of a submersible vehicle with preset tracking precision according to claim 1, wherein z 4(t)＝u-ud,z5(t)＝r-rd,
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