CN112230666B - Drift angle correction course control method based on self-adaptive extended state observer - Google Patents
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Abstract
The invention discloses a drift angle correction course control method based on a self-adaptive extended state observer, which at least comprises the following steps: step 1: establishing a water surface ship course control nonlinear model with drift angles; step 2: obtaining a smooth instruction course angle and a derivative signal thereof by using a target course angle through a second-order filter; step 3: acquiring a course angle deviation signal; step 4: designing a course control rule based on the self-adaptive extended state observer and the self-adaptive backstepping control method; step 5: judging whether the course control effect is satisfactory or not, ending the control if yes, and returning the update state to the step 3 to recalculate the course control signal if no.
Description
Technical Field
The invention relates to the field of ship motion control, in particular to a drift angle correction course control method based on a self-adaptive extended state observer.
Technical Field
The ship sails on the sea and is disturbed by random wind and wave to generate swinging motion, wherein the bow swinging motion determines the ship course maintenance precision, and course control is an important problem in ship navigation and control engineering, so that a course control system taking an automatic rudder as an actuating mechanism is required to be installed by a conventional ship on the water surface in order to ensure that the ship reaches a destination smoothly. The course control of the water surface ship comprises course maintenance control and steering control, and the ship bow movement under the horizontal plane coordinate system is shown in figure 1. The bow generates a small transverse drift angle beta to change the fluid distribution state at two sides of the ship body due to the action of transverse drift force during steering movement of the ship, the drift angle is usually less than 5 degrees and is not easy to measure, and steady-state errors of course tracking control are increased due to the existence of the drift angle. The current ship course control algorithm basically ignores the drift angle effect, the course tracking deviation adopted in the control algorithm is in a measurement deviation form psi e＝ψ-ψd, and the course control accuracy is reduced due to the fact that the stable state error of course tracking is increased due to the existence of the drift angle, so that drift angle correction is needed for the course tracking deviation in the control algorithm. The most widely applied heading control model is a first-order linear heading model, which is suitable for heading maintenance control, but high-order nonlinear conditions need to be considered for steering control. On the other hand, the commercial course control system is usually only provided with a measuring device of course angle signals, the course angle speed, the course angle acceleration and other signals are obtained through a state estimation method, and meanwhile, the ship body is affected by unknown time-varying disturbance effects of sea waves and the like, so that the problems of model dynamic uncertainty (unmodeled dynamic state), parameter time-varying and the like are necessarily existed, and the problems are solved by adopting an adaptive control method.
Disclosure of Invention
The invention mainly solves the technical problems that: the drift angle correction course control method based on the self-adaptive extended state observer solves the problems of drift angle correction, state estimation, model dynamic uncertainty and parameter time-varying in ship course control.
The solution provided by the technology of the invention is as follows: the drift angle correction course control method based on the self-adaptive extended state observer comprises the following specific steps:
Step 1: based on the first-order drift angle model and the second-order nonlinear course model, establishing a water surface ship course control state space nonlinear model with drift angles;
Step 2: obtaining a smooth instruction heading angle phi d and a first derivative thereof by using a target heading angle phi r through a second-order filter
Step 3: acquiring a course angle deviation signal phi e＝ψ-ψd according to the command course angle phi d and the course angle phi signals acquired in the step 1 and the step 2;
step 4: the course control law is designed based on the self-adaptive extended state observer and the self-adaptive backstepping control method, and the course control signal u drives steering through a steering engine servo system to finally realize course control;
step 5: judging whether the course control effect is satisfactory or not, ending the control if yes, and returning the update state to the step 3 to recalculate the course control signal if no;
The second order nonlinear heading model in step 1 is represented by the following formula:
wherein: and psi is the heading angle, psi (3) is the third derivative of psi, Is the second derivative of psi,/>Is the first derivative of ψ, δ is the rudder angle,/>As the first derivative of δ, a 1,a2,a3,b1 and b 2 are heading model parameters;
the first-order drift angle model in step 1 is expressed by the following formula:
Wherein: the psi is the heading angle of the vehicle, For the first derivative of ψ, β is the drift angle, Δ β is the drift angle model uncertainty, c 1 and c 2 are model nominal values and satisfy 0 < c 1＜1,0＜c2 < 1;
The non-linear model of the course control state space of the water surface ship in the step 1 is expressed by the following formula:
Wherein: the system states x 1,x2,x3 and x 4 are defined as, respectively, x 1 =ψ represents the heading angle, x 2 =β represents the drift angle, Representing the angular velocity of the heading,/>Representing course angular acceleration, delta β representing drift angle model uncertainty, d (t) representing combined system dynamic uncertainty, t representing time, g (t) being a time-varying control coefficient, u being a course control signal, c 1 and c 2 being model nominal values and satisfying 0 < c 1＜1,0＜c2 < 1;
the adaptive extended state observer in step 4 uses the following formula to calculate:
Wherein: For an estimate of the extended state vector x= [ x 1 x2 x3 x4 x5]Τ and extended state of x 5 =d (t), d (t) represents the combined system dynamics uncertainty, t represents time, y=cx is the measurement output, B＝[0 0 0 1 0]Τ，C＝[1 0 0 0 0]，/>C 1 and c 2 are model nominal values and satisfy 0 < c 1＜1,0＜c2 < 1, u is a heading control signal,/>Is an observer gain vector and the parameters satisfy alpha 1＞0,α2＞0,α3＞0,α4＞0,α5 >0 and 0 < epsilon < 1;
the time-varying control coefficient self-adaptive rule of the self-adaptive extended state observer in the step 4 is calculated by adopting the following formula:
Wherein: u is a course control signal, C= [ 100 00 ], epsilon is a parameter of the self-adaptive extended state observer and satisfies 0 < epsilon < 1, a g and sigma g are designed positive constants, g 0 is an initial value of g, For redefined system state estimation error vector, the original state estimation error vector is/>X= [ x 1 x2x3 x4 x5]Τ ] is a system expansion state vector,/>Estimating a state vector for the system extension;
the heading control signal in step4 is expressed by the following formula:
Wherein: And/> Is a virtual error signal,/>For the estimation of the system state x 3,/>For the estimation of the system state x 4,/>For the estimation of the system expansion state x 5, k 3 is the designed positive constant, q 1 and q 2 are virtual control signals,/>Is the first derivative of the virtual control signal q 2;
The virtual control signals q 1 and q 2 in the above control law are calculated by the following formulas, respectively:
Wherein: k 1 and k 2 are positive constants of the design, And/>Is a virtual error signal,/>For the estimation of the system state x 1,/>For the estimation of the system state x 2,/>For the estimation of system state x 3, ψ d is the instruction heading angle,/>Is the first derivative of psi d,/>For estimation of uncertainty Δ β of drift angle model,/>For the first derivative of the virtual control signal q 1, c 1 and c 2 are model nominal values and satisfy 0 < c 1＜1,0＜c2 < 1.
The beneficial effects of the invention are as follows: the drift angle correction course control of the water surface ship is realized by establishing a nonlinear course model with drift angle and a self-adaptive control method based on a self-adaptive extended state observer, so that the course tracking steady-state error and a steering command signal under course maintenance control are effectively reduced.
Drawings
FIG. 1 is a schematic view of a bow-tie motion coordinate system of a surface vessel;
FIG. 2 is a block diagram of a heading control system in accordance with the present invention;
FIG. 3 is a flow chart of a drift angle correction course control method based on an adaptive extended state observer provided by the invention;
FIG. 4 is a schematic diagram of the ship course control result in an embodiment;
Fig. 5 is a schematic view of the rudder angle calculation result of the ship in the embodiment.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the attached drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention.
Please refer to fig. 2-5. It should be noted that, the illustrations provided in the present embodiment merely illustrate the basic concept of the present invention by way of illustration, and only the components related to the present invention are shown in the drawings and are not drawn according to the number, shape and size of the components in actual implementation, and the form, number and proportion of the components in actual implementation may be arbitrarily changed, and the layout of the components may be more complex.
Fig. 2 is a block diagram of a course control system in the present invention, fig. 3 is a flowchart of a drift angle correction course control method based on an adaptive extended state observer, fig. 4 is a schematic diagram of a ship course control result in an embodiment, and fig. 5 is a schematic diagram of a ship rudder angle calculation result in an embodiment, where the drift angle correction course control method based on an adaptive extended state observer disclosed in the present invention is specifically implemented as follows:
Step 1: based on the first-order drift angle model and the second-order nonlinear course model, establishing a water surface ship course control state space nonlinear model with drift angles;
the second-order nonlinear heading model is in the form of the following formula (1):
Wherein: psi is heading angle, delta is rudder angle, a 1,a2,a3,b1 and b 2 are model parameters, specific values of which can be determined or estimated according to the specific vessel selected.
The first-order drift angle model is in the form of the following formula (2):
Wherein: For bounded model uncertainty (i.e., |Δ β|≤Δβmax and Δ βmax are unknown positive constants), c 1 and c 2 are model nominal values and satisfy 0 < c 1＜1,0＜c2 < 1, the specific values can be estimated based on ship model experiments or system identification methods.
According to the formula (1) and the formula (2), the state space nonlinear model of the heading control of the water surface ship with the drift angle is represented by the following formula (3):
wherein: the system state is defined as x 1 =ψ representing the heading angle, x 2 =β representing the drift angle, Representing the angular velocity of the heading,/>Representing the heading angular acceleration. /(I)For the system unmodeled dynamics (dynamic uncertainty), w is the external time-varying disturbance, g (t) =b 1 is the time-varying control coefficient. /(I)For system control signals, i.e. input to steering engine servo system/>And outputs the rudder angle.
Combining the system unmodeled dynamics f (x) with the external time-varying disturbance w, the model (3) is transformed into the following formula (4):
wherein: d (t) =f (x) +w represents the combined system dynamic uncertainty.
Defining a new state x 5 =d (t), the state space model (4) can be converted into an extended state space model as represented by the following equation (5):
Step 2: obtaining a smooth instruction heading angle phi d and derivatives thereof by using a target heading angle phi r through a second-order filter
The second order filter is calculated using the following equation (6):
Wherein: ζ is the filter damping and ω is the filter frequency.
Step 3: acquiring an instruction course angle phi d and course angle phi signals according to the step 1 and the step 2, and acquiring a course angle deviation signal phi e(t)＝ψ-ψd;
step 4: based on the self-adaptive extended state observer and the self-adaptive backstepping control method, a course control rule is designed, and a course control signal u (t) drives steering through a steering engine servo system to finally realize course control;
The adaptive extended state observer is calculated using the following equation (7):
Wherein: For the estimation of the extended state vector x= [ x 1 x2 x3 x4 x5]Τ, y=cx is the measurement output,/> B＝[0 0 0 1 0]Τ，C＝[1 0 0 0 0]，V x＝[0 Δβ 0 0 h(t)]Τ is the disturbance vector and,Is an observer gain vector and the parameters satisfy alpha 1＞0,α2＞0,α3＞0,α4＞0,α5 >0 and 0 < epsilon < 1.
The time-varying control coefficient self-adaptive rule of the self-adaptive extended state observer is calculated by the following formula (8):
Wherein: a g and sigma g are positive constants of design, g 0 is an initial value of g, For redefined error vector, the raw state estimation error vector is/>
The heading control signal is calculated by the following formula (9):
Wherein: And/> For the virtual error signal, k 3 is the positive constant of the design,/>Is the derivative of the virtual control signal q 2.
The virtual control signals q 1 and q 2 in the heading control law (9) are calculated by the following formulas, respectively:
Wherein: k 1 and k 2 are positive constants of the design, For the uncertain estimation of the drift angle model,/>Is the derivative of the virtual control signal q 1.
Estimation of drift angle model uncertaintyThe calculation can be performed by adopting a proper self-adaptive method according to the needs or by adopting the following self-adaptive rule:
Wherein: a β and σ β are positive constants of the design.
Step 5: judging whether the course control effect is satisfactory or not, ending the control if yes, and returning the update state to the step 3 to recalculate the course control signal if no.
The beneficial effects of the invention are as follows: the drift angle correction course control of the water surface ship is realized by establishing a nonlinear course model with drift angle and a self-adaptive control method based on a self-adaptive extended state observer, so that the course tracking steady-state error and a steering command signal under course maintenance control are effectively reduced.
Examples: in order to verify the effectiveness of the invention, a ship in a literature "J V Amerongen,A J U T Cate.Model reference adaptive autopilots for ship.Automatica,1975,11:441-449." is taken as a research object, a MATLAB is utilized to carry out a simulation experiment, a nonlinear heading model is adopted as shown in a formula (3), specific parameters in the model are shown in a literature "Lokukaluge P Perera,C Guedes Soares.Lyapunov and Hurwitz based controls for input and output linearization applied to nonlinear vessel steering.Ocean Engineering,2013,66:58-68.". and are internal disturbance caused by simulation parameter time variation, and random noise is added into a control coefficient b 1, namely the control coefficient is expressed as g (t) =b 1 [1+0.5randn (1) ]. External unknown environmental disturbances are modeled by w=0.3 [0.1+0.1cos (0.3 t) +0.1sin (0.5 t) ] and dynamic uncertainty in the drift angle model is modeled by Δ β =0.015 [0.1sin (0.2 t) +0.1cos (0.3 t) ]. The initial state of the nonlinear heading model at the time t=0 is thatThe parameters of the controller are set as follows:
k1＝0.6 k2＝2 k3＝2 γ1＝0.8 γ2＝0.1
aβ＝5 σβ＝1 ag＝0.1 σg＝0.1 α1＝3
α2＝3 α3＝3 α4＝3 α5＝1 ε＝0.2
ξ＝1.2 ω＝0.4 g0＝0.24
The target heading angle is expressed by the following formula:
fig. 4 and 5 show the results of the drift angle correction course control of the surface vessel based on the adaptive extended state observer under the above simulation experiment conditions. Fig. 4 is a real ship course tracking contrast curve, and it can be seen that the real ship course can quickly and accurately track the target course, and the stable steering at the inflection point has no obvious course overshoot, which illustrates that the control strategy has good robustness to unknown disturbance of external environment and uncertain system dynamics. Fig. 5 shows a rudder angle time change curve calculated by a control law of the formula (9), and the rudder angle curve is smooth without random violent buffeting phenomenon, which indicates that the control strategy can well process the random disturbance in the system caused by the time variation of the control parameters, and further enhances the robustness of the control system. It can be seen that the course control of the water surface ship, which is realized by the method, meets the actual requirements of ship motion control engineering, can effectively ensure the course control precision to reduce tracking errors, avoid the course overshoot phenomenon at inflection points and the rudder angle buffeting problem caused by random noise in the system, and improve the robustness of the course control of the water surface ship under complex sea conditions.
The above embodiments are merely illustrative of the principles of the present invention and its effectiveness, and are not intended to limit the invention. Modifications and variations may be made to the above-described embodiments by those skilled in the art without departing from the spirit and scope of the invention. Accordingly, it is intended that all equivalent modifications and variations of the invention be covered by the claims, which are within the ordinary skill of the art, be within the spirit and scope of the present disclosure.
Claims (1)
1. The drift angle correction course control method based on the adaptive extended state observer is characterized by comprising the following steps of:
Step 1: based on the first-order drift angle model and the second-order nonlinear course model, establishing a water surface ship course control state space nonlinear model with drift angles;
Step 2: obtaining a smooth instruction heading angle phi d and a first derivative thereof by using a target heading angle phi r through a second-order filter
Step 3: acquiring a course angle deviation signal phi e＝ψ-ψd according to the command course angle phi d and the course angle phi signals acquired in the step 1 and the step 2;
step 4: the course control law is designed based on the self-adaptive extended state observer and the self-adaptive backstepping control method, and the course control signal u drives steering through a steering engine servo system to finally realize course control;
step 5: judging whether the course control effect is satisfactory or not, ending the control if yes, and returning the update state to the step 3 to recalculate the course control signal if no;
The second order nonlinear heading model in step 1 is represented by the following formula:
wherein: and psi is the heading angle, psi (3) is the third derivative of psi, Is the second derivative of psi,/>Is the first derivative of ψ, δ is the rudder angle,/>As the first derivative of δ, a 1,a2,a3,b1 and b 2 are heading model parameters;
the first-order drift angle model in step 1 is expressed by the following formula:
Wherein: the psi is the heading angle of the vehicle, For the first derivative of ψ, β is the drift angle, Δ β is the drift angle model uncertainty, c 1 and c 2 are model nominal values and satisfy 0 < c 1＜1,0＜c2 < 1;
The non-linear model of the course control state space of the water surface ship in the step 1 is expressed by the following formula:
Wherein: the system states x 1,x2,x3 and x 4 are defined as, respectively, x 1 =ψ represents the heading angle, x 2 =β represents the drift angle, Representing the angular velocity of the heading,/>Representing course angular acceleration, delta β representing drift angle model uncertainty, d (t) representing combined system dynamic uncertainty, t representing time, g (t) being a time-varying control coefficient, u being a course control signal, c 1 and c 2 being model nominal values and satisfying 0 < c 1＜1,0＜c2 < 1;
the adaptive extended state observer in step 4 uses the following formula to calculate:
Wherein: For an estimate of the extended state vector x= [ x 1 x2 x3 x4 x5]Τ and extended state of x 5 =d (t), d (t) represents the combined system dynamics uncertainty, t represents time, y=cx is the measurement output, B＝[0 0 0 1 0]Τ，C＝[1 0 0 0 0]，/>C 1 and c 2 are model nominal values and satisfy 0 < c 1＜1,0＜c2 < 1, u is a heading control signal,/>Is an observer gain vector and the parameters satisfy alpha 1＞0,α2＞0,α3＞0,α4＞0,α5 >0 and 0 < epsilon < 1;
the time-varying control coefficient self-adaptive rule of the self-adaptive extended state observer in the step 4 is calculated by adopting the following formula:
Wherein: u is a course control signal, C= [ 100 00 ], epsilon is a parameter of the self-adaptive extended state observer and satisfies 0 < epsilon < 1, a g and sigma g are designed positive constants, g 0 is an initial value of g, For redefined system state estimation error vector, the original system state estimation error vector is/>X= [ x 1 x2x3 x4 x5]Τ ] is a system expansion state vector,/>Estimating a state vector for the system extension;
the heading control signal in step4 is expressed by the following formula:
Wherein: And/> Is a virtual error signal,/>For the estimation of the system state x 3,/>For the estimation of the system state x 4,/>For the estimation of the system expansion state x 5, k 3 is the designed positive constant, q 1 and q 2 are virtual control signals,/>Is the first derivative of the virtual control signal q 2;
The virtual control signals q 1 and q 2 in the above control law are calculated by the following formulas, respectively:
Wherein: k 1 and k 2 are positive constants of the design, And/>Is a virtual error signal,/>For the estimation of the system state x 1,/>For the estimation of the system state x 2,/>For the estimation of system state x 3, ψ d is the instruction heading angle,/>Is the first derivative of psi d,/>For estimation of uncertainty Δ β of drift angle model,/>For the first derivative of the virtual control signal q 1, c 1 and c 2 are model nominal values and satisfy 0 < c 1＜1,0＜c2 < 1.
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