CN112230666A - Drift angle correction course control method based on self-adaptive extended state observer - Google Patents

Drift angle correction course control method based on self-adaptive extended state observer Download PDF

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CN112230666A
CN112230666A CN202011187641.4A CN202011187641A CN112230666A CN 112230666 A CN112230666 A CN 112230666A CN 202011187641 A CN202011187641 A CN 202011187641A CN 112230666 A CN112230666 A CN 112230666A
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drift angle
course
control
extended state
course control
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刘志全
储瑞婷
秦毅峰
朱云浩
张依恋
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Shanghai Maritime University
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Shanghai Maritime University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/0206—Control of position or course in two dimensions specially adapted to water vehicles

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 non-linear model of course control of a water surface ship with a drift angle; step 2: acquiring a smooth instruction course angle and a derivative signal thereof by using the target course angle through a second-order filter; and step 3: acquiring a course angle deviation signal; and 4, step 4: designing a course control rule based on the self-adaptive extended state observer and the self-adaptive backstepping control method; and 5: and judging whether the course control effect is satisfactory or not, if yes, ending the control, and if not, updating the state, returning to the step 3, and recalculating the course control signal.

Description

Drift angle correction course control method based on self-adaptive extended state observer
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 generates swing motion under the disturbance action of random wind waves when sailing on the sea, wherein the heading motion determines the heading maintaining precision of the ship, and heading control is an important problem in ship navigation and control engineering, and in order to ensure that the ship can successfully arrive at a destination, a heading control system taking an autopilot as an actuating mechanism is required to be installed on a conventional ship on the water surface. The course control of the water surface ship comprises course keeping control and steering control, and the ship yawing motion under a horizontal plane coordinate system is shown in figure 1. When the ship steers, the ship bow generates one under the action of transverse drift forceThe small transverse drift angle beta changes the fluid distribution state on two sides of the ship body, the drift angle is usually less than 5 degrees and is not easy to measure, and the existence of the drift angle can increase the steady-state error of course tracking control. The current ship course control algorithm basically ignores the drift angle effect, and the course tracking deviation adopted in the control algorithm is in a measuring deviation form psie＝ψ-ψdBecause the drift angle can increase the steady-state error of course tracking and reduce the course control precision, the drift angle correction needs to be carried out on the course tracking deviation in the control algorithm. The most applied course control model at present is a first-order linear Nomoto model which is suitable for course keeping control, but a high-order nonlinear condition needs to be considered for steering control. On the other hand, commercial course control systems are usually only provided with a measuring device of a course angular signal, the signals such as course angular speed, course angular acceleration and the like are obtained by a state estimation method, meanwhile, the problems of model dynamic uncertainty (unmodeled dynamic state), parameter time variation and the like inevitably exist when the ship body is subjected to unknown time-varying disturbance action such as sea waves and the like, and the problems need to be solved by a self-adaptive control method.
Disclosure of Invention
The invention mainly solves the technical problems that: the method overcomes the defects of the prior art, provides a drift angle correction course control method based on a self-adaptive extended state observer, and solves the problems of drift angle correction, state estimation, model dynamic uncertainty and parameter time variation in ship course control.
The technology of the invention provides a solution scheme that: a drift angle correction course control method based on a self-adaptive extended state observer specifically comprises the following steps:
step 1: establishing a heading control state space nonlinear model of the water surface ship with a drift angle based on a first-order drift angle model and a second-order nonlinear Nomoto model;
the non-linear model of the course control state space of the surface ship in the step 1 is represented by the following formula:
Figure BDA0002751797530000021
Figure BDA0002751797530000022
Figure BDA0002751797530000023
Figure BDA0002751797530000024
wherein: the system state is defined as x1Phi denotes heading angle, x2Beta represents the drift angle and the drift angle is represented by beta,
Figure BDA0002751797530000025
which represents the angular velocity of the heading,
Figure BDA0002751797530000026
representing the heading angular acceleration. DeltaβRepresenting uncertainty of drift angle model, d (t) representing uncertainty of merged system dynamics, g (t) being time-varying control coefficient, u being system control signal, c1And c2Nominal values of the drift angle model parameters which are normal numbers.
Step 2: using the target heading angle psirObtaining a smooth commanded heading angle psi through a second order filterdAnd derivatives thereof
Figure BDA0002751797530000027
And step 3: according to the command course angle psi acquired in step 1 and step 2dAnd acquiring a heading angle deviation signal psie(t)＝ψ-ψd；
And 4, step 4: designing a course control rule based on the self-adaptive extended state observer and the self-adaptive backstepping control method, and driving a steering engine through a steering engine servo system by a course control signal u (t) to finally realize course control;
the adaptive extended state observer in the step 4 is calculated by adopting the following formula:
Figure BDA0002751797530000028
wherein:
Figure BDA0002751797530000029
for expanding the state vector x ═ x1 x2 x3 x4 x5]TIs estimated and the extended state is x5Y Cx is a measurement output (d (t)),
Figure BDA00027517975300000210
B＝[0 0 0 1 0]T，C＝[1 0 0 0 0]，
Figure BDA00027517975300000211
vx＝[0 Δ β 0 0 h(t)]Tin order to be a disturbance vector,
Figure BDA00027517975300000212
is an observer gain vector and the parameter satisfies alpha1＞0,α2＞0,α3＞0,α4＞0,α5> 0 and 0 < epsilon < 1.
The time-varying control coefficient adaptive law of the adaptive extended state observer in the step 4 is calculated by adopting the following formula:
Figure BDA00027517975300000213
wherein: a isgAnd σgFor the designed normal number, g0Is the initial value of g and is,
Figure BDA0002751797530000031
for the redefined error vector, the original state estimate error vector is
Figure BDA0002751797530000032
The course control signal in step 4 is represented by the following formula:
Figure BDA0002751797530000033
wherein:
Figure BDA0002751797530000034
and
Figure BDA0002751797530000035
for virtual error signals, k3In order to be a normal number for the design,
Figure BDA0002751797530000036
for the dummy control signal q2The derivative of (c).
Virtual control signal q in the above control law1And q is2Respectively calculated by the following formula:
Figure BDA0002751797530000037
Figure BDA0002751797530000038
wherein: k is a radical of1And k2In order to be a normal number for the design,
Figure BDA0002751797530000039
Figure BDA00027517975300000310
for an estimation of the uncertainty of the drift angle model,
Figure BDA00027517975300000311
for the dummy control signal q1The derivative of (c).
And 5: and judging whether the course control effect is satisfactory or not, if yes, ending the control, and if not, updating the state, returning to the step 3, and recalculating the course control signal.
The invention has the beneficial effects that: the method has the advantages that the drift angle correction course control of the water surface ship is realized by establishing the nonlinear course model with the drift angle and the self-adaptive control method based on the self-adaptive extended state observer, the course tracking steady-state error and the steering instruction signal under course keeping control are effectively reduced, only the course angle signal needs to be measured, excessive measuring devices are not needed, meanwhile, the method does not need specific modeling information of a nonlinear part in the model and prior information of a time-varying control coefficient, and the robustness of the course control of the water surface ship under severe sea conditions can be improved.
Drawings
FIG. 1 is a schematic view of a surface vessel heading motion coordinate system;
FIG. 2 is a schematic diagram of a heading control system according to 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 heading control result in the embodiment;
FIG. 5 is a schematic diagram of the calculation result of the rudder angle of the ship in the embodiment.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the invention may be more readily understood by those skilled in the art. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention.
Please refer to fig. 2-5. It should be noted that the drawings provided in the present embodiment are only for illustrating the basic idea of the present invention, and the components related to the present invention are only shown in the drawings rather than drawn according to the number, shape and size of the components in actual implementation, and the type, quantity and proportion of the components in actual implementation may be changed freely, and the layout of the components may be more complicated.
FIG. 2 is a structure diagram of a heading control system in the present invention, FIG. 3 is a flowchart of a drift angle correction heading control method based on an adaptive extended state observer provided by the present invention, FIG. 4 is a schematic diagram of a heading control result of a ship in an embodiment, FIG. 5 is a schematic diagram of a rudder angle calculation result of a ship in an embodiment, and a drift angle correction heading control method based on an adaptive extended state observer disclosed by the present invention is specifically implemented as follows:
step 1: establishing a heading control state space nonlinear model of the water surface ship with a drift angle based on a first-order drift angle model and a second-order nonlinear Nomoto model;
the second-order nonlinear Nomoto model is in the form of the following equation (1):
Figure BDA0002751797530000041
wherein: psi is the heading angle, delta is the rudder angle, a1,a2,a3,b1And b2For model parameters, specific values of the model parameters may be determined or estimated according to the specific vessel selected.
The first-order drift angle model is in the form of the following equation (2):
Figure BDA0002751797530000042
wherein:
Figure BDA0002751797530000043
model uncertainty for bounded (i.e. | Δ)β|≤ΔβmaxAnd ΔβmaxIs an unknown normal number), c1And c2Is a model nominal value and satisfies 0 < c1＜1,0＜c2< 1, the specific value can be estimated according to ship model experiments or system identification methods.
According to the formula (1) and the formula (2), the heading control state space nonlinear model of the water surface ship with the drift angle is represented by the following formula (3):
Figure BDA0002751797530000051
wherein: the system state is defined as x1Phi denotes heading angle, x2Beta represents the drift angle and the drift angle is represented by beta,
Figure BDA0002751797530000052
which represents the angular velocity of the heading,
Figure BDA0002751797530000053
representing the heading angular acceleration.
Figure BDA0002751797530000054
For unmodeled dynamics of the system (dynamics uncertainty), w is the external time-varying disturbance, g (t) b1Is a time varying control coefficient.
Figure BDA0002751797530000055
For system control signals, i.e. input to steering engine servo system
Figure BDA0002751797530000056
And outputs the rudder angle.
Combining the unmodeled dynamics f (x) of the system with the external time-varying disturbance w, and converting the model (3) into the following formula (4):
Figure BDA0002751797530000057
wherein: d (t) ═ f (x) + w represents the combined system dynamics uncertainty.
Defining a new state x5D (t), the state space model (4) can be converted into an extended state space model as shown in the following equation (5):
Figure BDA0002751797530000058
step 2: using the target heading angle psirObtaining a smooth commanded heading angle psi through a second order filterdAnd the guide thereofNumber of
Figure BDA0002751797530000059
The second order filter is calculated using the following equation (6):
Figure BDA00027517975300000510
wherein: ξ is the filter damping and ω is the filter frequency.
And step 3: collecting the command course angle psi according to the step 1 and the step 2dAnd acquiring a heading angle deviation signal psie(t)＝ψ-ψd；
And 4, step 4: designing a course control rule based on the self-adaptive extended state observer and the self-adaptive backstepping control method, and driving a steering engine through a steering engine servo system by a course control signal u (t) to finally realize course control;
the adaptive extended state observer is calculated using the following equation (7):
Figure BDA0002751797530000061
wherein:
Figure BDA0002751797530000062
for expanding the state vector x ═ x1 x2 x3 x4 x5]TX is the measurement output,
Figure BDA0002751797530000063
B＝[0 0 0 1 0]T，C＝[1 0 0 0 0]，
Figure BDA0002751797530000064
vx＝[0 Δ β 0 0 h(t)]Tin order to be a disturbance vector,
Figure BDA0002751797530000065
for observersGain vector and parameter satisfying alpha1＞0,α2＞0,α3＞0,α4＞0,α5> 0 and 0 < epsilon < 1.
The time-varying control coefficient self-adaptive law of the self-adaptive extended state observer is calculated by adopting the following formula (8):
Figure BDA0002751797530000066
wherein: a isgAnd σgFor the designed normal number, g0Is the initial value of g and is,
Figure BDA0002751797530000067
for the redefined error vector, the original state estimate error vector is
Figure BDA0002751797530000068
The heading control signal is calculated by the following equation (9):
Figure BDA0002751797530000069
wherein:
Figure BDA00027517975300000610
and
Figure BDA00027517975300000611
for virtual error signals, k3In order to be a normal number for the design,
Figure BDA00027517975300000612
for the dummy control signal q2The derivative of (c).
Virtual control signal q in course control law (9)1And q is2Respectively calculated by the following formula:
Figure BDA00027517975300000613
Figure BDA0002751797530000071
wherein: k is a radical of1And k2In order to be a normal number for the design,
Figure BDA0002751797530000072
Figure BDA0002751797530000073
for an estimation of the uncertainty of the drift angle model,
Figure BDA0002751797530000074
for the dummy control signal q1The derivative of (c).
Estimation of uncertainty in a drift model
Figure BDA0002751797530000075
The calculation can be carried out by adopting a proper self-adaptive method or the following self-adaptive rule according to the requirement:
Figure BDA0002751797530000076
wherein: a isβAnd σβIs a designed normal number.
And 5: and judging whether the course control effect is satisfactory or not, if yes, ending the control, and if not, updating the state, returning to the step 3, and recalculating the course control signal.
The invention has the beneficial effects that: the method has the advantages that the drift angle correction course control of the water surface ship is realized by establishing the nonlinear course model with the drift angle and the self-adaptive control method based on the self-adaptive extended state observer, the course tracking steady-state error and the steering instruction signal under course keeping control are effectively reduced, only the course angle signal needs to be measured, excessive measuring devices are not needed, meanwhile, the method does not need specific modeling information of a nonlinear part in the model and prior information of a time-varying control coefficient, and the robustness of the course control of the water surface ship under severe sea conditions can be improved.
Example (b): to verify the effectiveness of the present invention, a ship in the document "J V Amerongen, A J U T Cat. model reference adaptive autocompletes for ship, Automatica,1975,11: 441-. For simulating internal disturbance caused by time variation of parameters, at control coefficient b1Adding random noise, i.e. the control coefficient is expressed as g (t) ═ b1[1+0.5randn(1)]. The external unknown environment is disturbed by w ═ 0.3[0.1+0.1cos (0.3t) +0.1sin (0.5t)]Simulation, dynamic uncertainty in drift angle model is represented by Δβ＝0.015[0.1sin(0.2t)+0.1cos(0.3t)]And (6) simulating. The initial state of the nonlinear heading model at the moment when t is 0 is
Figure BDA0002751797530000077
The parameter settings of the controller are 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 represented by the following formula:
Figure BDA0002751797530000081
fig. 4 and 5 show the heading control result of the drift angle correction of the surface ship based on the adaptive extended state observer under the above simulation experiment condition. FIG. 4 is a real ship course tracking comparison curve, which shows 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 shows that the control strategy has good robustness to the unknown disturbance of the external environment and the system dynamic uncertainty. Fig. 5 shows a rudder angle time variation curve calculated by the control law of the formula (9), and the rudder angle curve is smooth and has no random severe buffeting, which shows 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. Therefore, the course control of the water surface ship realized by the invention conforms to the actual requirement of ship motion control engineering, can effectively ensure the course control precision, reduce the tracking error, avoid the problem of rudder angle buffeting caused by course overshoot at turning points and random noise in a system, and improve the robustness of the course control of the water surface ship under complex sea conditions.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or change the above-mentioned embodiments without departing from the spirit and scope of the present invention. Accordingly, it is intended that all equivalent modifications or changes which can be made by those skilled in the art without departing from the spirit and technical spirit of the present invention be covered by the claims of the present invention.

Claims (5)

1. A drift angle correction course control method based on a self-adaptive extended state observer is characterized by comprising the following steps:
step 1: establishing a heading control state space nonlinear model of the water surface ship with a drift angle based on a first-order drift angle model and a second-order nonlinear Nomoto model;
step 2: using the target heading angle psirObtaining a smooth commanded heading angle psi through a second order filterdAnd derivatives thereof
Figure FDA0002751797520000011
And step 3: according to the instruction acquired in step 1 and step 2Direction angle psidAnd acquiring a heading angle deviation signal psie(t)＝ψ-ψd；
And 4, step 4: designing a course control rule based on the self-adaptive extended state observer and the self-adaptive backstepping control method, and driving a steering engine through a steering engine servo system by a course control signal u (t) to finally realize course control;
and 5: and judging whether the course control effect is satisfactory or not, if yes, ending the control, and if not, updating the state, returning to the step 3, and recalculating the course control signal.
2. The drift angle correction course control method based on the adaptive extended state observer is characterized in that: the non-linear model of the course control state space of the surface ship in the step 1 is represented by the following formula:
Figure FDA0002751797520000012
Figure FDA0002751797520000013
Figure FDA0002751797520000014
Figure FDA0002751797520000015
wherein: the system state is defined as x1Phi denotes heading angle, x2Beta represents the drift angle and the drift angle is represented by beta,
Figure FDA0002751797520000016
which represents the angular velocity of the heading,
Figure FDA0002751797520000017
representing the heading angular acceleration. DeltaβRepresenting uncertainty of drift angle model, d (t) representing uncertainty of merged system dynamics, g (t) being time-varying control coefficient, u being system control signal, c1And c2Nominal values of the drift angle model parameters which are normal numbers.
3. The drift angle correction course control method based on the adaptive extended state observer is characterized in that: the adaptive extended state observer in the step 4 is calculated by adopting the following formula:
Figure FDA0002751797520000018
wherein:
Figure FDA0002751797520000019
for expanding the state vector x ═ x1 x2 x3 x4 x5]TIs estimated and the extended state is x5Y Cx is a measurement output (d (t)),
Figure FDA00027517975200000110
B＝[0 0 0 1 0]T，C＝[1 0 0 0 0]，
Figure FDA0002751797520000021
vx＝[0 Δβ 0 0 h(t)]Tin order to be a disturbance vector,
Figure FDA0002751797520000022
is an observer gain vector and the parameter satisfies alpha1＞0,α2＞0,α3＞0,α4＞0,α5> 0 and 0 < epsilon < 1.
4. The drift angle correction course control method based on the adaptive extended state observer is characterized in that: the time-varying control coefficient adaptive law of the adaptive extended state observer in the step 4 is calculated by adopting the following formula:
Figure FDA0002751797520000023
wherein: a isgAnd σgFor the designed normal number, g0Is the initial value of g and is,
Figure FDA0002751797520000024
for the redefined error vector, the original state estimate error vector is
Figure FDA0002751797520000025
5. The drift angle correction course control method based on the adaptive extended state observer is characterized in that: the course control signal in step 4 is represented by the following formula:
Figure FDA0002751797520000026
wherein:
Figure FDA0002751797520000027
and
Figure FDA0002751797520000028
for virtual error signals, k3In order to be a normal number for the design,
Figure FDA0002751797520000029
for the dummy control signal q2The derivative of (c).
Virtual control signal q in the above control law1And q is2Respectively calculated by the following formula:
Figure FDA00027517975200000210
Figure FDA00027517975200000211
wherein: k is a radical of1And k2In order to be a normal number for the design,
Figure FDA00027517975200000212
Figure FDA00027517975200000213
for an estimation of the uncertainty of the drift angle model,
Figure FDA00027517975200000214
for the dummy control signal q1The derivative of (c).
CN202011187641.4A 2020-10-30 2020-10-30 Drift angle correction course control method based on self-adaptive extended state observer Pending CN112230666A (en)

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