CN112363393B - Model-free self-adaptive preset performance control method for unmanned ship dynamic positioning - Google Patents
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Abstract
The invention provides a model-free self-adaptive preset performance control method for unmanned ship dynamic positioning. Firstly, a novel preset performance function is provided, and a foundation is laid for preset performance error conversion; and then the dynamic positioning system with limited error performance is converted into a system with non-limited error performance based on the proposed preset performance function, and based on a controller designed by the conversion system, the closed loop signal of the system is consistent and finally bounded, and the transient performance of the system can be ensured. And finally, developing the controller design based on the instruction filtering back-stepping method, and introducing an adaptive method to obtain the model-free adaptive preset performance controller. The designed controller gets rid of the requirement of accurately modeling the hydrodynamic force and the additional quality items of the unmanned ship, and can also realize the preset performance control of the unmanned ship under the external time-varying disturbance and the input saturation constraint.
Description
Technical Field
The invention relates to the technical field of unmanned ship control, in particular to a model-free self-adaptive preset performance control method for dynamic positioning of unmanned ships (including underwater vehicles, underwater robots, water-surface unmanned ships and the like).
Background
In recent years, with the exhaustion of land fuel resources, the strategic position of the ocean occupying about 71% of the earth's area is increasing. To fully explore and exploit marine resources, development of marine equipment technology is indispensable. Marine intelligent equipment represented by unmanned vessels (including underwater vehicles, underwater robots, unmanned vessels on water surfaces and the like) is a main carrier for offshore operation at present, and the conventional mooring/anchoring positioning cannot meet the positioning requirement of the operation of the marine intelligent equipment due to the limitation of mooring lines and anchor chain lengths. The dynamic positioning is a positioning method capable of automatically maintaining the position by means of power propulsion, the working process of the dynamic positioning method does not need the assistance of a system/anchoring system, the limitation of working water depth is eliminated, sea waves and sea wind interference of sea can be resisted, and the accurate dynamic positioning of the unmanned ship is ensured.
A series of advanced control methods such as inversion control, sliding mode control and fuzzy control are applied to the design of the unmanned ship power positioning controller, but the traditional controller designs only can ensure that the unmanned ship can finally converge to a desired position and heading, and transient performance in the power positioning process cannot be considered. The operation requirement of the unmanned power positioning craft in the complex ocean environment is oriented, and a plurality of environment boundary constraints exist in the action process of the unmanned power positioning craft, so that the design of the preset performance control method considering the transient performance in the power positioning process is worthy of intensive study.
Disclosure of Invention
The invention aims to solve the problem of model-free self-adaptive preset performance control of unmanned ship dynamic positioning under the constraint of external time-varying disturbance and actuator input saturation.
In order to achieve the above purpose, the invention firstly introduces a preset performance function, converts the unmanned ship dynamics system with limited error performance into a new system with unlimited error performance, and can realize unmanned ship dynamics positioning requirement by only designing a controller to enable the system to finally converge on a desired signal, and can also ensure transient performance of the system. Then, the controller is designed based on a back-step design method, and virtual intermediate control variables are obtained through recursion. To avoid complex differential operations, instruction filter filters are introduced to convert differential operations into simple algebraic operations. The error compensation auxiliary system is constructed to process in consideration of instruction filtering errors brought by introducing an instruction filter. The robust term is designed for disturbance caused by external time variation to calm. Model adaptation is achieved based on adaptation techniques. And finally, obtaining unsaturated control output through the constructed auxiliary dynamic system when solving the control force/moment, and realizing model-free self-adaptive preset performance control of the unmanned ship under external time-varying disturbance and input saturation constraint.
Drawings
FIG. 1 is a general control block diagram of a fuzzy adaptive preset performance control method for unmanned boat dynamic positioning in the present invention.
FIG. 2 is a complement to FIG. 1, detailing the command filtering process for the robust adaptive controller design in the fuzzy adaptive preset performance control method for unmanned boat dynamic positioning.
Fig. 3 is a plot of the speed duration of a dynamically positioned unmanned boat.
Fig. 4 is a plot of dynamically positioned unmanned boat horizontal plane position and heading duration.
Fig. 5 is a graph of the output thrust/torque duration of a dynamically positioned unmanned boat actuator.
Fig. 6 is a plot of the vector duration of the power positioning unmanned boat transition position error plane.
Fig. 7 is a plot of the velocity error vector for a dynamically positioned unmanned boat.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Step one: based on the novel preset performance function, the dynamic positioning system with limited error performance is converted into a novel system with unrestricted error performance, and a foundation is laid for the back-step design.
The specific implementation process is as follows
The three-degree-of-freedom mathematical model of the dynamic positioning unmanned ship in the horizontal plane considering the dynamic state of the propeller can be expressed as follows
Wherein D is a damping matrix, M is a mass matrix of the unmanned ship,external time-varying disturbance caused by wind, wave and flow, < >>Thrust and moment provided for unmanned ship propulsion system, A tr For the propeller dynamic matrix of the system, +.>Unsaturated thrust and moment are obtained for the output of the controller, Δτ=τ p -τ c ，τ p The actual output signal obtained after the controller output torque is subjected to saturation limiting is specifically shown as follows.
Defining a pose error vector e 1 ＝x-x d ,e 2 ＝y-y d ,Based on the new error conversion function
Representing conversion errors of three degrees of freedom of heave, surge and yaw respectively. Wherein, e i represents the longitudinal position error, the transverse position error and the heading error of the unmanned ship, e i,l And e i,u Represent the lower and upper limits, epsilon, of the range of preset performance errors in each degree of freedom i Is the new error variable after conversion. This preset performance error transfer function has the following important properties:
1) When e i →-e i,l Time epsilon i -infinity. When e i →e i,u Time epsilon i →∞
2) If and only if e i When=0, ε i ＝0
Wherein the boundary limiting function is defined as follows
Where ρ (t) = (ρ) 0 -ρ ∞ )e -kt +ρ ∞ Is a positive function with respect to a strictly monotonic decrease in time t, ρ 0 、ρ ∞ 、k、δ i,l 、δ i,u Are all positive constants set. The converted system is obtained after deriving
Wherein,
let ε= [ ε ] 1 ,ε 2 ,ε 3 ] T ，f＝[f 1 ,f 2 ,f 3 ] T ，g＝diag[g 1 ,g 2 ,g 3 ]Is available in the form of
Step two: adopting a back-step design method to calculate a control law
The specific implementation process is as follows
Error variables in defining the back-step design process are as follows
Selecting a first Liapunov function
Can obtain the derivation
The following virtual control quantity is obtained through recursion
α 1 ＝g -1 (-K 1 z 1 -f)
Wherein K is 1 ＝diag([K 11 ,K 12 ,K 13 ]) A symmetric matrix is designed for positive definite.
To avoid complex derivation processes, the following instruction filters are introduced
Wherein omega n1 Is that the natural frequency of the filter satisfies omega n1 ＞0，ζ 1 Is designed to satisfy ζ 1 ∈(0,1]。For the filter output, phi 12 Is a filter state vector. The virtual control amount is used as a filter input, and the output of the filter is obtained to replace the virtual control amount. This approach successfully converts complex differential operations into simple algebraic operation problems. In order to overcome the filtering error brought by the instruction filter, the filtering error is defined as delta 1 ＝φ 11 -α 1 And is constructed as follows
Wherein, xi 1 、ξ 2 Is a state vector, ζ 2 Will be defined below. The conversion position error face vector after the filtering error is considered can be redefined as
s 1 ＝z 1 -ξ 1
For the second error plane vector, the following Liapunov function is defined
Is derived and available
The following virtual control quantity is obtained through recursion
Wherein τ rob Is a robust term designed for composite errors caused by external time-varying disturbances. K (K) 2 ＝diag([K 21 ,K 22 ,K 23 ]) Designing a symmetric matrix for positive determination, λ and l being positive determination design constantsAnd->Is an adaptive model parameter whose matrix-to-vector form conversion is as follows:
wherein m is i And d i Column vectors representing the i-th row elements of the inertia matrix and the damping matrix, respectively. Theta (theta) 1 And theta (theta) 2 The corresponding adaptive law of (a) is designed as follows
Wherein K is D 、K M 、Γ D 、Γ M A positive diagonal matrix is defined for the design to be made.
A second command filter is introduced, the virtual control quantity is taken as a filter input, and the filter output is taken as an actual control quantity.
Wherein omega n2 Is that the natural frequency of the filter satisfies omega n2 ＞0，ζ 2 Is designed to satisfy ζ 2 ∈(0,1]。For the filter output, phi 22 Is a filter state vector. Definition of the filtering error delta 2 ＝φ 21 -α 2 Designing a model-free error compensation auxiliary system as
Wherein, xi 3 ∈R 3 Is a compensation vector and meets the requirement of xi 3 (0) =0 sumThe velocity error plane vector after consideration of the filtering error can be redefined as
s 2 ＝z 2 -ξ 2
For the third error plane vector, the following Liapunov function is defined
After substitution, the final control law can be obtained as
Wherein K is 3 ＝diag([K 31 ,K 32 ,K 33 ]) And K c ＝diag([K c1 ,K c2 ,K c3 ]) Designing a symmetric matrix for positive determination, wherein theta is an auxiliary dynamic system variable
Wherein K is θ ＝diag([K θ1 ,K θ2 ,K θ3 ]) Is a positive design matrix.
Implementation case: in order to verify the effect of the control method, the following simulation test is carried out by taking a certain unmanned ship model as a simulation object: initial position of unmanned shipThe desired position is [ u (0), v (0), r (0)]＝[0m/s,0m/s,0m/s]. Is set as follows
τ dx ＝1+0.2m 11 d(t),τ dy ＝1+0.2m 22 d(t),τ dpsi ＝1+0.003m 33 d(t)
d(t)＝0.1sin(0.2t)
Wherein m is 11 、m 22 、m 33 Is the quality item of the unmanned ship. In the dynamic updating process, the inertia matrix of the system is made to be
M＝diag([5.3122×10 6 +t×10 3 ,8.2831×10 6 +t×10 3 ,3.7454×10 9 +t×10 3 ])
To simulate the variable load process of an unmanned boat.
The simulation results are as follows, fig. 3 shows a speed calendar curve of unmanned ship power positioning, fig. 4 shows a horizontal plane position and heading angle calendar curve of unmanned ship power positioning, and fig. 5 shows a calendar curve output by an actuator during unmanned ship power positioning. The unmanned ship can be finally converged to the expected pose, and the pose of the unmanned ship in the transient process is always under the constraint of the upper and lower boundaries of the preset performance function. Fig. 6 and 7 show the time history curves of the unmanned boat dynamic positioning conversion position error surface vector and the speed error surface vector after the filtering errors are considered, and the errors are close to 0 under the control of the designed controller.
Claims (8)
1. The model-free self-adaptive preset performance control method for unmanned ship dynamic positioning is characterized by comprising the following steps of:
based on the proposed novel preset performance function, converting the dynamic positioning system with limited error performance into a new system with non-limited error performance;
developing controller backstepping design work by combining linearization feedback and robust self-adaptive technology to obtain a preliminary virtual intermediate variable;
the virtual intermediate variable is filtered by an instruction filter to avoid differential operation, and a corresponding model-free filtering error elimination auxiliary system is designed to compensate errors;
the self-adaptive technology is adopted to carry out the self-adaptive updating of the model, so that the controller effect under the variable load working condition is ensured;
the novel preset performance function is provided as follows
Wherein, e i respectively representing the longitudinal position error, the transverse position error and the heading error of the unmanned ship on the horizontal plane, e i,l And e i,u Represent the lower and upper limits, epsilon, of the range of preset performance errors in each degree of freedom i To pass byThe new error variable after conversion.
2. The model-free adaptive preset performance control method for unmanned ship dynamic positioning according to claim 1, wherein the preset performance control method is introduced based on a third-order dynamic positioning unmanned ship model, the transient and steady performance of the dynamic positioning unmanned ship taking the propeller dynamics into consideration is limited within the following preset upper and lower limits,
wherein e i,l (t) and e i,u (t) represents the upper and lower performance limits, δ, of the three degrees of freedom, respectively i,l And delta i,u Is a preset performance parameter ρ i (t) is an exponential function of the attenuation.
3. A model-free adaptive preset performance control method for unmanned ship dynamic positioning as claimed in claim 1, wherein the new system has unrestricted error performance, and the design controller enables the system to be stably equivalent to preset performance range control, and the new system with unrestricted error performance is obtained after derivative and matrix form arrangement, which lays a foundation for back-step design,
wherein f is a continuous function, g is a velocity gain, D is a damping matrix, M is a mass matrix of the unmanned boat,external time-varying disturbance caused by wind, wave and flow, < >>Thrust and moment provided for unmanned ship propulsion system, A tr For the dynamic moment of the propeller of the systemThe array of which is arranged in a row,
unsaturated thrust and moment are obtained for the output of the controller, Δτ=τ p -τ c ，τ p Is the actual output signal obtained after the controller output torque is subjected to lower saturation limiting.
4. The model-free adaptive preset performance control method for unmanned ship dynamic positioning of claim 1, wherein the virtual intermediate control variables used in the back-step design process are as follows:
α 1 ＝g -1 (-K 1 z 1 -f)
wherein f is a continuous function, K 2 Is a positive design of the diagonal matrix,and->For adaptive system model parameters, < >>For the output of one of the filters, s 1 Is a conversion position error taking into account the filtering error, τ rob Is a robust term designed for external time-varying disturbances.
5. The model-free adaptive preset performance control method for unmanned ship dynamic positioning according to claim 4, wherein the calculation method for processing the robust term of unmanned ship wind and wave interference is as follows:
wherein, xi 2 Is a state variable of the model-free filter compensation system, and l and lambda are normal numbers to be designed.
6. The model-free adaptive preset performance control method for unmanned ship dynamic positioning as claimed in claim 5, wherein the adaptive update law of system model parameters M and D is that
Wherein K is D 、K M 、Γ D 、Γ M A diagonal matrix is defined for the design to be made,and->Representing the damping matrix and the inertia matrix adaptive estimation vector, respectively.
7. The model-free adaptive preset performance control method for unmanned ship dynamic positioning according to claim 1, wherein the model-free instruction filter designed for the virtual intermediate variable in the back-step design process is as follows:
considering unavoidable filtering errors, the corresponding model-free filtering compensation auxiliary system is designed as follows:
ξ 3 ＝0
wherein K is 1 And K 2 Is a positive design diagonal matrix, ω n1 And omega n2 In order for the natural frequency of the filter to be present,and->In order to design the constant(s),is an adaptive inertia matrix, delta 1 ＝φ 11 -α 1 And delta 2 ＝φ 21 -α 2 The filtering errors of the two filters, respectively, xi 1 、ξ 2 And xi 3 The state variables of the model-free filter compensation system are respectively calculated.
8. The model-free adaptive preset performance control method for unmanned ship dynamic positioning according to claim 1, wherein the model-free preset performance controller output control force/moment calculation method is as follows
Wherein K is 3 And K c Is positive toDetermining a design matrix, τ being the thrust/torque output without consideration of input saturation limit, s 2 In order to consider the velocity error face vector after the command filter compensates the error, θ is the auxiliary dynamic system variable, A tr Is an actuator dynamic matrix.
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