CN114265308A - Anti-saturation model-free preset performance track tracking control method for autonomous water surface vehicle - Google Patents
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Abstract
The invention discloses an anti-saturation model-free preset performance track tracking control method for an autonomous water surface vehicle, and belongs to the technical field of unmanned ship anti-interference control. The anti-saturation model-free preset performance track tracking control method of the autonomous water surface vehicle comprises the following steps: step one, establishing an unmanned ship dynamic model considering external interference; step two, establishing a saturation function model; designing an anti-saturation controller independent of model information; and step four, verifying the stability and robustness of the unmanned ship control system. The invention can realize saturation tracking control only by adjusting the preset performance parameters by designing the error conversion equation and the saturation function model, has simple structure and few design parameters, and has good applicability in the aspect of engineering.
Description
Technical Field
The invention relates to an anti-saturation model-free preset performance track tracking control method for an autonomous water surface vehicle, and belongs to the technical field of unmanned ship anti-interference control.
Background
In recent decades, with the scarcity of land resources, marine resources have received attention from more and more scholars. In marine exploration, an unmanned ship can arrive and keep on a desired track within a specified time, a specified engineering task is completed, and the unmanned ship has excellent performance in tasks such as oil production, pipe laying and supply and the like by virtue of low cost and high efficiency, so that the tracking control problem of the unmanned ship is undoubtedly of high practical significance.
However, with the ever-increasing sophistication of work environments, the design of unmanned boat tracking control is becoming a challenge. Since drone tracking performance depends largely on control system interference rejection and stability, the design of high performance drone controllers still faces many challenges. On one hand, due to the complex operation environment and the high coupling and nonlinearity of the unmanned ship, an accurate model is difficult to obtain, and accurate tracking cannot be achieved. On the other hand, since a large control deviation and an estimated tracking error are often encountered during the task execution, it is difficult to effectively implement tracking control by the conventional adaptive control method and the like.
Disclosure of Invention
The invention aims to provide an anti-saturation model-free preset performance track tracking control method of an autonomous surface vehicle, which designs an unmanned ship anti-saturation tracking control method completely independent of model information by selecting a proper preset performance function under the condition of not needing on-line estimation of external interference so as to realize track tracking of the unmanned ship and solve the problems in the prior art.
An anti-saturation model-free preset performance track tracking control method of an autonomous water surface vehicle is characterized by comprising the following steps of:
step one, establishing an unmanned ship dynamic model considering external interference;
step two, establishing a saturation function model;
designing an anti-saturation controller independent of model information;
and step four, verifying the stability and robustness of the unmanned ship control system.
Further, in the step one, specifically:
the unmanned ship dynamics model established in the first step is as follows:
wherein eta is [ x, y, psi ═ x, y, psi]TRepresenting the position and the yaw angle of the unmanned ship under the geocentric coordinate system;representing linear and angular velocities in a body coordinate systemIs the inertial matrix of the system;is an unknown nonlinear function including hydrodynamic and model parameter perturbations;representing the actual control force;indicating a desired control input; r (ψ) is a coordinate transformation matrix defined as follows:
further, in the second step, specifically:
the following matrices and lemmas are defined:
for non-linear systemsWherein For a non-empty set, if f (t, x (t)) satisfies RippSitz continuity, it is found that there is a maximum solution for x (t) as follows:
theorem 2 is introduced as follows:
for continuous positive definite function V (x) if k is satisfied1||x||≤V(x)≤k2L x l, andwhereinα, β are both positive numbers, then x (t) satisfies a semi-global uniform final bounding,
aiming at the singularity problem brought by a hard equation adopted by the traditional saturation control, the saturation control is realized by designing a smooth saturation function, and the definition is as follows:
in the formula of alphai>0,β>0,In a limited interval approachingAnd is positive,/i(beta), i is 1,2,3, the density function satisfies li(β)≥0,
substituting the designed smooth saturation function to obtain:
namely, for the condition that the upper bound of the control input signal is known, the saturation control is realized by reasonably adjusting the parameters so as to avoid the occurrence of the singular condition.
Further, in step three, specifically:
establishing an unconstrained tracking error control function comprising:
the target tracking trajectory is defined as follows:
wherein etad=[xd,yd,ψd]TIn order to be the target track,in order to be able to set the desired motion parameters,
the tracking error is further defined as:
wherein E ═ RWRT,As a known non-linearity parameter of the system,representing an unknown disturbance outside, and being bounded,
designing an unconstrained error conversion equation as follows:
wherein mui=ηe,i/ρi,i=1,2,3,ηe=[ηe,1,ηe,2,ηe,3]TIndicating tracking error, rho (t) ═ rho1(t),ρ2(t),ρ3(t)]TThe performance function representing the preset is defined as follows:
ρi(t)=(ρ0,i-ρ∞,i)exp(-κit)+ρ∞,i,i=1,2,3
in the formula, a preset parameter rho0,i>|ηe,i(0)|,ρ∞,iIs a preset maximum value of the tracking error, κiThe convergence speed of the tracking error can be adjusted, the set parameters are positive numbers,
thus, an unconstrained error transfer function is derivedIs smooth and strictly increasing, and satisfiesAndfurther obtaining an inverse function of the error transformation function to obtain etaeAnd ω (μ) as follows:
wherein ω is-1(μi) Also satisfies the requirements of smoothness and strict increment and satisfiesAnd-1 < omega-1(μi)<1,
Therefore, ω is predefined-1(μi) And obtaining that the tracking error meets the following properties:
the tracking error problem studied translates into ω (μ)i) Stability problem, design unconstrained error control equation as follows:
wherein K is diag { K ═ K1,K2,K3},KiIf the tracking error is more than 0, the following equation is obtained by derivation:
And the controller is designed as follows:
where k is the strict positive control gain, Θ ═ diag { θ }1,θ2,θ3Is a matrix that can be designed by the user, and satisfies θi> 0, i-1, 2, 3.
Further, in step four, specifically:
to verify the stability and robustness of the unmanned boat control system, μ is definediThe time derivative of (a) is as follows:
satisfies the continuous and local integrability of Liphoz, and omega (mu)i) I is 1,2,3 is predetermined and is limited to Γiμ by introducing theorem 1 (═ 1,1)i(t) in the interval ΓiWithin a maximum value, i.e.
The Lyapunov function was chosen as follows:
the derivation can be:
due to ηd,All satisfy [0, tmax) Bounded within the interval, thus givingM-1And E is also bounded by the sum of,
by defining the following parameters:
wherein a isi,biI ═ 1,2,3 and qiWhere i is 1 and 2 are both positive numbers, substituting the derivative of the function of Helapunov, by defining sT(0) Thetas (0) < 1, eventually proving that the tracking error will converge to within the specified range.
The invention has the following beneficial effects: the invention can realize saturation tracking control only by adjusting the preset performance parameters by designing an error conversion equation and a saturation function model, has simple structure and few design parameters, and has good applicability in the aspect of engineering.
Drawings
FIG. 1 is a flow chart of an anti-saturation model-free default performance trajectory tracking control method of an autonomous surface vehicle of the present invention;
FIG. 2 is a saturated input model;
FIG. 3(a) is a two-dimensional plane tracking diagram, and FIGS. 3(b), 3(c) and 3(d) are forward, yaw and yaw velocity diagrams, respectively;
fig. 4(a), fig. 4(b) and fig. 4(c) are tracking errors of x, y and heading, and fig. 4(d), fig. 4(e) and fig. 4(f) are control moment diagrams of three directions of forward movement, rolling and heading respectively.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention is described in further detail below with reference to the accompanying drawings and the detailed description.
As shown in fig. 1, the limited time tracking control method for the under-actuated unmanned ship comprises the following steps:
firstly, establishing an unmanned ship dynamics model as follows:
where eta is [ x, y, psi [ ]]TRepresenting the position and the yaw angle of the unmanned ship under the geocentric coordinate system;representing linear and angular velocities in a body coordinate systemIs the inertial matrix of the system;is an unknown nonlinear function including hydrodynamic and model parameter perturbations;representing the actual control force;indicating a desired control input; r (ψ) is a coordinate transformation matrix defined as follows:
secondly, defining a saturation function:
for the convenience of subsequent derivation, we define the following matrices and lemmas:
for non-linear systemsx(0)∈ΩxWherein f (t, x (t)):for a non-empty set, if f (t, x (t)) satisfies RippSitz continuity, it can be concluded that there is a maximum solution for x (t) as follows:
theorem 2 is introduced as follows:
for continuous positive definite function V (x) if k is satisfied1||x||≤V(x)≤k2L x l, andwherein k is1,k2:And alpha and beta are positive numbers, x (t) satisfies the semi-global consistent final bounded.
Aiming at the singularity problem caused by a hard equation adopted by the traditional saturation control, the invention realizes the saturation control by designing a smooth saturation function, and the definition is as follows:
in the formula of alphai>0,β>0,In a limited interval approachingAnd is positive,/i(beta), i is 1,2,3, the density function satisfies li(β)≥0。
substituting the designed smooth saturation function can obtain:
that is, for the case that the upper bound of the control input signal is known, the singular case can be avoided by reasonably adjusting the parameters to realize saturation control.
Thirdly, establishing an unconstrained tracking error control function, which comprises the following steps:
the target tracking trajectory is defined as follows:
The tracking error is further defined as:
wherein E ═ RWRT,As a known non-linearity parameter of the system,represents an unknown disturbance of the outside world and is bounded.
Establishing an unconstrained tracking error control function comprising:
designing an unconstrained error conversion equation as follows:
wherein mui=ηe,i/ρi,i=1,2,3,ηe=[ηe,1,ηe,2,ηe,3]TIndicating tracking error, rho (t) ═ rho1(t),ρ2(t),ρ3(t)]TThe performance function representing the preset is defined as follows:
ρi(t)=(ρ0,i-ρ∞,i)exp(-κit)+ρ∞,i,i=1,2,3
in the formula, a preset parameter rho0,i>|ηe,i(0)|,ρ∞,iIs a preset maximum value of the tracking error, κiThe convergence speed of the tracking error can be adjusted, and the set parameters are positive numbers.
Therefore we can derive an unconstrained error transfer functionIs smooth and strictly increasing, and meetsAndfurther obtaining an inverse function of the error transformation function to obtain etaeAnd ω (μ) are as follows:
wherein ω is-1(μi) Also satisfies the requirements of smoothness and strict increment and satisfiesAnd-1 < omega-1(μi)<1。
Therefore, only ω is predefined-1(μi) We can conclude that the tracking error satisfies the following property:
the tracking error problem studied thus translates into ω (μ)i) Stability issues, and therefore design an unconstrained error control equation, as follows:
wherein K is diag { K ═ K1,K2,K3},KiIf the tracking error is more than 0, the following equation is obtained by derivation:
And the controller is designed as follows:
where k is the strict positive control gain, Θ ═ diag { θ }1,θ2,θ3Is a matrix that can be designed by the user, and satisfies θi>0,i=1,2,3。
Fourthly, defining mu in order to verify the stability and robustness of the unmanned boat control systemiThe time derivative of (a) is as follows:
it can be known thatSatisfies the continuous and local integrability of Liphoz, and omega (mu)i) I is 1,2,3 is predetermined and is limited to ΓiBy lemma 1, we derive μi(t) in the interval ΓiWithin a maximum value, i.e.
The Lyapunov function was chosen as follows:
the derivation can be:
due to ηd,All satisfy [0, tmax) Bounded within the interval, and thus can be derivedM-1And E is also bounded.
By defining the following parameters:
wherein a isi,biI ═ 1,2,3 and qiWhere i is 1 and 2 are both positive numbers, substituting the derivative of the function of Helapunov, by defining sT(0) Thetas (0) < 1, eventually proving that the tracking error will converge to within the specified range.
The performance of the above controller is then demonstrated and verified by a simulation example.
The control parameters and constraint boundaries are shown in table 1:
TABLE 1
The desired trajectory is defined as follows:
fd,1(t)=0.01cos(0.015πt)
fd,2(t)=-0.05sin(0.1πt)
fd,3(t)=0.01cos(0.02πt)
The initial state vector is defined as:
by defining model perturbations and external perturbations as follows:
to model a more realistic external perturbation, a second order Gaussian-Markov process is designed as follows:
τd=z1
The detailed simulation results are shown in fig. 2-4. These results demonstrate that the proposed controller is able to guarantee the desired performance index and has good disturbance resistance and robustness.
The above embodiments are only for assisting understanding of the method of the present invention and the core idea thereof, and a person skilled in the art may make several modifications and decorations on the specific embodiments and application scope according to the idea of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (5)
1. An anti-saturation model-free preset performance track tracking control method of an autonomous water surface vehicle is characterized by comprising the following steps of:
step one, establishing an unmanned ship dynamic model considering external interference;
step two, establishing a saturation function model;
designing an anti-saturation controller independent of model information;
and step four, verifying the stability and robustness of the unmanned ship control system.
2. The anti-saturation model-free preset performance trajectory tracking control method for the autonomous surface vehicle according to claim 1, characterized in that in step one, specifically:
the model of the unmanned ship dynamics established in step one is as follows:
wherein eta is [ x, y, psi ═ x, y, psi]TRepresenting the position and the yaw angle of the unmanned ship under the geocentric coordinate system; theta ═ u, v, r]TRepresenting linear and angular velocities in a body coordinate systemIs the inertial matrix of the system;is an unknown nonlinear function including hydrodynamic and model parameter perturbations; t (tau)θ)=[T(τθ,1),T(τθ,1),T(τθ,1)]TRepresenting the actual control force; tau isθIndicating a desired control input; r (ψ) is a coordinate transformation matrix defined as follows:
3. the anti-saturation model-free preset performance trajectory tracking control method of the autonomous surface vehicle according to claim 1, characterized in that in step two, specifically:
the following matrices and lemmas are defined:
theorem 1 is introduced as follows:
for non-linear systemsWhereinFor a non-empty set, if f (t, x (t)) satisfies RipHitz continuity, it is found that there is a maximum solution for x (t) as follows:
theorem 2 is introduced as follows:
for continuous positive definite function V (x) if k is satisfied1||x||≤V(x)≤k2L x l, andwhereinα, β are both positive numbers, then x (t) satisfies a semi-global uniform final bounding,
aiming at the singularity problem brought by a hard equation adopted by the traditional saturation control, the saturation control is realized by designing a smooth saturation function, and the definition is as follows:
T(τθ,i)=ciτθ,i-di,i=1,2,3
in the formula of alphai>0,β>0,Approaches to tau in a finite intervalθ,maxiI is 1,2,3 and is positive, li(beta), i is 1,2,3, the density function satisfies li(β)≥0,
By defining the controller z (τ)θ,i,β)=max(τθ,i-β,min(0,τθ,i+ β)) gives the formula:
substituting the designed smooth saturation function to obtain:
namely, for the condition that the upper bound of the control input signal is known, the saturation control is realized by reasonably adjusting the parameters so as to avoid the occurrence of the singular condition.
4. The anti-saturation model-free preset performance trajectory tracking control method of the autonomous surface vehicle according to claim 1, characterized in that in step three, specifically:
establishing an unconstrained tracking error control function comprising:
the target tracking trajectory is defined as follows:
wherein etad=[xd,yd,ψd]TIs a target track, θd=[ud,vd,rd]TIn order to be able to set the desired motion parameters,
the tracking error is further defined as:
wherein E ═ RWRT,As a known non-linearity parameter of the system,representing an unknown disturbance outside, and being bounded,
designing an unconstrained error conversion equation as follows:
wherein mui=ηe,i/ρi,i=1,2,3,ηe=[ηe,1,ηe,2,ηe,3]TIndicating tracking error, rho (t) ═ rho1(t),ρ2(t),ρ3(t)]TThe representative preset performance function is defined as follows:
ρi(t)=(ρ0,i-ρ∞,i)exp(-κit)+ρ∞,i,i=1,2,3
in the formula, a preset parameter rho0,i>|ηe,i(0)|,ρ∞,iIs a preset maximum value of the tracking error, κiThe convergence rate of the tracking error can be adjusted, the set parameters are positive numbers,
thus, an unconstrained error transfer function is derivedIs smooth and strictly increasing, and satisfiesAndfurther obtaining an inverse function of the error transformation function to obtain etaeAnd ω (μ) as follows:
wherein ω is-1(μi) Also satisfies the requirements of smoothness and strict increment and satisfiesAnd-1 < omega-1(μi)<1,
Therefore, ω is predefined-1(μi) And obtaining that the tracking error meets the following properties:
the tracking error problem studied translates into ω (μ)i) Stability problem, design unconstrained error control equation as follows:
wherein K is diag { K ═ K1,K2,K3},KiIf the tracking error is more than 0, the following equation is obtained by derivation:
And the controller is designed as follows:
where k is the strict positive control gain, Θ ═ diag { θ }1,θ2,θ3Is a matrix that can be designed by the user, and satisfies θi> 0, i-1, 2, 3.
5. The anti-saturation model-free preset performance trajectory tracking control method of the autonomous surface vehicle according to claim 1, characterized in that in step four, specifically:
to verify the stability and robustness of the unmanned boat control system, μ is definediThe time derivative of (a) is as follows:
satisfies the continuous and local integrability of Liphoz, and omega (mu)i) I is 1,2,3 is predetermined and is limited to Γiμ by introducing theorem 1 (═ 1,1)i(t) in the interval ΓiWithin a maximum value, i.e.
The Lyapunov function was chosen as follows:
the derivation can be:
due to ηd,θdAll satisfy [0, tmax) Bounded within the interval, thus givingM-1And E is also bounded by the sum of,
by defining the following parameters:
wherein a isi,biI ═ 1,2,3 and qiWhere i is 1 and 2 are both positive numbers, substituting the derivative of the function of Helapunov, by defining sT(0) Thetas (0) < 1, eventually proving that the tracking error will converge to within the specified range.
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