CN116449695A - Event-driven based full-drive ship preset performance tracking control method and system - Google Patents
Event-driven based full-drive ship preset performance tracking control method and system Download PDFInfo
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Abstract
The invention discloses a method and a system for tracking and controlling the preset performance of a full-drive ship based on event driving, and relates to the technical field of tracking and controlling the preset performance. The method comprises the following steps: acquiring parameter information of a target ship, and establishing a ship model based on a closed-loop system of the full-drive ship; the auxiliary system is constructed to generate a compensation signal to compensate adverse effects of the ship model due to input saturation; designing an adaptive fixed time tracking controller according to the compensation signal; setting parameters of a self-adaptive fixed time tracking controller, inputting a control target in preset time to the self-adaptive fixed time tracking controller, and outputting a control instruction to an actuator by the controller so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint. Aiming at a full-drive water surface ship, the invention realizes the control of the preset performance of fixed time based on event driving under the conditions of full-state constraint, lumped interference and input saturation.
Description
Technical Field
The invention relates to the technical field of preset performance tracking control, in particular to a method and a system for tracking control of preset performance of a full-drive ship based on event driving.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
Ship control has been an important place in control theory and control engineering. Ocean surface vessels can be classified into full-drive and under-drive, and full-drive vessels have a simple and intuitive form compared to under-driven vessels. In 2005, the ocean control laboratory of Norway science and technology successfully built a full-drive ship named Cybership II, the size of which is designed according to the proportion of 1:70 of a certain replenishment ship, and experimental results show that the ship has a simple structure and flexible operation. Since then, all-drive marine vessels have received attention.
In order for a fully driven vessel to meet certain performance and safety requirements, the system state often needs to be limited to a certain range. For example, vessels operating around offshore platforms, are severely constrained in terms of speed and position in order to avoid collision accidents with the platform. In actual ship control, however, it is sometimes necessary to complete desired tasks, such as ship docking and interception, in a limited time. Terminal Sliding Mode Control (TSMC) was first used to achieve limited time control of the robotic arm due to its robustness to interference. Subsequently, for various finite time control targets, a disturbance observer-based TSMC, a high-order TSMC, and a TSMC to which a power integrator is added are respectively proposed.
Although time-driven based control is easy to implement, it is a conservative approach and may lead to overload of the communication channel. The above problems do not occur with event driven control. However, in existing approaches to event driven control, the inventors found that:
the vessel is always inevitably affected by lumped disturbances when sailing at sea and is constrained in position and speed. In addition, in the ship propulsion system, the engine speed can only be changed within a certain range, so that the propeller has limited power supply and the input saturation phenomenon occurs. Whereas existing event-driven control does not take into account the lumped disturbance and input saturation conditions described above. And in the case of a fully driven vessel, there is a lack of control research for a fixed time in the case of a state constraint.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a method and a system for tracking and controlling the preset performance of a full-drive ship based on event driving, and aims at controlling the preset performance of fixed time based on event driving under the conditions of full-state constraint, lumped interference and input saturation for a type of full-drive water surface ship.
In order to achieve the above object, the present invention is realized by the following technical scheme:
the invention provides a full-drive ship preset performance tracking control method based on event driving, which comprises the following steps:
acquiring parameter information of a target ship, and establishing a ship model based on a closed-loop system of the full-drive ship;
the auxiliary system is constructed to generate a compensation signal to compensate adverse effects of the ship model due to input saturation;
designing an adaptive fixed time tracking controller according to the compensation signal;
setting parameters of a self-adaptive fixed time tracking controller, inputting a control target in preset time to the self-adaptive fixed time tracking controller, and outputting a control instruction to an actuator by the controller so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint.
The second aspect of the invention provides a full-drive ship preset performance tracking control system based on event driving, which comprises the following components:
the model building module is configured to collect parameter information of a target ship and build a ship model based on a closed-loop system of the full-drive ship;
the model optimization module is configured to construct an auxiliary system to generate a compensation signal so as to compensate adverse effects of the ship model due to input saturation;
a controller design module configured to design an adaptive fixed time tracking controller based on the compensation signal;
the system comprises a preset performance tracking control module, a self-adaptive fixed time tracking controller and a controller, wherein the preset performance tracking control module is configured to set parameters of the self-adaptive fixed time tracking controller, a control target in preset time is input into the self-adaptive fixed time tracking controller, and the controller outputs a control instruction to an actuator, so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint.
A third aspect of the present invention provides a medium having stored thereon a program which when executed by a processor performs the steps of the event driven based all-drive marine vessel predetermined performance tracking control method according to the first aspect of the present invention.
A fourth aspect of the invention provides an apparatus comprising a memory, a processor and a program stored on the memory and executable on the processor, the processor implementing the steps in the event driven based all-terrain marine vessel predetermined performance tracking control method according to the first aspect of the invention when the program is executed.
The one or more of the above technical solutions have the following beneficial effects:
aiming at a full-drive water surface ship, the invention realizes the control of the preset performance of fixed time based on event driving under the conditions of full-state constraint, lumped interference and input saturation. In the control design, the effect of input saturation on the system is compensated by introducing auxiliary signals and the state constraints are guaranteed by using the Barrier Lyapunov Function (BLF). In order to achieve a given tracking performance, error transformation based on a speed function is introduced, so that the proposed algorithm can ensure expected transient and steady-state tracking performance without violating full-state constraints, and the remarkable characteristics of the proposed method are that convergence speed, tracking accuracy, and settling time can be preset in advance, and the communication cost of the controller is low.
Additional aspects of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention.
FIG. 1 is a schematic view of a full-drive vessel in the earth and hull coordinate systems according to a first embodiment of the invention;
FIG. 2 is a schematic diagram of a closed loop system state meeting constraints in a simulation verification experiment according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a tracking error reaching a predetermined accuracy in a simulation verification experiment according to an embodiment of the present invention;
FIG. 4 is a schematic diagram showing the finite nature of adaptive parameters in a simulation verification experiment according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of the output of the forward actuator and the signal transmission time in a simulation verification experiment according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of the output of the lateral drift force actuator and the signal transmission time in a simulation verification experiment according to an embodiment of the present invention;
fig. 7 is a schematic diagram of output and signal transmission time of a helm swing actuator in a simulation verification experiment according to an embodiment of the invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
The definition and quotation of the related assumptions used in the event-driven full-drive ship preset performance tracking control method are as follows:
suppose 1: for vector d (x 1 ,x 2 T) there is an unknown positive constant θ and a known positive smoothing function ψ (x 1 ,x 2 T) such that d (x) 1 ,x 2 ,t)|| 2 ≤θψ(x 1 ,x 2 ,t)。
Suppose 2: x is x d (t) and its derivative with respect to time are continuous, while there is a positive continuous functionAnd positive constant->Satisfy->
Suppose 3: with a constant K a ，K b So that k is a (t)＜K a And k is b (t)＜K b . In addition, there is a positive constantAnd->So that k is a (t) and k b The derivative of (t) satisfies->And->
Definition 1: nonlinear systemIs practically stable under constraint for a fixed time (CPFTS), if for all η (t 0 )＝η 0 E.OMEGA.with scalar epsilon > 0, so that when t.gtoreq.t 0 +t 1 When, there is ||eta (t) | < epsilon, and eta (t) ∈omega is satisfied throughout the control process. Omega is a constraint set given in advance, t 1 Is the upper limit of the rest time T (η (0)) independent of the initial value of the system.
Note 1: in the control problem with state constraints, constraint function k a (t) and k b (t) is predetermined. One of the design goals of the controller is to keep all states of the system from violating given constraints throughout the control process, i.e., inequality x 1 (t)||＜k a (t)，||x 2 (t)||＜k b (t) holds true for any time. Thus, definition 1 has a stable property, not an attractive property.
Lemma 1: if there is a positive functionThe method meets the following conditions: 1)/>2)Wherein alpha is 1 ＞0，α 2 ＞0，0＜p 1 ＜1，p 2 ＞1，/>Are all constant. The system is CPFTS, i.e. when t.gtoreq.t 1 There is->Is true, whereinAnd 0 < c < 1 is a constant. When->In the time-course of which the first and second contact surfaces,when->When (I)>
And (4) lemma 2: definition open setAnd->Wherein k is ci Is a normal number, and l is a positive integer. Consider the system->Definition of the function->Wherein f is atThe upper pair η is local lipschitz. Assuming that there is a positive and continuously differentiable function +.>AndAnd satisfies the following over the respective domains:
W i (w i )→∞，|w i |→k ci ，
α 1 (||ξ||)≤W(t,ξ)≤α 2 (||ξ||)， (1)
wherein alpha is 1 And alpha 2 Is thatA function. Based on this, V (η) =w (t, ζ) +w is further defined i (w i ) At the same time define w i (0)∈Π i . Furthermore, if V is in the set->Satisfy the following requirements
Wherein 0 < p 1 ＜1，p 2 > 1. Then: 1) The system being CPFTS, 2) w i ∈Π i ，
And (3) lemma 3: assuming d and e are normal numbers, then the sum of the arbitrary real numbers x, y and the function γ (x, y) >0, establish |x| d |y| e ≤(dγ|x| d+e +eγ -d/e |y| d+e )/(d+e)。
And 4, lemma: for vectorsIf the equation x </b is satisfied, the following inequality holds: 0 < ln (b) T b/(b T b-x T x))≤x T x/(b T b-x T x), wherein l > 0.
And (5) lemma: for positive real numbersk=1, …, n, and an arbitrary constant l, if l > 1, there isIf 0 < l < 1, there is +.>
And (3) lemma 6: for any oneIs satisfied that 0 is less than or equal to |U| -Utanh (U +) * )≤k ** Wherein k is * = 0.2785 and e * And > 0 is a real number.
And (4) lemma 7: definition of a functionThe expression is as follows: y (x) =sign (x) |x|x|n 2k-1 tanh(|x| 2k /∈ * ) Wherein E is * > 0,3/4 < k < 1. Let the first derivative be ψ (x) and the second derivative be G (x). Y (x), ψ (x), and G (x) are at +.>The upper part is continuous.
And lemma 8: defining a vector:the following inequality holds: - χ T Ξ≤-(χ T χ) k +n∈ * k * Wherein->
And (3) proving: directly available by means of the lemma 5 and lemma 6
The verification of lemma 8 is complete.
Embodiment one:
the embodiment of the invention provides a full-drive ship preset performance tracking control method based on event driving, which comprises the following steps:
step 1: and acquiring parameter information of the target ship, and establishing a ship model based on a closed-loop system of the full-drive ship.
Step 2: the auxiliary system is constructed to generate a compensation signal to compensate adverse effects of the ship model due to input saturation;
step 3: designing an adaptive fixed time tracking controller according to the compensation signal;
step 4: setting parameters of a self-adaptive fixed time tracking controller, inputting a control target in preset time to the self-adaptive fixed time tracking controller, and outputting a control instruction to an actuator by the controller so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint.
In step 1, a ship model is built for a closed-loop system of a fully-driven ship based on an earth coordinate system, and the relationship between the earth coordinate system and a ship body coordinate system is shown in fig. 1. The method comprises the following specific steps:
the fully driven surface vessel models the closed loop system according to the following formula:
wherein the bit shape vectorWherein (x, y) represents the position of the vessel in the earth coordinate system, < >>Representing the heading angle. Speed vector->The elements of (a) represent forward speed, lateral speed, and yaw speed, respectively. Vector->To represent lumped disturbances, possible modeling bias, and ignored dynamics. f (τ) = [ f 1 (τ 1 ),f 2 (τ 2 ),f 3 (τ 3 )] T Is the actuator output with saturation characteristics, τ= [ τ ] 1 ,τ 2 ,τ 3 ] T Is the original control signal to be designed. J (eta) is the rotation matrix, D (v) is the damping matrix,/and (eta)>Is a symmetrical and positive inertia matrix, +.>Is a centripetal force and coriolis force matrix, < +.>Is a restoring force caused by gravity, ocean currents, and buoyancy. J (η), M, C (v), D (v) has the detailed expression:
each element in M is respectively:each element in C (v) is respectively:each element in D (v) is respectively: d, d 11 (v)＝-X u -X |u|u |u|-X uuu u 2 ，d 22 (v)＝-Y ν -Y |ν|ν |ν|-Y |r|ν |r|，d 23 (v)＝-Y r -Y |ν|r |ν|-Y |r|r |r|，d 32 (v)＝-N ν -N |ν|ν |ν|-N r|ν |r|，d 33 ＝-N r -N |ν|r |ν|-N |r|r R is the same as the standard. Coefficient X (·) ，Y (·) ，N (·) Is the hydrodynamic coefficient. m is the mass of the vessel, I z Moment of inertia about yaw rotation, x g Represents O b Distance to the center of gravity of the vessel. f (f) i (τ i ) Can be described as:
wherein f imax > 0 and f imin < 0 is a known saturation parameter. It is readily apparent that J (η) has the following properties: j (J) T ＝J -1 And ||j (η) |=1.
By selecting x 1 =η and x 2 =v, the equivalent of (3) can be obtained, i.e. a ship model of closed-loop system:
wherein H (x) 1 ,x 2 )＝M -1 (-C(x 2 )x 2 -D(x 2 )x 2 -g(x 1 ))。
The present embodiment aims at implementing 1) all signals of a closed loop system (4) are bounded based on an event driven adaptive control strategy. 2) Desired trajectory x d ＝[x d1 ,x d2 ,x d3 ] T Can be systematically profiled with the trajectory x 1 ＝[x 11 ,x 12 ,x 13 ] T Tracking is completed before a pre-specified time T, while the tracking error satisfies lim t→T |x 1i -x di I < ε and I x 1i -x di | t≥T < ε (i=1, 2, 3), where ε is a predetermined arbitrary small constant. 3) The system state does not violate the desired constraints: ||x 1 (t)||＜k a (t)，||x 2 (t)||＜k b (t) wherein k a (t) and k b (t) is a strictly positive continuous function.
In step 2, in order to compensate the adverse effect of input saturation on the closed loop system, the present embodiment constructs the following auxiliary systems to generate the compensation signalAnd->
Wherein the method comprises the steps of
In the middle ofΔτ＝M -1 f(τ)-M -1 τ，λ 1 ＝βξ 1 ，λ 2 ＝βξ 2 ，Ξ 1 ＝[Y 11 ,Y 12 ,Y 13 ] T ，3/4＜r 1 ＜1，r 2 ≥2，Ξ 2 ＝[Y 21 ,Y 22 ,Y 23 ] T ，ω 1 ＞0。
In the auxiliary system (5), Δτ is the input, ζ 1 And xi 2 Is the output. Before control design, the compensation signal ζ needs to be proved 1 And xi 2 Is limited by the nature of the (c).
Selecting Lyapunov functions as:
the derivative thereof can be determined by calculation as:
combining the lemma 4 and applying Young's inequality to obtain
Thereby having the following characteristics
It can be obtained that the auxiliary system (5) is practically stable for a fixed time, while ζ is at the same time given a bounded Δτ 1 And xi 2 Can be at a fixed time t 1* Into an arbitrarily small bounded set.
The principle is as follows: using the quotation 5, (6) can be written asWherein the method comprises the steps ofq 2 ＝min{2q 21 ，2q 22 And (3) 1 ＝ω 1 max t≥0 {‖Δτ(t)‖ 2 }+3k * (q 11*1 +q 12*2 )。
Setting T to be greater than or equal to T 1* Can obtainThis means
By means of the primer 2, the closed loop system (4) is practically stable for a fixed time and the upper boundary t of the rest time 1* Can be expressed asOr-> In->And 0 < c < 1.
By combining the above analyses, for arbitrarily small constants ε > 0, the method can be performed by settingThere will be ζ i And the L is less than or equal to epsilon/2 and is equal to or greater than T.
In step 3, the specific design process of the adaptive fixed time tracking controller is as follows:
introducing a speed function and a velocity function based on tracking control performance;
combining the compensation signals to obtain error transformation based on a speed function;
constructing a BLF according to the constraint state;
designing a fixed time self-adaptive tracking control algorithm based on event triggering;
and analyzing according to a tracking control algorithm, and designing a tracking controller.
More specifically, a speed function beta (t) is introduced to ensure the tracking performance of the system, the tracking performance is designed according to actual requirements, and the specific formula is as follows:
wherein ρ (t) is a rate function, 0 < b f The term "1" is a design parameter, T is more than 0 infinity is pre-allocation time.
Combining the compensation signals, obtaining error transformation based on a speed function:
z 1 ＝x 1 -x d -ξ 1 ，z 2 ＝x 2 -α 1 -ξ 2 ，
e 1 ＝βz 1 ，e 2 ＝βz 2 ， (9)
wherein alpha is 1 Is a virtual control signal.
The construction of the BLF according to the constraint state is divided into the following two steps:
step 1: constraint status is guaranteed by constructing the BLF. The BLFV of the following form 1 ：
Wherein the method comprises the steps ofFor the sake of simplicity, define->Calculating BLFV 1 Is derived from:
using Young's inequality to obtain:
middle l 1 > 0 is a design parameter.
Recording deviceAnd constructing xi 3 ＝[Y 31 ,Y 32 ,Y 33 ] T Wherein the method comprises the steps ofAnd 3/4 < k < 1.
The virtual controller is designed as follows:
wherein the method comprises the steps of
At the same time, k is more than 3/4 and less than 1, mu 11 > 0, and mu 12 ＞0。
Based on beta.gtoreq.1, the further combinations of formulae (11), (12), and (13) give:
note 2 the xi introduced in the virtual controller is known from the lemma 8 1 ，Ξ 2 And xi 3 Are all well defined and Y 1i ，Y 2i And Y 3i (i=1, 2, 3) are also continuously differentiable, and alpha is found 1 Is continuously differentiable.
Step 2: consider a second candidate BLF:
wherein k is 2 (t) > 0, andat the same time->Representing an estimate of θ.
Definition of the definitionAnd to V 2 The derivation can be obtained:
l-shaped memory 1 ＝(σ-K 2 (t))e 2 ，The method (15) can be rewritten as:
note beta 2 1. Gtoreq., then the Young's inequality can be used to obtain the following result:
wherein l 2 Is a positive design parameter.
By means of the quotation 6, it is possible to obtain:
wherein the method comprises the steps of
Bringing formulae (17) and (18) to (16) gives:
next, a virtual control signal alpha is constructed 2 The following are provided:
wherein is of the type 4 ＝[Y 41 ,Y 42 ,Y 43 ] T ， Is vector->Is the i-th element of (2), and->∈ *5 ＞0，i＝1，2，3。
By using the lemma 8, (19) can be rewritten as:
thus, the adaptive fixed time tracking controller may be designed to:
wherein τ i (t) is the ith component, alpha, of the control signal τ 2i Is alpha 2 Is selected from the group consisting of the (i) th element,representing the control signal τ i Update time of (t).
The event driven strategy is taken as:
wherein,,representing the control signal τ i Update time of (t),> representing the sampling error of the ith actuator, < +.>Is the corresponding signal transmission time, M i Represents the ith row of matrix M, while M 1 > 0 is a design parameter and i=1, 2,3.
It should be noted that, in the event-driven strategy, updating and transmission of the control signal are separated. Since the control signal is affected by saturation, whenWhen the control signals before and after updating are in the saturation stage, the output f of the actuator i (τ i ) Is kept unchanged, and no signaling is necessary at this time. Briefly, in event triggering mechanisms (22) - (24), if trigger condition (23) is activated, control signal τ is applied i (t) update toOn the basis of this, if it is satisfied againThe control signal tau is further processed i To the ith actuator. Thus, signal transmission time +.>Is the trigger time +.>This also allows the proposed event driven strategy to further alleviate the communication burden. On the other hand, the control signal τ i (t) update at trigger time, guaranteed +.>This holds for all t.
If it is assumed that 1-3 holds, and the initial value of the closed loop system (4) meets the value x 1 (0)||＜k a (0)，||x 2 (0)||＜k b (0) Applying the event-based control strategy (21) - (24) may achieve the control objective: 1) All signals of the closed loop system (4) are bounded. 2) Desired trajectory x d ＝[x d1 ,x d2 ,x d3 ] T Can be x 1 ＝[x 11 ,x 12 ,x 13 ] T Tracking is completed before a pre-specified time T, while the tracking error satisfies lim t→T |x 1i -x di I < ε and I x 1i -x di | t≥T < ε (i=1, 2, 3), where ε is a predetermined arbitrary small constant. 3) System state does not violate desired constraints：||x 1 (t)||＜k a (t)，||x 2 (t)||＜k b (t) wherein k a (t) and k b (t) is a strictly positive continuous function.
The deduction process is as follows: from equations (22) and (24), it can be derived:
wherein |θ 1 (t)|≤1，|θ 2 And (t) |is less than or equal to 1, and is two time-varying parameters. Thus there is τ (t) =τ s (t)/(1+θ 1 δ 1 ) +n holds, where n= [ (-m) 1 θ 2 (t))/(1+θ 1 (t)δ 1 ),(-m 1 θ 2 (t))/(1+θ 1 (t)δ 1 ),(-m 1 θ 2 (t))/(1+θ * (t)δ 1 )] T 。
Due to the assurance ofThereby have->It is further known that:
on the basis of (25), it can be deduced that
Carrying (26) into (20) to obtain
For the coupling term in (27), the embodiment has
Order thex＝1，d＝1-k，e＝k，γ＝k k/(1-k) Then +.>
I.e. the
Also, there will be
Simultaneous inequalities (27) - (29) can be obtained:
equation (30) can be further written by way of quotation 4 and quotation 5 as:
wherein sigma 1 ＝min{2 k μ 11 ,2 k μ 21 ,μ 31 }，σ 2 ＝min{(4/3)μ 12 ,(4/3)μ 22 ,(1/3)μ 32 }， Because of V 2 More than or equal to 0, there is
Definition of the definitionIt can be seen that there is +.0 for any t>Thus->And->
Further, the method comprises the steps of, as long as it is initially error satisfies ||e 1 (0)||＜k 1 (0)，||e 2 (0)||＜k 2 (0) Just there is Also, since β (t) is bounded, there is +.>And->Review (9) know->And->Furthermore, can get +.>And->According to->And combining the above analysis with->And->Thereby reflecting +.>And->Further, it can be summarized that: all signals of the closed loop system (4) are bounded. The certification of the control target 1) is completed.
Analysis of (31) by means of primer 1 and primer 2 shows that the closed loop system (4) is CPFTS. Definition of the definitionAfter some simple calculation, it is not difficult to obtain the time t is more than or equal to t 2* At the time, there are
Wherein the method comprises the steps ofAnd K is * ＝max t≥0 {k 1 (t),k 2 (t) }. When->In the time-course of which the first and second contact surfaces,when->When (I)>j＝1,2。
The parameters of the speed function are set as follows:
T≥max{t 1* ,t 2* }，
then (32) can be rewritten as:
this means a generalized error z j (T) decays to an arbitrarily small value before being able to precede a preset time T and does not escape after T.
For tracking error z 1i* ＝x 1i -x di The method can be obtained on the basis of the analysis: z 1i* |≤||x 1 -x d ||≤||z 1 ||+||ξ 1 I. The links (9) and (34) can be obtained
|z 1i* |≤(1-b f )ρ -1 (t)Θ 1 +ε，max{t 1* ,t 2* }≤t＜T，
|z 1i* |≤ε，t≥T，
Wherein the method comprises the steps ofThus, there are
The above results indicate that the tracking error can be attenuated to be arbitrarily small within T to accomplish the desired tracking, and that the attenuation speed is not slower than ((T-T)/T) 4 e -t . The certification concerning the control target 2) is completed.
From the above analysis, it can be seen that for any t.gtoreq.0, as long as the initial conditions of the system satisfy the constraintIs established and combine with V 2 Is further aware of the structure of +.> And->Also, since all signals of the system are bounded, there must be a positive constantMake->Thus, only select +.>Will haveSimilarly, select +.>Will haveThis means that all states are subject to constraints throughout the control process, thereby achieving the control objective 3).
Finally, it is necessary to explain that the gano phenomenon does not occur in the whole control. τ si The derivative of (i=1, 2, 3) can be expressed as
Wherein the method comprises the steps of
From the lemma 7, it can be known that α 1i ，And->(i=1, 2, 3) are continuous functions. Based on this, alpha can be directly derived 2i ，/>And->Further, it is known that +.>Is also continuous. For sampling errorsThe following inequality holds:
due toIn section->Continuity of the upper and the definition of the total signal, it is not difficult to deduce +.>Is limited by the nature of the (c). Thus there is a positive constant iota i Make->For any->This is true. For (36)>To->Can be obtained by integration of (C)
Due toAnd->Then->Always hold. Thereby have->I.e. the gano phenomenon is circumvented in the control process.
And (4) injection: formula (33) gives T and b in the conserved case f In fact, due to the fixed time-stable nature of the closed-loop system, it is possible for the system to achieve a tracking of a given precision before the pre-allocation time T, which is reflected inThe fixed time adjustment properties of the control algorithm in this embodiment are shown.
And (5) injection: although the lemma 2 is denoted by p in the present embodiment 2 Form application of =2, in fact, p 2 Any integer greater than 1 may be taken. This can be achieved by a control design similar to the present embodiment. For example, will A 2 In (a) and (b)Replaced by->While in the law of adaptationReplaced by->Then (31) will be rewritten as +.>I.e. p 2 Implementation=3.
And (3) performing simulation verification according to the step (4), wherein the specific verification process is as follows:
the effectiveness of the algorithm was verified using the existing full drive ship cybershipii. The main physical parameters of CyberShip II are shown in Table 1, and the other parameters are Y |r|ν ＝-0.805，Y |ν|r ＝-0.845，Y |r|r ＝3.45，N |r|ν ＝-0.13，N r ＝1.9，N |ν|r ＝0.08，N |r|r -0.75. The restoring force vector is set as: g (x) 1 )＝[0.36sin(x 13 )+0.2cos(x 13 ),0.36cos(x 13 )+0.2sin(x 13 ),0.18]. The control targets are as follows: reference trace x d ＝[0.5sin(t),0.5cos(t),0.5sin(t)] T At disturbance x d ＝[0.5sin(t),0.5cos(t),0.5sin(t)] T Position output x of lower capable of being used by ship system 1 Tracking is completed within a pre-specified time t=4s, and the tracking accuracy thereof is set to epsilon=0.001. System state x 1 And x 2 Is required to respectively satisfy constraint k a (t) =0.15 sin (t) +0.9 and k b (t)＝0.15sin(t)+1。
TABLE 1 major physical parameters of CyberShip II
The corresponding control parameters are taken as follows: l (L) 1 ＝l 2 ＝0.002，q 11 ＝q 12 ＝q 21 ＝q 22 ＝10000，r 1 ＝k＝0.8，r 2 ＝3，ω 1 ＝0.001，μ 11 ＝μ 12 ＝2，μ 21 ＝μ 22 ＝μ 31 ＝μ 32 ＝15，δ＝0.5，m 1 ＝0.3， *1 ＝ *2 ＝ *3 ＝0.0001， *4 ＝ *5 ＝ *6 =0.01. Saturation characteristic function f i Is set to f max ＝[50,17,4] T N，f min ＝[-13,-50,-0.5] T N. The initial value of the system is set as x 1 (0)＝[0.08,0.45,0.1] T m，x 2 (0)＝[0,0,0] T m/s，ξ 1 (0)＝ξ 2 (0)＝[0,0,0] T ，In addition, take k 1 (t)＝0.15sin(t)+0.3，k 2 (t) =0.15 sin (t) +0.4. The simulation results are shown in fig. 2-7.
From fig. 2 and 3, it can be seen that the closed loop system not only accomplishes the desired tracking, but that its state is always subject to constraints. Fig. 4 illustrates the limitations of adaptive parameters. The forward force actuator, the yaw force actuator, and the helm swing force actuator under saturation influence output signals and their corresponding update times are shown in fig. 5-7. Specifically, the three actuators transmit signals 588, 669, and 707, respectively, within 20 seconds. Obviously, simulation results prove that the technical scheme in the embodiment can ensure expected transient state and steady state tracking performance under the condition of not violating full state constraint, and the method provided by the invention has the characteristics of being capable of presetting convergence speed, tracking precision and stabilizing time in advance, and is low in communication cost of the controller.
Embodiment two:
the second embodiment of the invention provides a full-drive ship preset performance tracking control system based on event driving, which comprises the following components:
the model building module is configured to collect parameter information of a target ship and build a ship model based on a closed-loop system of the full-drive ship;
the model optimization module is configured to construct an auxiliary system to generate a compensation signal so as to compensate adverse effects of the ship model due to input saturation;
a controller design module configured to design an adaptive fixed time tracking controller based on the compensation signal;
the system comprises a preset performance tracking control module, a self-adaptive fixed time tracking controller and a controller, wherein the preset performance tracking control module is configured to set parameters of the self-adaptive fixed time tracking controller, a control target in preset time is input into the self-adaptive fixed time tracking controller, and the controller outputs a control instruction to an actuator, so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint.
Embodiment III:
the third embodiment of the present invention provides a medium, on which a program is stored, the program when executed by a processor implementing the steps in the event-driven based all-drive ship predetermined performance tracking control method according to the first embodiment of the present invention, where the steps are as follows:
step 1: and acquiring parameter information of the target ship, and establishing a ship model based on a closed-loop system of the full-drive ship.
Step 2: the auxiliary system is constructed to generate a compensation signal to compensate adverse effects of the ship model due to input saturation;
step 3: designing an adaptive fixed time tracking controller according to the compensation signal;
step 4: setting parameters of a self-adaptive fixed time tracking controller, inputting a control target in preset time to the self-adaptive fixed time tracking controller, and outputting a control instruction to an actuator by the controller so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint.
The detailed steps are the same as those of the event-driven full-drive ship preset performance tracking control method provided in the first embodiment, and are not repeated here.
Embodiment four:
the fourth embodiment of the invention provides a device, which comprises a memory, a processor and a program stored in the memory and capable of running on the processor, wherein the processor realizes the steps in the event-driven full-drive ship preset performance tracking control method according to the first embodiment of the invention when executing the program, and the steps are as follows:
step 1: and acquiring parameter information of the target ship, and establishing a ship model based on a closed-loop system of the full-drive ship.
Step 2: the auxiliary system is constructed to generate a compensation signal to compensate adverse effects of the ship model due to input saturation;
step 3: designing an adaptive fixed time tracking controller according to the compensation signal;
step 4: setting parameters of a self-adaptive fixed time tracking controller, inputting a control target in preset time to the self-adaptive fixed time tracking controller, and outputting a control instruction to an actuator by the controller so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint.
The detailed steps are the same as those of the event-driven full-drive ship preset performance tracking control method provided in the first embodiment, and are not repeated here.
The steps involved in the second, third and fourth embodiments correspond to the first embodiment of the method, and the detailed description of the second embodiment refers to the relevant description of the first embodiment. The term "computer-readable storage medium" should be taken to include a single medium or multiple media including one or more sets of instructions; it should also be understood to include any medium capable of storing, encoding or carrying a set of instructions for execution by a processor and that cause the processor to perform any one of the methods of the present invention.
It will be appreciated by those skilled in the art that the modules or steps of the invention described above may be implemented by general-purpose computer means, alternatively they may be implemented by program code executable by computing means, whereby they may be stored in storage means for execution by computing means, or they may be made into individual integrated circuit modules separately, or a plurality of modules or steps in them may be made into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
While the foregoing description of the embodiments of the present invention has been presented in conjunction with the drawings, it should be understood that it is not intended to limit the scope of the invention, but rather, it is intended to cover all modifications or variations within the scope of the invention as defined by the claims of the present invention.
Claims (10)
1. The event-driven full-drive ship preset performance tracking control method is characterized by comprising the following steps of:
acquiring parameter information of a target ship, and establishing a ship model based on a closed-loop system of the full-drive ship;
the auxiliary system is constructed to generate a compensation signal to compensate adverse effects of the ship model due to input saturation;
designing an adaptive fixed time tracking controller according to the compensation signal;
setting parameters of a self-adaptive fixed time tracking controller, inputting a control target in preset time to the self-adaptive fixed time tracking controller, and outputting a control instruction to an actuator by the controller so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint.
2. The event-driven total drive ship predetermined performance tracking control method according to claim 1, wherein the ship model of the closed-loop system is:
wherein H (x) 1 ,x 2 )＝M -1 (-C(x 2 )x 2 -D(x 2 )x 2 -g(x 1 ))。
3. The event-driven total drive marine vessel scheduled performance tracking control method of claim 1, wherein the compensation signal generated by the auxiliary system is bounded.
4. The event-driven based all-drive ship predetermined performance tracking control method according to claim 1, wherein the system tracking performance is ensured by introducing a speed function when designing the adaptive fixed time tracking controller.
5. The event-driven full-driven ship preset performance tracking control method according to claim 1, wherein the specific design process of the adaptive fixed time tracking controller is as follows:
introducing a speed function and a velocity function based on tracking control performance;
combining the compensation signals to obtain error transformation based on a speed function;
constructing a BLF according to the constraint state;
designing a fixed time self-adaptive tracking control algorithm based on event triggering;
and analyzing according to a tracking control algorithm, and designing a tracking controller.
6. The event-driven based all-drive marine vessel predetermined performance tracking control method of claim 1, wherein the adaptive fixed time tracking controller is designed to:
wherein τ i (t) is the ith component, alpha, of the control signal τ 2i Is alpha 2 Is selected from the group consisting of the (i) th element,representing the control signal τ i The update time of (t);
the event driven strategy of the adaptive fixed time tracking controller is taken as follows:
wherein,,representing the control signal τ i Update time of (t),>representing the sampling error of the i-th actuator,is the corresponding signal transmission time, M i I.e. row i of M, while M 1 > 0 is a design parameter and i=1, 2,3.
7. The event-driven based all-drive marine vessel predetermined performance tracking control method according to claim 1, wherein the objective of the adaptive control strategy implementation comprises:
1) All signals in the ship model of the closed-loop system are bounded;
2) Desired trajectory x d ＝[x d1 ,x d2 ,x d3 ] T Quilt x 1 ＝[x 11 ,x 12 ,x 13 ] T Tracking is completed before a pre-specified time T, while the tracking error satisfies lim t→T |x 1i -x di I < ε and I x 1i -x di | t≥T < ε (i=1, 2, 3), where ε is a predetermined arbitrary small constant;
3) The closed loop system state does not violate the desired constraints: ||x 1 (t)||＜k a (t)，||x 2 (t)||＜k b (t) wherein k a (t) and k b (t) is a strictly positive continuous function.
8. The event-driven full-driven ship preset performance tracking control system is characterized by comprising the following components:
the model building module is configured to collect parameter information of a target ship and build a ship model based on a closed-loop system of the full-drive ship;
the model optimization module is configured to construct an auxiliary system to generate a compensation signal so as to compensate adverse effects of the ship model due to input saturation;
a controller design module configured to design an adaptive fixed time tracking controller based on the compensation signal;
the system comprises a preset performance tracking control module, a self-adaptive fixed time tracking controller and a controller, wherein the preset performance tracking control module is configured to set parameters of the self-adaptive fixed time tracking controller, a control target in preset time is input into the self-adaptive fixed time tracking controller, and the controller outputs a control instruction to an actuator, so that a closed-loop system of the ship completes expected tracking under the condition of obeying constraint.
9. A computer readable storage medium, characterized in that a plurality of instructions are stored, which instructions are adapted to be loaded by a processor of a terminal device and to perform the event driven based all-drive marine vessel reservation performance tracking control method of any of claims 1-7.
10. A terminal device comprising a processor and a computer readable storage medium, the processor configured to implement instructions; a computer readable storage medium for storing a plurality of instructions adapted to be loaded by a processor and to perform the event driven based all-drive marine vessel predetermined performance tracking control method of any of claims 1-7.
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