CN106444370B - A kind of predictive control algorithm based on movement linear model and region performance index - Google Patents
A kind of predictive control algorithm based on movement linear model and region performance index Download PDFInfo
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Abstract
The present invention relates to a kind of predictive control algorithms based on movement linear model and region performance index, and steps are as follows: 1) linearisation assumes；2) the ship equation of motion of incremental form；3) region performance index；4) predictive equation；5) constraint condition；6) equation solution.The present invention has the advantages that method of the present invention is the method for linearisation, solving will simply relative to non-linear class predictive control algorithm, and result is reliable.Because it is solved simply, so the calculating time is shorter, it is suitable for the higher field of this requirement of real-time of ship control.Method of the invention is based on region performance index, meets the concept of green control at present, can effectively avoid the abrasion of propeller, reduces energy consumption.
Description
Technical field
The present invention relates to a kind of Dynamic Positioning Control System fields, in particular to a kind of based on movement linear model and region performance
The predictive control algorithm of index.
Background technique
Dynamic positioning system refers to ship using dynamical system provisioned in automatic control algorithm controller itself --- such as
Paddle, rudder etc. make ship keep certain position and angle or transport according to desired trajectory to resist the external forces such as wind, wave stream
It is dynamic.General dynamic positioning system includes operating system, position and bow to frame of reference, power-positioning control system, dynamical system
Equal subsystems, wherein power-positioning control system is its key subsystem, is responsible for such as transducing signal processing, path planning, ship
Oceangoing ship motion control and thrust distribution etc. work.
Marine vehicle movement control algorithm substantially experienced three developing stage: original adoption traditional PID control algorithm；20th century
Since the seventies, the optimum control based on modern control theory is used widely；So far start the 1990s to adopt
With control algolithms such as robust control, fuzzy control, ANN Control, Nonlinear Model Predictive Controls.
Model Predictive Control is generated from the 1970s so far in Industry Control as a kind of advanced control technology
Field, which achieves, to be widely applied, and after introducing ship control field, also obtains good effect.Due to the complexity of ship movement
Property, the application of Nonlinear Model Predictive Control will often be related to complicated nonlinear equation optimization problem, may cause solution
Overlong time, and there is the shortcomings that falling into local optimum.
Summary of the invention
The technical problem to be solved in the present invention is to provide a kind of predictions based on movement linear model and region performance index
Control algolithm.
In order to solve the above technical problems, the technical solution of the present invention is as follows: a kind of based on movement linear model and region performance
The predictive control algorithm of index, innovative point are: the following steps are included: 1) linearisation assumes: the present invention is based on following 4 lines
Propertyization is assumed；
Assuming that 1: based on ship under dynamic positioning operating condition, ship movement velocity is lower, ignores the influence of coriolis force；
Assuming that 2: it is assumed that ship viscous hydrodynamic forces power is directly proportional to speed of the ship in metres per second；
Assuming that 3: turning bow movement slowly in view of ship, ignore ship in predicted time and turn the bow movement coupling mobile to position
It influences, that is, thinks the hereafter ship equation of motion.In spin matrix take prediction walk in keep constant；
Assuming that 4: it is assumed that ship is equipped with enough positions and bow to sensor, vessel position and bow to considerable, in this paper mould
Quasi- calculating is when being, using Unscented kalman filtering method [4] obtain ship low frequency position and bow to；
2) the ship equation of motion of incremental form
According to assuming 1,2, under with ship coordinate system, the ship equation of motion is as follows:
Wherein M is the inertia matrix of ship, and D is linear damping matrix, η=[x y ψ]TFor with ship coordinate origin complete
Position and bow under office's horizontal coordinates is to angle, τenvIt is respectively the environmental forces and control force in three directions with τ；According to hypothesis
3, it is believed that R (ψ) is constant in limited predicted time step number, fixed further at the beginning of the every step of MPC algorithm calculates
Adopted global coordinate system is overlapped with level with ship coordinate system, then R (ψ) is unit battle array；Thus the incremental form of discretization can be derived
Ship movement and predictive equation it is as follows:
Wherein
yp=[x y ψ]T
C0=[I3×3 03×3 03×3]
X is state variable, and component x, y, ψ are the position of ship and bow to u, v, r respectively indicate the longitudinal, horizontal of ship
To speed and angular speed, ax、ay、For the longitudinally, laterally acceleration and angular acceleration of ship；ypTo control aim parameter, i.e. ship
Position and bow to；ΔτenvFor environmental load increment；Δ τ is control force (square) increment；
Here with the current state x (k) of equation and outer load increment Delta τenv(k) known；
3) region performance index
The optimization aim of ship motion controller is to seek control sequence Δ τ (k), and Δ τ (k+1) ... Δ τ (k+N-1) makes
Following objective function is minimized:
N is prediction step number in formula；λ is three-dimensional diagonal matrix, indicates that the cost coefficient of three control amounts, r are Three dimensions control mesh
Mark vector, δmaxIt is vessel position and bow to region difference limit value, ε is the control amount and aim parameter after deducting region difference limit value
Deviation；
4) predictive equation
Definition:
Wherein δ is three-dimensional relaxation vector corresponding with control target, this slack variable must meet additional constraint :-δmax,i
≤δi≤δmax,i
Then original equation is written as follow form:
Wherein
B2=[L0 09×3]
B3=[B0 09×3]
Former optimization aim then becomes seeking control sequence u (k), and u (k+1) ... u (k+N-1) makes following objective function
Minimalization
Wherein
Indicate the pre-estimation under given control sequence to the value of z.
Definition
Then have
Wherein:
Corresponding optimization aim are as follows:
Wherein
5) constraint condition
The following two kinds constraint is considered, first is that the variation of one-step control power is no more than a certain limit value, first is that total control force
No more than a certain limit value；
Its expression-form is constrained to the first are as follows:-Δ τmax,i≤Δτi≤Δτmax,i, definition
Then the constraint can be written as follow form together with the constraint previously for slack variable δ:
lb< u (k+j) < ubJ=1,2 ..., N-1
It re-defines:
Then single step thrust constraint can be expressed as follows:
Total thrust limit value constraint is discussed now, for this purpose, it is assumed that the thrust size τ (k-1) of last moment it is known that
Remember I0=[I3×3 03×3], definition:
Then total thrust limit value constraint is equivalent to constrain as follows:
6) equation solution
MPC control problem of the ship movement based on region performance index can be summarized as follows:
System for being described by following equation
In the case where meeting following constraint condition:
Seek optimum control amountSo that following objective function is minimized.The locally optimal solution of the above problem is the overall situation
Optimal solution.
The present invention has the advantages that method of the present invention is the method for linearisation, solve pre- relative to non-linear class
It is simple to survey control algolithm, and result is reliable.Because its solve it is simple, so it is shorter to calculate the time, be suitable for ship control this
The kind higher field of requirement of real-time.Method of the invention is based on region performance index, meets the concept of green control at present, energy
Enough abrasions for effectively avoiding propeller, reduce energy consumption.
Detailed description of the invention
Fig. 1 is that the power in a kind of predictive control algorithm based on movement linear model and region performance index of the present invention is fixed
The control principle drawing of position system.
Specific embodiment
1) linearisation is it is assumed that the present invention is based on following 4 linearisations hypothesis.
Assuming that 1: based on ship under dynamic positioning operating condition, ship movement velocity is lower, ignores the influence of coriolis force；
Assuming that 2: it is assumed that ship viscous hydrodynamic forces power is directly proportional to speed of the ship in metres per second；
Assuming that 3: turning bow movement slowly in view of ship, ignore ship in predicted time and turn the bow movement coupling mobile to position
It influences, that is, thinks the hereafter ship equation of motion.In spin matrix take prediction walk in keep constant；
Assuming that 4: it is assumed that ship is equipped with enough positions and bow to sensor, vessel position and bow to considerable, in this paper mould
Quasi- calculating is when being, using Unscented kalman filtering method [4] obtain ship low frequency position and bow to.
2) the ship equation of motion of incremental form
According to assuming 1,2, under with ship coordinate system, the ship equation of motion is as follows:
Wherein M is the inertia matrix of ship, and D is linear damping matrix, η=[x y ψ]TFor with ship coordinate origin complete
Position and bow under office's horizontal coordinates is to angle, τenvIt is respectively the environmental forces and control force in three directions with τ.According to hypothesis
3, it is believed that R (ψ) is constant in limited predicted time step number, fixed further at the beginning of the every step of MPC algorithm calculates
Adopted global coordinate system is overlapped with level with ship coordinate system, then R (ψ) is unit battle array.Thus the incremental form of discretization can be derived
Ship movement and predictive equation it is as follows:
Wherein
yp=[x y ψ]T
C0=[I3×3 03×3 03×3]
X is state variable, and component x, y, ψ are the position of ship and bow to u, v, r respectively indicate the longitudinal, horizontal of ship
To speed and angular speed, ax、ay、For the longitudinally, laterally acceleration and angular acceleration of ship；ypTo control aim parameter, i.e. ship
Position and bow to；ΔτenvFor environmental load increment；Δ τ is control force (square) increment.
Here it is not related to observational equation, when ship is equipped with sensor enough and appropriate, always can choose side appropriate
Method such as Unscented kalman filtering method obtains the motion state of ship and estimation obtains outer load, therefore here with equation
Current state x (k) and outer load increment Delta τenv(k) known.
3) region performance index
In ship motion controller, in general be control the next one section of moment ship of ship position and bow to
A certain previously given target sequence is consistent, and certainly, the physical location and bow of ship are to it is not possible that can not with target sequence
Need not be completely coincident, it is believed that as long as its difference thinks to reach control target in the range of a certain preset, this and
The so-called Con trolling index based on region performance.Based on this, the optimization aim of ship motion controller is to seek control sequence Δ τ (k),
Δ τ (k+1) ... Δ τ (k+N-1) is minimized following objective function:
N is prediction step number in formula；λ is three-dimensional diagonal matrix, indicates that the cost coefficient of three control amounts, r are Three dimensions control mesh
Mark vector, δmaxIt is vessel position and bow to region difference limit value, ε is the control amount and aim parameter after deducting region difference limit value
Deviation.We do not account for the constraint to input quantity above, this problem we will be considered below.
4) predictive equation
Definition:
Wherein δ is three-dimensional relaxation vector corresponding with control target, this slack variable must meet additional constraint :-δmax,i
≤δi≤δmax,i
Then original equation is written as follow form:
Wherein
B2=[L0 09×3]
B3=[B0 09×3]
Former optimization aim then becomes seeking control sequence u (k), and u (k+1) ... u (k+N-1) makes following objective function
Minimalization
Wherein
Indicate the pre-estimation under given control sequence to the value of z.
Definition
Then have
Wherein:
Corresponding optimization aim are as follows:
Wherein
5) constraint condition
Here only consider the following two kinds constraint, first is that the variation of one-step control power is no more than a certain limit value, first is that
Total control force is no more than a certain limit value.
Its expression-form is constrained to the first are as follows:-Δ τmax,i≤Δτi≤Δτmax,i, definition
Then the constraint can be written as follow form together with the constraint previously for slack variable δ:
lb< u (k+j) < ubJ=1,2 ..., N-1
It re-defines:
Then single step thrust constraint can be expressed as follows:
Discuss that total thrust limit value constraint, the constraint can be expressed as now, for this purpose, it is assumed that last moment push away
Power size τ (k-1) is it is known that note I0=[I3×3 03×3], definition:
Then total thrust limit value constraint is equivalent to constrain as follows:
6) equation solution
By above-mentioned derivation, MPC control problem of the ship movement based on region performance index can be summarized as follows:
System for being described by following equation
In the case where meeting following constraint condition:
Seek optimum control amountSo that following objective function is minimized.The above problem is the two of a convex constraint condition
Secondary planning problem, the locally optimal solution of the problem are globally optimal solution.
As shown in Figure 1, using the control principle drawing of dynamic positioning system of the invention.
Basic principles and main features of the invention have been shown and described above.It should be understood by those skilled in the art that
The present invention is not limited to the above embodiments, and the above embodiments and description only illustrate the principle of the present invention, In
Without departing from the spirit and scope, various changes and improvements may be made to the invention, these changes and improvements are all fallen
Enter in scope of the claimed invention.The scope of the present invention is defined by the appended claims and its equivalents.
Claims (1)
1. a kind of predictive control algorithm based on movement linear model and region performance index, it is characterised in that: including following step
It is rapid:
1) linearisation assumes: the algorithm is assumed based on following 4 linearisations；
It is assumed that 1: based on ship under dynamic positioning operating condition, ship movement velocity is lower, ignores the influence of coriolis force；
It is assumed that 2: it is assumed that ship viscous hydrodynamic forces are directly proportional to speed of the ship in metres per second；
It is assumed that 3: turning bow movement slowly in view of ship, ignore ship in predicted time and turn the bow movement coupling shadow mobile to position
It rings, that is, thinks that the spin matrix in the ship equation of motion is kept constant in taking prediction step；
It is assumed that 4: it is assumed that ship is equipped with enough positions and bow to sensor, vessel position and bow to considerable, simulate calculate when,
Using Unscented kalman filtering method obtain ship low frequency position and bow to；
2) the ship equation of motion of incremental form
According to assuming 1,2, under with ship coordinate system, the ship equation of motion is as follows:
Wherein M is the inertia matrix of ship, and D is linear damping matrix, η=[x y ψ]TFor with ship coordinate origin in global water
Position and bow under flat coordinate system are to angle, τenvIt is respectively the environmental forces and control force in three directions with τ；According to assuming 3, recognize
For in limited predicted time step number R (ψ) it is constant, further at the beginning of the every step of MPC algorithm calculates, define global sit
Mark system is overlapped with level with ship coordinate system, then R (ψ) is unit battle array；Thus the ship fortune of the incremental form of discretization can be derived
Dynamic and predictive equation is as follows:
Wherein
yp=[x y ψ]T
C0=[I3×3 03×3 03×3]
X is state variable, and component x, y, ψ are the position of ship and bow to u, v, r respectively indicate the longitudinally, laterally fast of ship
Degree and angular speed, ax、ay、For the longitudinally, laterally acceleration and angular acceleration of ship；ypTo control aim parameter, the i.e. position of ship
Set with bow to；ΔτenvFor environmental load increment；Δ τ is control force increment；
The current state x (k) of equation and outer load increment Delta τenv(k) known；
3) region performance index
The optimization aim of ship motion controller is to seek control sequence Δ τ (k), and Δ τ (k+1) ... Δ τ (k+N-1) makes as follows
Objective function be minimized:
N is prediction step number in formula；λ is three-dimensional diagonal matrix, indicates the cost coefficient of three control amounts, r be Three dimensions control target to
Amount, δmaxIt is vessel position and bow to region difference limit value, ε is the control amount and aim parameter deviation deducted after region difference limit value；
4) predictive equation
Definition:
Wherein δ is three-dimensional relaxation vector corresponding with control target, this slack variable must meet additional constraint :-δmax,i≤δi
≤δmax,i
Then original equation is written as follow form:
Wherein
B2=[L0 09×3]
B3=[B0 09×3]
Former optimization aim then becomes seeking control sequence u (k), and u (k+1) ... u (k+N-1) makes following objective function take pole
Small value
Wherein
Indicate the pre-estimation under given control sequence to the value of z；
Definition
Then have
Wherein:
Corresponding optimization aim are as follows:
Wherein
5) constraint condition
The following two kinds constraint is considered, first is that the variation of one-step control power is no more than a certain limit value, first is that total control force cannot
More than a certain limit value；
Its expression-form is constrained to the first are as follows:-Δ τmax,i≤Δτi≤Δτmax,i, definition
Then the constraint is written as follow form together with the constraint previously for slack variable δ:
lb< u (k+j) < ubJ=1,2 ..., N-1
It re-defines:
Then single step thrust constraint representation is as follows:
Total thrust limit value is constrained, it is assumed that the thrust size τ (k-1) of last moment is it is known that note I0=[I3×3 03×3], it is fixed
Justice:
Then total thrust limit value constraint is equivalent to constrain as follows:
6) equation solution
MPC control problem of the ship movement based on region performance index is summarized as follows:
System for being described by following equation
In the case where meeting following constraint condition:
Seek optimum control amountSo that objective functionIt is minimized, the locally optimal solution of the above problem
As globally optimal solution.
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| CN107357168B (en) * | 2017-06-01 | 2019-12-31 | 同济大学 | Unmanned vehicle obstacle avoidance method based on opportunity constraint model predictive control |
| CN108445762B (en) * | 2018-03-21 | 2021-09-14 | 青岛科技大学 | Dynamic positioning control method based on UKF filtering and constraint model predictive control |
| CN109683472B (en) * | 2018-08-30 | 2022-02-01 | 上海海事大学 | Model prediction control-based thrust distribution method for ship electric propulsion system |
| CN109799826B (en) * | 2019-02-20 | 2022-02-25 | 上海振华重工(集团)股份有限公司 | Thrust distribution method of ship propeller system |
| CN112256026B (en) * | 2020-10-14 | 2022-11-29 | 中国船舶重工集团公司第七0七研究所九江分部 | Ship course model predictive control algorithm design method under multi-constraint condition |
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