CN114924480A - Ship course tracking self-adaptive control method - Google Patents
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Abstract
The invention discloses a ship course tracking self-adaptive control method, which combines a differential tracker with model reference self-adaptive control, designs a differential tracking model reference self-adaptive control method, enables a ship to turn at a constant angular speed, and ensures the convergence of course and angular speed signal tracking by a Lyapunov function; meanwhile, considering that the steering energy consumption is reduced while the ship requires higher steering control precision in the course keeping process, the Gaussian adaptive linear quadratic optimal controller is designed, and higher steering control precision can be achieved under the condition of lower steering energy consumption. The control performance comparison test is carried out on the self-adaptive rudder software respectively embedded with the two control algorithms by using various sea conditions and ship types of the ship semi-physical simulation platform, and the stability of the two controllers is verified. The performance index result shows that the differential tracking model reference adaptive controller has better steering control performance, and the adaptive linear quadratic Gaussian optimal controller has better course keeping performance.
Description
Technical Field
The invention belongs to the field of self-adaptive rudder ship course control, and particularly relates to a ship course tracking self-adaptive control method.
Background
Ships play an important role in the development and utilization of marine resources as a main transport means at sea. The self-adaptive control of the ship course is a very basic research problem in the field of ship motion control.
Ship autopilots were originally derived from 1890 research efforts on Hopkins electric gyroscopes. Elmer Sperry in 1911 first proposed the use of feedback control and automatic gain adjustment for marine steering, and subsequently Nicholas Minorsky designed a position feedback controller using three control laws, called Proportional Integral Derivative (PID) control. The PID controller has the advantages of simple design and strong robustness, but the course control precision and the steering energy consumption are difficult to meet the current requirements of automatic steering, and the algorithm has poor adaptability to the ship speed, loading and sea conditions and needs to adjust parameters repeatedly.
Disclosure of Invention
The invention aims to provide a ship course tracking self-adaptive control method for solving the problems of course control precision and steering energy consumption.
The self-adaptive control method for ship course tracking comprises the following steps:
step 1: according to the course set value psi s Calculating the desired heading ψ of the ship using a saturated differential tracker d And desired steering angular velocity
Step 2: calculating the state of a differential tracking system according to the current heading psi and the yawing angular speed r of the ship;
and 3, step 3: selecting whether to switch an STC-LQG controller or an STD-MRAC controller according to the current control mode and the system state of the ship;
and 4, step 4: according to the current control mode, calculating a control command by using an STC-LQG controller or an STD-MRAC controller and updating an algorithm or a model parameter;
and 5: and (5) circulating the steps 1 to 4 to realize the ship course keeping and the constant angular speed steering.
Further, the step 1 specifically comprises: when the second derivative of the input signal is within the TD amplitude limiting value, the TD can quickly track the input signal and estimate the first derivative value of the tracking signal; the differential tracker has the following form:
wherein u (k) is an input signal, m 1 (k) For tracking signal output, m 2 (k) For the differential output of the tracking signal, h is the filter factor, r is the velocity factor, T is the tracking step length, and the fst function calculates the second derivative of the tracking signal:
δ＝rh
δ 0 ＝δh
y＝x 0 -u+hm 2
according to the requirement of the ship for constant angular speed steering, the differential signal m is applied 2 (k) Adding saturation clipping, a saturated differential tracker can be obtained:
wherein sat is a saturation clipping function, v m Is a differential signal m 2 (k) The clipping value of (1). Application of STD to ship course control has u psi s ，m 1 ψ d ，
v m A desired steering angular velocity set point for the vessel;
further, the step 2 specifically includes: the ship maneuvering model may employ a first-order linear Nomoto model:
wherein r is the ship bow angular velocity,
selecting a system state x for the yaw acceleration, psi for the ship heading angle, delta for the rudder angle, K, T for the ship turning capacity and turning inertia parameters, influenced by the ship load condition and navigation speed 1 ＝ψ-ψ d ，
x＝(x 1 x 2 ) T Considering the requirements of course keeping and constant angular speed steering
Then the original system state space equation is:
further, the step 3 specifically includes: if the course setting is changed, switching to the STD-MRAC control mode; if the course setting is not changed, the current control mode is STC-LQG control, the mode is not switched, the current control mode is STD-MRAC control mode, x is checked 1 ,x 2 If the absolute value is small enough, switching to STC-LQG control, otherwise, keeping STD-MRAC control;
further, the step 4 specifically includes:
(1) if the current control mode is the STD-MRAC control mode, calculating a control angle order according to the following control laws:
updating control law parameters through the parameter adaptive law of the STD-MRAC control mode:
(2) if the current control mode is STC-LQG control
a. Estimating time-varying ship course model parameters by using a full rank decomposition least square method, and parameterizing ship states and inputs:
the parameter estimation of the full rank decomposition least square method comprises two components of total iteration and principal component iteration, wherein the total iteration formula is as follows:
the principal component iterative formula is:
the two component relations of the total iteration and the principal component iteration are as follows:
wherein, V k1 For a full rank decomposition matrix, the k-th measurement data { h } can be obtained by k ,z k The corresponding transformation matrix is V k ＝[V k1 V k2 ]
Wherein h is ki As a vector of data h k The ith component of (c), h s Is a dead zone threshold;
b. estimating the state of the ship course model by using a state expansion Kalman filter, and predicting the state of the Kalman filter in a state space model form:
wherein h is the sampling period, w r And v r For interference and measuring noise
The state prediction equation is:
x k+1|k ＝φ k x k|k +B k u k +w k
the calculation steps of the state expansion Kalman filter are as follows:
wherein: p is a state estimation error variance matrix, Q is a model error variance matrix, and R is a measurement noise variance matrix.
c. Calculating a rudder angle command according to a control law:
the invention has the beneficial effects that:
(1) the method has the advantages of high course keeping precision, few times of rudder striking for keeping the course for a long time and energy consumption saving.
(2) The steering at constant angular speed is realized, the steering process is stable, and no obvious overshoot is caused.
(3) The parameters do not need to be adjusted repeatedly, and the ship speed, sea conditions and loading are better adaptive.
Drawings
FIG. 1 is a block diagram of a differential tracking model of the system of the present invention;
FIG. 2 is a flow chart of the control mode switching of the present invention;
FIG. 3 is a diagram of a simulation platform of the present invention;
FIG. 4 is a block diagram of a steering apparatus of the present invention;
FIG. 5 is a graph of the course change of the course keeping test of the present invention;
FIG. 6 is a graph of the variation of the angular velocity of the course keeping test according to the present invention;
FIG. 7 is a plot of rudder angle variation for the course hold test of the present invention;
FIG. 8 is a graph showing the course change of the positive 30 degree steering test according to the present invention;
FIG. 9 is a graph of the change in angular velocity for a positive 30 ° turn test according to the present invention;
FIG. 10 is a graph of the rudder angle variation in a positive 30-degree steering test;
FIG. 11 is a graph of negative 30 ° steering test course change;
FIG. 12 is a graph of the variation of angular velocity for a minus 30 ° steering test;
FIG. 13 is a graph of the negative 30 ° steering test rudder angle variation;
FIG. 14 is a graph of positive 30 ° steering versus test course change;
FIG. 15 is a graph of positive 30 ° steering versus test angular velocity variation;
FIG. 16 is a plot of positive 30 steering versus test rudder angle change.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Step 1: according to the course set value psi s Calculating the desired heading ψ of the ship using a saturated differential tracker d And desired steering angular velocity
A differential Tracker (TD) can convert a step input signal into a continuous fastest Tracking signal under the second derivative amplitude limit, and output the first derivative of the Tracking signal at the same time. When the second derivative of the input signal is within the limit value of TD, TD can track the input signal quickly and estimate the first derivative value of the tracked signal. The classical differential tracker has the following form:
where u (k) is an input signal, m 1 (k) For tracking signal output, m 2 (k) Is the differential output of the tracking signal. h is a filtering factor, r is a speed factor, T is a tracking step length, the fst function calculates the second derivative of the tracking signal, and the calculation process is as follows:
δ＝rh
δ 0 ＝δh
y＝x 0 -u+hm 2
according to the requirement of the ship for constant angular speed steering, the differential signal m in the formula is 2 (k) A Saturation differential tracker (STD) can be obtained by adding Saturation clipping.
Wherein sat is a saturation limiting function, v m Is a differential signal m 2 (k) The clipping value of (c). Application of STD in ship course control s ，m 1 ＝ψ d ，
v m A steering angular velocity setting is desired for the vessel.
Step 2: calculating the state x of the differential tracking system according to the current course psi and the yaw angular velocity r of the ship 1 ＝ψ-ψ d ，x 2 ＝r-r d ；
The ship maneuvering motion model can adopt a first-order linear Nomoto model:
wherein r is the ship bow angular velocity,
the heading angle acceleration phi is the ship heading angle psi, the rudder angle delta and the ship turning capacity and turning inertia parameters K, T, and the parameters are influenced by the ship load condition and the navigation speed. Selecting the system state as x 1 ＝ψ-ψ d ，
x＝(x 1 x 2 ) T Considering the requirements of course keeping and constant angular speed steering
The original system state space equation can be written as:
and step 3: selecting whether to switch the control mode according to the current control mode of the ship and the system state;
if the course setting is changed, switching to the STD-MRAC control mode; if the course setting is not changed, the current control mode is STC-LQG control, the mode is not switched, the current control mode is STD-MRAC control mode, x is checked 1 ,x 2 If the absolute value is small enough, switching to STC-LQG control, otherwise, keeping STD-MRAC control.
And 4, step 4: calculating a steering order according to the current control mode and updating an algorithm or a model parameter;
(1) if the current control mode is the STD-MRAC control mode, calculating a control angle order according to the following control laws:
updating control law parameters through the parameter adaptive law of the STD-MRAC control mode:
(2) if the current control mode is STC-LQG control;
a. estimating time-varying ship course model parameters by using a full rank decomposition least square method, and parameterizing ship states and inputs:
the parameter estimation of the full-rank decomposition least square method comprises two components of total iteration and principal component iteration, wherein the total iteration formula is as follows:
the principal component iterative formula is:
the two part relation is as follows:
wherein, V k1 For a full rank decomposition matrix, the k-th measurement data { h } can be obtained by k ,z k The corresponding transform matrix is V k ＝[V k1 V k2 ]
Wherein h is ki As a vector of data h k The ith component of (c), h s Is the dead band threshold.
b. The state of a ship course model is estimated by using a state expansion Kalman filter, and a Kalman filter state prediction equation in the form of a state space model is as follows
Wherein h is the sampling period, w r And v r For interference and measuring noise, order
The state prediction equation can be abbreviated as
x k+1|k ＝φ k x k|k +B k u k +w k
The calculation steps of the state expansion Kalman filter are as follows: state prediction, variance matrix prediction, gain matrix calculation, innovation calculation, state updating, expansion state tracking and variance matrix updating.
Wherein, P is a state estimation error variance matrix, Q is a model error variance matrix, and R is a measurement noise variance matrix.
c. The rudder angle order is calculated according to the following control laws:
and 5: judging and controlling to finish adjustment;
and judging whether the current control mode is switched to manual mode, if so, ending the control circulation, and otherwise, circulating the step 1 to the step 4.
The method is tested as follows:
the heading of the ship A is kept and tested, the navigational speed is 20 knots, and the sea state is 5 level; the course of the ship B is kept and tested, the navigational speed is 20 knots, and the sea state is 5 grade; c, keeping the ship course to be tested, wherein the ship speed is 10 knots, and the sea state is 5 grades. The running time 540s and A, B, C of the simulation platform are shown in the course of ship course keeping test, such as course change, angular speed change and rudder angle change curves in the figures 1, 2 and 3, and the course keeping performance statistical table is shown in the table one, wherein each index in the table indicates: 1) and (3) steering frequency: the rudder angle command is recorded as one rudder striking time when the rudder angle command changes 0.1 degree per minute; 2) steering amplitude: the amplitude is the maximum rudder angle amplitude in the course keeping process; 3) course control precision: is the mean absolute course error in course of course keeping. The experimental result shows that the designed course keeping algorithm has the advantages of less rudder striking times, high control precision and the like, and has excellent course keeping control effect for different ship types.
The steering test is divided into a ship A steering test, the navigational speed is 20 knots, and the sea condition is 5 level; b, ship steering test, navigational speed of 20 knots, 5-level sea state; and C, carrying out ship steering test, carrying out navigational speed 10 sections, and carrying out 5-level sea state grouping. A ship steering test, the navigational speed of 20 knots, 5-level sea state, and the adaptive LQG control algorithm and the linear quadratic optimal control algorithm are applied to a course steering test. The course change and rudder angle change curves of the steering test process are shown in figures 4, 5 and 6, and the running time 380s of the simulation platform is tested by positive 30 degrees steering from 180 degrees to 210 degrees. A. B, C course change and rudder angle change of the ship from 210 DEG to 180 DEG during the negative 30 DEG steering test, and the simulation platform running time 420s are shown in figures 7, 8 and 9. The A vessel turns faster in 210 to 180 turns and data acquisition stops at 200 s.
And a steering performance comparison test is carried out, wherein an A ship is used, the navigational speed is 20 knots, the 5-level sea condition is adopted, and an STC-LQG control algorithm and an STD-MRAC control algorithm are applied to a course steering test. The course change and rudder angle change curves in the steering test process are shown in figures 10, 11 and 12 by the steering test of positive 30 degrees from 180 degrees to 210 degrees, and the comparison indexes of all steering performance indexes and the steering performance are shown in a second table. Turning to experimental performance index description: 1) steering rapidity: adjustment time per turn; 2) stability in the steering process: whether stagnation and rollback and other phenomena occur in the steering process; 3) turning over and undershooting: the degree of under-modulation was exceeded at each turn-around experiment. According to the performance index statistical result, the steering time of the ship adopting the STD-MRAC control algorithm is short, the overshoot is small, the steering stability is high, the good control precision can be achieved under the interference of five-level sea conditions aiming at different ship types and different steering angles, and the self-adaptive capacity and the robustness are excellent; the ship course keeping performance adopting the STC-LQG control algorithm meets the requirement of the adaptive rudder standard, and has the advantages of high control precision and less rudder hitting times.
Table one: heading holding test performance statistical table
A second table: steering experiment performance statistical table
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (5)
1. The self-adaptive control method for the ship course tracking is characterized by comprising the following steps of:
step 1: according to the course set value psi s Calculating the desired heading ψ of the ship using a saturated differential tracker d And desired steering angular velocity
And 2, step: calculating the state of a differential tracking system according to the current heading psi and the yaw angular speed r of the ship;
and step 3: selecting whether to switch an STC-LQG controller or an STD-MRAC controller according to the current control mode of the ship and the system state;
and 4, step 4: calculating a control command and updating an algorithm or a model parameter by using an STC-LQG controller or an STD-MRAC controller according to the current control mode;
and 5: and (5) circulating the steps 1 to 4 to realize the ship course keeping and the constant angular speed steering.
2. The adaptive control method for ship heading tracking according to claim 1, wherein the step 1 specifically comprises: when the second derivative of the input signal is within the TD amplitude limiting value, the TD can quickly track the input signal and estimate the first derivative value of the tracking signal; the differential tracker has the following form:
wherein u (k) is an input signal, m 1 (k) For tracking signal output, m 2 (k) For the differential output of the tracking signal, h is the filter factor, r is the velocity factor, T is the tracking step length, and the fst function calculates the second derivative of the tracking signal:
δ＝rh
δ 0 ＝δh
y＝x 0 -u+hm 2
according to the requirement of ship constant angular speed steering, differential signal m is added 2 (k) Adding saturation clipping, a saturated differential tracker can be obtained:
wherein sat is a saturation clipping function, v m Is a differential signal m 2 (k) The clipping value of (1). Application of STD in ship course control s ，m 1 ＝ψ d ，
v m For shipsA desired steering angular velocity setting.
3. The adaptive control method for ship course tracking according to claim 1, wherein the step 2 is specifically: the ship maneuvering motion model can adopt a first-order linear Nomoto model:
wherein r is the ship bow angular velocity,
selecting a system state x for the yaw angular acceleration, psi for the ship heading angle, delta for the rudder angle, K, T for the ship turning capacity and turning inertia parameters under the influence of the ship load condition and the navigation speed 1 ＝ψ-ψ d ，
x＝(x 1 x 2 ) T Considering the requirements of course keeping and constant angular speed steering
Then the original system state space equation is:
4. the adaptive control method for ship course tracking according to claim 1, wherein the step 3 is specifically: if the course setting is changed, switching to the STD-MRAC control mode; if the course setting is not changed, the current control mode is STC-LQG control, the mode is not switched, the current control mode is STD-MRAC control mode, and x is checked 1 ,x 2 If the absolute value is small enough, if yes, the method is executedAnd switching to STC-LQG control, otherwise, continuing to maintain STD-MRAC control.
5. The adaptive control method for ship course tracking according to claim 1, wherein the step 4 is specifically:
(1) if the current control mode is the STD-MRAC control mode, calculating a control angle order according to the following control laws:
updating control law parameters through the parameter adaptive law of the STD-MRAC control mode:
(2) if the current control mode is STC-LQG control
a. Estimating time-varying ship course model parameters by using a full rank decomposition least square method, and parameterizing ship states and inputs:
the parameter estimation of the full rank decomposition least square method comprises two components of total iteration and principal component iteration, wherein the total iteration formula is as follows:
the principal component iterative formula is:
the two component relations of the total iteration and the principal component iteration are as follows:
wherein, V k1 For a full rank decomposition matrix, the k-th measurement data { h } can be obtained by k ,z k The corresponding transformation matrix is V k ＝[V k1 V k2 ]
Wherein h is ki As a vector of data h k The ith component of (a), h s Is a dead zone threshold;
b. estimating the state of the ship course model by using a state expansion Kalman filter, and predicting the state of the Kalman filter in a state space model form:
where h is the sampling period, w r And v r For interference and measuring noise
The state prediction equation is:
x k+1|k ＝φ k x k|k +B k u k +w k
the calculation steps of the state expansion Kalman filter are as follows:
wherein: p is a state estimation error variance matrix, Q is a model error variance matrix, and R is a measurement noise variance matrix.
c. And (3) calculating a rudder angle order according to a control law:
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115469553A (en) * | 2022-11-02 | 2022-12-13 | 中国船舶集团有限公司第七〇七研究所 | Ship motion state reconstruction method, device, equipment and storage medium |
| CN115685751A (en) * | 2022-10-20 | 2023-02-03 | 聊城大学 | Event trigger control method based on Nomoto nonlinear ship model |
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| Title |
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| 包政凯，朱齐丹，杨司浩，刘永超: "船舶航向模型参考自适应和最优控制研究", 《应用科技》, 18 January 2022 (2022-01-18) * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115685751A (en) * | 2022-10-20 | 2023-02-03 | 聊城大学 | Event trigger control method based on Nomoto nonlinear ship model |
| CN115685751B (en) * | 2022-10-20 | 2024-05-14 | 聊城大学 | Event trigger control method based on Nomoto nonlinear ship model |
| CN115469553A (en) * | 2022-11-02 | 2022-12-13 | 中国船舶集团有限公司第七〇七研究所 | Ship motion state reconstruction method, device, equipment and storage medium |
| CN115469553B (en) * | 2022-11-02 | 2023-03-24 | 中国船舶集团有限公司第七〇七研究所 | Ship motion state reconstruction method, device, equipment and storage medium |
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