CN105197185A - Iterative learning control algorithm for ship steering engine - Google Patents

Abstract

The invention discloses an iterative learning control algorithm for a ship steering engine, and relates to the technical field of iterative learning control, ship steering engine movement control and the like. The iterative learning control comprises three aspects of iterative learning, convergence analysis and robustness analysis. The ship steering engine system control algorithm based on iterative learning control is provided for solving the problems that randomness of environmental disturbance on a ship is strong, course complexity is high, a classic PID ship steering engine controller cannot change control parameters in real time, and the performance index requirement of a control system is difficult to meet. On the condition that only the original state is given, a control object can be completely tracked only by searching for an appropriate learning law. The iterative learning control algorithm has the advantages of being high in flexibility, good in convergence performance, high in speed, strong in robustness and the like.

Description

A kind of Iterative Learning Control Algorithm of ship steering engine

Technical field

The present invention relates to a kind of Iterative Learning Control Algorithm of ship steering engine, include the realization of the ship steering engine systematic control algorithm controlled based on iterative learning, elaboration, the convergence of ship steering engine dynamic equation and corresponding law of learning and the analytic demonstration of robustness of the principle of work that iterative learning controls.Belong to the technical fields such as iterative learning control, ship steering engine motion control.

Background technology

Steering wheel is the core system that manoeuvre of ship controls, and ship steering engine control system determines the main performance of ship steering engine.During ship's navigation, require that the ship steering engine control system controlling course must have good stability, robustness and alerting ability.Steering gear system is a nonlinear system, and work the load variations and interference caused under different operating mode and different water environment, and classical PID controller can not change controling parameters in real time, is difficult to the performance figure requirement meeting control system.

Iterative learning control theory is proposed by Japanese scholars Arimoto, be suitable for the research object that a class has the characteristic that reruns, its task finds control inputs, make the actual output trajectory of Study system perfect tracking along whole desired output path implementation zero error in finite time interval, and whole process entails completes fast.Iterative learning controls not require to set up the accurate math modeling of control object, more do not need the correlation parameter determining math modeling, only having under given initial condition condition, finding the perfect tracking that suitable law of learning can realize control object, be applicable to ship steering engine and control.

Fuzzy control and nerual network technique are used for the speed of response and the control accuracy that improve steering wheel by general steering gear control system, based on many sliding formworks Adaptive Fuzzy Control algorithms to improve ship tracking error, Agent thought is adopted to build steering gear system, realize that stronger flight path keeps, auto-steering and collision prevention ability, be used for strengthening the robustness of Marine Autopilot by respectively nonlinear ship being handled math modeling and discrete-time variable structure.But be below all difficult to set up ship steering engine mathematical models, can not determine the correlation parameter of math modeling, the effective control to ship's navigation can not be realized.

Summary of the invention

For the problems referred to above, the object of this invention is to provide a kind of Iterative Learning Control Algorithm of ship steering engine, comprise the realization of the ship steering engine systematic control algorithm controlled based on iterative learning, ship steering engine dynamic equation and the convergence of corresponding law of learning and the analytic demonstration of robustness, overcome and be difficult to set up the accurate math modeling problem of ship steering engine, the ship steering engine control system realizing controlling course has good stability, robustness and alerting ability.

For achieving the above object, the present invention takes following technical scheme:

For the feature of ship steering engine motion control, analyze the math modeling of ship steering engine system, propose the ship steering engine systematic control algorithm controlled based on iterative learning, set forth the principle of work that iterative learning controls, the convergence of analytic demonstration ship steering engine dynamic equation and corresponding law of learning and robustness.Algorithm realization concrete steps are as follows:

(1) state space model Ship dynamic situation math modeling is built.Choose state variable x ₁=ψ, x ₃=θ, it is boats and ships course made good ψ that system exports y.The Ship dynamic situation state-space expression comprising steering gear control system characteristic is obtained by nonlinear second order Ship dynamic situation response model and Rudder Servo System dynamic equation:

${\stackrel{\·}{x}}_1=x_2$

${\stackrel{\·}{x}}_2=-\frac{1}{T}{x}_2-\frac{\mathrm{\γ}}{T}{x}_2^3+\frac{K}{T}{x}_3---\left(1\right)$

${\stackrel{\·}{x}}_3=-\frac{1}{T_E}{x}_3+\frac{K_E}{T_E}{\mathrm{\θ}}_E$

y＝x ₁

Model parameter T in formula, K, γ are unknown constant.This is the non-matching uncertain nonlinear system of control coefficient the unknown of a single-input single-output.

(2) dynamic process of ship steering engine system builds.Ship steering engine system be one nonlinear time become SISO system, its dynamic process is described as:

$\left\{\begin{array}{c}\stackrel{\·}{x}\left(t\right)=f(t,x(t\left)\right)+B\left(t\right)u\left(t\right))\\ y\left(t\right)=C\left(t\right)\left(X\right(t\left)\right)\end{array}\right.---\left(2\right)$

Wherein, x (t) ∈ R ^{n × 1}, u (t) ∈ R ^{m × 1}, y (t) ∈ R ^{m × 1}correspond to the state of system, control and output signal respectively, the vectorial sum matrix that f (), B (t), C (t) are corresponding dimension, system architecture and unknown parameters but determine.

(3) foundation of iterative control process.Represent iterations with k, when kth time iteration is run, expression formula is:

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_k\left(t\right)=f(t,x_k(t\left)\right)+B\left(t\right)u_k\left(t\right))\\ y_k\left(t\right)=C\left(t\right)\left(x_k\right(t\left)\right)\end{array}\right.---\left(3\right)$

Output error is:

e _k＝y _d(t)-y _k(t)(4)

In formula, y _dt () is desired output.

The control policy of open loop structure is as follows:

A () initialization, puts k=0, given and store desired trajectory y _d(t) and initially control u ₀(t), t ∈ [0, T];

B () gets kth time iteration control u _kt () send ship steering engine system;

C () sampling exports y _kt (), calculates output error e _k(t);

D () judges y _k(t) whether accurate tracking y _dt (), is, iteration terminates, otherwise enters next step.

(e) e _kt () delivers to law of learning controller, calculate the u next time run _k+1t () also stores, for kth+1 iterative learning;

F () repeats and step (b), (c), process that (d) is identical, until output error converges within desired scope.

The present invention is owing to taking above technical scheme, and it has the following advantages:

1, algorithm concisely easily realizes.Do not need to set up the accurate math modeling of steering gear system, more do not require the correlation parameter determining math modeling, only having under given initial condition condition, find the perfect tracking that suitable law of learning can realize control object.

2, high flexibility.Controling parameters can be changed in real time according to service condition, reach actual behavior index.

3, constringency performance is high, fast convergence rate.Give the High-order Closed Loop PID law of learning with forgetting factor herein, checking shows that its convergence and robustness are comparatively strong, and gain factor diminishes, and convergence rate also greatly improves.

4, strong robustness.When system works the load variations and interference that cause under different operating mode and different water environment, through iterating control, the perfect tracking of zero error can be realized.

Accompanying drawing explanation

Fig. 1 is ship steering engine control system.

Fig. 2 is the schematic diagram of the ship steering engine control system based on iterative learning control.

Fig. 3 is open loop PID law of learning (K _p=0.15, K _i=0.1, K _d=0.2).

Fig. 4 is closed loop PID law of learning (K _p=0.15/3, K _i=0.1/3, K _d=0.2/3).

Fig. 5 is open and close ring PID law of learning (K _p=0.15/3, K _i=0.1/3, K _d=0.2/3).

Fig. 6 is band forgetting factor 3 rank PID law of learning (K _p=0.15/3, K _i=0.1/5, K _d=0.2/3).

Detailed description of the invention

The preferred embodiments of the present invention accompanying drawings is as follows:

As shown in Figure 1, ship steering engine control system inside is actually feedback closed loop system more than, comprise: control system (1), actuating unit (2), controll plant (3), be wherein also subject to uncertain disturbance and error in measurement.Control system (1) comprises course setting link, setting and course made good comparing element, course deviation and rudder angle and feeds back comparing element, rudder angle feedback mechanism etc.; Actuating unit (2) comprises rudder; Controll plant (3) i.e. ship.But externally, ship steering engine control system is a single input/mono-output (SISO) system.

Embodiment one:

As shown in Figure 2, the ship steering engine control system open loop control strategy based on iterative learning control is as follows:

A () initialization, puts k=0, given and store desired trajectory y _d(t) and initially control u ₀(t), t ∈ [0, T];

B () gets kth time iteration control u _kt () send ship steering engine system;

C () sampling exports y _kt (), calculates output error e _k(t);

D () judges y _k(t) whether accurate tracking y _dt (), is, iteration terminates, otherwise enters next step;

(e) e _kt () delivers to law of learning controller, calculate the u next time run _k+1t () also stores, for kth+1 iterative learning;

F () repeats and step (b), (c), process that (d) is identical, until output error converges within desired scope.

Embodiment two:

Consider to have uncertainty and disturbance, steering gear control system dynamic process is expressed as

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_k\left(t\right)=f(t,x_k(t\left)\right)+B\left(t\right)u_k\left(t\right))+w_k\left(t\right)\\ y_k\left(t\right)=C\left(t\right)\left(x_k\right(t\left)\right)+v_k\left(t\right)\end{array}\right.---\left(5\right)$

In formula, w _k(t), v _k(t) state disturbances and output noise.

This paper is that object has carried out emulation experiment with the nonlinear model shown in following formula (5).

$\left\{\begin{array}{c}{\stackrel{\·}{x}}_k\left(t\right)=0.6\sin \left(x_k\right(t\left)\right)+u_k\left(t\right))+w_k\left(t\right)\\ y_k\left(t\right)=0.8\left(x_k\right(k\left)\right)+v_k\left(t\right)\end{array}\right.---\left(6\right)$

In formula, $w_k\left(t\right)=\left\{\begin{array}{c}0.15sin\left(0.1t\right),k=1,3,L,N/+1\\ 0.25sin\left(0.1t\right),k=0,2,L,N/2\end{array}\right.$

$v_k\left(t\right)=\left\{\begin{array}{c}0.2sin\left(0.1t\right),k=1,3,L,N/+1\\ 0.1\sin \left(0.1t\right),k=0,2,L,N/2\end{array}\right.$

Law of learning: open loop PID type iterative learning control law is:

$\begin{array}{c}{u}_{k+1}\left(t\right)=u_k\left(t\right)+\\ K_P{e}_k\left(t\right)+K_I{\∫}_0^t{e}_k\left(\mathrm{\τ}\right)+K_D\frac{{\mathrm{de}}_k\left(t\right)}{dt}\end{array}---\left(7\right)$

Closed loop PID type iterative learning control law is:

$\begin{array}{c}{u}_{k+1}\left(t\right)=u_k\left(t\right)+\\ K_P{e}_{k+1}\left(t\right)+K_I{\∫}_0^t{e}_{k+1}\left(\mathrm{\τ}\right)d\mathrm{\τ}+K_D\frac{{\mathrm{de}}_{k+1}\left(t\right)}{dt}\end{array}---\left(8\right)$

Open and close ring PID type iterative learning control law is:

$\begin{array}{c}{u}_{k+1}\left(t\right)=u_k\left(t\right)+K_P{e}_{k+1}\left(t\right)+K_I{\∫}_0^t{e}_{k+1}\left(\mathrm{\τ}\right)d\mathrm{\τ})+\\ K_D\frac{{\mathrm{de}}_{k+1}\left(t\right)}{dt}+K_P{e}_k\left(t\right)+K_I{\∫}_0^t{e}_k\left(\mathrm{\τ}\right)d\mathrm{\τ}+K_D\frac{{\mathrm{de}}_k\left(t\right)}{dt}\end{array}---\left(9\right)$

Open and close ring PID type iterative learning control law with forgetting factor:

$\begin{array}{c}{u}_{k+1}\left(t\right)=(1-\mathrm{\α})u_k\left(t\right)+K_P{e}_{k+1}\left(t\right)+K_I{\∫}_0^t{e}_{k+1}\left(\mathrm{\τ}\right)d\mathrm{\τ})\\ +K_D\frac{{\mathrm{de}}_{k+1}\left(t\right)}{dt}+K_P{e}_k\left(t\right)+K_I{\∫}_0^t\left(\mathrm{\τ}\right)d\mathrm{\τ})+K_D\frac{{\mathrm{de}}_k\left(t\right)}{dt}\end{array}---\left(10\right)$

High-order Closed Loop PID type iterative learning control law with forgetting factor:

$\begin{array}{c}{u}_{k+1}\left(t\right)=(1-\mathrm{\α})u_k\left(t\right)+\\ \underset{i=1}{\overset{N}{\Σ}}\[K_P{e}_{k-i+1}\left(t\right)+K_I{\∫}_0^t{e}_{k-i+1}\left(\mathrm{\τ}\right)d\mathrm{\τ}+K_D\frac{{\mathrm{de}}_{k-i+1}\left(t\right)}{dt}\]\end{array}---\left(11\right)$

Giving the desired trajectory y of fixed system _d=t ², t ∈ [0,100] the initial condition of initialization system and initial input are respectively x _k(0)=0, u _k(0)=0, in the situation of forgetting factor α=0.5, with when iterations is enough large, algorithm convergence uniform.

Simulation result is as in Fig. 3 ~ Fig. 6, figure, and mark 1 is y _dt (), mark 2 is y ₅t (), mark 3 is y ₈t (), mark 4 is y ₁₁(t).

From Fig. 3 ~ Fig. 6, when there is uncertain disturbance, error in measurement and initial condition (IC) deviation in ship steering engine control system, open loop PID law of learning, closed loop PID law of learning, open and close ring PID law of learning, with the closed loop PID law of learning of forgetting factor, strengthen successively with the convergence of the High-order Closed Loop PID law of learning of forgetting factor, robustness, corresponding gain factor diminishes, and convergence rate also greatly improves.

Claims (4)

1. an Iterative Learning Control Algorithm for ship steering engine, is characterized in that comprising iterative learning, convergence, robust analysis three aspects.

2. the Iterative Learning Control Algorithm of ship steering engine according to claim 1, is characterized in that described iterative learning finds suitable law of learning, makes it to expect input u in hypothesis _d(t), namely under given initial condition x (0), output y (the t)=y of ship steering engine system _dt incoming signal time (), by repeated operation, makes u (t) → u under this law of learning _d(t), y (t) → y _d(t).

3. the Iterative Learning Control Algorithm of ship steering engine according to claim 1, is characterized in that described convergence is exactly that research learning rule and controlled system are in the condition of convergence of iterative learning control process.

Theorem 1: controlled system dynamic equation is the non-linear process shown in formula (2), and meets following condition in t ∈ [0, T]:

(1) f (t, x) meets Lipschitz condition for x, namely there is M > 0, makes:

||f(t,x ₁(t))-f(t,x ₂(t))||≤M||x ₁(t)-x ₂(t)||；

$\∀t\∈\[0,T\],\∀x_1\left(t\right),x_2\left(t\right)\∈R^{n\×1}$

(2) initial condition error { δ x during each run _k(0) } _k>=0it is a sequence converging to zero;

(3) the desirable control u of existence anduniquess _dt (), makes the state of system and exports as expectation value;

(4) in t ∈ [0, T] exist, and B (t), C (t), bounded.

4. the Iterative Learning Control Algorithm of ship steering engine according to claim 1, is characterized in that described robust analysis mainly refers to when system exists interference, under various law of learning, and the convergence problem of iterative learning control process.

Theorem 2: there is the ship steering engine control system of uncertainty and disturbance for shown in formula (5), and meet following condition in t ∈ [0, T]:

(1) f (t, x) meets Lipschitz condition for x, namely there is M > 0, makes:

||f(t,x ₁(t))-f(t,x ₂(t))||≤M||x ₁(t)-x ₂(t)||；

$\∀t\∈\[0,T\],\∀x_1\left(t\right),x_2\left(t\right)\∈R^{n\×1}$

(2) initial condition error during each run meets:

(3) output error bounded, state disturbances and output noise meet || w _k(t) ||≤b _w, || v _k(t) ||≤b _v1, $\left|\right|{\stackrel{\·}{V}}_k\left(t\right)\left|\right|\≤b_{v2};$

(4) there is R ₀∈ R ^{m × r}make || I _m+ R ₀cB|| ≠ 0.