Sign function-based dynamic positioning fixed time control method
A dynamic positioning and symbolic function technology, applied in two-dimensional position/channel control, non-electric variable control, vehicle position/route/height control, etc., can solve the problem that dynamic positioning ships cannot achieve synchronous convergence and achieve optimal motion path, avoiding anomalies, and reducing energy consumption
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[0064] Step 1: Establish the kinematics and dynamics model of the dynamic positioning vessel:
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[0067] Where: R(η(t)) represents the coordinate system transformation matrix, η=[x,y,ψ] T Indicates the position and heading angle of the dynamically positioned ship; υ=[u,v,r] T Indicates the velocity and angular velocity of the dynamically positioned ship; M 0 Indicates the mass and moment of inertia of the dynamic positioning ship; C 0 (ν) represents the Coriolis centripetal force matrix, D 0 (ν) represents the damping coefficient matrix; τ represents the control force and control torque. The initial values of the position and velocity vectors are set to
[0068] Then combine the system (1) and (2) to establish a second-order mathematical model:
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[0070] in,
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[0074] In the formula,
[0075] M(η(t))=R(η(t))M 0 R -1 (η(t)) (7)
[0076] The second step is to design a new type of direction sign f...
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