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Tutorial 8 – Ship Autopilot (JEE344 Applied Control Engineering) Aim • To design and simulate an PID- based autopilot system • To use simulation as a diagnostic tool to improve autopilot performance and select control gains Learning Outcomes • Simulate a ship’s steering dynamics with LabVIEW • Simulate PID autopilot with Auto/Man switch mode for course keeping and changing Ship 1: Autopilot system for Shioji Maru using Nomoto’s model Problem Statement Let’s consider the Nomotor’s first order manoeuvring model: Tr + r = Kδ (or Tψ + ψ = Kδ ) & && & (1) ψ=r & (2) where ψ is yaw angle (rad) and δ is rudder angle (rad, −40π /180 to +40π /180 , T = 7.5 seconds and K = 0.11. Ship speed is constant, v = 15 knots (1 NM = 1,852.00 m). The steering machine model is & δc − δ δ= (3) δ c − δ TRUD + a where TRUD is rudder constant, TRUD = 11.9 (sec), and a is constant chosen as 1 to avoid zero dividing. The ship’s heading is control by a PID autopilot system with control gains of KP, KI and KD. It is assumed that the rudder angle for the PID autopilot is in range of -10o (port) to +10o (starboard), rudder rate in range of -5 deg/s to +5 deg/s, error (between the actual yaw angle and set course) in range of -180o to +180o, and yaw angle in range of 0-360o. The position of the ship is represented by the following model: x = u sin ψ + v cos ψ & (4) y = u cos ψ − v sin ψ & (5) where u is surge velocity and v is sway velocity (assuming that v = 0). Make simulation program/s with LabVIEW. Solution 1. Ship’s open-loop system U (knot) x δc Steering δ Ship hull ψ Ship y machine dynamics trajectory -40 to +40 0 to 360 Figure 1 Block diagram of the open-loop system 1 2. Block diagram algorithm for the ship’s hull dynamics: 1 K r=− + δ & (6) T T ψ=r & (7) Sum × & r r [rad/s] ψ [rad] × × ÷ ∫ ∫ δ [rad] K T Divide Integrator Integrator Display ψ Figure 2 Block diagram algorithm for ship’s hull dynamics 3. Block diagram algorithm for ship’s trajectory on the earth-fixed reference frame: x = u sin ψ + v cos ψ & (9) y = u cos ψ − v sin ψ & (9) ψ [rad] cos × + × & y y ∫ x sin × – Integrator × u [m/s] (0,0) × + XY-Chart v [m/s] × & x x ∫ y × + Integrator × Figure 3 Block diagram for the ship’s trajectory (x – latitude, y – longitude) 4. Block diagram algorithm for the steering machine & δc − δ δ= (10) δ c − δ TRUD + a δc + δc − δ & δ δ × ∫ – abs × + × ÷ Integrator + Trud a Figure 4 Block diagram algorithm for the steering machine 2 5. Ship’s Closed-loop Control System (Autopilot with Auto/Man Switch) U (knot) SP ψ d -40 to +40 0 to 360 x PID δc Steering δ Ship hull ψ Ship Autopilot machine dynamics trajectory y GPS ψm Gyro- compass Figure 5 Block diagram of the closed-loop autopilot system The block diagram algorithm for PID autopilot with Auto/Man mode is below: PID Autopilot Comparator Sum (Compound SP ψ d Subtract Multiply Arithmetic) PV ψ + Auto/Man Kp P Multiply Select Integral uin OP + Auto I KI (Control signal) Multiply Commanded uin Man + rudder angle To Steering Derivative D KD Machine Figure 6 Block diagram algorithm for PID autopilot with Auto/Man switch mode Hands-on Exercise 1 (Save as ShipSimulator01.vi) Open-loop system without the steering machine & trajectory: Refer to Figure 2 and the following sample code: Figure 7 Sample code for the open-loop system without SM & trajectory 3 • Save the VI. • Do testing of its functionality. Hands-on Exercise 2 (Save as ShipSimulator02.vi) Open-loop system with the trajectory (without steering machine): Refer to Figure 3 and the following sample code: Figure 8 Sample code for the open-loop with trajectory (without the SM) Hint: When using the XY Graph for ship’s trajectory, uncheck “Clear data on each call”: Figure 9 Setting the Build XY Graph • Save the VI. • Do testing of its functionality. Hands-on Exercise 3 (Save as ShipSimulator03.vi) Open-loop system with steering machine and trajectory: Refer to Figure 4 and the following sample code: 4 Figure 10 Sample code for the steering machine • Save the VI. • Do testing of its functionality. Note: You can add indicator/s and/or a waveform chart to display the commanded rudder and actual rudder. Hands-on Exercise 4 (Save as ShipSimulator04.vi) Program a gyrocompass and set limits for ship’s heading in range 0 to 360o. Algorithm to set limits: If psi >= 2 π then psi = psi – 2 π , Else if psi < 0 then psi = psi + 2 π Else psi = psi C language code (Formula Node): If psi >= 2*pi { psi = psi – 2*pi;} Else if (yaw < 0) { psi = psi + 2*pi;} Else { psi = psi} MATLAB language code (MathScripts Node): if (psi >= 2*pi) psi = psi – 2*pi; elseif (psi < 0) psi = psi + pi*2; else psi = psi; end Hands-on Exercise 5 (Save as ShipSimulator05.vi) Closed-loop system (Autopilot with Auto/Man) • Save the VI. • Do testing of its functionality. 5 Conclusions At this point the following LOs have been satisfied: • Simulate a ship’s steering dynamics with LabVIEW • Simulate PID autopilot with Auto/Man switch mode for course keeping and changing Follow-up Exercise Modify the above program for ship autopilot system in consideration of the trajectory with initial latitude and longitude (the Control Lab’s latitude and longitude!): x(0) = current latitude = 41o27.179’ S y(0) = current longitude = 147o04.246’ E such that the ship’s position is expressed with latitude and longitude. One nautical mile is approximately 1852 m, and equivalent to one minute of arc. Refer to Nautical mile: http://en.wikipedia.org/wiki/Nautical_mile 6

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posted: | 7/30/2010 |

language: | English |

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