00 CONTROLLER TUNING METHOD FOR SHIP

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#00 CONTROLLER TUNING METHOD FOR SHIP AUTOPILOT A. Consegliere, M. J. López

Deptartamento de Ingeniería de Sistemas y Automática Facultad de Ciencias Náuticas Universidad de Cádiz, Spain

Abstract: In this work we present a raethod for tuning Hx controllers for ship autopilots. Weighting transfer functions are calculated by means of ship mathematical model parameters, and these parameters are experimentally obtained using the turning circle test. Simulation results are presented for different ship types. Controller fine tuning depends on two parameters only, so that tuning procedure may be carried out by an operator using the design and analysis software developed for that task. Robustness and performance analysis are obtained for each ship and regulador. Copyright (c) 2000 . Keywords: Robust control, ífoo optimization, course control.

1. INTRODUCTION In this paper we expound a method to tune H) \m and high frequency), pS = médium frequency cross point, pSl = low frequency cross point. With respect to the operation point, ship dynamics equivalent uncertainty is bounded by the following transfer function: WT(s) =

s+pT pTl KT pT

where, pTl and pT depend on valúes of a. It is considered an uncertainty level up to KT 100% at low frequency (where the ship dynamics is better known), and a level up to (pTl KT)/pT 100% at high frequency. This transfer function is used to test robust stability with respect to equivalent multiplicative uncertainty for each controller. To take into account limitations in actuator (steering gear) WR(s) is used. This weighting transfer function depends on the stationary gain K, and a new tuning parameter fx is used too. Both tun-

Zero order hold approximation is used to get a discrete time model of ship, and inverse bilinear transformation previously to obtain analogic Hx controller, since the infinity norm of a given discrete problem is preserved under such a transformation in the continuous domain. The resulting contiuous HOO controller is then transformed back to the discrete domain via bilinear transformation. A sample time of 0.2 seconds is used for controllers. The final implementation of the control system is represented in Figure 1, which shows the structure used in computer simulations. In this figure a filter (G/i) for set-point changes can be seen, which is used to carry out large changes in the set-point (course-changing). Another filter (G/2) is used for heading sensor noise. To analyze robustness of each controller, some numeric indicators are calculated: gain margin (MG), phase margin (MF), delay margin (MR), multiplicative stability margin (MSM). These indicators are given in Table 1 for each ship and for each controller. As it can be seen, these indicators are satisfactory for both controllers, and may be modified acting on tuning parameters (¿ía and

fK). Figure 3 shows control system response for 90 degress SP change. Manouvre is made fast and in a clear way for other ships (without overshoot). Figures 4 (without filter) and 5 (with filter) show yaw angle and rudder angle for course-keeping operation. Filter efect is very much significative to reduce control signal effort, but the price is that additional phase lag is introduced and lower stability margins (see Table 1) are obtained. The 2 ZOH: 3'bilin:

Zero Order Hold approximation. Bilinear transformation.

—> G(z)

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Figure 8: Time response for course-changing controller (ship 3)

employs " H^ design toolbox" for Matlab, which we have developed to carry out design, analisys and simulation with ship mathematical models and ífoo controllers. Design method uses two paramenters to get controller's fine tuning, and needs that toolbox. Tuning procedure achieves controllers with good performance and robustness properties. In next works we will set out the adaptation procedure of the controller. Acknowledgement: The authors want to thank the Spanish CICYT for its partial support to this work through project TAP98-1214.

References [1] R, Y. Chiang and M.G. Safonov (1992), Robust Control Toolbox. The MathWorks Inc.

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Figure 9: Time response for course-keeping controller (ship3) HOO controllers, for this ship, are the following: Course-changing controller: Gr(s) =

0.0041084s2 + 14.864s + 0.579 s 2 +2.2929s +0.42314

Course-keeping controller (with filter):

Gr(s) =

19.458s3 + 6.159s2 + 0.31964s + 0.002666 2.7908s3 + 1.3012s2 + 0.34964s

Figures 5 to 8 show respective time responses for ships 2 and 3, for course-changing and coursekeeping operation Our H