Cop}right © (FAC 9 1h Triennial World Congress Budapest, Hungary. (984 DESIGN CONSIDERATIONS, ANALYSIS AND PRACTICAL EXPERIENCE WITH AN ADAPTIVE SHIP'S AUTOPILOT S. Saelid*, T. Svanes**, T. Onshus* ** and N. A. Jenssen* *Kongsberg Vdpenfabrikk AIS, Kongsberg, N01way **Robertson AIS Radio Eleklro, Egersund, N01way ***Division oJ Engineering Cybernetics, NTH, Trondheim, Nonvay Abstract. The paper describes an adaptive autopilot. The autopilot is based on a mathematical model which uses a priori information to find initial parameter estimates. The autopilot also includes a model of wave induced yaw-motion. The estimates of the oscillating yaw components are used to minimize their influence on the rudder motions . It is shown in the paper that a Kalman filter gain for a vessel of unit length can be computed once and for all . Based upon this unit vessel Kalman filter gain, formulas for computing the gain for a general vessel are given. A vector of variable forgetting factors are introduced. This completely eliminates the blow up problem . The autopilot is tested on board the coastal steamer M/S MIDNATSOL and results from these tests are given. Keywords. Adaptive autopilot; experiments; ship model. INTRODUCTION In recent years adaptive autopilots have been mar- keted and sold by at least three different compa- nies. These autopilots are all based on adaption of the parameters in a black box model , where the paramters have no direct physical interpretation. An autopilot based on a mathematical model develo- ped from physical and hydrodynamical principles, will be described and analyzed in this paper . This autopilot will be claimed to have the following ad- vantages , compared to an autopilot based on black box models. A priori estimates of the parameters can be ob- tained based on physical and hydrodynamic laws. For a given model order , the number of parame- ters to be estimated will be smaller. In order to minimize unwanted rudder action, the heading is modelled as the added outputs of a steering model and a model representing the wave induced, oscillatory yaw components. When the autopilot feedback is taken only from the steer- model, a very effective wave filtering of the. rudder control signal results. (Saelid et al. 1983, a, b; Balchen et al . 1980). Section 11 of this paper describes the physically based HF - and LF-models of oscillatory motion and the steering dynamics based on physical and hydro- dynamical laws. The model is used in an adaptive control structure . A fixed gain Kalman filter is used for state esti- mation . In the paper it is shown that the Kalman filter gain matrix can be computed with sufficient accuracy for a general vessel of length L based on the gain for a nominal vessel of unit length. Hence, the Kalman filter gain matrix can be compu- 2895 ted once and for all and modfied for a sepcific vessel, based on the knowledge of the actual vessel length L. The innovation process of the Kalman filter is used in a prediction error parameter estimation algo- rithm for estimation and tracking of the model pa- rameters. The estimation of the parameters are used to compute the control gains of the control law. A serious problem, which can arise in adaptive con- trollers is the "blow-up" of the covariance matrices associated with a constant exponential weighting of past data. A partial solution to this problem has been deviced in Fortescue et al. (1981), where a variable forgetting fact or is introduced. In this paper a vector of variable forgetting factors are introduced (Saelid and Foss, 19 8 3), and it is shown how this is implemented. It is als o shown that the algorithm totally eliminates the possibility of blow-up. Results from full scale sea trials on board the Norwegian Coastal steamer M/s MIDNATSOL are re- ported. THE MATHEMATICAL MODEL As already mentioned, the heading measurement model is given by y = tj. + iJ; H + w where y is measured heading in radians, iJ; is the LF-part and iJ; H is the HF-pa rt of the heading. w is assumed to be whit e measurement noise . The well known form of a linearized LF-model is given in Compstock (1967):