Note that the hydrodynamic coefficients given, are not known by the control law, and are assumed to be the actual values that the estimations must converge to.
Simulation results are presented for two cases: one to examine the effectiveness of the proposed control law in the presence of disturbance waves (which result from ocean currents), and another to study the variation of parameters. The initial condition is assumed to be [y 0,y0] = [0,30° ] in all simulations. It is assumed that the disturbance acts as a step wave that is actuated at some time t1 and is ended at time 12. Two types of disturbances are examined: one 10% of maximum input value, and the other 20% of maximum input value. In order to examine parameter variations, it is assumed that the variations are sinusoidal with a relatively low frequency (which corresponds to gradual variations). We have assumed that the parameter p varies according to p (t) = p + a sin mt.
Two cases are considered. For the first case, it is assumed that m = 0.5 and dp = 10% , whereas for the second case we consider m = 0.5 and dp = 50%. In other words, a 10% variation pertains to p (t ) = p (1 + 0.1sin0.5t), and a 50% variation pertains to p (t ) = p (1 + 0.5sin0.5t).
Note that the control law is not aware of the parameter changes, i.e. the control law is designed for parameters of constant value p , and that the variations are due to unknown environmental effects.
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