Pn

drag coefficient, only that a constant multiplying term appears. Again, inertia term can be calculated based on the parameters which are known from before.

Static system

In this case we can observe the value of the steady-state response, Kss = lim£^+ra ¿^(¡0 and some characteristic points of the response. If a linear model (constant drag coefficient) is assumed, one degree of freedom of an underwater vehicle can be described with (16) and the response is explicitly given with (17).

The steady state value of the response is clearly Kss = -j-. Just as in the astatic case, given enough experimental data, drag can be determined as precisely as needed. The calculation of inertia term is somewhat different than in the astatic case. Here we can use a classical method for determining system's time constant based on the fact that at the time instance t=TL=y system response achieves around 63% of the steady state value.

Therefore if TL is determined, based on the known constant drag coefficient, inertia term can be easily calculated.

If the system is described as nonlinear, i.e. with linear drag, then the SISO equation is (19) and the response is explicitly given with (20) (see Appendix A for derivation of the term).

The steady state value of the response is Kss = sgn(r) 1—, and linear drag can be calculated

\ Pw using this value. Similarly as in the case with constant drag coefficient, at the time instance t =TN = , a the system response achieves around 76% of the steady state value. VAvM

Therefore if TN is determined, based on the known linear drag coefficient, inertia term can be easily calculated. Table 2. gives a short overview of equations for determining model parameters using the open loop experiments. 