Velocity tracking controller for simulation analysis of underwater vehicle model

Figures & data

Table 1. Parameters of the underwater vehicle.

Symbol	Value	Unit
L	2.0	m
b	0.5	m
m	250	kg
$I_x$	20	kg m^2
$I_y$	150	kg m^2
$I_z$	140	kg m^2
$J_{xy}$	0	kg m^2
$J_{xz}$	−30	kg m^2
$J_{yz}$	0	kg m^2

Table 2. Hydrodynamic derivatives and damping terms.

Symbol	Value	Unit
$X_{\dot{u}}$	−50	kg
$Y_{\dot{v}}=Z_{\dot{w}}$	−250	kg
$X_{\dot{q}}=Y_{\dot{r}}=M_{\dot{u}}=N_{\dot{v}}$	10	kg m
$Y_{\dot{p}}=Z_{\dot{q}}=K_{\dot{v}}=M_{\dot{w}}$	−10	kg m
$K_{\dot{p}}$	−20	kg m^2
$M_{\dot{q}}=N_{\dot{r}}$	−30	kg m^2
$K_{\dot{r}}=N_{\dot{p}}$	1	kg m^2
$X_u$	−50	N
$Y_v$	−100	N
$Z_w$	−100	N
$K_p$	−200	N m
$M_q$	−300	N m
$N_r$	−300	N m
$X_{\left|u\right|u}$	−50	Ns/m
$X_{\left|v\right|v}$	−100	Ns/m
$Z_{\left|w\right|w}$	−100	N
$K_{\left|p\right|p}$	−200	N m s
$M_{\left|q\right|q}$	−300	N m s
$N_{\left|r\right|r}$	−300	N m s

Figure 1. Simulation results using GVC for underwater vehicle: (a) linear velocity errors; (b) angular velocity errors.

Figure 2. Simulation results using the classical (CL) controller for underwater vehicle: (a) linear velocity errors; (b) angular velocity errors.

Figure 3. Simulation results using GVC for underwater vehicle: (a) lumped dynamics estimation errors $\text{w}$ related to linear velocities; (b) lumped dynamics estimation errors $\text{w}$ related to angular velocities.

Figure 4. Simulation results using GVC for underwater vehicle: (a) the quantity $\mathrm{\Delta }\xi$ time history related to linear velocities; (b) the quantity $\mathrm{\Delta }\xi$ related to angular velocities.

Figure 5. Simulation results using GVC for underwater vehicle: (a) the quantity $\mathrm{\Delta }\pi$ time history related to linear velocities; (b) the quantity $\mathrm{\Delta }\pi$ related to angular velocities.

Figure 6. Case 2: simulation results using (29(29) $\begin{array}{rl}\tau & =M{\dot{\nu }}_r+C\left(\nu \right){\nu }_r+D\left(\nu \right){\nu }_r+g\left(\eta \right)\\ & +k_{D}s+k_{I}z+\tilde{f},\end{array}$(29) ) controller for underwater vehicle: (a) linear velocity errors; (b) angular velocity errors; (c) lumped dynamics estimation errors $\text{w}$ related to linear velocities; (d) lumped dynamics estimation errors $\text{w}$ related to angular velocities; (e) control forces τ; (f) control torques τ.

Figure 7. Case 2: simulation results using GVC for underwater vehicle: (a) control forces τ; (b) control torques τ.