Modeling and Control of a Spherical Underwater Robot Vehicle by Using a Variable Ballast Mechanism

A mechanism of variable ballast system which manipulates volume of water in the
ballast tank is designed and modeled in this thesis. The mechanism is designed to
make water always fulfill space in the variable ballast tank with varying volume.
Therefore the internal dynamic that is caused by the movement of water in the tank
can be avoided. The variable ballast is utilized for vertical motion actuator of a
spherical URV by controlling the difference between buoyant force and gravitational
force. In this thesis, the VBS can change the weight of URV body, ΔW, in range
± 9.96N in order to make URV in positive buoyancy, neutral buoyancy or negative
buoyancy. The buoyancy of URV is considered as a constant value. By using this
mechanism, then the URV can move in vertical plane in the range of velocity
±1.019ms−1 .
Two approaches, i.e. linearized approximation and nonlinear approach, are presented
to design the controller of the dynamic model which behaves as nonlinear system. In
linearized approximation, the nonlinear model is linearized about the equilibrium
point by using Taylor series. Since the linearized model is controllable then a linear
control strategy is applied. In order to analyze the stability of the system, Lyapunov’s
linearization method is used. Since the eigenvalues of the linearized model is zero,
λ = 0, then the Lyapunov’s linearization method cannot determine whether the
nonlinear system is stable or unstable. The second method of Lyapunov stability
analysis, i.e. Lyapunov direct method, is also applied. By using this method, it can be
known that the equilibrium point of this depth positioning system is unstable,
furthermore, nonlinear approach, i.e. state-space feedback linearization and inputoutput
feedback linearization, are also used to stabilize this system.
These control strategies are then simulated in MATLAB/Simulink. All control
strategies designed in this thesis can asymptotically stabilize the equilibrium point, for
t →∞ , e→0 . The linearized approximation approach is the fastest to reach steady
state compare to the others, but it consumes more power. For tracking a trajectory,
input-output linearization gives better performance compare to the others by resulting
smallest error. If the change of trajectory is constant, then error of input-output
feedback linearization converges to zero. For linearized approach and state-space
feedback linearization, if change of input is 0.1ms−1 then absolute error converge to
2.408m and 6.082m respectively, and if change input is 0.2ms−1 then absolute
error converge to 6.361m and 12.163m respectively.