A General Approach to Discrete-Time Adaptive Control Systems with Perturbed Measures for Complex Dynamics. Case Study: Unmanned Underwater Vehicles

MARIO A. JORDÁN; JORGE L. BUSTAMANTE

Discrete Time Systems

In-Tech

Lugar: Rijeka; Año: 2011; p. 255 - 280

In this work a novel design of adaptive control systems was presented. This is based on speed-gradient techniques which are widespread in the form of continuous-time designs in the literature. Here, we had focused their counterparts namely sampled-data adaptive controllers. The work was framed into the path tracking control problem for the guidance of vehicles in many degrees of freedom. Particularly, the most complex dynamics of this class corresponding to unmanned underwater vehicles was worked through in this work. Noisy measures as well as model uncertainties were considered by the design and analysis. Formal proofs for stability of the digital adaptive control system and convergence of the path error trajectories were presented and an extensive analysis of the control performance was given. It was shown that it is possible to stabilize the control loop adaptively in the six degrees of freedom without any a-priori knowledge of the vehicle system matrices with the exception of a lower bound for inertia matrix. Providing the noisy measures remain bounded, the adaptive controller can reduce asymptotically the path errors up to a residual set in the space state by small errors. The residual set contains the null equilibrium point and its magnitude depends on the upper bounds of the measure noises and on the sampling time. This signalizes the quality of the control performance. However, as generally occurs by digital controllers, it was observed that a large sampling time is an instabilizing factor. It was also indicated the plausibility of obtaining a lower bound of the inertia matrix by simply calculating the inertia matrix of the body only. We will emphasize that the design presented here was completely carried out in the discrete time domain. Other usual alternative design is the direct translation of a homologous but analog adaptive controller by digitalizing both the control and the adaptive laws. Recent results like in (Jordán & Bustamante, 2011) have shown that this alternative may lead to unstable behaviors if the sampling time is particularly not sufficiently small. This fact stands out the usefulness of our design here. Finally, a case study was presented for an underwater vehicle in simulated sampling mission. The features of the implemented adaptive control system were highlighted by an all-round very good quality in the control performance.