Nonlinear adaptive trajectory control of multi-input multi-output submarines with input constraints

Abstract

The paper presents a new nonlinear adaptive control system for the dive-plane control of multi-input multi-output submarine models with input constraints, in the presence of external disturbances. It is assumed that all the system parameters, except the signs of the principal minors of the input matrix, are unknown. The objective is to design an adaptive control law for the tracking of reference depth and pitch angle trajectories, despite constraints on the rotation angles of the bow and stern hydroplanes. For the derivation of a singularity-free adaptation law, the decomposition of the input matrix as a product of a positive-definite symmetric matrix, a diagonal matrix, and an upper triangular matrix (termed SDU decomposition) is obtained. Then an adaptive control system is designed which accomplishes uniform ultimate boundedness of the closed-loop system trajectories. The control system includes an auxiliary dynamic system to counter the effect of control input saturation. Simulation results show that the designed adaptive law accomplishes precise depth and pitch angle trajectory control, despite symmetric and non-symmetric input constraints, parametric uncertainties and external disturbance inputs. These results also show that the designed saturating adaptive controller can accomplish certain dive-plane maneuvers using either of the hydroplanes; but the bow hydroplane can execute larger maneuvers than the stern hydroplane. The robust performance of the controller, despite non-symmetric input constraints, is useful in situations in which partial failure of actuators causes rotation of the hydroplanes in unequal ranges.

Composite adaptive control of submarine and parameter identification by integral regressor excitation

“…Thus, the composite adaptation law uses information on the tracking error and on two model prediction errors. Substituting equation (51) for _ ĥc in equation (50) gives…”

“…48,49 An adaptive law has also been proposed for a submarine model with input constraints. 50 The adaptive control systems for AUVs [29][30][31][32][33][34][35][36][37][38][41][42][43] and submarine models [46][47][48][49][50] have only been designed for trajectory control and stabilization. Of course, the identification of uncertain parameters is also important.…”

“…1. In contrast to the adaptive systems for AUVs [29][30][31][32][33][34][35][36][37][38][41][42][43] and submarines [46][47][48][49][50] published in the literature, this composite adaptive system includes an RMI estimator to achieve enhanced parameter excitation. 2.…”

Diving Adaptive Position Tracking Control for Underwater Vehicles

“…The positive parameters k i , τ * j (i = 1, 2, ..6, j = 1, 2, 3, 4) provide a guideline for designers that increasing k i , τ * j would increase η 1 , subsequently reduce the upper bound of the errors δ * 1 η 1 . Remark 2: The dynamic model in (1) could be reduced down to that in [14] with the constant surge velocity constraint and to that in [12] with the constant surge velocity and zero heave velocity constraints. It could be further reduced down to that in [7] with the constant surge velocity, zero heave velocity and small pitch angle constraints.…”

“…However, the heave velocity was neglected in those literatures and the diving dynamic model was regarded as a signal-input signal-output (SISO) system. Then the multi-input multi-output (MIMO) diving model was investigated in [14] with the heave velocity considered. The proposed controller could accomplish depth tracking and pitch angle tracking keeping all signals uniformly ultimately boundedness.…”