Abstract
This article presents a robust stabilizing control for nonholonomic underwater systems that are affected by uncertainties. The methodology is based on adaptive integral sliding mode control. Firstly, the original underwater system is transformed in a way that the new system has uncertainties in matched form. A change of coordinates is carried out for this purpose, and the nonholonomic system is transformed into chained form system with matched uncertainties. Secondly, the chained form system with uncertainties is transformed into a special structure containing nominal part and some unknown terms through input transformation. The unknown terms are computed adaptively. Afterward, the transformed system is stabilized using integral sliding mode control. The stabilizing controller for the transformed system is constructed which consists of the nominal control plus some compensator control. The compensator controller and the adaptive laws are derived in a way that the derivative of a suitable Lyapunov function becomes strictly negative. Two different cases of perturbation are considered including the bounded uncertainty present in any single control input and the uncertainties present in the overall system model of the underwater vehicle. Finally, simulation results show the validity and correctness of the proposed controllers for both cases of nonholonomic underwater system affected by uncertainties.
Highlights
In recent years, there has been an increasing interest in design and implementation of robust control laws for underwater vehicles
In the study by Bi et al.,[4] a tracking control of under-actuated autonomous underwater vehicles (AUVs) was designed in the presence of unknown ocean currents, whereas positionbased control of underwater robotic system for maintaining position in the presence of ocean currents was presented by Kim et al.[5]
Kyriakopoulos,[6] and a second order sliding mode controller was designed for AUV in the presence of unknown disturbances in the study by Joe et al.[7]
Summary
There has been an increasing interest in design and implementation of robust control laws for underwater vehicles. X_6 1⁄4 v4 þ Dðx; tÞ where Dðx; tÞ is unknown scalar function bounded with first time derivatives and with known bound, that is, jDðx; tÞj < M. and pð; tÞ 2 spanfg1ðÞ ; g2ðÞ; g3ðÞ ; g4ðÞ g; 8 t According to Liang and Jianying,[24] if pð; tÞ 2 spanfg1ðÞ ; g2ðÞ; g3ðÞ ; g4ðÞ g is in matched form, under coordinate change and state feedback (11) can be locally or globally transformed into x_1 1⁄4 v1 þ p1ðx; tÞ x_2 1⁄4 v2 þ p2ðx; tÞ x_3 1⁄4 x2ðv[1] þ p1ðx; tÞÞ (12). The perturbed chained form system is further transformed into a special structure containing nominal part and some unknown terms through input transformation. S_ 1⁄4 s_ 0 þ _ 1⁄4 x_1 þ 5x_2 þ 10x_3 þ 10x_4 þ 5x_5 þ x_6 þ _ 1⁄4 x2 þ x1’1ðx; tÞ~1 þ 5x3 þ 5x2’2ðx; tÞ~2 þ 10x4 þ 10F^3 þ 10F~3 þ 10x2x1’1ðx; tÞ~1 þ 10x5 þ 10x4’3ðx; tÞ~3 þ 5x6 þ 5F^5 þ 5F~5 þ 5x2x1’1ðx; tÞ~1 þ x6’4ðx; tÞ~4 þ v0 þ vs þ _
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