Optimal control of underwater vehicle using LQR controller driven by new matrix decision control algorithm

This paper introduces an optimal control system to control the depth and pitch angle of an Autonomous Undersea Vehicle (AUV). The paper considers the design of a 4th-order AUV model using state space technique to represent the behavior of depth and pitch angle states. A closed-loop control scheme-based Linear Quadratic Regulator (LQR) is designed to manipulate the depth and pitch states by reducing a cost function defined for this purpose. In this paper, LQR method is employed to guarantee the control of different states of AUV model at the same time. In addition, a new control algorithm, called Matrix Decision Control (MDC) algorithm, is presented to ensure that the search algorithm always achieves positive semidefinite Q matrix which is crucial for LQR design. Simulation results are obtained by integrating the LQR approach to the model with different control parameters. Results are benchmarked by comparing the results of LQR based PSO and MDC algorithms with the response from optimal and robust controllers in the presence of white noise and wide range of system uncertainties. Simulation results show that the proposed control scheme delivers better performance and strong robustness in terms of reducing the overshoot, improving the pitch behavior, and covering wide range of system uncertainties.