A sliding-mode speed controller for output tracking of underactuated surface vessels is presented based on a new manifold definition. The new sliding-mode control algorithm relies on a conventional sliding manifold and its time derivative. The states/outputs are estimated with the extended Kalman filter as an observer. The new controller is compared with its integral-type sliding-mode counterpart in terms of performance in tracking the outputs where the estimator is driven by respective control inputs and observed states involved with arbitrarily correlated process and measurement errors.Introduction: Owing to recent progress on self-deployed underactuated surface vessels (USVs), which are considered non-holonomic, stabilisation control methods for underactuated systems have attracted a great deal of attention from the standpoint of autonomous tracking and guidance operations [1]. Non-holonomic systems that fail to meet Brockett's requirement for the existence of a linearised system representation are not controllable with conventional continuous state-feedback control law, thereby most USV control approaches adopt discontinuous control strategies [2]. As a favoured choice, sliding-mode control (SMC) has been a widely used variable-structure control method in tracking a desired trajectory given a plant. Its main strengths are its inherent adaptive nature and robustness against bounded modelling uncertainties and unmodelled external disturbances [3]. Tracking with SMC mainly consists of reaching and sliding-mode phases. In the former, the system trajectory launched from an arbitrary initial state is forced to converge to a predefined sliding surface, while the latter refers to the behaviour of system dynamics on the sliding surface. The resulting control law is expressed as the superposition of a nominal control and a discontinuous term ensuring robustness. The nominal control term is calculated by setting the time derivative of the sliding manifold expression to zero under the nominal model. With conventional SMC where the error term is not explicitly included in the nominal control calculation, the major problem is the chattering in tracking time-varying target trajectories due to a lag between the control to be applied and the error. Such lagging in control causes a challenge in conventional SMC as a hindering elimination of constant or slowly varying errors [4]. On the other hand, tracking fast time-varying trajectories will be subject to excessive chattering. A solution may be to use the integral-type SMC (ISMC) which includes the error in nominal control calculation [5]. In [6], ISMC was employed as a USV speed controller for tracking successfully with adaptive characteristics and robustness with coupled and nonlinear operation conditions in water. However, tracking performance in navigation and guidance involving sensory measurements with unavoidable uncertainties will depend on how correctly the states and outputs are estimated. Despite its shortcomings against errors in initial estimation and for the case...
A new sliding-mode control method is presented in which the nominal control is derived from a manifold consisting of the standard sliding manifold expression and its derivative. It is shown that the new method yields a faster reach time. Simulation results also show that it performs with smaller error and less control effort compared to standard counterparts in tracking an autonomous nonlinear affine system. Introduction: Sliding-mode control (SMC) is an adaptive and robust variable-structure (VS) control method in tracking a specified target trajectory for a given plant model involving uncertainties and external disturbances [1]. It mainly consists of reaching and sliding-mode phases. In the former, the system trajectory launched from any initial condition is forced towards a sliding surface while the latter refers to dynamics on the sliding surface presumably reached [2]. The associated control law contains nominal and discontinuous control terms. The nominal control term in standard SMC is calculated by setting the time derivative of the sliding manifold expression to zero. A major problem in this approach is high-frequency chattering in tracking fast time-varying target trajectories due to lag between the control to be applied and the error dynamics.In this Letter, a new sliding manifold definition and associated control law are introduced to alleviate the above shortcoming. The new manifold consists of an exponentially stable combination of standard conventional sliding manifold and its time derivative. The new and standard approaches with associated control laws are applied to a second-order nonlinear system and their performances are presented.
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