Finite-time sliding mode control strategies and their applications

In many engineering applications, faster convergence is always sought, such as manufacturing plants, defence sectors, mechatronic systems. Nowadays, most of the physical systems are operated in a closed-loop environment in conjunction with a controller. Therefore, the controller plays a critical role in determining the speed of the convergence of the entire closed-loop system. Linear controllers are quite popular for their simple design. However, linear controllers provide asymptotic convergence speed, i.e., the actual convergence is obtained when the time reaches an infinitely large amount. Furthermore, linear controllers are not entirely robust in the presence of non-vanishing types of disturbances. It is always important to design robust controllers because of the presence of model imperfections and unknown disturbances in almost all kinds of systems. Therefore, it is necessary to design controllers that are not only robust, but will also provide faster convergence speed. Out of many robust non-linear control strategies, a further development in sliding mode control (SMC) strategy is considered in this thesis because of its simplicity and robustness. There have been many contributions in the SMC field in the last decade. Many existingmethods are available for the SMC design for second-order systems. However, the SMC design becomes extremely complex if the system order increases. Therefore, the first part of this thesis focuses on developing arbitrary-order SMC strategies with a relatively simpler design while providing finite-time convergence. Novel methods are developed with both continuous and discontinuous control structures. The second part of this thesis focuses on developing algorithms to provide even faster convergence speed than that of finite-time convergent algorithms. Some practical applications need strict constraints on time response due to security reasons or to ameliorate the productiveness. For example, a missile or any aerial launch vehicle can be hugely affected by a strong wind gust deviating it from the desired trajectory, thus yielding a significant degree of initial tracking error. It is worth mentioning that the state convergence achieved in SMC during sliding can be either asymptotic or in finite-time, depending on the selection of the surface. Furthermore, it primarily depends on the initial conditions of the states. This provides a motivation to focus on developing SMC controllers where the convergence time does not depend on initial conditions, and a well-defined theoretical analysis is provided in the thesis regarding arbitrary-order fixed-time convergent SMC design. Subsequently, a predefined-time convergent second-order differentiator and observer are proposed. The main advantage of the proposed differentiator is to calculate the derivative of a given signal in fixed-time while the least upper bound of the fixed stabilisation time is equal to a tunable parameter. Similarly, the proposed predefined-time observer is robust with respect to bounded uncertainties and can also be used to estimate the uncertainties. The final part of the thesis is focused on the applications of the proposed algorithms. First of all, a novel third-order SMC is designed for a piezoelectric-driven motion systems achieving better accuracy and control performance. Later on, an experimental validation of the proposed controller is conducted on an induction motor setup. Later, a fixed-time convergent algorithm is proposed for an automatic generation control (AGC) of a multi-area interconnected power system while considering the non-linearities in the dynamic system. The final part is focused on developing fixed-time convergent algorithms in a co-operative environment. The reason for selecting such a system is the presence of the highest degree of uncertainties. To this end, a novel distributed algorithm is developed for achieving second-order consensus in the multiagent systems by designing a full-order fixed-time convergent sliding surface

Robust exact differentiators with predefined convergence time

The problem of exactly differentiating a signal with bounded second derivative is considered. A class of differentiators is proposed, which converge to the derivative of such a signal within a fixed, i.e., a finite and uniformly bounded convergence time. A tuning procedure is derived that allows to assign an arbitrary, predefined upper bound for this convergence time. It is furthermore shown that this bound can be made arbitrarily tight by appropriate tuning. The usefulness of the procedure is demonstrated by applying it to the well-known uniform robust exact differentiator, which the considered class of differentiators includes as a special case

A Robust Consensus Algorithm for Current Sharing and Voltage Regulation in DC Microgrids

In this paper a novel distributed control algorithm for current sharing and voltage regulation in Direct Current (DC) microgrids is proposed. The DC microgrid is composed of several Distributed Generation units (DGUs), including Buck converters and current loads. The considered model permits an arbitrary network topology and is affected by unknown load demand and modelling uncertainties. The proposed control strategy exploits a communication network to achieve proportional current sharing using a consensus-like algorithm. Voltage regulation is achieved by constraining the system to a suitable manifold. Two robust control strategies of Sliding Mode (SM) type are developed to reach the desired manifold in a finite time. The proposed control scheme is formally analyzed, proving the achievement of proportional current sharing, while guaranteeing that the weighted average voltage of the microgrid is identical to the weighted average of the voltage references.Comment: 12 page

Technical report on Optimization-Based Bearing-Only Visual Homing with Applications to a 2-D Unicycle Model

We consider the problem of bearing-based visual homing: Given a mobile robot which can measure bearing directions with respect to known landmarks, the goal is to guide the robot toward a desired "home" location. We propose a control law based on the gradient field of a Lyapunov function, and give sufficient conditions for global convergence. We show that the well-known Average Landmark Vector method (for which no convergence proof was known) can be obtained as a particular case of our framework. We then derive a sliding mode control law for a unicycle model which follows this gradient field. Both controllers do not depend on range information. Finally, we also show how our framework can be used to characterize the sensitivity of a home location with respect to noise in the specified bearings. This is an extended version of the conference paper [1].Comment: This is an extender version of R. Tron and K. Daniilidis, "An optimization approach to bearing-only visual homing with applications to a 2-D unicycle model," in IEEE International Conference on Robotics and Automation, 2014, containing additional proof