Optimal second order sliding mode control for nonlinear uncertain systems

In this paper, a chattering free optimal second order sliding mode control (OSOSMC) method is proposed to stabilize nonlinear systems affected by uncertainties. The nonlinear optimal control strategy is based on the control Lyapunov function (CLF). For ensuring robustness of the optimal controller in the presence of parametric uncertainty and external disturbances, a sliding mode control scheme is realized by combining an integral and a terminal sliding surface. The resulting second order sliding mode can effectively reduce chattering in the control input. Simulation results confirm the supremacy of the proposed optimal second order sliding mode control over some existing sliding mode controllers in controlling nonlinear systems affected by uncertainty.     

Recent trends on the development of photobiological processes and photobioreactors for the improvement of hydrogen production

Hydrogen production through biological routes is promising because they are environmentally friendly. Hydrogen production through biophotolysis or photofermentation is usually a two stage process. In the first stage CO₂ is utilized for biomass production which is followed by hydrogen production in the second stage in anaerobic/sulfur-deprived conditions. In addition, one-stage photobiological hydrogen production process can be achieved using selected cyanobacterial strains. The major challenges confronting the large scale production of biomass/hydrogen are limited not only on the performance of the photobioreactors in which light penetration in dense cultures is a major bottleneck but also on the characteristics of the organisms. Other dependable factors include area/volume (A/V) ratio, mode of agitation, temperature and gas exchange. Photobioreactors of different geometries are reported for biohydrogen production: Tubular, Flat plate, Fermentor type etc. Every reactor has its own advantages and disadvantages. Airlift, helical tubular and flat plate reactors are found most suitable with respect to biomass production. These bioreactors may be employed for hydrogen production with necessary modifications to overcome the existing bottlenecks like gas hold up, oxygen toxicity and poor agitation. This review article attempts to focus on existing photobioreactors with respect to biomass generation and hydrogen production and the steps taken to improve its performance through engineering innovation that definitely help in the future design and construction of photobioreactors.     

Designing lenses to correct peripheral refractive errors of the eye.

The purpose of this work was to design ophthalmic lenses that correct peripheral refractive errors of human eyes along a meridian. We designed lenses with the tangential section of one surface based on a figured spheroid but figured in the tangential section only. The curvature of the sagittal section of this surface was adjusted separately. A merit function was used to modify these surfaces until the lenses had power errors that corrected the eye. Examples are presented of lenses that correct a schematic eye. They do excellent jobs of correcting the peripheral power errors of the eye and are relatively insensitive to small changes in fitting distance. We conclude that it is theoretically feasible to design lenses to correct peripheral refractive errors.     

A fast converging robust controller using adaptive second order sliding mode

This paper proposes an adaptive second order sliding mode (SOSM) controller with a nonlinear sliding surface. The nonlinear sliding surface consists of a gain matrix having a variable damping ratio. Initially the sliding surface uses a low value of damping ratio to get a quick system response. As the closed loop system approaches the desired reference, the value of the damping ratio gets increased with an aim to reducing the overshoot and the settling time. The time derivative of the control signal is used to design the controller. The actual control input obtained by integrating the derivative control signal is smooth and chattering free. The adaptive tuning law used by the proposed controller eliminates the need of prior knowledge about the upper bound of system uncertainties. Simulation results demonstrate the effectiveness of the proposed control strategy.     

Lau effect and beam collimation

Abstract

We report a new phenomenon in showing that the rotation sensitivity of Lau fringes depends not only on spatial coherence of the illumination used but also on its convergence or divergence. This finding could be usefully applied to beam collimation and focal length measurement.     

Integral backstepping sliding mode control for underactuated systems: Swing-up and stabilization of the Cart–Pendulum System

In this paper an integral backstepping sliding mode controller is proposed for controlling underactuated systems. A feedback control law is designed based on backstepping algorithm and a sliding surface is introduced in the final stage of the algorithm. The backstepping algorithm makes the controller immune to matched and mismatched uncertainties and the sliding mode control provides robustness. The proposed controller ensures asymptotic stability. The effectiveness of the proposed controller is compared against a coupled sliding mode controller for swing-up and stabilization of the Cart–Pendulum System. Simulation results show that the proposed integral backstepping sliding mode controller is able to reject both matched and mismatched uncertainties with a chattering free control law, while utilizing less control effort than the sliding mode controller.     

Actuator fault‐tolerant control (FTC) design with post‐fault transient improvement for application to aircraft control

A robust fault‐tolerant control scheme is proposed for uncertain nonlinear systems with zero dynamics, affected by actuator faults and lock‐in‐place and float failures. The proposed controller utilizes an adaptive second‐order sliding mode strategy integrated with the backstepping procedure, retaining the benefits of both the methodologies. A Lyapunov stability analysis has been conducted, which unfolds the advantages offered by the proposed methodology in the presence of inherent modeling errors and strong eventualities of faults and failures. Two modified adaptive laws have been formulated, to approximate the bounds of uncertainties due to modeling and to estimate the fault‐induced parametric uncertainties. The proposed scheme ensures robustness towards linearly parameterized mismatched uncertainties, in addition to parametric and nonparametric matched perturbations. The proposed controller has been shown to yield an improved post‐fault transient performance without any additional expense in the control energy spent. The proposed scheme is applied to the pitch control problem of a nonlinear longitudinal model of Boeing 747‐100/200 aircraft. Simulation results support theoretical propositions and confirm that the proposed controller produces superior post‐fault transient performance compared with already existing approaches designed for similar applications. Besides, the asymptotic stability of the overall controlled system is also established in the event of such faults and failures. Copyright © 2015 John Wiley & Sons, Ltd.