Design of PID controllers using Filippov's method for stable operation of DC–DC converters

A lot of work has taken place into the design and control of DC–DC converters, and various methodologies have been proposed. While traditionally only P or PI controllers have been employed, recent applications that require a fast transient performance impose the usage of the derivative, D, term. As it is well known, using the D‐term can cause numerous problems in such converters that greatly downgrade their performance and lifetime. Having said that, in this paper, we first prove that by using the D‐term, it is possible to increase the stability margin (and hence keep a low current ripple), and then, we present a novel method to tune the PID controller that guarantees a fast and stable response over a wide range of parameter values without using an unreasonably high value of the derivative gain that magnifies the presence of noise in the system. The controller is designed utilising Filippov's method, and a simple and easy to implement strategy is proposed. Furthermore, an adaptive PID controller is designed whose gains are changed depending on the value of the supply voltage or output load. Another important contribution of this work is the derivation of the saltation matrix when the switching manifold is discontinuous, the complete proof is presented, and the results validated. Copyright © 2015 John Wiley & Sons, Ltd.     

Characterization of age-related variation in corneal biomechanical properties

An experimental study has been conducted to determine the stress–strain behaviour of human corneal tissue and how the behaviour varies with age. Fifty-seven well-preserved ex vivo donor corneas aged between 30 and 99 years were subjected to cycles of posterior pressure up to 60 mm Hg while monitoring their behaviour. The corneas were mechanically clamped along their ring of scleral tissue and kept in physiological conditions of temperature and hydration. The tissue demonstrated hyper-elastic pressure-deformation and stress–strain behaviour that closely matched an exponential trend. Clear stiffening (increased resistance to deformation) with age was observed in all loading cycles, and the rate of stiffness growth was nonlinear with bias towards older specimens. With a strong statistical association between stiffness and age (p < 0.05), it was possible to develop generic stress–strain equations that were suitable for all ages between 30 and 99 years. These equations, which closely matched the experimental results, depicted corneal stiffening with age in a form suitable for implementation in numerical simulations of ocular biomechanical behaviour.