G. Bartolini

A combined backstepping/second order sliding mode approach to control a class of nonlinear systems

A combined adaptive/variable structure control approach is presented in this note, which exploits the good properties of the backstepping procedure, on one side, and of a second order sliding mode control algorithm, on the other. It retains the stability and convergence features of the original adaptive strategy, allowing, in addition, the presence of nonparametric uncertainties in the last two equations of the system, as well as ensuring robustness and a reduction of the computational load.

Load swing damping in overhead cranes by sliding mode technique

Moving a suspended load is not an easy task when strict specifications on the swing angle and on the transfer time need to be satisfied. Nevertheless, these type of requirements are always present in industry because they are related to operation safety and cost. Intuitively, minimizing the cycle time and the load swing are conflicting requirements, and their satisfaction requires proper control actions, especially if some uncertainties in the system dynamics are present. In this paper we propose a simple control scheme based on second order sliding modes which is proved to be effective also in the case of poor knowledge of the system dynamics and/or parameters. Such controller has been tested on a laboratory-size model of an overhead crane by means of commercial devices, and some experimental results are reported within the paper.

Mediterranean warming is especially due to summer season

We created a new homogenized daily minimum and maximum temperature data set (1955–2007) for the central Mediterranean area of Tuscany (Italy). Yearly and seasonal long-term trends of some climatic and extreme climatic indices were investigated. The results highlighted a positive trend for mean temperature of about 0.9°C per 50xa0years with a slightly more pronounced increase in maximum temperature. Seasonal analysis revealed a by far much greater increase in summer (June, July, August) and spring (March, April, May) temperature in respect of autumn and winter, this finding consistent with most recent Mediterranean evidences. Warm extremes showed an overall tendency to increase, while a slight not significant decrease trend was found in regard to frost days and cold extremes. Comparisons with different patterns of Mediterranean warming confirmed the magnitude of recent very fast rise in temperature, especially during summer. This change could be due to last decades modifications of general circulation patterns and land–temperature, land–precipitation positive feedback processes dependent from soil moisture. All these results confirm that the Mediterranean is a region especially responsive and thus very vulnerable to climate change.

Sliding mode output-feedback stabilization of uncertain nonlinear nonaffine systems

The paper considers the variable-structure output-feedback stabilization of nonlinear uncertain nonaffine systems when the state vector is not completely available and the use of observers is required. The strategy of introducing integrators in the input channel is exploited to enlarge the class of tractable control systems. A full-order observer is designed and the control problem is solved by forcing a sliding regime for the observer. Depending on the type of uncertainties, conditions are found under which convergence to the unique ideal solution of both the system and the observer, either exponentially or with a bounded error, is proven.

A backstepping second order variable structure control design for a class of uncertain nonlinear systems

The problem of the stabilization of uncertain nonlinear systems expressible in the perturbed-chain-of-integrators form is considered. Under suitable assumptions, the control problem is solved via a combined backstepping/variable structure control strategy which retains n-1 steps of a backstepping like procedure, and associates with them a final step aimed at generating a second order sliding regime on a suitably selected sliding manifold.

Second order VSC for non linear systems subjected to a wide class of uncertainty conditions

The problem of the control of a class of second order SISO systems with incompletely available state and uncertain bounded dynamics is addressed. For this class of systems an output-feedback VSC has been presented and a sufficient condition for its finite time convergence has been proved. The effectiveness of this control strategy is shown for different control problems such as model reference control and chattering elimination in VSC.

Recent trends in seasonal and annual precipitation indices in Tuscany (Italy)

Global warming alters the hydrological cycle since a rise in temperature leads to an increase in the moisture-holding capacity of the atmosphere at a rate of about 7xa0%/°C. This fact can influence the global, but also local characteristics of precipitation, such as total amount and intensity. Therefore, it is important to study changes in rainfall regime in regions with complex orography, like Tuscany, where there are strong spatial gradients in precipitation amounts. The aim of this study is to look for temporal change in precipitation from 1955 to 2007 searching for spatial differences. Daily data of 21 meteorological stations were analyzed to identify trends in seasonal and annual precipitation indices. Cluster analysis applied to principal components was applied to identify homogeneous groups of stations. A decrease in precipitation was observed at annual time scale, during winter and spring, especially in northwestern areas. Wet days highlighted a decrease in all of Tuscany, due to the same seasons. In northern Tuscany, the decrease in rainfall amount was mainly determined by a lower frequency of rainy events which in turn caused a decrease in the occurrence of extreme daily precipitation events (75th, 90th, and 95th percentile). In central-southern Tuscany, no significant changes were observed except for an increase in precipitation fraction, due to extreme events and in mean daily total amount for wet days. These results are consistent with recent findings for the Mediterranean area and confirm the usefulness of cluster analysis for the analysis of the spatial distribution of precipitation.

Nested backward compensation of unmatched perturbations via HOSM observation

Abstract This paper tackles the compensation problem of linear time invariant systems affected by unmatched perturbations. The proposed methodology exploits a high order sliding mode observer, guaranteeing theoretically exact state and perturbation estimation. A compensation based strategy is proposed to cope with the unmatched perturbations. The compensation of the desired coordinate is carried through a nested backward sliding surface design, which compensates some of the non-actuated state components, while the remaining states are maintained to be bounded. The feasibility of the technique was tested in an active suspension vehicle system. 1

Global tracking control for a class of nonlinear uncertain systems

In this paper the exponential tracking problem for a class of single-input nonlinear uncertain systems expressed in canonical Brunowsky form, with nonaffine dependence on the control, is addressed and solved by a second-order sliding-mode control methodology. The presence of unmodelled first-order actuators is considered in the design procedure, and the proposed controller provides for a global domain of attraction and counteracts the typical transient peaking of the state trajectory. Computer simulations confirm the feasibility of the proposed approach.

On multi-input second order sliding mode control of nonlinear systems with uncertainty

Some works presented in the literature have shown the effectiveness of second order sliding modes (i.e. a sliding regime on a set s(x(t))=s/spl dot/(x(t))=0 enforced by a control signal directly acting on s/spl uml/(t)) in controlling uncertain systems. Such an approach, in its native formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In this paper the validity of a second order sliding mode control algorithm, previously presented by the authors (1997, 1999), is extended to some classes of multi-input nonlinear uncertain systems, covering a wide class of real processes. The chattering avoidance feature of the proposed second order sliding mode control scheme is presented as an example for a class of multi-input systems.