Piecewise

About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.

Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation

Abstract: In this note, the problem of observer design for linear descriptor systems with faults and unknown inputs is considered. First, it is considered that the fault vector function f is s~ times piecewise continuously differentiable. If the s~th time derivative of f is null, then s~ integral actions are included into a Luenberger observer, which is designed such that it estimates simultaneously the state, the fault, and its finite derivatives face to unknown inputs. Second, when the fault is not time piecewise continuously differentiable but bounded (like actuator noise) or s~th time derivative of fault is not null but bounded too, a high gain observer is derived to attenuate the fault impact in estimation errors. The considered faults may be unbounded, may not be determinist, and faults and unknown inputs may affect the state dynamic and plant outputs. Sufficient conditions for the existence of such observer are given. Results are illustrated with a differential algebraic power system.

Border collision bifurcations in two-dimensional piecewise smooth maps

Abstract: Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps that cannot be classified among the generic cases like saddle-node, pitchfork, or Hopf bifurcations occurring in smooth maps. In this paper we first present experimental results to establish the need for the development of a theoretical framework and classification of the bifurcations resulting from border collision. We then present a systematic analysis of such bifurcations by deriving a normal form - the piecewise linear approximation in the neighborhood of the border. We show that there can be eleven qualitatively different types of border collision bifurcations depending on the parameters of the normal form, and these are classified under six cases. We present a partitioning of the parameter space of the normal form showing the regions where different types of bifurcations occur. This theoretical framework will help in explaining bifurcations in all systems, which can be represented by two-dimensional piecewise smooth maps.

Adaptive Control of Hydraulic Actuators With LuGre Model-Based Friction Compensation

Abstract: This paper concerns high-accuracy tracking control for hydraulic actuators with nonlinear friction compensation Typically, LuGre model-based friction compensation has been widely employed in sundry industrial servomechanisms However, due to the piecewise continuous property, it is difficult to be integrated with backstepping design, which needs the time derivation of the employed friction model Hence, nonlinear model-based hydraulic control rarely sets foot in friction compensation with nondifferentiable friction models, such as LuGre model, Stribeck effects, although they can give excellent friction description and prediction In this paper, a novel continuously differentiable nonlinear friction model is first derived by modifying the traditional piecewise continuous LuGre model, then an adaptive backstepping controller is proposed for precise tracking control of hydraulic systems to handle parametric uncertainties along with nonlinear friction compensation In the formulated nonlinear hydraulic system model, friction parameters, servovalve null shift, and orifice-type internal leakage are all uniformly considered in the proposed controller The controller theoretically guarantees asymptotic tracking performance in the presence of parametric uncertainties, and the robustness against unconsidered dynamics, as well as external disturbances, is also ensured via Lyapunov analysis The effectiveness of the proposed controller is demonstrated via comparative experimental results

A multiplicative model for efficiency analysis

Abstract: This paper develops theory and algorithms for a “multiplicative” Data Envelopment Analysis (DEA) model employing virtual outputs and inputs as does the CCR ratio method for efficiency analysis. The frontier production function results here are of piecewise log-linear rather than piecewise linear form.