Robust Positively Invariant Cylinders in Constrained Variable Structure Control

This paper proposes the use of cylinders as primary invariant sets to be used in certain state-constrained control designs. Following the idea originally introduced by O\u27Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions. Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding-mode control (SMC) using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A numerical example for a third-order plant illustrates the method

Modeling Nonlinear Behavior in a Piezoelectric Actuator

A piezoelectric tube actuator is employed as a sample positioning device in Nanocut, a cutting instrument conceived to study the mechanics of nanometric cutting. Extension of functionality of the instrument as a nanometric machine tool motivates the search for an accurate model of the actuator for implementing feedback control. A simple nonlinear model describing longitudinal expansion of the piezoelectric tube actuator is presented in this paper. The model derivation is based on a non-formal analogy with nonlinear viscoelastic materials under uniaxial extension, for which the responses to a step input are similar to the piezoelectric tube. Suitability of the model structure for arbitrary inputs is tested by cross-verification between time and frequency domains. Two parameter estimation procedures are examined and the results of the experimental work for characterization, estimation and validation are presented

Robust Positively Invariant Cylinders in Constrained Variable Structure Control

This paper proposes the use of cylinders as primary invariant sets to be used in certain state-constrained control designs. Following the idea originally introduced by O\u27Dell, the primary invariant set is intersected with the state constraints to yield sets which retain the invariance under some conditions. Although several results presented here apply to fairly general nonlinear systems and primary invariant sets of any shape, the focus is on constrained sliding-mode control (SMC) using infinite cylinders as the primary invariant set. Their use is motivated by a coordinate transformation where the sliding motion is decoupled from the overall convergence to the origin. Robust positive invariance conditions are given for cylinders having convex and compact cross sections. For the case of cylinders with ellipsoidal cross sections, the invariance condition is given in the form of a linear matrix inequality. Further, a decision procedure to qualify each state constraint is given as a tool for the selection of the switching gain. A numerical example for a third-order plant illustrates the method

Delphi consensus on bile duct injuries during laparoscopic cholecystectomy:An evolutionary cul-de-sac or the birth pangs of a new technical framework?

Bile duct injury (BDI) during laparoscopic cholecystectomy remains a serious iatrogenic surgical complication. BDI most often occurs as a result of misidentification of the anatomy; however, clinical evidence on its precise mechanism and surgeons' perceptions is scarce. Surgeons from Japan, Korea, Taiwan, and the USA, etc. (n=614) participated in a questionnaire regarding their BDI experience and near-misses; and perceptions on landmarks, intraoperative findings, and surgical techniques. Respondents voted for a Delphi process and graded each item on a five-point scale. The consensus was built when 80% of overall responses were 4 or 5. Response rates for the first- and second-round Delphi were 60.6% and 74.9%, respectively. Misidentification of local anatomy accounted for 76.2% of BDI. Final consensus was reached on: (1) Effective retraction of the gallbladder, (2) Always obtaining critical view of safety, and (3) Avoiding excessive use of electrocautery/clipping as vital procedures; and (4) Calot's triangle area and (5) Critical view of safety as important landmarks. For (6) Impacted gallstone and (7) Severe fibrosis/scarring in Calot's triangle, bail-out procedures may be indicated. A consensus was reached among expert surgeons on relevant landmarks and intraoperative findings and appropriate surgical techniques to avoid BD

Boundary Layer Eigenvalues in SISO Discrete-Time Sliding Mode Control with Observer

A result that allows us to specify the sliding manifold in observer based discrete-time sliding mode control is presented. Selection of coefficients is done by analyzing the tracking error dynamics inside the boundary layer, where the closed-loop system has a linear state feedback configuration, rather than assuming that ideal sliding occurs. The result facilitates assignment of eigenvalues for the system matrix which defines such linear dynamics

ACL-98-005 Comparison of the Sliding Observer to Several State Estimators Using a Rotational Inverted Pendulum

Because of the inherent characteristics of nonlinear systems, state estimation of these systems continues to pose difficult problems. The objective of this paper is to test the Sliding Mode Observer techniqe on a highly nonlinear non-minimum phase system. The chosen system is the rotaional inverted pendulum system of Misawa, Arrington, and Ledgerwood [7]. In addition, the observer technique is compared to that of other techniques: the Linear Kalman Filter, Thau's Method, the Adaptive Observer, the High Gain Observer, the Multistage Nonlinear Observer, and the Equivalent Control-Based Sliding Mode Observer. The bases of comparison is performance, robustness against disturbances and modeling errors, stability, and ease of application. 1 Introduction Due to its complex behavior, the test system was chosen to be the rotaional inverted pendulum (RIP) developed by Misawa et. al. [7] The RIP is a fourth order nonlinear coupled system. It consists of a control link and a pendulum link connect..

Discrete Variable Structure Control for Linear Multivariable Systems: The State Feedback Case

This paper presents a state feedback discrete variable structure controller for linear multivariable systems with unmatched additive uncertainties, a generalization of the controller for single-input systems by Misawa (1997). It is shown that the controller guarantees the attractiveness and invariance of the boundary layer. In contrast to existing schemes, it utilizes one sliding hyperplane regardless of the number of inputs. This attribute enhances the design freedoms of tracking error dynamics inside the boundary layer while preserving robustness. It allows the use of well-established linear control design strategies under an eigenvalue constraint. A numerical example is used to illustrate the proposed technique