Discontinuous State Research Articles

Asymptotic stabilization with locally semiconcave control Lyapunov functions on general manifolds

Asymptotic stabilization on noncontractible manifolds is a difficult control problem. If a configuration space is not a contractible manifold, we need to design a time-varying or discontinuous state feedback control for asymptotic stabilization at the desired equilibrium.For a system defined on Euclidean space, a discontinuous state feedback controller was proposed by Rifford with a semiconcave strict control Lyapunov function (CLF). However, it is difficult to apply Rifford’s controller to stabilization on general manifolds.In this paper, we restrict the assumption of semiconcavity of the CLF to the “local” one, and introduce the disassembled differential of locally semiconcave functions as a generalized derivative of nonsmooth functions. Further, we propose a Rifford–Sontag-type discontinuous static state feedback controller for asymptotic stabilization with the disassembled differential of the locally semiconcave practical CLF (LS-PCLF) by means of sample stability. The controller does not need to calculate limiting subderivative of the LS-PCLF.Moreover, we show that the LS-PCLF, obtained by the minimum projection method, has a special advantage with which one can easily design a controller in the case of the minimum projection method. Finally, we confirm the effectiveness of the proposed method through an example.

Study on the Solidified Microstructures of AZ61 Magnesium Alloys under Electromagnetic Fields

The solidified microstructures of AZ61 magnesium alloy under different electromagnetic fields were investigated. Optical microstructure revealed that the solidified microstructure of AZ61 under single static magnetic field and combination of static magnetic field and alternating current (AC) consisted of basically equiaxed grains; when the alloy solidified under static magnetic field and direct current (DC), dendrite in solidified microstructure increases with certain orientation. The constituent phase at grain boundary consists of mainly magnesium matrix and continuous cellular compound under the static field, and the one consists of mainly magnesium matrix, cellular and spotted Mg-Al-Zn intermetallic compound under the action of static magnetic field and combination of static magnetic field and alternating current, the continuous cellular structure disappears thoroughly under static magnetic field and DC, compound in magnesium matrix distributes in discontinuous lamellar state.

In Vivo Identification of Skeletal Muscle Dynamics with Nonlinear Kalman Filter: Comparison between EKF and SPKF

Skeletal muscle system has nonlinear dynamics and subject-specific characteristics. Thus, it is essential to identify the unknown parameters from noisy biomedical signals to improve the modeling accuracy in neuroprosthetic control. The objective of this work is to develop an experimental identification method for subject-specific biomechanical parameters of a physiological muscle model which can be employed to predict the nonlinear force properties of stimulated muscle. Our previously proposed muscle model, which can describe multiscale physiological system based on the Hill and Huxley models, was used for the identification. The identification protocols were performed on two rabbit experiments, where the medial gastrocnemius was attached to a motorized lever system to record the force by the nerve stimulation. The muscle model was identified using nonlinear Kalman filters: sigma-point and extended Kalman filter. The identified model was evaluated by comparison with experimental measurements in the cross-validation manner. The feasibility could be demonstrated by comparison between the estimated parameter and the measured value. The estimates with SPKF showed 5.7% and 2.9% error in each experiment with 7 different initial conditions. It reveals that SPKF has great advantage especially for the identification of multiscale muscle model which accounts for the high nonlinearity and discontinuous states between muscle contraction and relaxation process.

The solids concentration distribution in the deep cone thickener: A pilot scale test

Cemented backfill or surface deposition of paste tailings is increasingly being considered as a simple and effective means of reducing the hazards of conventional slurry deposition and recovering water for recycle. Although gravity thickening has been widely used in the mineral industry to increase the solids concentration of tailings, the accurate prediction of the concentration distribution in three-dimensions and discontinuous operational state has proven to be difficult. We investigated the axial and radial solids concentration distribution at discontinuous state in a pilot deep cone thickener as a function of bed height and residence time. The feed flux of lead/zinc tailings was 0.254 t·h−1· m−2 with a flocculant (high molecular weight anionic polyacrylamide) dose of 20 g/t. The thickened solids bed was sheared by a rotating rake at a rate of 0.2 rpm. The underflow was recirculated at a flux of 0.5 t·h−1·m−2, which can introduce additional shear stresses into the bed. The results of the bed density profile showed that, beside the clarification zone, the area below the feedwell could be divided into four zones: the dilution zone caused by free settling and diffusing action, the hindered settling zone in which the concentration was lower than the gel point, the unraked bed zone with a large concentration gradient and, finally, the raking zone with the highest slurry concentration and lower concentration gradient.

A Wire Feed Control System Based on Detecting Induced Electromotive Force of the Motor

A stable and even wire feed speed is a guarantee of good quality welding. A new wire feed system, without any speed-measuring equipment, has been designed. And the motor current of this system works in a discontinuous state. When the motor current is zero, it detects the induced electromotive force; acquires the motor speed according to the relationship between the induced electromotive force and the motor speed; calculates and compares with the given speed then changes the duty cycle of the voltage added on the motor by PWM technology, that control the motor speed. Then a stable and even wire feed speed can be achieved. Verified by testing resistance, the change rate of the wire feed speed is slightly, which proves that the new system has good mechanical properties and a stable speed. Besides, it runs reliably.

Jorge Amado: Exile and Literature

Because exile, unlike nationalism, is fundamentally a discontinuous state of being. Exiles are cut off from their roots, their land, their past. They generally do not have armies or states, although they are often in search of them. Exiles feel, therefore, an urgent need to reconstitute their broken lives, usually by choosing to see themselves as part of a triumphant ideology or a restored people.

Schrödinger current for discontinuous states from the first-passage-time decomposition

We revisit the problem of calculating the probability current for discontinuous states, such as those that may arise in atom trapping or as a result of projective measurements. In the first-passage-time representation, the problem reduces to an evaluation of a localized wave originating from the discontinuity, whose interference with the initial state determines the transfer of probability. Depending on the type of discontinuity, the current behaves as ${t}^{1/2}$, ${t}^{3/2}$, or $\text{const}(t)$. Our approach generalizes earlier work on this subject.

Study on Probability Prediction Approach to Holistic Life Based on Fracture Theory

Fatigue life can be divided into crack initiation life and crack propagation life in fatigue damage process. Fatigue crack comes of the initial discontinuity states （IDS） of material, and goes through short crack , long crack and rupture failure. A estimation model based on fracture theory is built, in which includes of IDS, short crack, long crack and rupture failure. A fatigue holistic life (including fatigue life, the residual life and the calendar life ) estimation model was built on the basis of IDS in which the aircraft structures had not been corrosion damage. A lot of fatigue tests with different stress level and different stress ratio are carried out to validate the model. The results demonstrate that the approach is reasonable and feasible.

Investigation of the near-grazing behavior in hard-impact oscillators using model-based TS fuzzy approach

An impact oscillator is a non-smooth dy- namical system with discontinuous state jumps whose dynamical behavior illustrates a variety of non-linear phenomena including a grazing bifurcation. This spe- cific phenomenon is difficult to analyze because it co- incides with an infinite stretching of the phase space in the neighborhood of the grazing orbit, resulting in the well-known problem of the square-root singular- ity of the Jacobian of the discrete-time map. A novel Takagi-Sugeno fuzzy model-based approach is pre- sented in this paper to model a hard impacting system as a non-smooth dynamical system including discon- tinuous jumps. Employing non-smooth Lyapunov the- ory, the structural stability of the system is analyzed to predict the onset of the destabilizing chaotic be- havior. The proposed stability results, formulated as a Linear Matrix Inequality (LMI) problem, demonstrate how the new method can detect the loss of stability just before the grazing bifurcation.

Stability analysis of interconnected event-based control loops

In event-based control the feedback link within a control loop is only closed when an event indicates the need for information exchange among the sensors, controller and actuators to maintain a required loop performance. The event-based control loop is a hybrid dynamical system, which is characterized by a sequence of continuous state flows and discontinuous state jumps at the event times. This paper analyzes the stability of interconnected decentralized event-based control loops where events are triggered asynchronously. A stability criterion is derived using the comparison principle. It is shown that conditions that are sufficient to prove the stability of the continuous control system imply ultimate boundedness of the event-based state-feedback loop. The conservatism of the proposed stability test is evaluated for a thermofluid process.

The Effects of Exfoliation Corrosion on Upper Wing Skins Structural Integrity

Based on initial discontinuity state (IDS) of material, this paper presents a preliminary analytical model which was developed to evaluate the effect of exfoliation corrosion on the residual fatigue life of upper wing skins. A life prediction was then carried out using constant amplitude compression dominated loading for various exfoliation corrosion levels by AFGROW, and the prediction agreed reasonably with the available test data. The result suggest that exfoliation can be treated as a process zone located initially at a surface, and then at the base of an evolving general stress concentration representing the loss of material in the exfoliation region. The major effect of the exfoliation corrosion on fatigue life is to cause a dramatic reduction in life with small corrosion depths, and most of the fatigue effect is associated with the introduction of small pits, rather than more general stress concentration associated with the bulk of the exfoliation attack. But the effect of pit on fatigue life is gradually reduced with increasing pit size. A pit with a constant depth can be applied to the model described in this paper for long exposure structure. A preliminary recommendation for the pit depth is about 0.3mm for LY12CZ.

Automatic generation of equations of motion for multibody system in discrete event simulation framework

In this paper, the development of a simulation program that can automatically generate equations of motion for mutibody systems in the discrete event simulation framework is presented. The need to analyze the dynamic response of mechanical systems that are under event triggered conditions is increasing. General mechanical systems can be defined as multibody systems that are collections of interconnected rigid bodies, consistent with various types of joints that limit the relative motion of pairs of bodies. For complex multibody systems, a systematic approach is required to efficiently set up the mathematical models. Therefore, a dynamics kernel was developed to automatically generate the equations of motion for multibody systems based on multibody dynamics. The developed dynamics kernel also provides the numerical solver for the dynamic analysis of multibody systems. The general multibody dynamics kernel cannot deal with discontinuous state variables, event triggered conditions, and state triggered conditions, though. To enable it to deal with multibody systems in discontinuous environments, the multibody dynamics kernel was integrated into a discrete event simulation framework, which was developed based on the discrete event system specification (DEVS) formalism. DEVS formalism is a modular and hierarchical formalism for modeling and analyzing systems under event triggered conditions, which are described by discontinuous state variables. To verify the developed program, it was applied to an block-lifting and transport simulation, and dynamic analysis of the system is carried out.

Hybrid automata: an insight into the discrete abstraction of discontinuous systems

We develop a novel computational–dynamical framework for the modelling of a class of discontinuous dynamical systems (DDSs). In particular, what is referred to as the DDS hybrid automaton with inputs and outputs is proposed. This is a general hybrid automaton that provides a suitable mathematical model for DDSs with discontinuous state derivatives and sliding motions. The chief characteristic of this model is that, following the computational divide-and-conquer principle, a system with multiple discontinuous elements can be represented by the composition of several DDS hybrid automata. Although discontinuous, non-smooth or switched dynamical systems have been well-investigated within different frameworks, it is still a challenge to give satisfactory solutions for specifying the transitions between the different modes of operation of these systems. We propose a new way of solving this problem, which is especially effective for systems with multiple switching elements. An example is used to illustrate these ideas. Several simulations are presented. The simulations results are obtained with Stateflow® and Modelica®.

Study on the Initial Discontinuity State Distribution of LY12CZ Aluminum Alloy

The initial discontinuity state (IDS) concept was developed just several years ago in an attempt to describe the as-manufactured or as-produced state of material. As a geometric and material characteristic, IDS is the major parameter of holistic life assessment methodology which establishes the initial analysis condition. In this paper, a number of IDS values were determined for several types of smooth specimens. A crack growth analysis software was used to develop the IDS. The results obtained indicate that the calculated IDS values scatter widely. A statistical analysis shows that the distribution of the calculated IDS values fit well with Weibull distribution.

不連続な状態遷移を考慮した学習最適制御による歩行軌道の生成手法

This paper is concerned with a gait generation framework for legged robots based on iterative learning control (ILC) of Hamiltonian systems. This method allows one to obtain solutions to a class of optimal control problems by iteration of laboratory experiments and, furthermore, precise knowledge of the plant model is not required for it by taking advantage of a symmetric property of Hamiltonian systems. Generally in walking motion, there are discontinuous state transitions caused by collision between the foot and the ground. The proposed framework can also deal with such state transitions without using the parameters of the transition model by combining ILC method and the least-squares. It is applied to a compass-like biped robot to generate optimal gait on the level ground. Some numerical examples demonstrate the effectiveness of the proposed method.

Special relativistic effects revealed in the Riemann problem for three-dimensional relativistic Euler equations

We consider the Riemann problem of three-dimensional relativistic Euler equations with two discontinuous initial states separated by a planar hypersurface. Based on the detailed analysis on the Riemann solutions, special relativistic effects are revealed, which are the variations of limiting relative normal velocities and intermediate states and thus the smooth transition of wave patterns when the tangential velocities in the initial states are suitably varied. While in the corresponding non-relativistic fluid, these special relativistic effects will not occur.

In Memoriam: James K. Knowles 1931–2009

In Memoriam: James K. Knowles 1931–2009

Decentralised energy-based hybrid control for the multi-RTAC system

The concept of decentralised energy-based hybrid control involves hybrid dynamic subcontrollers with discontinuous states that individually control each subsystem of a large interconnected dynamical system. Specifically, each subcontroller accumulates the emulated energy and when the states of the subcontroller coincide with a high emulated energy level, then we can reset these states to remove the emulated energy so that the emulated energy is not returned to the subsystem. The real physical energy of each subsystem in this case is constantly dissipated through the motion of the actuators due to the subcontroller state resettings. In this article, we experimentally implement the decentralised energy-based hybrid control framework on the multi-rotational/translational proof mass actuator (RTAC) system. We discuss the hardware used and the experimental testbed involving three RTAC carts connected by the springs. This testbed presents a unique experimental platform for studying benchmark problems in decentralised nonlinear control design. Finally, we present experimental results using decentralised energy-based hybrid controllers.

Scenario-based strategy maps

Strategy maps are designed to help execute strategy and bring predictive qualities to key performance indicators by linking them according to perceived cause-and-effect relationships. However, in our experience strategy maps are often extrapolations of past performance and are seldom sufficiently linked to possible future states. In this article, we argue that scenario analysis could play an important role in the design of strategy maps, as it is an effective method to look at the future. Through the development of scenarios, organizations can think creatively about possible discontinuous future states and can prepare themselves for multiple plausible futures, not only the one they expect to happen. Therefore, scenario-based strategy maps could enable organizations to face strategic uncertainty in a more effective way and make them more sustainable in the longer term. This article highlights the strengths and weaknesses of strategy maps and scenario analysis, and outlines a method to develop scenario-based strategy maps both in theory and by presenting a significant example.

Research on Initial Discontinuity State of an Advanced Aluminum Alloy Rolling Alclad Sheet

Initial Discontinuity State is the characteristic of aluminum alloy, it is a random parameter. According to an advanced aluminum alloy rolling alclad sheet, the coupons were carried out tension and fatigue test, stress ratio R=0.06, 0.2, 0.5 and the maximum stress level σmax=403, 370, 330, 310, 280, 260, 240, 220MPa through Material Test System 810. By use of scanning electron microscope, the tension and fatigue fracture surface was analyzed and the flaw size was obtained. The metallographic coupons were prepared, the constituent particles were surveyed using KH-7700 optical microscope and particulate size was gained. Based on measuring data, different distributions (Normal, Lognormal, Weibull, Logistic, Gumbel) were verified, the best-fit distributions of tension and fatigue facture flaw size is Lognormal distribution, as same as that of θ phase. However, that of S phase size is Weibull distribution.