Switching Curve Research Articles

SIMPLE HYBRID SYSTEMS

A hybrid system is one which can instantaneously switch between a number of phase portraits. Switching occurs when trajectories hit prescribed switching curves. This type of system is highly applicable to digital controls such as robotic controls. A working definition of such a system is given, as well as a method for stabilizing periodic orbits and several examples.

Effects of X-Ray irradiation upon switching in potassium dihydrogen phosphate.

Abstract Ferroelectric polarization reversal in radiation damaged KH2PO4, (KDP) was monitored using the switching current technique first developed by Merz. The experimental results show extinction of the switching curve after an 8hr exposure to x-rays. The switching curve returns after annealing at room temperature. Approximately one hundred switching transients were recorded for seven samples with applied electric fields of 90 V/cm to 850 V/cm. Samples were irradiated, annealed at room temperature, again exposed to radiation, and then again annealed. After each exposure the switching curve vanished and then returned after annealing.

Stability Based Design of Fuzzy Logic Controller

There are presented some methods for the stability analysis of the control system with fuzzy logic controller. The methods are based on classical methods and they require fuzzy logic controller, satisfying the sector condition. The necessary structure of fuzzy controller, satisfying this requirement is proposed. For this controller, the method for tuning the controller parameters is developed. The method is based on stability analysis and guarantees the stability of the system. The analogy with switching curve is used to tune the remaining degrees of freedom of the controller. The method is documented on a d.c. velocity servosystem.

Stability Analysis of Fuzzy Controller and Implications for Design

Some techniques for the stability analysis of the control system with fuzzy logic controller are presented. The techniques are based on classical methods and they require the fuzzy controller, satisfying the sector condition. The structure of fuzzy controller, satisfying this requirement is proposed. For this controller, the analytical dependence between the stability margin and controller parameters is developed and the technique for tuning the controller parameters is also developed. The analogy with switching curve is used to tune the remaining degrees of freedom of the controller. The method is documented on a d.c. velocity servosystem.

A New Design Method of Sliding Mode Control Systems Based on the Construction of Liapunov Functions

A new design method of sliding mode control based on the construction of Liapunov function is proposed in this paper. This method enables us to generate linear and nonlinear switching curves. Numerical simulations and pilot plant experiments on strongly endothermic NH4-alum pyrolysis reactor were carried out using Ibis design method. Good control performances were obtained in both cases.

Investment Mathematics and Statistics.

Part 1 Investment mathematics: compound interest fixed-interest bonds equities and real estate real returns index-linked bonds foreign currency investments numerical approximation techniques. Part 2 Statistics: data collection and presentation descriptive statistics probability some particular probability distributions confidence intervals and hypothesis testing correlation and regression. Part 3 More advanced applications: portfolio theory market indices and performance measurement bond portfolio management bond switching curve fitting theoretical pricing of futures and forwards theoretical pricing of options the stochastic approach to the theory of interest.

Jointly optimal admission and routing controls at a network node

We consider the problem of jointly optimal admission and routing at a data network node. Specifically, a message arriving at the buffer of a node in a data network is to be transmitted over one of two channels with different transmission times. Under suitably chosen criteria, two decisions have to be made: Whether or not to admit an incoming message into the buffer, and under what conditions should the slower channel be utilized. A discounted infinite-horizon cost as well as an average cost are considered. These costs consist of a linear combination of the blocking probability and the queueing delay at the buffer. The optimal admission and routing strategies are shown to be characterized almost completely by means of “switching curves”

Characterization of anodically formed polypyrrole/tungsten trioxide composites

Composite PPy/WO3 materials were synthesized anodically under various conditions. The cyclovoltammetric switching curves are very close to the blank polypyrrole. The redox behaviour of the filler is only detected through electrochromism, leading to a yellow grey colour at +0.4 V vs SCE and to a green surface at −0.6 V. For overoxidation of the composite, a degree of overoxidation Y = 5 is found, the same as for the matrix alone. Photoelectrochemical response is due to the conducting polymer at negative potentials and even at 0 V vs SCE. A strong effect at positive potentials is due to the WO3 pigment. From this, a flat band potential of +0.15 V vs SCE is determined for aqueous 0.1 m LiClO4. Some non-electrochemical properties are also reported. Surface roughness increases with increasing WO3 concentration, but for thicker layers, from MeCN, it decreases. SEM micrographs reveal homogeneous distribution of WO3. Large secondary particles are observed in NBu4BF4 electrolyte. True and nominal thicknesses differ by up to a factor 1.65 due to the porous structure and this explains differences between densities measured by the flotation and the jump method. X-ray diffraction analysis exhibits unchanged WO3-lines, but no PPy-lines due to the amorphous character. The conductivity of the composite from MeCN is much lower than expected by the volume filling of the WO3.

On the asymptote of the optimal routing policy for two service stations

It has been previously proved that the optimal routing control of a two-station Markovian network with linear cost is described by a monotone switching curve. With the discounted cost objective function, it is proven in this paper that the optimal switching curve has a finite asymptotic limit when c/sub 1/ not=c/sub 2/, where c/sub i/ is the unit inventory cost at station i. Whereas, for the case with c/sub 1/=c/sub 2/, as well as the case with the long-run average objective function, the switching curve does not have a finite asymptote. >

Simple analytical description of performance of Y-junctions

Simple analytical expressions, describing the performance of the Y-junction as a function of only one parameter, the mode conversion factor (MCF), are derived. The expressions are based on numerical studies of Y-junctions with varying MCFs by means of the finite-difference beam propagation method (FDBPM). The simple expressions are compared with published switching curves of electro-optic Y-junction switches and found to be in excellent agreement.

The Effects of External Bending Moments on Lumbar Muscle Force Distribution

A detailed biomechanical model of the low-back musculature that predicts muscle-force distribution in response to external loading is presented. The paper shows that the class of loading tasks that involve an erect posture and an arbitrary load placed on the upper limbs can be described as a loading plane whose axes are the flexion and lateral bending moments. Under these conditions, the individual muscle forces are described as a three-dimensional surface defined by the loading plane and termed the muscle activity surface (MAS). The MAS and the loading plane intersect along the switching curve which separates the load combinations that activate the muscle from those that do not. The paper suggests the existence of a recruitment order of low back muscles in response to external loads and presents a comprehensive framework for examining earlier studies that used EMG measurements to validate physiological and mechanical predictions.

Experimental determination of switching curves of lumbar muscles

Experimental determination of switching curves of lumbar muscles

Time optimization of the continuous-path motions of industrial robots

This paper presents an engineering approach to the time optimization of robotic motions with specified paths and trapezoidal velocity profiles. Optimizations of this type occur when dealing with continuous-path motions of commercial manipulators. Parameterized path equations and full non-linear robot dynamics are used in conjunction with the actuator limitations and the specified path and velocity profile in order to transform the problem into a non-linear programming form. The optimal velocity profile and the corresponding joint torques/forces are obtained via a simple search algorithm, without resorting to any constrained optimization technique, numerical integration, or search for the switching curve. Three examples of time-optimized robotic motions are presented.

Shifts in lumbar muscles switching curves due to non-zero axial torques

Shifts in lumbar muscles switching curves due to non-zero axial torques

Combined time/location optimization of robotic motions with specified paths and velocity profiles

SUMMARYA parameter optimization approach to the time-minimization of robotic motions along specified paths is presented for the case when: (i) the velocity profile is a prescribed sequence of constant acceleration/deceleration segments with unspecified, but bounded vertex velocities at given path stations; (ii) the relative robot/path location can be varied. Such optimizations occur when technological requirements impose a certain velocity profile along the path due to velocity and acceleration constraints. Full nonlinear manipulator dynamics and path parameterization are used to determine the optimal velocity profile and robot location consistent with the actuator/configuration limitations. No numerical integration or search for switching curve are involved in the solution. Examples of time-and-location optimized robotic motions with specified velocity profile are presented.

1989 Volvo Award in biomechanics. Mechanical recruitment of low-back muscles. Theoretical predictions and experimental validation.

A biomechanical model for studying lumbar muscle load sharing for a class of physical tasks that involve gravitational loading (holding weights) of the upper body in an erect posture is presented. The model assumes that the lumbar muscles balance the externally applied flexion and lateral bending moments. The concept of a 'loading plane' whose axes are the two bending moments is introduced. Any point in the plane can be viewed as a 'loading-point' describing a combination of bending moments that are applied to the body. The study of lumbar-muscle load sharing revealed loading conditions that required activation or deactivation of a particular muscle. The loading plane thus could be divided into regions of activity and inactivity for each muscle, separated by a 'switching curve.' The concept of 'switching curves' proved very useful for examining previously described physiologic assumptions on the loading conditions of particular muscle groups, and for grouping the 22 muscles described in the model into ten functional units. Electromyographic validation studies were conducted and showed a high degree of correlation between the model predictions and actual measurements for the contralateral (with respect to the load) muscles and to a lesser degree of correlation for the ipsilateral muscles.

A Control Strategy for the AC/DC Power System Under Large Disturbances

In the proposed control system, a parallel continuously adjustable PI control loop is used with a time optimal control loop. Different combinations of the control loop are used for different time intervals for the DC transmission system. This forces the system output to change along the pre-selected switch curve and to reach the predetermined final state. The proposed controller has the advantages of time optimum" largest stable region, short transient period and self-tuning capability. Numerical simulation gives the satisfactory results.

Effect of space charge on polarization reversal in a copolymer of vinylidene fluoride and trifluoroethylene

Polarization-reversal phenomena in ferroelectric copolymers of vinylidene fluoride and trifluoroethylene are affected by the time interval elapsed after poling of samples. Measurements of switching current demonstrated that this waiting effect is enhanced with the increase of space charges and switching curves with different waiting intervals satisfy the scaling rule when each switching curve is scaled by the switching time. These facts suggest that the electric field that reverses the spontaneous polarization decreases due to the electric field coming from space charges in the amorphous phase. A model with a prolate ellipsoid crystal and space charges in the amorphous phase explains such experimental facts. The difference of the waiting effect among samples crystallized under different conditions is also explained through the difference in the depolarization field coefficient of crystals.

A Robust Approach to Bang-bang Control for Unmodeled Systems with Time-delay

The maximum principle suggests a bang-bang control law to the time optimal control systems. However, the performance of the resulting closed loop system is extremely sensitive to the variation of modeling parameters, and it is almost impossible to achieve stability for unmodeld systems. A simple method of adaptive time-optimization which compromises regulating speed and stability in a common class of regulating systems is discussed in this paper. Our focus is on how close and how fast the system is driven to the equilibrium, irrespective of the parameter estimation. The basic idea of the solution is that the actual switching curve can be generated after drawing a section of almost any trajectory of the system for a subclass of systems, and then extend it to obtain the switching curve of any system in the full class considered. The control law has robustness in the sense of the system parameters varying slowly, since the real switching curve is constantly adjusted as the disturbance occurs. Perhaps, the significance of the results developed in this paper arises a potential application for the bang-bang control law to solving technical diffculties caused by time-delay and variations of system parameters

Modes with switchings of increasing frequency in the problem of controlling a robot

Trajectories that are optimal with respect to high-speed response are constructed for a system for controlling a two-component manipulator (a robot). It is shown that when the initial conditions lie within a certain open region of the phase space, all optimal trajectories will have a segment of switchings of increasing frequency (SIF), i.e. a segment in which the control will undergo an infinite number of switchings in a finite time interval. The synthesis of the optimal control in the R 2 plane containing the mode of SIF was first constructed by Fuller /1/. It was shown in /2/ that the synthesis is structurally stable in the sense that adding terms of higher order of smallness to the integrand and to the right-hand sides of the system of differential constraints does not affect the qualitative pattern of the optimal synthesis in the neighbourhood of the origin of coordinates. The present paper explains that the synthesis in the problem of optimal control (relative to the high speed response) of the motion of the robot appears, in a certain sense, a direct product of the synthesis appearing in the Fuller problem and of the synthesis in the simplest problem of high-speed response (/3/, pp.38–47). The special aspect of the present paper consists of the proof of the proposition that switching surface is a piecewise-smooth manifold. The presence of the SIF mode is connected only with the fact that every trajectory intersects this surface an infinite number of times. In existing papers, the piecewise smoothness of the switching curve was proved for the two-dimensional problems using the SIF mode only for problems admitting of a one-parameter group of symmetries /1, 4–6/. A proof of the presence of SIF was given in /7, 8/.