State Space Notation Research Articles

Epileptic seizure suppression: A computational approach for identification and control using real data.

Epilepsy affects millions of people worldwide every year and remains an open subject for research. Current development on this field has focused on obtaining computational models to better understand its triggering mechanisms, attain realistic descriptions and study seizure suppression. Controllers have been successfully applied to mitigate epileptiform activity in dynamic models written in state-space notation, whose applicability is, however, restricted to signatures that are accurately described by them. Alternatively, autoregressive modeling (AR), a typical data-driven tool related to system identification (SI), can be directly applied to signals to generate more realistic models, and since it is inherently convertible into state-space representation, it can thus be used for the artificial reconstruction and attenuation of seizures as well. Considering this, the first objective of this work is to propose an SI approach using AR models to describe real epileptiform activity. The second objective is to provide a strategy for reconstructing and mitigating such activity artificially, considering non-hybrid and hybrid controllers - designed from ictal and interictal events, respectively. The results show that AR models of relatively low order represent epileptiform activities fairly well and both controllers are effective in attenuating the undesired activity while simultaneously driving the signal to an interictal condition. These findings may lead to customized models based on each signal, brain region or patient, from which it is possible to better define shape, frequency and duration of external stimuli that are necessary to attenuate seizures.

Limit cycles in relay systems with fractional order plants

In this paper, limit cycle frequency, pulse width and stability analysis are examined using different methods for relay feedback nonlinear control systems with integer or fractional order plant transfer functions. The describing function (DF), A loci, a time domain method formulated in state space notation and Matlab/Simulink simulations are used for the analysis. Comparisons of the results of using these methods are given in several examples. In addition, the work has been extended to fractional order systems with time delay. Programs have been developed in the Matlab environment for all the theoretical methods. In particular, Matlab programs have been written to obtain a graphical solution for the A loci method, which can precisely calculate the limit cycle frequency. The developed solution methods are shown in various examples. The major contribution is to look at finding limit cycles for relay feedback systems having plants with a fractional order transfer function (FOTF). However, en route to this goal new assessments of limit cycle stability have been done for a rational plant transfer function plus a time delay.

Analytical Solution of Compression, Free Swelling and Electrical Loading of Saturated Charged Porous Media

Analytical solutions are derived for one-dimensional consolidation, free swelling and electrical loading of a saturated charged porous medium. The governing equations describe infinitesimal deformations of linear elastic isotropic charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoupled introducing a set of normal parameters, being a linear combination of the eigenvectors of the diffusivity matrix. The magnitude of the eigenvalues of the diffusivity matrix correspond to the time scales for Darcy flow, diffusion of ionic constituents and diffusion of electrical potential.

Curving simulation and stability of a creep-controlled wheelset for high speed rail-vehicles

Higher travel speeds of rail vehicles will be possible by developing sophisticated top performance bogies having creep-controlled wheelsets. In this case the torque transmission between the right and the left wheel is realized by an actively controlled creep coupling. To investigate hunting stability and curving capability the linear equations of motion are written in state space notation. Simulation results are obtained with realistic system parameters from industry and various controller gains. The advantage of the „creep-controlled wheelset" is discussed by comparison the simulation results with the dynamic behaviour of the special cases „solid-axle wheelset" and „loose wheelset" (independent rotation of the wheels). The stability is also investigated with a root-locus analysis.

AC machine dynamics described by space vectors using state-space notation

Asynchronous machines represent by now the majority of applications in the sector of variable speed drives. The demands on the performance of their control have risen as they by now replace DC machines with sophisticated control. Therefore it is necessary to describe the dynamic behaviour of an AC machine correctly and at the same time as simply and graphically as possible, because efficient control schemes can be designed best based on a complete understanding of the AC machine dynamics. Such a simple and graphical description can be achieved by combining the space-vector theory introduced by Kovacs and Racz with the state-space notation. Additionally it is advantageous to introduce a rotating reference frame which can be selected according to the problem at hand. Combining space vectors and state-space notation leads to single complex eigenvalues instead of the usual pair of an eigenvalue and its conjugate. Changing the velocity of the reference frame naturally changes the eigenfrequencies, as can be seen from the eigenvalues in their analytic form calculated and discussed in this paper. It is shown that the effects caused by introducing a rotating reference frame in general have not necessarily to do with induced voltages and Faraday's law.

Fault Management in Discrete Manufacturing Processes via an Arithmetic Approach

Abstract In this paper discrete manufacturing processes are modelled by finite Boolean automata. Different from classical automata theory, however, an arithmetic state space notation is used such as to provide a close relationship to classical discrete-time control. A case study will focus on observer-based control and its potential for fault management.

Time Series Analysis of Groundwater Radon Using Stochastic Differential Equations.

This paper provides a new approach to detect changes in the groundwater radon concentration related to an earthquake. We express changes in radon concentration in a radon-detection chamber by using stochastic linear differential equations. These equations are represented by the state space notation, and then its solution is replaced by an estimation of the state vector at discrete points in time with an assumption that the coefficients describing the stochastic differential equations are constant for a sufficiently small time interval. Since the solubility of radon in water depends strongly on temperature, the separation of radon from liquid water, which is necessary for radon detection, causes fluctuations in the observed radon concentrations due to water temperature changes in the chamber. We applied our procedure to some actual data sets on groundwater radon concentration with those on simultaneously observed water temperature, and found that the temperature effects on the fluctuations in the observed radon concentration can be satisfactorily described by our procedure. Furthermore, we were able to estimate the original radon concentration in groundwater before it was introduced into the radon-detection chamber, which was not affected by water temperature changes. The obtained original radon concentrations are very stable during normal periods, and anomalous changes associated with earthquakes were easily detected. Our new method will be very useful to examine time-variation patterns of changes in groundwater radon and will provide important information about the mechanism of radon changes related to earthquakes.

System Simulation Using OCCAM

Methods are given for the mapping of a system representation into some standard form into an OCCAM program. Firstly, two different transform methods are converged into a standard canonical form. The different program elements, which extensively use the concept of OCCAM channels are demonstrated on a typical control problem. Secondly, the node-channel concepts used are extended to simulate MRAC scenarios which include state space notation.

PSYCHOBASIC: A BASIC dialect for the control of psychological experiments with the Commodore-64 and DELA interfacing

A modified version of BASIC for the control of psychological experiments is presented. PSYCHOBASIC runs on Commodore-64 computers with DELA interfacing, and it is based on Commodore BASIC. New commands control digital and analog input and output, centisecond timers, and counters. A control panel, which is displayed on the screen at all times, gives the status of many PSYCHOBASIC components. The interpreted nature of PSYCHOBASIC, as well as the control panel, makes the system easy to learn and use. The PSYCHOBASIC system is less expensive than equivalent systems for IBM·PC computers. A sample PSYCHOBASIC pro­ gram is given. The use of computers for the control of psycholog­ ical experiments has a history covering nearly three de­ cades (Leslie, 1981). Recently two systems SKED and MEDSTATE, both of which are based on the state-space notation system, have become dominant. The state-space approach is a clear method for describing experimental conditions, but it entails a number ofdifficulties. We were motivated to develop our own system by two drawbacks in the extant systems. First, they were too expensive; SKED and MEDSTATE are based on the IBM-PC com­ puter system with special interfacing (a minimum invest­ ment of over $2900 for 16 I/O lines with software). Sec­ ond, the two-stage compilation system of the state-space systems causes undesirable delays between the typing of a command and seeing its effect. We have found that many students and even colleagues still prefer to work with the solid-state logic units because they provide immediate feedback about their logical state. We therefore had three objectives: The system should (1) require a minimum of new learning of programming techniques; (2) be inexpensive enough to make it unneces­ sary to multitask several experiments on one computer, yet reliable enough to take the strain of dusty animal rooms; and (3) as far as was possible, provide immedi­ ate feedback of its state. Our solution is based on the Commodore-64 (C-64) computer with DELA interfacing and the BASIC pro­ gramming language. The C-64 is the cheapest computer that offers sufficient reliability for experimental purposes,

Some Aspects of ECM Performance and Control

This paper presents results of experimental investigation carried out to develop quantitative relationships for inter-electrode gap and surface characteristics in Electrochemical Machining (ECM). The effect of grain size on the machining gap and, therefore, on the ECM performance and tool design is discussed. The wavelength decomposition of surface profiles and current signals have been carried out with a view to develop a better understanding of surface generation and random occurrences of sparking in ECM respectively. The dynamics of ECM process is modeled in state space notation and the adequacy of the model has been verified by simulation.

Adjustment Time in the Neoclassical Growth model: An Optimal Control Solution

The long adjustment times implied by the neoclassical growth model are reviewed. The model is transformed into state-space notation, and the results of the minimum-time problem from optimal control theory are used as a basis for decreasing these adjustment times. This note illustrates the dynamic behaviour of a popular economic model and provides an example of applying optimal control theory to theoretical economics.

Feedback Control of Schooling Fish

The paper describes the principles suggested for a system for control of the movement of a school of fish in the ocean. A mathematical model using state space notation is developed, describing how the movement of a school is related to natural and artificial stimuli. Different kinds of natural and artificial stimuli are discussed and different ways of determination of direction in scalar and vector fields of stimuli are described. A mathematical expression is derived showing that the sensitivity of directional navigation of a large school is nearly proportional to the number of individuals in the school. A control structure is suggested using feed-back control stimuli from measured and estimated states of the school movement. The paper concludes with a survey of some practical applications of the techniques suggested in nerding of pelagic fish.