Multidimensional Control Systems Research Articles

New results on cycle–slipping in pendulum–like systems

n this paper, we examine dynamics of multidimensional control systems obtained as feedback interconnections of stable linear blocks and periodic nonlinearities. The simplest of such systems is the model of mathematical pendulum (with viscous friction), so we call such systems pendulum-like. Other examples include, but are not limited to, coupled vibrating units, networks of oscillators, Josephson junction arrays and numerous synchronization circuits used in radio and telecommunication engineering. Typically, a pendulum-like system has infinite sequence of equilibria, and one of the central problems addressed in the theory of such systems is to find the conditions of “global stability”, or gradient-like behavior ensuring that every solution converges to one of the equilibria points. If a system is gradient-like, another problem arises, being the main concern of this paper: can we find the terminal equilibrium, given the initial condition of the system? It is well known that solutions do not converge, in general, to the nearest equilibrium; this phenomenon is known as cycle-slipping. For a pendulum, cycle-slipping corresponds to multiple rotations of the pendulum about its suspension point. In this paper, we estimate the number of slipped cycles for general pendulum-like systems by means of periodic Lyapunov functions and the Kalman-Yakubovich-Popov lemma.

Mathematical Model of Heat-and-Mass Transfer for Steam Humidifier

The dynamical model of heat-mass exchange for a steam humidifier with lumped parameters, which can be used for synthesis of control systems by inflowing-exhaust ventilation installations, or industrial complexes of artificial microclimate, is considered. A mathematical description that represents thedynamical properties of a steam humidifier concerning the main channels of regulation and perturbation is presented. The resulting dynamical model of a humidification chamber can be the basis for the synthesis of automatic control systems and simulation of transients. A significant ad-vantage of the obtainedmathematical model in the state space is the possibility of synthesis and analysis of a multidimensional control system.

Development of the Robust Algorithm of Guaranteed Ellipsoidal Estimation and Its Application for Orientation of the Artificial Earth Satellite

The method for estimation of linear multidimensional dynamic control systems perturbed by only one of the phase coordinates is developed in the paper. Only one phase coordinate without perturbation is available for measurement in the system. A robust algorithm for ellipsoidal estimation is developed, which minimizes the trace of the matrix of ellipsoid that approximates admissible set of point estimates. Application of the method and efficiency of the algorithm are shown on the example of estimating the heading angle of an artificial Earth satellite during its orbital motion. The onboard local vertical reference and angular velocity sensors are used for the estimation.

Investigation of multidimensional control systems in the state space and wavelet medium

The notions are introduced of “one-dimensional-point” and “multidimensional-point” automatic control systems. To demonstrate the joint use of approaches based on the concepts of state space and wavelet transforms, a method for optimal control in a state space medium represented in the form of time-frequency representations (maps), is considered. The computer-aided control system is formed on the basis of the similarity transformation method, which makes it possible to exclude the use of reduced state variable observers. 1D-material flow signals formed by primary transducers are converted by means of wavelet transformations into multidimensional concentrated-at-a point variables in the form of time-frequency distributions of Cohen’s class. The algorithm for synthesizing a stationary controller for feeding processes is given here. The conclusion is made that the formation of an optimal control law with time-frequency distributions available contributes to the improvement of transient processes quality in feeding subsystems and the mixing unit. Confirming the efficiency of the method presented is illustrated by an example of the current registration of material flows in the multi-feeding unit. The first section in your paper.

Spline wavelets use for output processes analysis of multi-dimensional non-stationary linear control systems

Methods for solving systems of differential equations based on the use of wavelets have become very popular recently. Debeshy wavelets, coiflets were used among others. The disadvantage of such wavelets is that they do not have an analytical expression. Therefore, there are great difficulties in integrating and differentiating expressions containing these wavelets. The article presents an algorithm for the numerical solution of a system of differential equations with variable coefficients based on spline-wavelets on a interval. The algorithm presented generalizes the well-known method based on Haar wavelets which are a special case of spline-wavelets. The results of the article are used to analyze the output processes of multi-dimensional non-stationary linear control systems.

Parametric identification of the process of preparing ceramic mixture as an object of control

Manufacture of ceramic materials and products largely depends on the preparation of clay raw materials. The main process here is the process of mixing, which in industrial production is mostly done in cross-compound clay mixers of continuous operation with steam humidification. The authors identified features of dynamics of this technological stage, which in itself is a non-linear control object with distributed parameters. When solving practical tasks for automation of a certain class of ceramic materials production it is important to make parametric identification of moving clay. In this paper the task is solved with the use of computational models, approximated to a particular section of a clay mixer along its length. The research introduces a methodology of computational experiments as applied to the designed computational model. Parametric identification of dynamic links was carried out according to transient characteristics. The experiments showed that the control object in question is to a great extent a non-stationary one. The obtained results are problematically oriented on synthesizing a multidimensional automatic control system for preparation of ceramic mixture with specified values of humidity and temperature exposed to the technological process of major disturbances.

Control of multidimensional systems on complex network.

Multidimensional systems coupled via complex networks are widespread in nature and thus frequently invoked for a large plethora of interesting applications. From ecology to physics, individual entities in mutual interactions are grouped in families, homogeneous in kind. These latter interact selectively, through a sequence of self-consistently regulated steps, whose deeply rooted architecture is stored in the assigned matrix of connections. The asymptotic equilibrium eventually attained by the system, and its associated stability, can be assessed by employing standard nonlinear dynamics tools. For many practical applications, it is however important to externally drive the system towards a desired equilibrium, which is resilient, hence stable, to external perturbations. To this end we here consider a system made up of N interacting populations which evolve according to general rate equations, bearing attributes of universality. One species is added to the pool of interacting families and used as a dynamical controller to induce novel stable equilibria. Use can be made of the root locus method to shape the needed control, in terms of intrinsic reactivity and adopted protocol of injection. The proposed method is tested on both synthetic and real data, thus enabling to demonstrate its robustness and versatility.

Models of optimum multidimensional signals in the solid systems

Models of optimum multidimensional discrete signals using novel design based on the “perfect” vector combinatorial configurations, namely the concept of Ideal Ring Bundles (IRB)s for development of new directions in fundamental and applied research in vector information technologies presented. IRB means an n-stage cyclic sequence of semi-measured terms, e.g. integers for which the set of all circular sums enumerates row of natural numbers by fixed times. Development of vector multidimensional models and techniques, based on the remarkable geometric properties of rotational symmetry-asymmetry relationships allows configure optimum multidimensional control systems for reproduce the maximum number of combinatorial varieties in the systems with a limited number of basis vectors. The modular vector sums of connected basis vectors of an IRB-space enumerate the set of t-coordinates specified with respect to t-dimensional cyclic frame reference exactly R-times. The remarkable technical merits of IRB–space, which properties hold for the same set of the IRB-monolithic vector code in varieties permutations of its terms is demonstrated, and method for design of two- or multidimensional vector signals coded based on the optimum binary monolithic code is presented. Proposed vector models of optimum multidimensional discrete signals provide, essentially, a new approach to generalize them to great class of optimized problems in radio-telecommunications, navigation and vector information technology. Moreover, the optimization embedded in the underlying combinatorial models. The favourable qualities of the Optimum Multidimensional Ring code provides breakthrough opportunities to apply them to numerous branches of science and advanced technology, with direct applications to vector data telecommunications, vector encoded design, and optimal vector information technology.

Development of the mathematical modeling method for dynamics of the flexible tether as an element of the underwater complex

Mathematical modeling of flexible tethers (FT) is an integral part of the study of remotely operated vehicles and underwater complexes in general. In this paper, for the mathematical modeling of the FT dynamics in the flow of liquid, the FT is represented as a set of series-connected elements – solid bodies. The governing equation of the FT element motion is given; it takes into account the external gravity, buoyancy and hydrodynamic drag forces, and internal constraint reaction forces between adjacent elements. The main problem in the inextensible FT modeling is to determine the constraint reaction forces. There has been suggested the method of mathematical modeling of the flexible tether dynamics with automatic control of its elements axial motion (ACEAM). According to the ACEAM method, the flexible tether is represented as a multidimensional automatic control system. The controlled object is the set of the FT elements, the controlled parameters are the distances between adjacent elements, and the controlling parameters are the constraint reaction forces. With the help of the inverse dynamics method, the regulator of the FT elements axial motion is synthesized as a part of the FT mathematical model. The developed regulator provides highly precise control of the distances between the FT elements and, therefore, accurate modeling of the inextensible flexible tether dynamics. The method of the flexible tether simulation considering that its length varies during its operation is suggested. The basis of the method is the dynamic change of the number of the elements being involved in the calculation process, considering the current length of the released part of the FT. Changing the FT length causes additional loads on its inboard and running ends. Taking into account these loads allows accurate simulation of the dynamics of the FT impact on remotely operated vehicles and other components of underwater complexes. The flexible tether motion dynamics is then modeled with the developed method. The modeling results are compared with the method of lumped masses springs. It is established that when the equal precision of the inextensible FT simulation is provided, the suggested method operates about 25 times faster than the method of lumped masses and springs.

An Investigation into using SAP-PS as a Multidimensional Project Control System (MPCS)

This paper investigates the effectiveness of using a corporate enterprise resource planning (ERP) system as a multi-dimensional project control system (MPCS) to monitor and control the work performed on projects, meet the needs and expectations of the project managers and support the requirements of other key stakeholders. A qualitative approach i.e. case study interviews and literature review accompanied by a quantitative computer system validation test approach was deployed. The results from this study suggest that the corporate ERP system is effective at monitoring and controlling the project stakeholder success criteria within a fully integrated environment. The system does however need to be setup and configured for the purpose of MPCS. This study contributes to the field by providing empirical evidence that corporate ERP systems are likely one of the only systems truly capable of solving the age old problem of how to expand the traditional singular dimensional approaches commonly used in project control, thus multiple control dimensions are integrated with each other and other business systems to form a multi-dimensional project control system.

Research methods of simulate digital compensators and autonomous control systems

The peculiarity of the present stage of development of the production is the need to control and regulate a large number of process parameters, the mutual influence on each other that when using single-circuit systems significantly reduces the quality of the transition process, resulting in significant costs of raw materials and energy, reduce the quality of the products. Using a stand-alone digital control system eliminates the correlation of technological parameters, to give the system the desired dynamic and static properties, improve the quality of regulation. However, the complexity of the configuration and implementation of procedures (modeling) compensators autonomous systems of this type, associated with the need to perform a significant amount of complex analytic transformation significantly limit the scope of their application. In this regard, the approach based on the decompo sition proposed methods of calculation and simulation (realization), consisting in submitting elements autonomous control part digital control system in a series parallel connection. The above theoretical study carried out in a general way for any dimension systems. The results of computational experiments, obtained during the simulation of the four autonomous control systems, comparative analysis and conclusions on the effectiveness of the use of each of the methods. The results obtained can be used in the development of multi-dimensional process control systems.

Scalability and extensionality of innovative Chinese medicine preparation under guidance of component structure theory

Chinese medicine preparation is a science to study how to make raw material into suitable dosage forms to be used in clinical operations. Its study scope is significantly different from traditional chemical drugs. As is known, the ingredients of Chinese medicine are complex and various, as a result, the composition of the ingredients is not clear and the property is not unified. The pre-treatment process is the key factor to affect the druggability, safety and efficacy of the Chinese medicine. The connotation of Chinese medicine is a huge systematic project, not only including the traditional dosage form design process but also including the components structure optimization process on material basis, components extraction, separation and purification process, components characterization process as well as the pharmacological and toxicological study processes which aim to select suitable dosage form to exert the maximum drug efficacy and evaluate the properties of preparations. Therefore, according to the requirement of modern innovative preparations and based on the integrity and systematicness of Chinese medicine, in this paper we will explore the scalability and extensionality of modern Chinese medicine, including the material basis of Chinese medicine based on component structure theory; separation, refining and purification of components; component structure optimization and network pharmacology and regulation, as well as biopharmaceutics properties of representative components, and we will construct the multi-unit drug delivery system and Chinese medicine multi-dimensional dynamic quality control system. This paper elaborates the scientific connotation and systematicness of modern Chinese preparation, and provides ideas and methods for the development of modern innovative Chinese preparations.

Synthesis of quasi-invariant controllers using pattern recognition methods

The study presents a new approach to the synthesis of multidimensional quasi-invariant control systems based on the formulation and solution of the synthesis problem as an pattern recognition problem. The capabilities and specific features of the new approach are illustrated by two mathematical models of control systems.

ACCURACY INCREASE OF DYNAMIC OBJECTS STATE ESTIMATION BY A COMPLEX MATLAB-ARDUINO WHEN CYBERPHYSICAL SYSTEMS DESIGNING

The problem of accuracy increase of MATLAB and Arduino interaction when cyber-physical systems designing by making changes into the implementation of the standard protocol of Arduino has been solved. It has been proposed to carry out the analog-digital conversion of all required analog pins with further sequential data transmission to MATLAB when requesting to read data from the first analog pin of Arduino. It allows improving control quality of dynamic processes by reducing the uncertainty range of a high-speed multi-dimensional control system state. In addition, it has been offered to perform the preprocessing of sensors data by means of Arduino that increases the flexibility of cyberphysical systems due to the possibility of the hardware changing without MATLAB software and protocol changing. A formal description of MATLAB and Arduino interaction allows realizing the communications protocol using wireless interfaces as well as microprocessor units and platforms, which are not compatible with Arduino.

Special issue on multidimensional systems applications

Although originally motivated by applications such as image processing, multidimensional (nD) systems have mainly attracted the attention of the research community due to the richness of new theoretical questions raised by their treatment, and are often replaced by other settings when it comes to modelling, identifying and controlling processes in practical situations. The aim of this special issue is to illustrate the application potential of nD systems by presenting several contributions where the nD framework is successfully used either to deal with practical problems or to solve practically relevant questions that arise in other contexts that are not at first sight related to multidimensional systems. In the paper Multidimensional Control Systems: Case Studies in Design and Evaluation, by Rogers et al., after introducing the most commonly used models for the analysis and control of discrete nD linear systems, a series of case studies is presented with the aim of demonstrating the advantages of the nD systems approach in solving certain control problems. Namely, applications in the fields of sensor grid networks, iterative learning control, civil engineering and agriculture are considered. The paper Two-dimensional Generalized Predictive Control (2D-GPC) Scheme for the Batch Processes with Two-dimensional (2D)Dynamics, Shi et al. studies the problem of iterative learning control (ILC) design for batch processes. Based on 2Dcontrolled auto-regressive moving average (2D-CARMA) model, a novel two-dimensional generalized predictive control (2D-GPC) is proposed. The feasibility and effectiveness of the proposed method is validated by the experimental results on packing pressure control of the injection molding process.

Multidimensional control systems: case studies in design and evaluation

Multidimensional control systems have been the subject of much productive research over more than three decades. In contrast to standard control systems, there has been much less reported on applications where the multidimensional setting is the only possible setting for design or produces implementations that perform to at least the same level. This paper addresses the latter area where case studies focusing on control law design and evaluation, including experimental results in one case, are reported. These demonstrate that movement towards the actual deployment of multidimensional control systems is increasing.

Development of requirements for accuracy of inertia compensation in gas temperature control loop of gas turbine engine control systems with a channel selector

The influence of thermocouple inertia compensation errors on the quality of channels selecting in multidimensional gas turbine engine control systems is analyzed. Based on the results obtained, the requirements to the accuracy of inertia thermocouple compensator realization are formulated. The study was carried out by means of mathematical modeling.

Establishment of industry promotion technology system in Chinese medicine secondary exploitation based on “component structure theory”

The purpose of the secondary exploitation of Chinese medicine is to improve the quality of Chinese medicine products, enhance core competitiveness, for better use in clinical practice, and more effectively solve the patient suffering. Herbs, extraction, separation, refreshing, preparation and quality control are all involved in the industry promotion of Chinese medicine secondary exploitation of industrial production. The Chinese medicine quality improvement and industry promotion could be realized with the whole process of process optimization, quality control, overall processes improvement. Based on the "component structure theory", "multi-dimensional structure & process dynamic quality control system" and systematic and holistic character of Chinese medicine, impacts of whole process were discussed. Technology systems of Chinese medicine industry promotion was built to provide theoretical basis for improving the quality and efficacy of the secondary development of traditional Chinese medicine products.

Algorithm for synthesis of multidimensional digital control system with irregular matrices

An algorithm of multi-dimensional cross-linked digital control system synthesis is given, that allows you to divide the channels and obtain the required quality of the process. We give a formula of the state feedback matrix for irregular matrices. The solution of the problem is illustrated by calculation and simulation of a third-order system using Matlab software. Referens 3, рис. 4.

Stabilization of unstable vertical position of plasma in T-15 tokamak. I

Consideration was given to the design and mathematical modeling of the stabilization system for unstable vertical position of plasma in the T-15 tokamak (Institute of Tokamak Physics, National Research Centre "Kurchatov Institute"). For suppression of vertical instability of plasma, the poloidal systems of vertically elongated tokamaks were analyzed with the aim of detecting the most efficient positioning of the winding of the horizontal magnetic field (fast winding) in the T-15 tokamak. The controllability domains of vertical shift of the plasma magnetic axis were estimated for various arrangements of the fast winding (i) outside the toroidal winding, (ii) between the toroidal winding and the vacuum chamber, (iii) inside the tokamak vacuum chamber. Part I considered the linear control system for vertical plasma position where the fast winding is located outside the tokamak toroidal winding. For the given configuration of the poloidal system, the control system of the T-15 tokamak was shown to be inherently unstable. Inherent system stability is attained by using a multidimensional control system where all windings of the central solenoid and the windings of the poloidal field are used to control the vertical plasma position and the current in the fast winding.