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By W. Wan

Diesel particulate matter (DPM) emitted from diesel engines is currently considered to be a health problem in underground mines. As a result, attempts have been made to control DPM both by reducing emission rates and by managing the DPM that gets into the mine atmosphere. This paper presents a method for modeling the generation, transfer and distribution of DPM in the mining sections through the use of a convection-based computer model so that controls for emitted DPM can be evaluated. A variety of ventilation strategies and diesel deployment schemes for room-and-pillar development sections were simulated to compare their effects on average DPM concentrations at several fixed and mobile personnel locations in the section. Input data for the model was gathered from actual diesel development sections and derived from experimental study results provided by other researchers. Studied using the model were ventilation schemes using vent tubing and brattice, exhaust location strategies on the vehicles, and the direction of ventilation at the feeder-breaker location. A summary of results from this study will be presented.

Jan 1, 1994

By Jorge Ferrero, Andreas Raedle, Uhland Konrad, Michael Dutton, Keivan Pak Iman, Walter Trisi

Strabag, in partnership with Arup, is constructing the Advance Tunnel for the Scarborough Subway Extension (ATSSE); a project by Metrolinx and Infrastructure Ontario (Sponsors). The 10.7 m internal diameter single bore tunnel represents a significant departure from the traditional arrangement of twin subway tunnels in North America. ATSSE is the first-time steel fibers are used to solely reinforce a tunnel of this size in Eastern Canada. This paper discusses the challenges with design and acceptance of SFRC segments and the state-of-the-art numerical models employed to check the joint performance. The advance procurement approach for TBM and PCTL’s procurement to accelerate the project schedule is also presented.

Jun 13, 2023

By A. Bascetin

Materials produced in quarries have been used for different intentions such as concrete and cement raw material, asphalt and embankment aggregates, railway ballast. Especially in cement manufacturing, the chemical composition and the uniformity of the raw materials play a strategic role in the economy and quality of the cement process. Therefore, it is necessary to achieve uniformity and desired chemical composition and maintain these at all production stages according to the type of cement produced. To achieve this goal the production planning and pit design play an essential role. This paper briefly outlines the production optimization of cement raw materials in a quarry in Istanbul western part of Turkey. For the purpose it was used the 3D ore body modeling and the geostatistical techniques. The variation of chemical components (%CaO, %Al2O3, %Fe2O3 etc.) and quality control parametres (LSF, SR, AR and etc.) obtained from the quarry were determined. Then the values of unknown chemical components and quality control parameters in the ore body were estimated using Kriging which is one of the geostatistical interpolation methods. The open pit design was also created by specifying wall slopes and taking into consideration of the grade distributions of the benches. The most important revolution in the paper is investigating the effects of the block dimensions in block modelling which is important for reserve estimation. The other important point in the study is using the different range values in variogram analysis for determination optimal reserve estimation. n this study, the effects of two parametres on reserve and waste amount estimation were determined according to CaO% distribution. The study was pointed out that the changing of the two parameters are very important for the optimal mine planning and environmental considerations.

Jan 1, 2010

By S. S. M. Chan

The design of most underground support systems has largely been based upon empirical rules. This design method has proven to be satisfactory in most cases as witnessed by the number of successfully completed works. However, the adequacy of this approach to the developing technology of ground support systems associated with deep excavation has not been substantiated. In cases where the material has definite time-dependent behavior parameters, rules of past experience become extremely vague and conservative. The Spokane Mining Research Center is currently engaged in extensive research to develop rational design methods for underground structures which will account for the many interacting factors such as in-situ properties of the rock mass, excavation methods, proposed types of support system, construction sequence, and environmental variables. The information presented in this paper pertains to only a segment of the research program,

Jan 1, 1971

By Alexander Darío Huamán Ccorahua, Cayo Fernando Soto Buendía, Jhonatan Raphael Rojas Ventura

Lithium is a top-quality mineral in the energy market, with growing demand. It has many applications in medical, nuclear, and energy industries. The purpose of this article is to quantify and analyze the economic potential and projected global demand for lithium annually. It aims to determine Peru’s (specifically Puno) positioning in the global context in 2025 and 2030. The article also seeks to identify the main regulatory, environmental, and social challenges to sustainably exploit lithium in Peru. The study employs applied research (mixed approach), descriptive-correlational scope, and observational, crosssectional design. The methodology demonstrates the use of statistical techniques to model and make predictions about this energy-transition metal. Academic sources were reviewed to enable a comparative approach and projection into the future of lithium for development in the mining industry. In the last 10 years, lithium demand has grown, noting a 600% increase in the economy and projected annual growth of +26%. Exponential growth in resources is projected, where econometric, R-multivariable and R-linear models estimate that Peru could supply 1.5% in 2025 and 3% in 2030 of global lithium. Estimated growth of 5–15% in socio-environmental conflicts is projected with the start of lithium exploitation (Peru – Puno). The global potential of lithium demonstrates exponential growth. Lithium reserves in Puno - Peru would rank 13th between 2025 and 2030. It is necessary to establish a clear regulatory framework to avoid excessive increase in socio-environmental conflicts.

Feb 1, 2024

By Emily Adelsohn, Robert Winn, Anthony Iannacchione

"Over 600 longwall panels have been mined in Pennsylvania in the last 50 years. Of those 600 panels, 25 panels undermined interstate highways. Despite this quantity of panels, much is still unknown regarding the detailed effects of undermining highways. The Gateway Mine, the Emerald Mine, and the Cumberland Mine undermined I-79 with 17 panels between 1982–1989 and 2003–2008, respectively; mine Eighty-Four undermined I-70 with 4 panels between 1987–2000.Through the examination of the panels that undermined I-70 and I-79, it is possible to determine which factors have most impacted the highway alignments. In some locations, the highway intersects with panels at angles ranging from 45 to 80 degrees, and at others, it runs between two panels, which simulates the effect of gateroads on the subsidence. The panels width to overburden ratio varies between 0.64 and 1.7, meaning that the interstates were influenced by both subcritical and supercritical subsidence basins. The face advance rates and overburden depths also vary between the panels.Unfortunately, specific information detailing highway impacts associated with unique characteristics of the subsidence basins are limited. However, using the profile function model and influence function model within the Surface Deformation Prediction System (SDPS), the effects of overburden, panel size, and orientation of the road to highway can be indirectly assessed by profile and influence models of subsidence basin formation.INTRODUCTIONCoal mining has been an integral part of Pennsylvania’s history. Room-and-pillar mines have been active since the late-1700s when coal was extracted from outcrops. By 1830, the city of Pittsburgh alone consumed more than 400 tons of bituminous coal each day for domestic and industrial use (PADEP, 2019). In the late 1960s, the face of mining in Pennsylvania changed with the development of full extraction longwall mines. Since that development, over 600 longwall panels have been mined in the Pittsburgh Coalbed in Pennsylvania alone (PADEP, 2019).As longwall mining and other forms of full extraction mining have increased in popularity, the amount of planned subsidence impacting the surface has also increased. The stresses and strains induced by longwall subsidence can cause damage to the surface as well any structures, water supplies, or water bodies that lie above the panel. Since the behavior of soils and structures vary, one way to study the surface effects of longwall mining is to analyze the impact on flat, rigid, pavement surfaces. Examining factors that vary the impact of subsidence with respect to highway alignment can demonstrate the favorable orientation of an alignment to avoid or mitigate damage and critical impact zones in a subsidence basin."

Jan 1, 2019

By Alastair R. Biggart

ABOUT BENTONITE TUNNELLING Much has been written and many learned papers given on this subject whose generic term is Slurry Tunnelling. This paper is about the particular form of slurry tunnelling known as the Bentonite Tunnelling System. This method. of tunnelling was invented by J.V. Bartlett of consulting engineers, Mott Hay and Anderson in 1964. The general principles are incorporated in British Patent No. 1083322. It was not until the early 1970's that serious experimental work was started to prove the technical feasibility of the process. In the U.K. in 1971 Edmund Nuttall Limited started on an experimental length of 3.8m diameter tunnel at New Cross in London. In Germany at about the same time Wayss and Freytag were starting on a 3.7m diameter collector sewer tunnel in Hamburg. In Japan early slurry tunnelling work was carried out in the 1960's. In the early 1970's a large number of slurry tunnels of various diameters were carried out in that country. This paper is being presented at a time when this system of tunnelling has become an accepted method throughout the developed world. As a result of the work carried out so far there is now a large amount of data existing regarding the effects on the ground in the immediate area of the tunnel, settlement at the surface and the ability of the system to cope with ground varying from clays to coarse gravels and containing large erratics such as granite boulders. The decade of the 1970's has therefore seen a very rapid pace

Jan 1, 1979

By Cheng Li, Yanlei Wang, Lingrui Kong, Jianxin Tang, Fang Yuan

Coal mined-out areas have a significant impact on mining safety and affect the pressure distributions of neighboring coal faces. The PFC3D software is used to study the goaf mechanical characteristics, and the core loading test verifies the rationality of the numerical simulation method. The results from the numerical modeling showed that the void ratio, particle size ratio, and particle size distribution of the rock particle sample (RPS) had a significantly remarkable influence on the compression deformation characteristics of the rock block. The parallel-bond tensile strength and parallel-bond cohesion had a notable impact on the compression deformation traits of the rock block only when the axial stress level was lower than 12 MPa. By contrast, when the axial stress exceeded 5 MPa, the effective modulus significantly influenced the compression deformation features. However, the stiffness ratio, loading rate, and parallel-bond friction angle had almost no effect on the compression deformation characteristics. Furthermore, when the stress level was less than 10 MPa, the stress–strain curves from the rock core samples’ numerical simulation and loading tests were approximately linear. In addition, the Pearson correlation coefficients of the stress–strain curves suggest that the goaf zone’s core numerical simulation results had a robust correlation with the loading test results. The findings of this study can serve as a reference for the field application of PFC3D software and safety assessments in goaves.

Jan 18, 2022

By K. E. Yassin, A. Yehia, M. Amar

Phosphate ores are the source of many commodities, such as phosphorus element, P2O5 and fertilizers. Discarding a large percentage of fine phosphate particles produced as slimes during phosphate ore processing represents a severe environmental problem, besides making the beneficiation process uneconomical. The phosphate industry is interested in a process that is efficient, with high grade and high recovery; ensures economical feasibility, with low operating cost; and is environmentally sound, with low toxicity. Numerous investigations have been conducted to try to find better processing techniques and reagents. However, reagent requirements and recovery limitations may be so high that the end does not justify the means. Reagents of biological origin are of special interest because they offer specific interactions with minerals, reduced operating costs, environmental acceptability and flexibility in adaptation. Recently, there has been a growing interest in using microorganisms as flocculants for mineral fines and as flotation collectors. 

By Bruno Mattle, Max John

For tunnels with low overburden, the shotcrete lining is the main element of ground support, which is why shotcrete behavior is of prime importance. Following its application, shotcrete not only gains strength and stiffness with time but—if loaded at an early stage—it is also subject to creep which in turn leads to stress relaxation. For two-dimensional FE calculations, a computational modulus of elasticity of shotcrete is to be used. Based on parameter studies it was found that the modulus of elasticity of shotcrete depends on both shotcrete mix and ground behavior. While the Young’s Modulus used for young shotcrete may range from 1,000 to 7,000 MPa, the Young’s Modulus used for hardened shotcrete is best represented by a value of 15,000 MPa.

Jan 1, 2003

By D. E. L. Zapata, O. J. R. Baena

"INTRODUCTION Mining is a fundamental part of the historical and economic development of a country. In Colombia, this is reflected from pre-Columbian jewelery, to being now one of the first exporters of coal worldwide, in 2017, the Colombian mining sector contributed approximately 6% of GDP (Ministerio de Minas y Energía, 2017). Coal, nickel, gold, platinum, emeralds, limestone, salt, phosphate rock, clays, siliceous sands and to a lesser extent copper, manganese, magnesite, barite, gypsum and various types of ornamental rocks, among others are produced (UPME, 2016). The contributions of mining activity in the economic dimension is more measurable, on the contrary in other dimensions, as the social and environmental, for this, every day there are new proposals and tools oriented to strengthen how to evaluate the contributions in terms of the sustainability and responsibility, with the aim of quantifying, concreting and non-utopian, to improve the life quality of a community and not only to comply with reporting and gaining prestige. Colombia has a generalized increase in the mining sector where the levels of informality and illegality are evident only 10% of mining activity is legal (UPME, 2014), also, the mining sector is accused of human rights violations, high levels of inequality, poverty and the affectation of ecosystems due to bad environmental management, among other situations (ACNUDH Colombia, 2015). This problem has generated rejection to the realization of the mining activity in many places of Colombia. At this point, it is important to clarify this problem is more complex, different actors are involved in this conflict, but it is an evidence that is needed a sustainability model for specific realities such as the Colombian mining. This situation in the current mining activity, is similar to the chemical industry situation three decades ago, because of an extensive problem in relation to repeated work accidents, natural disasters and indications as a highly polluting and unsustainable industry, with the aim of improving, not only this public perception, but also in the way of carrying out the business activity. Thus, in 1985, the Canadian Chemical Producers Association released the Responsible Care Program (RCP) (ICCA, 2015). Being aware that companies were responsible for the affected lives in some way by the operation and needed to improve workers safety, environmental protection and most importantly how legal persons should comply with the law, but go beyond this. RCP is most recognized sustainability initiative in the chemical sector, companies associated are recognized for having high quality standards, continuous improvement, visibility, corporate ethics, environmental and social management (ACC, 2015). In addition, to meeting the objectives is set out the creation of a model that increasing reputational sector levels. This initiative is considered to be a worldwide successful case of reporting corporate responsibility indicators and contributions to sustainability from the industry sector to local development (BASF Group, 2016)."

Jan 1, 2018

By Ruipeng Qian, Pengfei Wang, Guorui Feng, XianJie Du, Jun Guo, Yuxia Guo, Tingye Qi, JinWen Bai

"A numerical modeling was conducted to describe the behavior of overlying strata on the longwall top coal caving face for exploitation of a 16.8 m thick coal seam. Three typical structural models, including the Cantilever Structure (CS), Lower Cantilever and Upper Hinged Arch Structure (LC&UHA), and Lower Arch and Upper Voussoir Beam (LA&UVB), were developed. Based on mechanical analysis of the different structures of the key strata, and considering the behaviors of the broken igneous rock strata, a method was proposed and applied to estimate the structures of the overburden strata. The results had been verified by a field micro-seismic monitoring test. The paper provides a foundational method to determine the shield loadings for the top coal caving longwall face.INTRODUCTIONLongwall top coal caving (LTCC) is a highly productive underground mining technology which has been widely applied to the exploitation of the thick coal seams in China and other countries due to its high efficiency (Ju and Xu, 2013; Ju, Xu, and Wang, 2011; Liu et al., 2009). In recent years, a large amount of research on mining pressure forecast, strata control, and mechanical equipment improvement of the LTCC technology has been carried out, which greatly advances the field application of the technology (Liu et al., 2009; Yu, 2016; Dou et al., 2014; Feng et al., 2011; Chen and Li, 2011; Yin, Yan, and An, 2008). In 2006, the LTCC technology was first applied to the exploitation in a 20 m thick coal seam at the Tashan Coal Mine in China (Yan et al., 2011). Ten years of mining at the Tashan Coal Mine has highlighted the importance of the support management in controlling the roof strata on the extra-thick LTCC face. The mining pressure is closely related to the structural features of the overlying strata and its movement laws (Yu, 2016; Dou et al., 2014; Feng et al., 2011). However, the distributions of three zones—caving zone, fracture zone, and deformation zone—on the fully mechanized caving longwalls changed significantly with the increase in thickness of the coal seam (Chen and Li, 2011). The behavior changes of the roof strata led to abnormal pressure in the mining face and resulted in the difficulty of surrounding rock control (Yin, Yan, and An, 2008; Liu et al., 2009; Yan et al., 2011; Gong and Jin, 2008). Therefore, the theoretical research focused on the behavior of overlying strata to reveal the laws of mining pressure has important theoretical significance and practical value.Many classical studies (Qian and Shi, 2003; Feng, 2010; Yu, 2015; Yu, Yan, and Liu, 2012) had been done to describe the behavior of overlying strata in the mining process. It has also been reported that magma intrusion causes an important effect on the surrounding rock, coal, and methane (Wang et al., 2005; Liu et al., 2007). On the one hand, the property and structure of the coal seam was obviously changed by the magma intrusion and resulted in a potential danger of a gas outburst during the mining process (Chen et al., 2012; Wang et al., 2014). On the other hand, the hard igneous strata and the joints occurred with the magma cooled, causing an abnormal behavior of overlying strata and resulting in a series of dynamic disasters during mining (Xuan, Xu, and Lu, 2014; Lu et al., 2016). In fact, many coal fields in China are intruded by igneous sill, including the Datong, Shuozhou, Huainan, and Xuzhou coal fields (Chen et al., 2014; Wu, 2011). The 3–5 coal seam at Tashan Coal Mine in Datong coal field is very thick and is intruded by a large area of layered lamprophyre rock. Face falls and shield failures occurred frequently during the face retreat."

Jan 1, 2019

By D. H. Davidson

The basic principal in the ISL process involves the recovery of metal values by moving fluids through rock instead of moving rock. The process combines surface and sub-surface operations, with the economic performance controlled by four major factors; rates of fluid injection and production from wells; the rate of mineral solubilization; the volume of rock swept by the fluid; and the volume of solution processed through the system. This paper discusses various technical and economic parameters affecting these four factors and how they impact project costs.

Jan 1, 1985

By James E. Lawver

Response surface methodology is a well-known and powerful technique for determining optimum conditions in flotation systems. One disadvantage is the onerous task of the numerical calculations and curve platting. This paper describes a system in which the investigator simply selects the range of several flotation variables after which the design of the experiment, data analysis, generation of response surface equations, and response surface plats are automatically carried out using a digital computer and a computer-driven curve plotter. Several typical response surfaces of important variables in phosphate flotation are presented as examples. An overview of the flow charting of the system is provided in the addendum.

Jan 1, 1978

By Robert F. Randolph, Arnold C. Love

This study describes the positioning strategies used by operators of radio controlled underground mining machines. The observations have implications for task design to insure adequate visibility and task performance. Radio controlled continuous coal mining machines have allowed many mines to increase safety and production by placing human operators away from the hazards of an unsupported mine roof. The operator is no longer confined to an operators component and visibility can be enhanced with proper positioning. Also, the operator is no longer subjected to the shocks and vibrations of the mining machine. The operator's ability to move freely about the worksite requires a careful analysis of several competing safety and production considerations. Thirty-five operators of remotely controlled continuous mining machines were observed using work sampling followed by interviews to determine where the operator was positioned and what he or she was watching. These observations were separated according to the task being performed by the continuous mining machine and summarized as position density plots. The specific task of tramming in reverse through a crosscut is analyzed along with more general summaries of the time miners spend outside of the policy-defined operating positions while performing other production tasks. The operators were: observed to frequently vary from company standard operating procedures (SOP). Many of the variations from company SOPS were based on task demands. Interview responses indicated that portions of the mining task place visibility demands on the operators that are difficult to accommodate within existing procedures. An improved task design process would include these visibility requirements. Also, the operator's vision can be augmented thorough video cameras in future teleoperated mining systems, and the operator can be increasingly isolated from environmental hazards.

Jan 1, 1992

By E. V. Manlapig, B. K. Gorain, N. W. Johnson, K. Ward

A flotation model developed at the Julius Kruttschnitt Mineral Research Centre was used to predict the performance of copper rougher and scavenger circuits at the copper concentrator at Mount Isa Mines. The model describes the kinetic response of an ore in a flotation cell in terms of ore floatability, cell characteristics and froth recovery. The floatability parameters of the rougher feed ore were obtained directly from a detailed plant survey. Flotation analysis was carried out for twenty different size-by-liberation classes to account for the effects of particle size and liberation on flotation. This paper investigates the capability of the model to predict the flotation behavior of 20 different size-by liberation classes in the rougher and the scavenger banks.

Jan 1, 2000

By R. C. Bunge

A magnetogravimetric separation is the consequence of two competing forces with opposing directions, i.e., magnetic buoyancy and gravitation (or centrifugal force). While magnetic buoyancy is a function of particle volume, gravitational force depends on particle mass, thus permitting a separation according to specific gravity. Since magnetic buoyancy is not a phenomenon of common knowledge, this chapter is meant to briefly introduce the theory of magnetogravimetric separations. A particle that is suspended in a magnetic fluid which is exposed to an inhomogeneous magnetic field experiences a repulsive force -the so called magnetic buoyancy. In order to illustrate this effect, an analogy with the more familiar hydrostatic buoyancy is drawn. Hydrostatic buoyancy occurs due to unsymmetrical pressure distribution 'above' and 'below' a suspended particle (fig. 1).

Jan 1, 1990

By Bryan A. Bartley

About 1,000 machines around the world are breaking rock and hard abrasive materials by a very economic, high intensity, autogenous process, but this method is largely ignored by the mining industry. This vertical shaft autogenous impact crusher has impact velocities around 70 m/s, which compare with those of Cascade and SAG mills of up to 10 m/s. The autogenous impact, breakage processes are all at higher intensity levels and the products reflect this difference. The topic of liberation is breifly considered. A series of tests with a laboratory scale machine are reported to illustrate a number of the characteristics of the process. This paper highlights topics for further evaluation and research.

Jan 1, 1992

By D. Butler

Lateral density changes in the subsurface cause a change in the vertical pull of gravity at the surface. By very accurate measurement of gravity and the practical application of common sense, a microgravity survey can sometimes detect natural or man-made voids, bedrock profiles, and geologic structures of engineering interest. This paper will give some practical guidelines for the application of microgravity surveying. Emphasis in many papers (Blizkovsky, 1979, Fajklewicz, 1983) has been on the anomaly size: herein emphasis will be placed on detectability and signal-to-noise ratios. First, some easy to use curves for anomaly valuation are adapted from Arzi (1974). Secondly, the predictable noise sources are discussed. Thirdly, representative models of abandoned underground workings are evaluated for microgravity surveying given the probable noise in the survey results.

Jan 1, 1988

By N. J. Peberdy, C. N. Moreton, K. C. Garner

Introduction During the past decade a major objective of the process industry has been to use digital computer technology to improve plant operating efficiencies. This objective implied some form of optimization, a concept that has various interpretations depending on the view of the prospective user. For the purpose of this paper, optimization of a process plant is defined as the establishment and setting of plant operating conditions that maximize some mathematical yield function, i.e. maximum profit, minimum residue, etc. Analysis of these objectives and the available design and implementation techniques led to the conclusion that digital computer and optimization techniques are not the stumbling blocks, but rather the development and derivation of the mathematical models of the unit operations and process plants to be optimized. Such models should not only describe the optimized (steady-state) objective, but also how one steers to this state (control algorithm). Due to the multidisciplinary nature of the skills associated with the design and operation of process plants, the development of suitable models by a single discipline, such as the process control engineer, was found to be not only difficult but often impossible, due to budget and human resource limitations. To over-come these limitations, a computer aided design (CAD) tool has been developed. It aims to provide a productivity tool to the various disciplines, at the same time coordinating the technical input from each. The system described is but the starting point in an evolutionary development of a tool that, with use, is becoming more efficient and cost effective to use. Development has become an application engineering activity rather than the preserve of the computer specialist. Project phasing The development of a mathematical description of a process plant requires coordination of information from conceptual design to operation management. The activities required to build and operate a process plant are divided into four basic chronological activities or phases. These activities are often undertaken by different organizations and disciplines. As a result, continuity is often lost with the resultant loss of critical design data. The major activities are considered to be: conceptual and flowsheeting; detailing around the P & ID; building and commissioning; and plant operation. The CAD system described provides a design tool to be used for each of these activities, as well as providing continuity between the activities and the disciplines involved. The heart of the system is the dynamic simulation of the flowsheet. Each of the activities will be discussed, leading to two simple examples that demonstrate the use of the simulator. Figure 1 shows a schematic format of the various activities and the path followed by the dynamic flowsheet simulator in the life of a project. Flowsheet development The prime requirements in the design and develop¬ment of a process flowsheet are • selection of the correct unit operations to achieve the most economic (capital and operating) beneficiation of the specified reserve ; • the sizing of the unit operations to achieve the desired results, as a function of the projected feed rates etc., to handle the time related (dynamics) of the process; and • the production of a set of engineering documents showing the drawn and labeled flowsheet with an equipment list and process specification for each of the unit operations. The question may well be asked at this stage why dynamic flowsheet simulation should be considered when steady state modeling has been found to be adequate to date. With the increases encountered in the cost of capital, one often cannot afford the luxury of designing around the compounding worst case technique. Further, a more accurate design of the control surges can be achieved. No information is lost in that the steady state solution is in fact a subset of the dynamic model. In generalized state space modeling, the differential equations describing the process dynamics are illustrated in the following matrix notation: XDOT=A.X+B.U(1) Y =C.X+D.U(2) where XDOT describes the set of first order derivatives of the system state Vector, and X- is the system state Vector; A - is the system matrix operator which in the general nonlinear case is both a function of X and time ; U- is the process input vector; B - is the input mapping matrix; Y - is the set of observations; C - is the output mapping matrix which maps X - onto Y; and D- maps the input onto the observations. Thus, by time integration of the system dynamic equations, described in (1), the dynamic trajectory away from any set of initial conditions can be deter¬mined. Further, by finding the conditions at which XDOT = 0, the steady state solution can be determined.

Jan 1, 1987