Three-Stage Optimization Approach Using Nonlinear Programming and Simulation

This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-dependent inequality constraints. The method presented is illustrated with a model of a single-link manipulator. The method is suitable to be taught to advanced undergraduate and Master's level students in control engineering.

This paper presents a nonlinear circuit simulation program called EHBSim implemented in Matlab. This program offers as simulation methods the harmonic balance method, and mainly the nonlinear envelope method. Equations systems that allow the simulation of any circuit architecture were used. The program has original algorithms implemented to solve the associated equation systems. Performance comparison between several simulation methods, through the analysis of multi-excited circuits, is also carried out.

A simulation‐management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. Restrictions can be placed on hydraulic heads, stresses, and gradients, in addition to contaminant concentrations and fluxes. These restrictions can be distributed over space and time. Three design strategies are demonstrated for an aquifer that is polluted by a constant contaminant source: they are pumping for contaminant removal, water injection for in‐ground dilution, and a pumping, treatment, and injection cycle. A transient model designs either contaminant plume interception or in‐ground dilution so that water quality standards are met. The method is not limited to these cases. It is generally applicable to the optimization of many types of distributed parameter systems.

In this paper, a method based on stability boundary plot is considered for an unstable second order process with dead time. All the controllers that satisfy the gain margin and phase margin requirements are found by plotting the K p -K i curve. The technique is based on Kharitonov theorem for stability of interval plants. Limiting values of the controller parameters that stabilize the given system are found using the curves obtained. In addition to this, an optimization based design of robust Proportional-Integral-Derivative (PID) controller that guarantees both the stability and performance of an interval plant is proposed. The controller design involves two steps. First, a controller setting is obtained for the nominal plant and then optimization is done to find a setting which will work on the entire range of the uncertainties specified. Optimization is based on the necessary and sufficient conditions for a system to be Hurwitz stable. A set of constraints are framed based on these conditions and it is used to minimize an objective function using non-linear programming (NLP). This technique is applied to i) Stable FOPTD process ii) Unstable FOPTD process. Further, Nonlinear simulation is performed for an unstable CSTR plant under three operating regions. The results obtained show the effectiveness of optimization taking into account the uncertainties associated with the plant.

The air separation unit (ASU) is one of the core elements of integrated gasification combined cycle (IGCC) power plants. The ASU separates air into pure oxygen and nitrogen, to be sent to the gasifier and the gas turbine, respectively. This system consumes about 10% of the gross power output generated in IGCC, so its economical operation is important for lowering the overall power generation cost. The use of an elevated-pressure air separation unit (EP ASU), in which the operating pressure is higher than in a conventional ASU, is known to lead to significant energy savings. In this research, controlled variable selection for an EP ASU was studied, considering both the controllability and economics, that is, with the objective of maintaining economically near-optimal operations in the presence of anticipated load changes. The main tool used for this was the so-called “minimum singular value rule” within the overall framework of self-optimizing control (SOC). For the purpose of selecting and testing self-optimizing control structures, equation-based modeling of EP ASU was carried out and implemented on the commercial software platform gPROMS. Then, the minimum singular value rule was applied using steady-state gain matrices (obtained from the simulator) to select a small number of candidate sets for controlled variables, to which rigorous analyses based on nonlinear simulation and optimization could be applied to pick the top choice. Before the minimum singular value rule was applied, however, certain process insights and heuristics were used to reduce the number of candidate sets down to a manageable level. The economic losses as a result of adopting a fixed control structure were assessed by comparing the hourly operating costs achieved under SOC with the equivalent values obtained by performing full nonlinear optimizations for the given scenarios. In addition, for the suggested control structure, proportional plus integral (PI) control loops were designed, and their dynamic performance was tested in order to make sure that it is attractive in terms of not only economics but also controllability. The finally selected control structure is compared with those presented in previous works.

Dynamics of capillary fluid exchange: A nonlinear computer simulation

Parameters optimization of magnetic fluid micro-pressure sensor

This work fills an important gap in the literature by providing an important link between MAPLE and its successful use in solving problems in Operations Research (OR). The symbolic, numerical, and graphical aspects of MAPLE make this software package an ideal tool for treating certain OR problems and providing descriptive and optimization-based analyses of deterministic and stochastic models. Detailed is MAPLE's treatment of some of the mathematical techniques used in OR modeling: e.g., algebra and calculus, ordinary and partial differential equations, linear algebra, transform methods, and probability theory. A number of examples of OR techniques and applications are presented, such as linear and nonlinear programming, dynamic programming, stochastic processes, inventory models, queueing systems, and simulation. Throughout the text MAPLE statements used in the solutions of problems are clearly explained. At the same time, technical background material is presented in a rigorous mathematical manner to reach the OR novice and professional. Numerous end-of- chapter exercises, a good bibliography and overall index at the end of the book are also included, as well as MAPLE worksheets that are easily downloadable from the author's website at www.business.mcmaster.ca/msis/profs/parlar, or from the Birkhauser website at www.birkhauser.com/cgi-win/ISBN/0-8176-4165-3. The book is intended for advanced undergraduate and graduate students in operations research, management science departments of business schools, industrial and systems engineering, economics, and mathematics. As a self-study resource, the text can be used by researchers and practitioners who want a quick overview of MAPLE's usefulness in solving realistic OR problems that would be difficult or impossible to solve with other software packages.

This paper presents the methods of processing interactive data describing different forms of uncertainty. Data can be expressed in the form of interactive possibility distribution or the part of data can be expressed in the form of interactive possibility distribution and the part in the form of pr obability distribution. The procedure of processing combines stochastic simulation with nonlinear programming or simulation of fuzzy systems. The interaction between data are modeled by the correlation matrices and the interval regression. Presented practical example indicates that an interaction between data have a significant impact on results of calculations. Data processing without consideration of these interrelations would bear a considerable, systematic error.

This paper focuses on improving the active and reactive power control of Wind Energy Conversion System (WECS) by employing the Battery Energy Storage System (BESS) and controlling the frequency and voltage regulation instantaneously. The proposed power control scheme is composed of two control loops so that they are implemented and designed for active power control and controlling the reactive power, respectively, which both are equipped with PI type controllers. In addition, two control loops were utilized to control the frequency and voltage on the rotor side converter under balance and unbalance grid conditions. In this paper, the presented control strategy optimally tuned all the parameters of controllers at the same time by utilizing a mixed integer nonlinear optimization programming and solved by the ICA algorithm. Moreover, in order to demonstrate the effectiveness of the proposed strategy, non-linear time domain simulations were carried out in MATLAB software. The obtained simulation results verified that the proposed control scheme efficiently utilize BESS to control the active and reactive power control and confirm the effectiveness of the proposed strategy under the balanced and unbalanced grid conditions.

Coastal water regions represent some of the most fragile ecosystems, exposed to both climate change and human activities. While remote sensing provides unprecedented amounts of data for water quality monitoring on regional to global scales, the performance of satellite observations is frequently impeded by revisiting intervals and unfavorable conditions, such as cloud coverage and sun glint. Therefore, it is crucial to evaluate the impacts of varied sampling strategies (time and frequency) and insufficient observations on the monitoring of short-term and long-term tendencies of water quality parameters, such as suspended solids (SS), in highly dynamic coastal waters. Taking advantage of the first high-frequency in situ SS dataset (at 30 min sampling intervals from 2007 to 2008), collected in Deep Bay, China, this paper presents a quantitative analysis of the influences of sampling strategies on the monitoring of SS, in terms of sampling frequency and time of day. Dramatic variations of SS were observed, with standard deviation coefficients of 48.9% and 54.1%, at two fixed stations; in addition, significant uncertainties were revealed, with the average absolute percent difference of approximately 13%, related to sampling frequency and time, using nonlinear optimization and random simulation methods. For a sampling frequency of less than two observations per day, the relative error of SS was higher than 50%, and stabilized at approximately 10%, when at least four or five samplings were conducted per day. The optimal recommended sampling times for SS were at around 9:00, 12:00, 14:00, and 16:00 in Deep Bay. The “pseudo” MODIS SS dataset was obtained from high-frequency in situ SS measurements at 10:30 and 14:00, masked by the temporal gap distribution of MODIS coverage to avoid uncertainties propagated from atmospheric correction and SS models. Noteworthy uncertainties of daily observations from the Terra/Aqua MODIS were found, with mean relative errors of 19.2% and 17.8%, respectively, whereas at the monthly level, the mean relative error of Terra/Aqua MODIS observations was approximately 10.7% (standard deviation of 8.4%). Sensitivity analysis between MODIS coverage and SS relative errors indicated that temporal coverage (the percentage of valid MODIS observations for a month) of more than 70% is required to obtain high-precision SS measurements at a 5% error level. Furthermore, approximately 20% of relative errors were found with the coverage of 30%, which was the average coverage of satellite observations over global coastal waters. These results highlight the need for high-frequency measurements of geostationary satellites like GOCI and multi-source ocean color sensors to capture the dynamic process of coastal waters in both the short and long term.

A nonlinear flow reservoir mathematical model was established based on the flow characteristic of low-permeability reservoir. The well-grid equations were deduced and the dimensionless permeability coefficient was introduced to describe the permeability variation of nonlinear flow. The nonlinear flow numerical simulation program was compiled based on black-oil model. A quarter of five-spot well unit was simulated to study the effect of nonlinear flow on the exploitation of low-permeability reservoir. The comprehensive comparison and analysis of the simulation results of Darcy flow, quasi-linear flow and nonlinear flow were provided. The dimensionless permeability coefficient distribution was gained to describe the nonlinear flow degree. The result shows that compared with the results of Darcy flow, when considering nonlinear flow, the oil production is low, and production decline is rapid. The fluid flow in reservoir consumes more driving energy, which reduces the water flooding efficiency. Darcy flow model overstates the reservoir flow capability, and quasi-linear flow model overstates the reservoir flow resistance. The flow ability of the formation near the well and artificial fracture is strong while the flow ability of the formation far away from the main streamline is weak. The nonlinear flow area is much larger than that of quasi-linear flow during the fluid flow in low-permeability reservoir. The water propelling speed of nonlinear flow is greatly slower than that of Darcy flow in the vertical direction of artificial fracture, and the nonlinear flow should be taken into account in the well pattern arrangement of low-permeability reservoir.

In order to accurately calculate the braking efficiency factor of drum brake shoe of heavy truck, virtual prototyping of a heavy truck's brake is demonstrated. The requirements for brakes include not only its performance but also its comfort, serviceability and working lifetime, which must be high. The finite element analysis software ANSYS and the multi-body system simulation software MSC.ADAMS were used to establish the drum brake nonlinear 3D simulation model. The model was built by developing joint program module between the rigid shoe and the flexible lining and nonlinear contact force program module between the lining and the rigid drum. Using this model, the simulation was executed for the drum brake of 32t heavy duty truck. The results show that the simulated braking efficiency factor coincides with experimental results of the braking efficiency factor of the heavy truck drum brake.

A six degree of freedom nonlinear airship flight dynamic simulation program has been adapted to apply to nonrigid airships. This report discusses the physical and aerodynamic models that underlie the simulation. The principle of the simulation and the structure of the program are described. The simulation was used to model the flight behavior of a new technology blimp, the Airship Industries Skyship 500, for which flight test data were available. Simulation predictions follow the same trends indicated by the flight test data. The computer simulation performed well in a wide variety of maneuvers.

A nonlinear flow mathematical model is established and the grid equation is deduced. A nonlinear flow reservoir numerical simulation program is compiled. The permeability loss coefficient is used to describe the permeability loss. A pilot calculation is made on the basis of actual field data, which reflects the reservoir development characteristics. The numerical simulation program based on nonlinear flow can anticipate the dynamic characteristics of the ultra-low permeability reservoir exploitation more exactly.