On solving fuzzy delay differential equation using bezier curves

In this article, we plan to use Bezier curves method to solve linear fuzzy delay differential equations. A Bezier curves method is presented and modified to solve fuzzy delay problems taking the advantages of the fuzzy set theory properties. The approximate solution with different degrees is compared to the exact solution to confirm that the linear fuzzy delay differential equations process is accurate and efficient. Numerical example is explained and analyzed involved first order linear fuzzy delay differential equations to demonstrate these proper features of this proposed problem

Synthesis, optimisation and control of crystallization systems

Process systems engineering has provided with a range of powerful tools to chemical engineers for synthesis, optimisation and control using thorough understanding of the processes enhanced with the aid of sophisticated and accurate multi-faceted mathematical models. Crystallization processes have rarely benefited from these new techniques, for they lack in models that could be used to bridge the gaps in their perception before utilising the resulting insight for the three above mentioned tasks. In the present work, first a consistent and sufficiently complex models for unit operations including MSMPR crystallizer, hydrocyclone and fines dissolver are developed to enhance the understanding of systems comprising these units. This insight is then utilised for devising innovative techniques to synthesise, optimise and control such processes. A constructive targeting approach is developed for innovative synthesis of stage-wise crystallization processes. The resulting solution surpasses the performance obtained from conventional design procedure not only because optimal temperature profiles are used along the crystallizers but also the distribution of feed and product removal is optimally determined through non-linear programming. The revised Machine Learning methodology presented here for continual process improvement by analysing process data and representing the findings as zone of best average performance, has directly utilised the models to generate the data in the absence of real plant data. The methodology which is demonstrated through KNO₃ crystallization process flowsheet quickly identifies three opportunities each representing an increase of 12% on nominal operation. An optimal multi-variable controller has been designed for a one litre continuous recycle crystallizer to indirectly control total number and average size of crystals from secondary process measurements. The system identification is solely based on experimental findings. Linear Quadratic Gaussian method based design procedure is developed to design the controller which not only shows excellent set-point tracking capabilities but also effectively rejects disturbance in the simulated closed loop runs

Inclusion of input saturation in the design of dynamically operable plants

Bibliography: leaves 109-113.Dynamic operability reflects the quality with which a plant can be controlled using feedback, and is a function of both the design of the plant and its associated control system. A plant designed on the basis of steady-state considerations alone could exhibit poor dynamic characteristics, leading to a loss of economic performance and a reduced capacity to effectively handle safety and environmental constraints. This motivates the need for the development of quantitative techniques for dynamic operability assessment, as well as its incorporation into procedures for process plant design. Optimization-based approaches to dynamic operability assessment permit simultaneous consideration of performance-limiting factors of nonminimum phase characteristics, input constraints and model uncertainty, and also provide considerable flexibility in the choice of performance criteria, decision variables and constraints. Recent work has incorporated operability requirements as constraints within a single optimal plant design problem formulation (Mohideen et at., 1997; Bahri et at.,1996). Young and Swartz (1997) considered the rigorous inclusion of input saturation effects in optimizing control. Actuator saturation introduces discontinuities in the system model and, to avoid potential problems using a sequential optimization approach, two alternative formulations were proposed for solving the problem within a simultaneous solution framework. Input saturation discontinuities were handled by the introduction of slack variables and their inclusion in either bilinear or mixed-integer constraints resulting in a nonlinear or mixed-integer linear programming problem respectively. The formulations were applied to a linear system with dead time to find the economically optimal operating point for a controller with fixed structure and tunings when disturbance deviations are taken into account. It was shown that using a strictly linear controller in this case would lead to an overly conservative estimate of the feasible operating range and consequently, a suboptimal operating point

Convex optimization of launch vehicle ascent trajectories

This thesis investigates the use of convex optimization techniques for the ascent trajectory design and guidance of a launch vehicle. An optimized mission design and the implementation of a minimum-propellant guidance scheme are key to increasing the rocket carrying capacity and cutting the costs of access to space. However, the complexity of the launch vehicle optimal control problem (OCP), due to the high sensitivity to the optimization parameters and the numerous nonlinear constraints, make the application of traditional optimization methods somewhat unappealing, as either significant computational costs or accurate initialization points are required. Instead, recent convex optimization algorithms theoretically guarantee convergence in polynomial time regardless of the initial point. The main challenge consists in converting the nonconvex ascent problem into an equivalent convex OCP. To this end, lossless and successive convexification methods are employed on the launch vehicle problem to set up a sequential convex optimization algorithm that converges to the solution of the original problem in a short time. Motivated by the computational efficiency and reliability of the devised optimization strategy, the thesis also investigates the suitability of the convex optimization approach for the computational guidance of a launch vehicle upper stage in a model predictive control (MPC) framework. Being MPC based on recursively solving onboard an OCP to determine the optimal control actions, the resulting guidance scheme is not only performance-oriented but intrinsically robust to model uncertainties and random disturbances thanks to the closed-loop architecture. The characteristics of real-world launch vehicles are taken into account by considering rocket configurations inspired to SpaceX's Falcon 9 and ESA's VEGA as case studies. Extensive numerical results prove the convergence properties and the efficiency of the approach, posing convex optimization as a promising tool for launch vehicle ascent trajectory design and guidance algorithms

Activities of the Institute for Computer Applications in Science and Engineering

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April 1, 1985 through October 2, 1985 is summarized

Optimal control of a motor-integrated hybrid powertrain for a two-wheeled vehicle suitable for personal transportation

The present research aims to propose an optimized configuration of the motor integrated power-train with an optimal controller suitable for small power-train based two wheeler automobile which can increase the system level efficiency without affecting drivability. This work will be the foundation for realizing the system in a production ready vehicle for the two wheeler OEM TVS Motor Company in India. A detailed power-train model is developed (from first principles) for the scooter vehicle, which is powered by a 110 cc spark ignition (SI) engine and coupled with two types of transmission, a continuous variable transmission (CVT) and a 4-speed manual transmission (MT). Both models are capable of simulating torque and NOx emission output of the SI engine and dynamic response of the full power-train. The torque production and emission outputs of the model are compared with experimental results available from TVS Motor Company. The CVT gear ratio model is developed using an indirect method and an analytical model. Both types of powertrain models are applied to perform a simulated study of fuel consumption, NOx emission and drivability study for a particular vehicle platform. In the next stage of work, the mathematical model for a brush-less direct current machine (BLDC) with the drive system and Li-Ion battery are developed. The models are verified and calibrated with the experimental results from TVS Motor Company. The BLDC machine is integrated with both the CVT and MT powertrain models in parallel hybrid configurations and a drive cycle simulation is conducted for different static assist levels by the electrical machines. The initial test confirms the need of optimal sizing of the powertrain components as well as an optimal control system. The detailed model of the powertrain is converted to a control-oriented model which is suitable for optimal control. This is followed by multi-objective optimization of different components of the motor-integrated powertrain using a single function as well as Pareto-Optimal methods. The objective function for the multi-objective optimization is proposed to reduce the fuel consumption with battery charge sustainability with least impact on the increase of financial cost and weight of the vehicle. The optimization is conducted by a nested methodology that involves Particle Swarm Optimization and a Non-dominated sorting genetic algorithm where, concurrently, a global optimal control is developed corresponding to the multi-objective design. The global optimal controller is designed using dynamic programming. The research is concluded with an optimal controller developed using the hp-collocation method. The objective function of the dynamic programming method and hp-collocation method is proposed to reduce fuel consumption with battery charge sustainability.Open Acces

Astrophysical turbulence modeling

The role of turbulence in various astrophysical settings is reviewed. Among the differences to laboratory and atmospheric turbulence we highlight the ubiquitous presence of magnetic fields that are generally produced and maintained by dynamo action. The extreme temperature and density contrasts and stratifications are emphasized in connection with turbulence in the interstellar medium and in stars with outer convection zones, respectively. In many cases turbulence plays an essential role in facilitating enhanced transport of mass, momentum, energy, and magnetic fields in terms of the corresponding coarse-grained mean fields. Those transport properties are usually strongly modified by anisotropies and often completely new effects emerge in such a description that have no correspondence in terms of the original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic