Search results for: optimal control involving ODEs

Authors: Liang Bai, Yandong Xiao, Haorang Wang, Songyang Lao

Abstract:

The directedness of links is crucial to determine the controllability in complex networks. Even the edge directions can determine the controllability of complex networks. Obviously, for a given network, we wish to design its edge directions that make this network approach the optimal controllability. In this work, we firstly introduce two methods to enhance network by assigning edge directions. However, these two methods could not completely mitigate the negative effects of inaccessibility and dilations. Thus, to approach the optimal network controllability, the edge directions must mitigate the negative effects of inaccessibility and dilations as much as possible. Finally, we propose the edge direction for optimal controllability. The optimal method has been found to be successfully useful on real-world and synthetic networks.

Keywords: complex network, dynamics, network control, optimization

Procedia PDF Downloads 145

Authors: R. Dariani, S. Schmidt, R. Kasper

Abstract:

Based on a non-linear single track model which describes the dynamics of vehicle, an optimal path planning strategy is developed. Real time optimization is used to generate reference control values to allow leading the vehicle alongside a calculated lane which is optimal for different objectives such as energy consumption, run time, safety or comfort characteristics. Strict mathematic formulation of the autonomous driving allows taking decision on undefined situation such as lane change or obstacle avoidance. Based on position of the vehicle, lane situation and obstacle position, the optimization problem is reformulated in real-time to avoid the obstacle and any car crash.

Keywords: autonomous driving, obstacle avoidance, optimal control, path planning

Procedia PDF Downloads 342

Authors: Anne Schattel, Mitja Echim, Christof Büskens

Abstract:

Trajectory planning for deep space missions has become a recent topic of great interest. Flying to space objects like asteroids provides two main challenges. One is to find rare earth elements, the other to gain scientific knowledge of the origin of the world. Due to the enormous spatial distances such explorer missions have to be performed unmanned and autonomously. The mathematical field of optimization and optimal control can be used to realize autonomous missions while protecting recourses and making them safer. The resulting algorithms may be applied to other, earth-bound applications like e.g. deep sea navigation and autonomous driving as well. The project KaNaRiA ('Kognitionsbasierte, autonome Navigation am Beispiel des Ressourcenabbaus im All') investigates the possibilities of cognitive autonomous navigation on the example of an asteroid mining mission, including the cruise phase and approach as well as the asteroid rendezvous, landing and surface exploration. To verify and test all methods an interactive, real-time capable simulation using virtual reality is developed under KaNaRiA. This paper focuses on the specific challenge of the guidance during the cruise phase of the spacecraft, i.e. trajectory optimization and optimal control, including first solutions and results. In principle there exist two ways to solve optimal control problems (OCPs), the so called indirect and direct methods. The indirect methods are being studied since several decades and their usage needs advanced skills regarding optimal control theory. The main idea of direct approaches, also known as transcription techniques, is to transform the infinite-dimensional OCP into a finite-dimensional non-linear optimization problem (NLP) via discretization of states and controls. These direct methods are applied in this paper. The resulting high dimensional NLP with constraints can be solved efficiently by special NLP methods, e.g. sequential quadratic programming (SQP) or interior point methods (IP). The movement of the spacecraft due to gravitational influences of the sun and other planets, as well as the thrust commands, is described through ordinary differential equations (ODEs). The competitive mission aims like short flight times and low energy consumption are considered by using a multi-criteria objective function. The resulting non-linear high-dimensional optimization problems are solved by using the software package WORHP ('We Optimize Really Huge Problems'), a software routine combining SQP at an outer level and IP to solve underlying quadratic subproblems. An application-adapted model of impulsive thrusting, as well as a model of an electrically powered spacecraft propulsion system, is introduced. Different priorities and possibilities of a space mission regarding energy cost and flight time duration are investigated by choosing different weighting factors for the multi-criteria objective function. Varying mission trajectories are analyzed and compared, both aiming at different destination asteroids and using different propulsion systems. For the transcription, the robust method of full discretization is used. The results strengthen the need for trajectory optimization as a foundation for autonomous decision making during deep space missions. Simultaneously they show the enormous increase in possibilities for flight maneuvers by being able to consider different and opposite mission objectives.

Keywords: deep space navigation, guidance, multi-objective, non-linear optimization, optimal control, trajectory planning.

Procedia PDF Downloads 383

Authors: Davood Yazdani Cherati, Ali Pak, Mehrdad Jafarzadeh

Abstract:

This research contains the formulation of a two-dimensional analytical solution to transient heat, and moisture flow in a semi-infinite unsaturated soil environment under the influence of daily temperature changes. For this purpose, coupled energy conservation and mass fluid continuity equations governing hydrothermal behavior of unsaturated soil media are presented in terms of temperature and volumetric moisture content. In consideration of the soil environment as an infinite half-space and by linearization of the governing equations, Laplace–Fourier transformation is conducted to convert differential equations with partial derivatives (PDEs) to ordinary differential equations (ODEs). The obtained ODEs are solved, and the inverse transformations are calculated to determine the solution to the system of equations. Results indicate that heat variation induces moisture transport in both horizontal and vertical directions.

Keywords: analytical solution, heat conduction, hydrothermal analysis, laplace–fourier transformation, two-dimensional

Procedia PDF Downloads 186

Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

Abstract:

Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

Procedia PDF Downloads 138

Authors: Mahmoud Lot

Abstract:

In this article, we will discuss the solution of elliptic optimal control problem. First, by using the nite element method, we obtain the discrete form of the problem. The obtained discrete problem is actually a large scale constrained optimization problem. Solving this optimization problem with traditional methods is difficult and requires a lot of CPU time and memory. But split Bergman method converts the constrained problem to an unconstrained, and hence it saves time and memory requirement. Then we use the split Bregman method for solving this problem, and examples show the speed and accuracy of split Bregman methods for solving these types of problems. We also use the SQP method for solving the examples and compare with the split Bregman method.

Keywords: Split Bregman Method, optimal control with elliptic partial differential equation constraint, finite element method

Procedia PDF Downloads 115

Authors: Niklas Panten, Eberhard Abele

Abstract:

This paper presents a novel approach for real-time and near-optimal control of industrial smart grids by deep reinforcement learning (DRL). To achieve highly energy-efficient factory systems, the energetic linkage of machines, technical building equipment and the building itself is desirable. However, the increased complexity of the interacting sub-systems, multiple time-variant target values and stochastic influences by the production environment, weather and energy markets make it difficult to efficiently control the energy production, storage and consumption in the hybrid industrial smart grids. The studied deep reinforcement learning approach allows to explore the solution space for proper control policies which minimize a cost function. The deep neural network of the DRL agent is based on a multilayer perceptron (MLP), Long Short-Term Memory (LSTM) and convolutional layers. The agent is trained within multiple Modelica-based factory simulation environments by the Advantage Actor Critic algorithm (A2C). The DRL controller is evaluated by means of the simulation and then compared to a conventional, rule-based approach. Finally, the results indicate that the DRL approach is able to improve the control performance and significantly reduce energy respectively operating costs of industrial smart grids.

Keywords: industrial smart grids, energy efficiency, deep reinforcement learning, optimal control

Procedia PDF Downloads 167

Authors: Artem Sedov, Aigerim Uyzbayeva, Valeriya Tyo

Abstract:

The presented article is showing results of dynamic modeling with Mathlab software of optimal automatic room climate control system for two experimental houses in Astana, one of which has circle plan and the other one has square plan. These results are showing that building geometry doesn't influence on climate system PID-controls configuring. This confirms theoretical implication that optimal automatic climate control system parameters configuring should depend on building's internal space volume, envelope heat transfer, number of people inside, supply ventilation air flow and outdoor temperature.

Keywords: climate control system, climate physics, dome-like building, mathematical modeling

Procedia PDF Downloads 330

Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

A class of implicit systems is known as a more generalized class of systems than a class of explicit systems. To establish a control method for such a generalized class of systems, we adopt model predictive control method which is a kind of optimal feedback control with a performance index that has a moving initial time and terminal time. However, model predictive control method is inapplicable to systems whose all state variables are not exactly known. In other words, model predictive control method is inapplicable to systems with limited measurable states. In fact, it is usual that the state variables of systems are measured through outputs, hence, only limited parts of them can be used directly. It is also usual that output signals are disturbed by process and sensor noises. Hence, it is important to establish a state estimation method for nonlinear implicit systems with taking the process noise and sensor noise into consideration. To this purpose, we apply the model predictive control method and unscented Kalman filter for solving the optimization and estimation problems of nonlinear implicit systems, respectively. The objective of this study is to establish a model predictive control with unscented Kalman filter for nonlinear implicit systems.

Keywords: optimal control, nonlinear systems, state estimation, Kalman filter

Procedia PDF Downloads 168

Authors: P. Sawatnatee, S. Udomsuk, K-N. Areerak, K-L. Areerak, A. Srikaew

Abstract:

The paper presents how to design the indirect vector control of three-phase induction motor drive systems using the artificial intelligence technique called the adaptive tabu search. The results from the simulation and the experiment show that the drive system with the controller designed from the proposed method can provide the best output speed response compared with those of the conventional method. The controller design using the proposed technique can be used to create the software package for engineers to achieve the optimal controller design of the induction motor speed control based on the indirect vector concept.

Keywords: indirect vector control, induction motor, adaptive tabu search, control design, artificial intelligence

Procedia PDF Downloads 377

Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

Abstract:

Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: decentralized, optimal control, output, singular perturb

Procedia PDF Downloads 337

Authors: Minjeong Kim, Seungchul Lee, Iman Janghorban Esfahani, Jeong Tai Kim, ChangKyoo Yoo

Abstract:

A trajectory of set-point of ventilation control systems plays an important role for efficient ventilation inside subway stations since it affects the level of indoor air pollutants and ventilation energy consumption. To maintain indoor air quality (IAQ) at a comfortable range with lower ventilation energy consumption, the optimal trajectory of the ventilation control system needs to be determined. The concentration of air pollutants inside the station shows a diurnal variation in accordance with the variations in the number of passengers and subway frequency. To consider the diurnal variation of IAQ, an iterative dynamic programming (IDP) that searches for a piecewise control policy by separating whole duration into several stages is used. When outdoor air is contaminated by pollutants, it enters the subway station through the ventilation system, which results in the deteriorated IAQ and adverse effects on passenger health. In this study, to consider the influence of outdoor air quality (OAQ), a new performance index of the IDP with the passenger health risk and OAQ is proposed. This study was carried out for an underground subway station at Seoul Metro, Korea. The optimal set-points of the ventilation control system are determined every 3 hours, then, the ventilation controller adjusts the ventilation fan speed according to the optimal set-point changes. Compared to manual ventilation system which is operated irrespective of the OAQ, the IDP-based ventilation control system saves 3.7% of the energy consumption. Compared to the fixed set-point controller which is operated irrespective of the IAQ diurnal variation, the IDP-based controller shows better performance with a 2% decrease in energy consumption, maintaining the comfortable IAQ range inside the station.

Keywords: indoor air quality, iterative dynamic algorithm, outdoor air information, ventilation control system

Procedia PDF Downloads 481

Authors: Pawel Martynowicz

Abstract:

Vibrations are a crucial problem for slender structures such as towers, masts, chimneys, wind turbines, bridges, high buildings, etc., that is why most of them are equipped with vibration attenuation or fatigue reduction solutions. In this work, a slender structure (i.e., wind turbine tower-nacelle model) equipped with nonlinear, semiactive tuned vibration absorber(s) is analyzed. For this study purposes, magnetorheological (MR) dampers are used as semiactive actuators. Several optimal-based approaches to structural vibration attenuation are investigated against the standard ‘ground-hook’ law and passive tuned vibration absorber(s) implementations. The common approach to optimal control of nonlinear systems is offline computation of the optimal solution, however, so determined open loop control suffers from lack of robustness to uncertainties (e.g., unmodelled dynamics, perturbations of external forces or initial conditions), and thus perturbation control techniques are often used. However, proper linearization may be an issue for highly nonlinear systems with implicit relations between state, co-state, and control. The main contribution of the author is the development as well as numerical and experimental verification of the Pontriagin maximum-principle-based vibration control concepts that produce directly actuator control input (not the demanded force), thus force tracking algorithm that results in control inaccuracy is entirely omitted. These concepts, including one-step optimal control, quasi-optimal control, and optimal-based modified ‘ground-hook’ law, can be directly implemented in online and real-time feedback control for periodic (or semi-periodic) disturbances with invariant or time-varying parameters, as well as for non-periodic, transient or random disturbances, what is a limitation for some other known solutions. No offline calculation, excitations/disturbances assumption or vibration frequency determination is necessary, moreover, all of the nonlinear actuator (MR damper) force constraints, i.e., no active forces, lower and upper saturation limits, hysteresis-type dynamics, etc., are embedded in the control technique, thus the solution is optimal or suboptimal for the assumed actuator, respecting its limitations. Depending on the selected method variant, a moderate or decisive reduction in the computational load is possible compared to other methods of nonlinear optimal control, while assuring the quality and robustness of the vibration reduction system, as well as considering multi-pronged operational aspects, such as possible minimization of the amplitude of the deflection and acceleration of the vibrating structure, its potential and/or kinetic energy, required actuator force, control input (e.g. electric current in the MR damper coil) and/or stroke amplitude. The developed solutions are characterized by high vibration reduction efficiency – the obtained maximum values of the dynamic amplification factor are close to 2.0, while for the best of the passive systems, these values exceed 3.5.

Keywords: magnetorheological damper, nonlinear tuned vibration absorber, optimal control, real-time structural vibration attenuation, wind turbines

Procedia PDF Downloads 97

Authors: Brahim Berbaoui

Abstract:

In this paper, a new particle swarm optimization (PSO) based method is proposed for the implantation of optimal harmonic power flow in power systems. In this algorithm approach, proportional integral controller for reference compensating currents of active power filter is performed in order to minimize the total harmonic distortion (THD). The simulation results show that the new control method using PSO approach is not only easy to be implanted, but also very effective in reducing the unwanted harmonics and compensating reactive power. The studies carried out have been accomplished using the MATLAB Simulink Power System Toolbox.

Keywords: shunt active power filter, power quality, current control, proportional integral controller, particle swarm optimization

Procedia PDF Downloads 579

Authors: Vinko Lešić, Mario Vašak, Anita Martinčević, Marko Gulin, Antonio Starčić, Hrvoje Novak

Abstract:

With 40% of total world energy consumption, building systems are developing into technically complex large energy consumers suitable for application of sophisticated power management approaches to largely increase the energy efficiency and even make them active energy market participants. Centralized control system of building heating and cooling managed by economically-optimal model predictive control shows promising results with estimated 30% of energy efficiency increase. The research is focused on implementation of such a method on a case study performed on two floors of our faculty building with corresponding sensors wireless data acquisition, remote heating/cooling units and central climate controller. Building walls are mathematically modeled with corresponding material types, surface shapes and sizes. Models are then exploited to predict thermal characteristics and changes in different building zones. Exterior influences such as environmental conditions and weather forecast, people behavior and comfort demands are all taken into account for deriving price-optimal climate control. Finally, a DC microgrid with photovoltaics, wind turbine, supercapacitor, batteries and fuel cell stacks is added to make the building a unit capable of active participation in a price-varying energy market. Computational burden of applying model predictive control on such a complex system is relaxed through a hierarchical decomposition of the microgrid and climate control, where the former is designed as higher hierarchical level with pre-calculated price-optimal power flows control, and latter is designed as lower level control responsible to ensure thermal comfort and exploit the optimal supply conditions enabled by microgrid energy flows management. Such an approach is expected to enable the inclusion of more complex building subsystems into consideration in order to further increase the energy efficiency.

Keywords: price-optimal building climate control, Microgrid power flow optimisation, hierarchical model predictive control, energy efficient buildings, energy market participation

Procedia PDF Downloads 438

Authors: Eunice Christabel Chukwu

Abstract:

Introduction: Diabetes is a chronic medical condition which is characterized by high levels of glucose in the blood and urine; it is usually diagnosed by means of a glucose tolerance test (GTT). Diabetes can cause a range of health problems if left unmanaged, as it can lead to serious complications. It is essential to manage the condition effectively, particularly in the workplace where the impact on work productivity can be significant. This paper discusses the modelling of optimal control of diabetes in the workplace using a control theory approach. Background: Diabetes mellitus is a condition caused by too much glucose in the blood. Insulin, a hormone produced by the pancreas, controls the blood sugar level by regulating the production and storage of glucose. In diabetes, there may be a decrease in the body’s ability to respond to insulin or a decrease in insulin produced by the pancreas which will lead to abnormalities in the metabolism of carbohydrates, proteins, and fats. In addition to the health implications, the condition can also have a significant impact on work productivity, as employees with uncontrolled diabetes are at risk of absenteeism, reduced performance, and increased healthcare costs. While several interventions are available to manage diabetes, the most effective approach is to control blood glucose levels through a combination of lifestyle modifications and medication. Methodology: The control theory approach involves modelling the dynamics of the system and designing a controller that can regulate the system to achieve optimal performance. In the case of diabetes, the system dynamics can be modelled using a mathematical model that describes the relationship between insulin, glucose, and other variables. The controller can then be designed to regulate the glucose levels to maintain them within a healthy range. Results: The modelling of optimal control of diabetes in the workplace using a control theory approach has shown promising results. The model has been able to predict the optimal dose of insulin required to maintain glucose levels within a healthy range, taking into account the individual’s lifestyle, medication regimen, and other relevant factors. The approach has also been used to design interventions that can improve diabetes management in the workplace, such as regular glucose monitoring and education programs. Conclusion: The modelling of optimal control of diabetes in the workplace using a control theory approach has significant potential to improve diabetes management and work productivity. By using a mathematical model and a controller to regulate glucose levels, the approach can help individuals with diabetes to achieve optimal health outcomes while minimizing the impact of the condition on their work performance. Further research is needed to validate the model and develop interventions that can be implemented in the workplace.

Keywords: mathematical model, blood, insulin, pancreas, model, glucose

Procedia PDF Downloads 39

Authors: Hyeonkyeong Yang, Minseok Son, Taekbeom Yoo, Woojin Park

Abstract:

Human error is the most salient contributing factor to railway accidents. To reduce the frequency of human errors, many researchers and train designers have adopted ergonomic design principles for designing display-control layout in rail cab. There exist a number of approaches for designing the display control layout based on optimization methods. However, the ergonomically optimized layout design may not be the best design for train drivers, since the drivers have their own mental models based on their experiences. Consequently, the drivers may prefer the existing display-control layout design over the optimal design, and even show better driving performance using the existing design compared to that using the optimal design. Thus, in addition to ergonomic design principles, train drivers’ mental models also need to be considered for designing display-control layout in rail cab. This paper developed an ergonomic assessment system of display-control layout design, and an interactive layout design system that can generate design alternatives and calculate ergonomic assessment score in real-time. The design alternatives generated from the interactive layout design system may not include the optimal design from the ergonomics point of view. However, the system’s strength is that it considers train drivers’ mental models, which can help generate alternatives that are more friendly and easier to use for train drivers. Also, with the developed system, non-experts in ergonomics, such as train drivers, can refine the design alternatives and improve ergonomic assessment score in real-time.

Keywords: display-control layout design, interactive layout design system, mental model, train drivers

Procedia PDF Downloads 274

Authors: Akram Khaleghei Ghosheh Balagh, Viliam Makis, Leila Jafari

Abstract:

In this paper, we present a new maintenance model for a partially observable system subject to two failure modes, namely a catastrophic failure and a failure due to the system degradation. The system is subject to condition monitoring and the degradation process is described by a hidden Markov model. A cost-optimal Bayesian control policy is developed for maintaining the system. The control problem is formulated in the semi-Markov decision process framework. An effective computational algorithm is developed and illustrated by a numerical example.

Keywords: partially observable system, hidden Markov model, competing risks, multivariate Bayesian control

Procedia PDF Downloads 428

Authors: Wesam Jasim, Dongbing Gu

Abstract:

This paper presents an iterative linear quadratic regulator optimal control technique to solve the problem of quadrotors path tracking. The dynamic motion equations are represented based on unit quaternion representation and include some modelled aerodynamical effects as a nonlinear part. Simulation results prove the ability and effectiveness of iLQR to stabilize the quadrotor and successfully track different paths. It also shows that iLQR controller outperforms LQR controller in terms of fast convergence and tracking errors.

Keywords: iLQR controller, optimal control, path tracking, quadrotor UAVs

Procedia PDF Downloads 391

Authors: W. M. Ng, O. B. Iskender, L. Simonini, J. M. Gonzalez

Abstract:

A multitude of factors, including mechanical imperfections of the deployment system and separation instance of satellites from launchers, oftentimes results in highly uncontrolled initial tumbling motion immediately after deployment. In particular, small satellites which are characteristically launched as a piggyback to a large rocket, are generally allocated a large time window to complete detumbling within the early orbit phase. Because of the saturation risk of the actuators, current algorithms are conservative to avoid draining excessive power in the detumbling phase. This work aims to enable time-optimal switching of control modes during the early phase, reducing the time required to transit from launch to sun-pointing mode for power budget conscious satellites. This assumes the usage of B-dot controller for detumbling and PD controller for pointing. Nonlinear Euler's rotation equations are used to represent the attitude dynamics of satellites and Commercial-off-the-shelf (COTS) reaction wheels and magnetorquers are used to perform the manoeuver. Simulation results will be based on a spacecraft attitude simulator and the use case will be for multiple orbits of launch deployment general to Low Earth Orbit (LEO) satellites.

Keywords: attitude control, detumbling, small satellites, spacecraft autonomy, time optimal control

Procedia PDF Downloads 91

Authors: M. Pramila Devi, N. V. N. Indra Kiran

Abstract:

Control charts, predominantly in the form of X-bar chart, are important tools in statistical process control (SPC). They are useful in determining whether a process is behaving as intended or there are some unnatural causes of variation. A process is out of control if a point falls outside the control limits or a series of point’s exhibit an unnatural pattern. In this paper, a study is carried out on four training algorithms for CCPs recognition. For those algorithms optimal structure is identified and then they are studied for type I and type II errors for generalization without early stopping and with early stopping and the best one is proposed.

Keywords: control chart pattern recognition, neural network, backpropagation, generalization, early stopping

Procedia PDF Downloads 337

Authors: Amr Abdel Azim Ali, G. A. Elsheikh, Moutaz Hegazy

Abstract:

This paper presents verification of a modeling and simulation for a Spacecraft (SC) attitude and orbit control system. Detailed formulation of coupled SC orbital and attitude equations of motion is performed in order to achieve accepted accuracy to meet the requirements of multitargets tracking and orbit correction complex modes. Correction of the target parameter based on the estimated state vector during shooting time to enhance pointing accuracy is considered. Time-optimal nonlinear feedback control technique was used in order to take full advantage of the maximum torques that the controller can deliver. This simulation provides options for visualizing SC trajectory and attitude in a 3D environment by including an interface with V-Realm Builder and VR Sink in Simulink/MATLAB. Verification data confirms the simulation results, ensuring that the model and the proposed control law can be used successfully for large and fast tracking and is robust enough to keep the pointing accuracy within the desired limits with considerable uncertainty in inertia and control torque.

Keywords: attitude and orbit control, time-optimal nonlinear feedback control, modeling and simulation, pointing accuracy, maximum torques

Procedia PDF Downloads 297

Authors: Umar Salisu

Abstract:

This research presents the development of a hot air tomatoes drying system. To provide a more efficient and continuous temperature control, microcontroller-based optimal controller was developed. The system is based on a power control principle to achieve smooth power variations depending on a feedback temperature signal of the process. An LM35 temperature sensor and LM399 differential comparator were used to measure the temperature. The mathematical model of the system was developed and the optimal controller was designed and simulated and compared with the PID controller transient response. A controlled environment suitable for fruit drying is developed within a closed chamber and is a three step process. First, the infrared light is used internally to preheated the fruit to speedily remove the water content inside the fruit for fast drying. Second, hot air of a specified temperature is blown inside the chamber to maintain the humidity below a specified level and exhaust the humid air of the chamber. Third, the microcontroller disconnects the power to the chamber after the moisture content of the fruits is removed to minimal. Experiments were conducted with 1kg of fresh tomatoes at three different temperatures (40, 50 and 60 °C) at constant relative humidity of 30%RH. The results obtained indicate that the system is significantly reducing the drying time without affecting the quality of the fruits. In the context of temperature control, the results obtained showed that the response of the optimal controller has zero overshoot whereas the PID controller response overshoots to about 30% of the set-point. Another performance metric used is the rising time; the optimal controller rose without any delay while the PID controller delayed for more than 50s. It can be argued that the optimal controller performance is preferable than that of the PID controller since it does not overshoot and it starts in good time.

Keywords: drying, microcontroller, optimum controller, PID controller

Procedia PDF Downloads 267

Authors: Aigul Manapova

Abstract:

We consider an optimal control problem in the higher coefficient of nonlinear equations with a divergent elliptic operator and unbounded nonlinearity, and the Dirichlet boundary condition. The conditions imposed on the coefficients of the state equation are assumed to hold only in a small neighborhood of the exact solution to the original problem. This assumption suggests that the state equation involves nonlinearities of unlimited growth and considerably expands the class of admissible functions as solutions of the state equation. We obtain formulas for the first partial derivatives of the objective functional with respect to the control functions. To calculate the gradients the numerical solutions of the state and adjoint problems are used. We also prove that the gradient of the cost function is Lipchitz continuous.

Keywords: cost functional, differentiability, divergent elliptic operator, optimal control, unbounded nonlinearity

Procedia PDF Downloads 140

Authors: Radoslaw Pytlak, Damian Suski

Abstract:

The aim of the paper is to provide a computational tool for planning a haemodialysis process. It is shown that optimization methods can be used to obtain the most effective treatment focused on removing both urea and phosphorus during the process. In order to achieve that, the IV–compartment model of phosphorus kinetics is applied. This kinetics model takes into account a rebound phenomenon that can occur during haemodialysis and results in a hybrid model of the process. Furthermore, vector fields associated with the model equations are such that it is very likely that using the most intuitive objective functions in the planning problem could lead to solutions which include sliding motions. Therefore, building computational tools for solving the problem of planning a haemodialysis process has required constructing numerical algorithms for solving optimal control problems with hybrid systems. The paper concentrates on minimum time control of hybrid systems since this control objective is the most suitable for the haemodialysis process considered in the paper. The presented approach to optimal control problems with hybrid systems is different from the others in several aspects. First of all, it is assumed that a hybrid system can exhibit sliding modes. Secondly, the system’s motion on the switching surface is described by index 2 differential–algebraic equations, and that guarantees accurate tracking of the sliding motion surface. Thirdly, the gradients of the problem’s functionals are evaluated with the help of adjoint equations. The adjoint equations presented in the paper take into account sliding motion and exhibit jump conditions at transition times. The optimality conditions in the form of the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding modes and with piecewise constant controls are stated. The presented sensitivity analysis can be used to construct globally convergent algorithms for solving considered problems. The paper presents numerical results of solving the haemodialysis planning problem.

Keywords: haemodialysis planning process, hybrid systems, optimal control, sliding motion

Procedia PDF Downloads 167

Authors: Aleksandra Aleksandrovna Filimonova, Lev Sergeevich Kazarinov, Tatyana Aleksandrovna Barbasova

Abstract:

A method of effective planning and control of industrial facility energy consumption is offered. The method allows to optimally arrange the management and full control of complex production facilities in accordance with the criteria of minimal technical and economic losses at the forecasting control. The method is based on the optimal construction of the power efficiency characteristics with the prescribed accuracy. The problem of optimal designing of the forecasting model is solved on the basis of three criteria: maximizing the weighted sum of the points of forecasting with the prescribed accuracy; the solving of the problem by the standard principles at the incomplete statistic data on the basis of minimization of the regularized function; minimizing the technical and economic losses due to the forecasting errors.

Keywords: energy consumption, energy efficiency, energy management system, forecasting model, power efficiency characteristics

Procedia PDF Downloads 354

Authors: Mahmoud M. Othman, Almoataz Y. Abdelaziz, Yasser G. Hegazy

Abstract:

This paper presents a load control strategy based on modification of the Big Bang Big Crunch optimization method. The proposed strategy aims to determine the optimal load to be controlled and the corresponding time of control in order to minimize the energy purchased from substation. The presented strategy helps the distribution network operator to rely on the renewable energy sources in supplying the system demand. The renewable energy sources used in the presented study are modeled using the diagonal band Copula method and sequential Monte Carlo method in order to accurately consider the multivariate stochastic dependence between wind power, photovoltaic power and the system demand. The proposed algorithms are implemented in MATLAB environment and tested on the IEEE 37-node feeder. Several case studies are done and the subsequent discussions show the effectiveness of the proposed algorithm.

Keywords: big bang big crunch, distributed generation, load control, optimization, planning

Procedia PDF Downloads 320

Authors: Kevin Spencer G. Anglim, Zhenyu Zhang, Qingbin Gao

Abstract:

Reusable launch vehicles (RLVs) present a more environmentally-friendly approach to accessing space when compared to traditional launch vehicles that are discarded after each flight. This paper studies the recyclable nature of RLVs by presenting a solution method for determining minimum-fuel optimal trajectories using principles from optimal control theory and particle swarm optimization (PSO). This problem is formulated as a minimum-landing error powered descent problem where it is desired to move the RLV from a fixed set of initial conditions to three different sets of terminal conditions. However, unlike other powered descent studies, this paper considers the highly nonlinear effects caused by atmospheric drag, which are often ignored for studies on the Moon or on Mars. Rather than optimizing the controls directly, the throttle control is assumed to be bang-off-bang with a predetermined thrust direction for each phase of flight. The PSO method is verified in a one-dimensional comparison study, and it is then applied to the two-dimensional cases, the results of which are illustrated.

Keywords: minimum-fuel optimal trajectory, particle swarm optimization, reusable rocket, SpaceX

Procedia PDF Downloads 246

Authors: Khawar Ali

Abstract:

We present the numerical study of unsteady hydromagnetic (MHD) flow and heat transfer characteristics of a viscous incompressible electrically conducting water-based hybrid metallic nanofluid (containing Cu-Au/ H₂O nanoparticles) between two orthogonally moving porous coaxial disks with suction. Different from the classical shooting methodology, we employ a combination of a direct and an iterative method (SOR with optimal relaxation parameter) for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar nonlinear ODEs. Effects of the governing parameters on the flow and heat transfer are discussed and presented through tables and graphs. The findings of the present investigation may be beneficial for the electronic industry in maintaining the electronic components under effectiveand safe operational conditions.

Keywords: heat transfer enhancement, hybrid metallic nanofluid, viscous dissipation and joule heating effect , Two dimensional flow

Procedia PDF Downloads 203

Authors: Pornsiri Kaewpradit, Chalisa Pourneaw

Abstract:

Temperature control improvement of a membrane reactor with exothermic and reversible esterification reaction is studied in this work. It is well known that a batch membrane reactor requires different control strategies from a continuous one due to the fact that it is operated dynamically. Due to the effect of the operating temperature, the suitable control scheme has to be designed based reliable predictive model to achieve a desired objective. In the study, the optimization framework has been preliminary formulated in order to determine an optimal temperature trajectory for maximizing a desired product. In model predictive control scheme, a set of predictive models have been initially developed corresponding to the possible operating points of the system. The multiple predictive control moves have been further calculated on-line using the developed models corresponding to current operating point. It is obviously seen in the simulation results that the temperature control has been improved compared to the performance obtained by the conventional predictive controller. Further robustness tests have also been investigated in this study.

Keywords: model predictive control, batch reactor, temperature control, membrane reactor

Procedia PDF Downloads 439