Modeling and Optimal Control of Micro-CSP and a Building HVAC System to Minimize Electricity Cost

2018 ◽  
Author(s):  
Chethan R. Reddy ◽  
Mohamed Toub ◽  
Meysam Razmara ◽  
Mahdi Shahbakhti ◽  
Rush D. Robinett ◽  
...  
Keyword(s):  
Optimal Control ◽  
Energy Cost ◽  
Hvac System ◽  
Building Model ◽  
Electricity Cost ◽  
Energy Flows ◽  
The Cost ◽  
Technological University ◽  
Weather Variations ◽  
Seasonal Weather

This paper presents a model predictive control (MPC) framework to minimize the energy cost associated with the building heating, ventilation, and air-conditioning (HVAC) system integrated with a micro-scale concentrated solar power (MicroCSP) system. To this end, a MicroCSP model is developed and then integrated to the building model of an office building in Michigan Technological University. Then, an MPC framework is designed to optimize MicroCSP electrical and thermal energy flows for HVAC use in the building. The optimal control results show that the designed MPC framework reduces the HVAC energy cost by 37–42% for a sample sunny day by optimally utilizing the solar energy, compared to the HVAC system without MicroCSP with an MPC controller. The cost saving varies from 12% to 47% depending on seasonal weather variations.

Efficient walking with optimization for a planar biped walker with a torso by hip actuators and springs

Robotica ◽  
2010 ◽  
Vol 29 (4) ◽  
pp. 641-648 ◽  
Author(s):  
Terumasa Narukawa ◽  
Masaki Takahashi ◽  
Kazuo Yoshida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Energy Cost ◽  
Walking Speed ◽  
Numerical Approach ◽  
Hip Joints ◽  
Biped Walking ◽  
Ground Conditions ◽  
The Cost ◽  
Simple Feedback

SUMMARYThis paper focuses on the use of passive dynamics to achieve efficient walking with simple mechanisms. A torso is added to a biped walker; and hip actuators, instead of ankle actuators, are used. A numerical approach is used to find the optimal control trajectories. A comparison between the cost functions of simple feedback control and optimal control is presented. Next, springs are added to the biped walking model at the hip joints to demonstrate the advantage of hip springs in terms of energy cost and ground conditions. The comparison between the torque costs with and without hip springs indicates that hip springs reduce the torque cost, particularly at a high walking speed.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

scholarly journals Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 929
Author(s):  
Guiyun Liu ◽  
Jieyong Chen ◽  
Zhongwei Liang ◽  
Zhimin Peng ◽  
Junqiang Li
Keyword(s):  
Optimal Control ◽  
Rapid Development ◽  
Hamiltonian Function ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Optimal Control Strategy ◽  
Epidemic Dynamics ◽  
Optimization Control ◽  
The Cost ◽  
The Pontryagin Maximum Principle

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

Speed, stride frequency and energy cost per stride: how do they change with body size and gait?

1988 ◽  
Vol 138 (1) ◽  
pp. 301-318 ◽  
Author(s):  
N. C. Heglund ◽  
C. R. Taylor
Keyword(s):  
Body Size ◽  
Body Mass ◽  
Energy Cost ◽  
Reaction Force ◽  
Stride Frequency ◽  
Energetic Cost ◽  
Published Data ◽  
Frequency Change ◽  
Cost Of Locomotion ◽  
The Cost

In this study we investigate how speed and stride frequency change with body size. We use this information to define ‘equivalent speeds’ for animals of different size and to explore the factors underlying the six-fold difference in mass-specific energy cost of locomotion between mouse- and horse-sized animals at these speeds. Speeds and stride frequencies within a trot and a gallop were measured on a treadmill in 16 species of wild and domestic quadrupeds, ranging in body size from 30 g mice to 200 kg horses. We found that the minimum, preferred and maximum sustained speeds within a trot and a gallop all change in the same rather dramatic manner with body size, differing by nine-fold between mice and horses (i.e. all three speeds scale with about the 0.2 power of body mass). Although the absolute speeds differ greatly, the maximum sustainable speed was about 2.6-fold greater than the minimum within a trot, and 2.1-fold greater within a gallop. The frequencies used to sustain the equivalent speeds (with the exception of the minimum trotting speed) scale with about the same factor, the −0.15 power of body mass. Combining this speed and frequency data with previously published data on the energetic cost of locomotion, we find that the mass-specific energetic cost of locomotion is almost directly proportional to the stride frequency used to sustain a constant speed at all the equivalent speeds within a trot and a gallop, except for the minimum trotting speed (where it changes by a factor of two over the size range of animals studied). Thus the energy cost per kilogram per stride at five of the six equivalent speeds is about the same for all animals, independent of body size, but increases with speed: 5.0 J kg-1 stride-1 at the preferred trotting speed; 5.3 J kg-1 stride-1 at the trot-gallop transition speed; 7.5 J kg-1 stride-1 at the preferred galloping speed; and 9.4 J kg-1 stride-1 at the maximum sustained galloping speed. The cost of locomotion is determined primarily by the cost of activating muscles and of generating a unit of force for a unit of time. Our data show that both these costs increase directly with the stride frequency used at equivalent speeds by different-sized animals. The increase in cost per stride with muscles (necessitating higher muscle forces for the same ground reaction force) as stride length increases both in the trot and in the gallop.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Disentangling the energetic costs of step time asymmetry and step length asymmetry in human walking

2021 ◽  
Author(s):  
Jan Stenum ◽  
Julia T. Choi
Keyword(s):  
Energy Cost ◽  
Metabolic Cost ◽  
Step Length ◽  
Human Walking ◽  
Metabolic Power ◽  
Healthy Human ◽  
Time Asymmetry ◽  
Double Support ◽  
Post Stroke ◽  
The Cost

The metabolic cost of walking in healthy individuals increases with spatiotemporal gait asymmetries. Pathological gait, such as post-stroke, often has asymmetry in step lengths and step times which may contribute to an increased energy cost. But paradoxically, enforcing step length symmetry does not reduce metabolic cost of post-stroke walking. The isolated and interacting costs of asymmetry in step times and step lengths remain unclear, because previous studies did not simultaneously enforce spatial and temporal gait asymmetries. Here, we delineate isolated costs of asymmetry in step times and step lengths in healthy human walking. We first show that the cost of step length asymmetry is predicted by the cost of taking two non-preferred step lengths (one short and one long), but that step time asymmetry adds an extra cost beyond the cost of non-preferred step times. The metabolic power of step time asymmetry is about 2.5 times greater than the cost of step length asymmetry. Furthermore, the costs are not additive when walking with asymmetric step times and step lengths: metabolic power of concurrent asymmetry in step lengths and step times is driven by the cost of step time asymmetry alone. The metabolic power of asymmetry is explained by positive mechanical power produced during single support phases to compensate for a net loss of center of mass power incurred during double support phases. These data may explain why metabolic cost remains invariant to step length asymmetry in post-stroke walking and suggests how effects of asymmetry on energy cost can be attenuated.

scholarly journals Operational optimization of residential HVAC system using model predictive control strategy planning

2021 ◽  
Author(s):  
Nima Alibabaei ◽  
Alan S. Fung
Keyword(s):  
Cost Saving ◽  
Energy Cost ◽  
Carbon Dioxide Emissions ◽  
Hvac Systems ◽  
Conservation Strategy ◽  
Hvac System ◽  
Heating Season ◽  
Residential Sector ◽  
Simulation Engine ◽  
Strategy Planning

To date, the residential sector accounts for a major portion of consumption by consuming more than 40% of the entire world's energy and producing 33% of the carbon dioxide emissions. In North America, the residential sector energy consumptions are mainly related to heating, ventilation, and air conditioning (HVAC) systems, which are not operating in the most efficient ways due to existing on/off and conventional controllers. In Ontario, due to the variable price of electricity, variation in outdoor disturbances, and new Ontario Government sweeping mandate in overhauling the energy use in residential sector, there is an opportunity to develop intelligent control systems to employ energy conservation strategy planning model (ECSPM) in existing HVAC systems for reducing their operating cost, energy consumption, and GHG emission. In order to take advantage of these opportunities, two model-based predictive controllers (MPCs) were developed in this Ph.D. research. In the first MPC controller, a Matlab-TRNSYS co-simulator was developed to fill the lack of advanced controllers in building energy simulators. This cosimulator investigated the effectiveness of different novel ECSPMs on an HVAC system's energy cost saving during winter and summer seasons. This co-simulator offered 23.8% saving in the HVAC system's energy costs in the heating season. Regardless of the strong capabilities, employing this co-simulator for implementing comprehensive/complex optimization methods resulted in an unacceptably long optimization time due to the of TRNSYS simulation engine. Therefore, in the second PMC controller, simplified house thermal and HVAC system models were developed in Matlab. To design a grid-friendly house, this model was enhanced by integrating on-site renewable energy generation and storage systems. A novel algorithm was developed to reduce the MPC controller optimization time. The effectiveness of the novel MPC model in the HVAC system's energy cost saving was compared with a Simple Rule-based (SRB) controller, which itself is an efficient HVAC controller, while this controller offered 12.28% additional savings in the heating season.

scholarly journals Operational optimization of residential HVAC system using model predictive control strategy planning

2021 ◽  
Author(s):  
Nima Alibabaei ◽  
Alan S. Fung
Keyword(s):  
Cost Saving ◽  
Energy Cost ◽  
Carbon Dioxide Emissions ◽  
Hvac Systems ◽  
Conservation Strategy ◽  
Hvac System ◽  
Heating Season ◽  
Residential Sector ◽  
Simulation Engine ◽  
Strategy Planning

To date, the residential sector accounts for a major portion of consumption by consuming more than 40% of the entire world's energy and producing 33% of the carbon dioxide emissions. In North America, the residential sector energy consumptions are mainly related to heating, ventilation, and air conditioning (HVAC) systems, which are not operating in the most efficient ways due to existing on/off and conventional controllers. In Ontario, due to the variable price of electricity, variation in outdoor disturbances, and new Ontario Government sweeping mandate in overhauling the energy use in residential sector, there is an opportunity to develop intelligent control systems to employ energy conservation strategy planning model (ECSPM) in existing HVAC systems for reducing their operating cost, energy consumption, and GHG emission. In order to take advantage of these opportunities, two model-based predictive controllers (MPCs) were developed in this Ph.D. research. In the first MPC controller, a Matlab-TRNSYS co-simulator was developed to fill the lack of advanced controllers in building energy simulators. This cosimulator investigated the effectiveness of different novel ECSPMs on an HVAC system's energy cost saving during winter and summer seasons. This co-simulator offered 23.8% saving in the HVAC system's energy costs in the heating season. Regardless of the strong capabilities, employing this co-simulator for implementing comprehensive/complex optimization methods resulted in an unacceptably long optimization time due to the of TRNSYS simulation engine. Therefore, in the second PMC controller, simplified house thermal and HVAC system models were developed in Matlab. To design a grid-friendly house, this model was enhanced by integrating on-site renewable energy generation and storage systems. A novel algorithm was developed to reduce the MPC controller optimization time. The effectiveness of the novel MPC model in the HVAC system's energy cost saving was compared with a Simple Rule-based (SRB) controller, which itself is an efficient HVAC controller, while this controller offered 12.28% additional savings in the heating season.

Operation of a CCHP System Using an Optimal Energy Dispatch Algorithm

2008 ◽  
Author(s):  
Heejin Cho ◽  
Sandra D. Eksioglu ◽  
Rogelio Luck ◽  
Louay M. Chamra
Keyword(s):  
Energy Efficiency ◽  
Energy Cost ◽  
Network Flow ◽  
Flow Model ◽  
Energy Requirement ◽  
Optimal Operation ◽  
Operational Conditions ◽  
Optimal Energy ◽  
Network Flow Model ◽  
The Cost

The Combined Cooling, Heating, and Power (CCHP) systems have been widely recognized as a key alternative for thermal and electric energy generation because of the outstanding energy efficiency, reduced environmental emissions, and relative independence from centralized power grids. Nevertheless, the total energy cost of CCHP systems can be highly dependent on the operation of individual components and load balancing. The latter refers to the process of fulfilling the thermal and electrical demand by partitioning or “balancing” the energy requirement between the available sources of energy supply. The energy cost can be optimized through an energy dispatch algorithm which provides operational/control signals for the optimal operation of the equipment. The algorithm provides optimal solutions on decisions regarding generating power locally or buying power from the grid. This paper presents an initial study on developing an optimal energy dispatch algorithm that minimizes the cost of energy (i.e., cost of electricity from the grid and cost of natural gas into the engine and boiler) based on energy efficiency constrains for each component. A deterministic network flow model of a typical CCHP system is developed as part of the algorithm. The advantage of using a network flow model is that the power flows and efficiency constraints throughout the CCHP components can be readily visualized to facilitate the interpretation of the results. A linear programming formulation of the network flow model is presented. In the algorithm, the inputs include the cost of the electricity and fuel and the constraints include the cooling, heating, and electric load demands and the efficiencies of the CCHP components. This algorithm has been used in simulations of several case studies on the operation of an existing micro-CHP system. Several scenarios with different operational conditions are presented in the paper to demonstrate the economical advantages resulting from optimal operation.

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