Control Time Step Research Articles

Method for Coordinated Passenger Inflow Control Strategy of Metro with Flexible Control Time Step Considering Long–Short Route Pattern

Method for Coordinated Passenger Inflow Control Strategy of Metro with Flexible Control Time Step Considering Long–Short Route Pattern

A novel bi-level temporally-distributed MPC approach: An application to green urban mobility

Model predictive control (MPC) has been widely used for traffic management, such as for minimizing the total time spent or the total emissions of vehicles. When long-term green urban mobility is considered including e.g. a constraint on the total yearly emissions, the optimization horizon of the MPC problem is significantly larger than the control sampling time, and thus the number of the variables that should be optimized per control time step becomes very large. For systems with dynamics that involve nonlinear, non-convex, and non-smooth functions, including urban traffic networks, this results in optimization problems that are computationally intractable in real time. In this paper, we propose a novel bi-level temporal distribution of such complex MPC optimization problems, and we develop two mathematically linked short-term and long-term MPC formulations with small and large control sampling times that will be solved together instead of the original complex optimization problem. The resulting bi-level control architecture is used to solve the two MPC formulations online for real-time control of urban traffic networks with the objective of long-term green mobility. In order to assess the performance of the bi-level control architecture, we perform a case study where a rough version of the model of the urban traffic flow, S-model, is used by the long-term MPC level to estimate the states of the urban traffic networks, and a detailed version of the model is used by the short-term MPC level. The results of the simulations prove the effectiveness (with respect to the objective of control, as well as computational efficiency) of the proposed bi-level MPC approach, compared to state-of-the-art control approaches.

Unsteady Heat Flux Measurement and Predictions Using Long Short-Term Memory Networks

Energy consumption modeling has evolved along with building technology. Modeling techniques can be largely classified into white box, gray box, and black box. In this study, the thermal behavior characteristics of building components were identified through time-series data analysis using LSTM neural networks. Sensors were installed inside and outside the test room to measure physical quantities. As a result of calculating the overall heat transfer coefficient according to the international standard ISO 9869-1, the U value of the multi-window with antireflection coating was 1.84 W/(m2∙K). To understand the thermal behavior of multiple windows, we constructed a neural network using an LSTM architecture and used the measured data-set to predict and evaluate the heat flux through deep learning. From the measurement data, a wavelet transform was used to extract features and to find appropriate control time-step intervals. Performance was evaluated according to multistep measurement intervals using the error metric method. The multistep time interval for control monitoring is preferably no more than 240 s. In addition, multivariate analysis with several input variables was performed. In particular, the thermal behavior of building components can be analyzed through heat flux and temperature measurements in the transient state of physical properties of pre-installed building components, which were difficult to access with conventional steady-state measurement methods.

Calibration-free approach to reactive real-time control of stormwater storages

Stormwater systems will likely require major upgrades due to increases in peak flows caused by the combined effects of urbanization, densification (urban infill) and climate change. Recently, the real-time control (RTC) of storages has been considered as a means to reduce peak flows and potentially avoid major infrastructure upgrades. This paper introduces a RTC approach, the Target Flow Control (TFC) approach, which is able to maintain system outflows at or below specified target flows (e.g., existing system capacity). The key features of the approach are that it does not require calibration to catchment specific data, as is the case for existing approaches and is only based on storage level information measured in real-time during rainfall events. This makes the approach generally applicable to different catchments and able to respond to future changes in rainfall due to land use and/or climate change. The TFC approach is tested on a simple two-storage system for 750 design rainfall events from a range of climates, event durations, rainfall intensities and temporal patterns using a practically achievable control time step of 30 s. Results show that the TFC approach can achieve the desired target flows effectively, with 95% of the experiments having less than 10% errors in target flows. This is an exciting achievement, given the TFC approach does not require calibration and only requires measurable storage level information. The outcomes highlight the potential of the TFC approach as a practical RTC approach that can maximize the effectiveness of existing stormwater conveyance systems by maintaining stormwater system outflows at desired target flows, thereby potentially avoiding stormwater infrastructure upgrades due to land use and climate change.

Real-Time Optimization-Based Reference Calculation Integrated Control for MMCs Considering Converter Limitations

The paper addresses a real-time optimization-based reference calculation integrated with a control structure for Modular Multilevel Converters (MMC) operating under normal and constrained situations (where it has reached current and/or voltage limitations, as it may occur during system faults). Firstly, a nonlinear optimization problem has been developed in which it prioritizes to satisfy the AC grid current set-points imposed by the transmission System Operator (TSO). The constrained nonlinear optimization problem is formulated based on the steady-state model of the MMC, whereby the prioritization is achieved through distinct weights defined in the Objective Function’s (OF) terms. The resultant optimization problem, however, is highly nonlinear requiring high computation burden to be solved in real-time. To cope with this issue, this paper applies a Linear Time-Varying (LTV) approximation, which permits to represent the nonlinear dynamics of the system as constant parameters, while a Linear Time-Invariant (LTI) system is used to formulate the optimization constraints. The converter’s current references are determined in real-time by solving a constrained linearized optimization problem at each control time step, which considers the TSO’s demands, the current MMC operating point and its physical limitations. Theoretical analyses comparing the responses of the linear and nonlinear optimization problems are performed to validate the accuracy of the LTV approximation. Finally, the linearized-optimization problem is integrated with the MMC controllers, evaluated under different AC and DC network conditions and compared with conventional control strategies, where it is shown that the presented method can be potentially employed to obtain the MMC current references for distinct network scenarios.

Impact of Deep Reinforcement Learning on Variable Speed Limit strategies in connected vehicles environments

The Variable Speed Limit (VSL) control is considered in the context of connected vehicles acting as moving sensors, while their obedience to speed limit is enforced by a mandatory Intelligent Speed Adaptation (ISA) system. The objective of this study is to extend spatially static differential VSL control by introducing novel VSL strategies that are based on spatially dynamic speed limit zones. The spatial configuration of speed limit zones requires a novel traffic state representation based on the set of consecutive matrices which encode each vehicle position and speed within the controlled motorway during the control time step. The actions for all proposed VSL strategies are computed by the same Deep Reinforcement Learning (DRL) approach based on the Deep Deterministic Policy Gradient (DDPG) architecture. The DDPG learning models contain integration of Convolution and Long Short-Term Memory (LSTM) known as ConvLSTM layers, along with the Convolution and Fully Connected layers. Thus, those models can learn complex spatio-temporal traffic dynamics based on proposed traffic state representation. The results show that proposed VSL strategies have achieved higher overall motorway throughput compared to one which is based on the static speed limit zones and baseline cases (no-control and Simple Proportional Speed Controller algorithm). Simultaneously, they achieved a minimal increase in the number of aggressive braking, while the average headway is increased. All proposed VSL control approaches are simulated and analyzed by using a synthetic microscopic motorway model and characteristic traffic scenario for urban motorways.

Finite element solution of nonlocal Cahn–Hilliard equations with feedback control time step size adaptivity

AbstractIn this study, we evaluate the performance of feedback control‐based time step adaptivity schemes for the nonlocal Cahn–Hilliard equation derived from the Ohta–Kawasaki free energy functional. The temporal adaptivity scheme is recast under the linear feedback control theory equipped with an error estimation that extrapolates the solution obtained from an energy‐stable, fully implicit time marching scheme. We test three time step controllers with different properties: a simple Integral controller, a complete proportional‐integral‐derivative controller, and the PC11 predictive controller. We assess the performance of the adaptive schemes for the nonlocal Cahn–Hilliard equation in terms of the number of time steps required for the complete simulation and the computational effort measured by the required number of nonlinear and linear solver iterations. We also present numerical evidence of mass conservation and free energy decay for simulations with the three different time step controllers. The PC11 predictive controller is the best in all three‐dimensional test cases.

Parametrized Model Predictive Control Approaches for Urban Traffic Networks

Model Predictive Control (MPC) has shown promising results in the control of urban traffic networks, but unfortunately it has one major drawback. The, often nonlinear, optimization that has to be performed at every control time step is computationally too complex to use MPC controllers for real-time implementations (i.e. when the online optimization is performed within the control time interval of the controlled network). This paper proposes an effective parametrized MPC approach to lower the computational complexity of the MPC controller. Two parametrized control laws are proposed that can be used in the parametrized MPC framework, one based on the prediction model of the MPC controllers, and another is constructed using Grammatical Evolution (GE). The performance and computational complexity of the parametrized MPC approach is compared to a conventional MPC controller by performing an extensive simulation-based case study. The simulation results show that for the given case study the parametrized MPC approach is real-time implementable while the performance decreases with less than 3% with respect to the conventional MPC controller.

Stability analysis of non-linear sampled data systems with time varying sample period and delay in the feedback loop

In almost all practical applications of control, technological and economical considerations impose limits on communication speed, frequency of communication, and frequency of actuator adjustment. Such limits turned the analysis of sampled data systems into a flourishing field. Water systems pose a particular challenge: the systems are networks of canals and reservoirs spread over large areas, and the actuators are relatively large and exposed to the elements. In this study, a theorem on the local exponential stability of sampled data systems with variable control time step and variable delay in the communication between the non-linear continuous time process and the non-linear discrete time controller is presented. To illustrate the application of the theorem, it is applied to a simple water system.

ADAPTIVE TIME-STEP CONTROL FOR THE MODAL METHOD TO INTEGRATE THE MULTIGROUP NEUTRON DIFFUSION EQUATION

The distribution of the power inside a reactor core can be described by the time dependent multigroup neutron diffusion equation. One of the approaches to integrate this time-dependent equation is the modal method, that assumes that the solution can be described by the sum of amplitude function multiplied by shape functions of modes. These shape functions can be computed by solving a _-modes problems. The modal method has a great interest when the distribution of the power cannot be well approximated by only one shape function, mainly, when local perturbations are applied during the transient. Usually, the shape functions of the modal methods are updated for the time-dependent equations with a constant time-step size to obtain accurate results. In this work, we propose a modal methodology with an adaptive control time-step to update the eigenfunctions associated with the modes. This algorithm improves efficiency because of time is not spent solving the systems to a level of accuracy beyond relevance and reduces the step size if they detect a numerical instability. Step size controllers require an error estimation. Different error estimations are considered and analyzed in a benchmark problem with a out of phase local perturbation.

Adaptive time-step control for modal methods to integrate the neutron diffusion equation

The solution of the time-dependent neutron diffusion equation can be approximated using quasi-static methods that factorise the neutronic flux as the product of a time dependent function times a shape function that depends both on space and time. A generalization of this technique is the updated modal method. This strategy assumes that the neutron flux can be decomposed into a sum of amplitudes multiplied by some shape functions. These functions, known as modes, come from the solution of the eigenvalue problems associated with the static neutron diffusion equation that are being updated along the transient. In previous works, the time step used to update the modes is set to a fixed value and this implies the need of using small time-steps to obtain accurate results and, consequently, a high computational cost. In this work, we propose the use of an adaptive control time-step that reduces automatically the time-step when the algorithm detects large errors and increases this value when it is not necessary to use small steps. Several strategies to compute the modes updating time step are proposed and their performance is tested for different transients in benchmark reactors with rectangular and hexagonal geometry.

Model predictive control of building energy systems with thermal energy storage in response to occupancy variations and time-variant electricity prices

Developing effective operational strategies for commercial buildings is a high priority as the global community seeks to reduce energy usage and greenhouse gas emissions. This study aims to validate the feasibility of a model predictive control (MPC) strategy for commercial building in response to occupancy variations and time-variant electricity prices in comparison to a conventional rule-based control (RBC) strategy. The building energy system included an air-cooled chiller, stratified chilled water thermal energy storage, two fan coil units, three heat exchangers, and five pumps. The optimal operations of the chiller and storage system were determined with the goal of minimizing the operating cost while maintaining the zone temperature at a cooling set point temperature during cooling operation hours. Artificial neural network was utilized as prediction models and metaheuristics algorithm was employed as optimization solver to construct a reliable and computationally manageable MPC controller. The simulation was performed for four days during the cooling season with a confirmed optimal prediction time horizon of 24 h and a control timestep of 1 h intervals. In conclusion, MPC reduced the total operating cost by 3.4% compared to the RBC, which prioritized the storage system operation to manage the thermal load.

An improved vehicle to the grid method with battery longevity management in a microgrid application

This paper proposed an improved vehicle-to-grid (V2G) scheduling approach for the frequency control with the advantage of protecting the batteries hence saving the battery lifetime during grid connected service. The proposed methodology is improved in two ways. Firstly, to give a prediction of the available electric vehicle (EV) battery capacity in the control time-step for the V2G service, a deep learning based prediction is developed. Secondly, this study advances the previous V2G method by adding the quantitative analysis of the battery cycle life into the V2G optimization. The accurate prediction of the schedulable battery capacity based on the LSTM algorithm is shown very effective in the power system frequency control. Also, compared with the previous method that without battery lifetime control, the proposed method benefits in the reduction of charge/discharge cycles.

Logic-Based Traffic Flow Control for Ramp Metering and Variable Speed Limits—Part 1: Controller

This paper proposes a Logic-Based Traffic Flow Control algorithm (LB-TFC) for integrated control of Ramp Metering (RM) installations and Variable Speed Limits (VSLs) in order to reduce traffic jams created at bottlenecks. LB-TFC estimates, for each control time step, the number of vehicles that should be held back or released by the control measures (i.e. the VSLs and the RM rates) in order to avoid the capacity drop (maximizing the outflow of the bottleneck). Afterwards, based on the resulting estimated number of vehicles, the VSLs and/or the RM rates are increased or decreased in a pre-specified order. In order to avoid or reduce traffic breakdowns, the proposed controller (LB-TFC) anticipates the future evolution of the bottleneck density by using a feed-forward structure. As a result, the performance of the controller is very efficient and similar to the one obtained with an optimal controller while the implementation of the controller (with an almost instantaneous computation time) and the tuning of the parameters are easy. In the second part of this work, published in a separate paper (`Part 2: Simulation and Comparison'), LB-TFC is simulated, analyzed and compared for two freeways (one synthetic network and one stretch of the ring-road freeway SE-30 in Seville, Spain).

An adaptive PID control method to improve the power tracking performance of solar photovoltaic air-conditioning systems

In order to increase the utilization of solar energy to lower the effect of photovoltaic power output fluctuations on power grids, an adaptive PID control method to improve the power tracking performance of solar photovoltaic air-conditioners is proposed in this paper. In this method, a dynamic temperature set point of the indoor zone is generated at each control time step based on the difference between the air-conditioning load and photovoltaic generation. The theoretical analysis shows that the proposed control is essentially a feedforward feedback control where the air-conditioning system can predictably adjust the compressor frequency based on the knowledge of how the solar radiation affects the cooling load. A case study in Shanghai shows that the proposed control method is able to significantly improve the power tracking performance of the photovoltaic air-conditioner, where the Solar Fraction (SF) and the Self-Consumption Ratio (SCR) are improved from 82.74% to 88.11% and from 70.12% to 74.42% respectively, without violating the indoor thermal comfort, where Mean Absolute Error (MAE) from the temperature set point is decreased from 0.197 to 0.168. The tuning of the power difference factor ko will lead to monotonic changes of SF &SCR and a minimum MAE. When ko is well tuned, the proposed control can realize desirable system improvements of both the power tracking ability and the indoor temperature control accuracy. The idea of this paper could be easily modified to benefit other solar cooling applications and conventional air-conditioners.

Service pressure regulation in water distribution networks

Real time pressure control is commonly adopted in water distribution network management to reduce leakage. A numerical description of the dynamic behaviour of the water distribution network (WDN) is introduced, allowing simulations of different case studies. A local, linear model is then identified from simulated experiments in order to synthesise different control algorithms working with control time step of 1 s. A state-of-the-art control algorithm operating with control time step of some minutes is used as benchmark. Results prove that all the new controllers reduce the control error, suggesting that cost and communication overheads introduced by control time step reduction are well motivated by sensible benefits in terms of pressure regulation.

Testing behavior and effects of PRVs and RTC valves during hydrant activation scenarios

This paper provides an insight into behavior and effects of pressure reducing valves (PRVs) and of valves controlled in real time (RTC) during hydrant activation scenarios, which determine high-flow conditions in water distribution networks (WDNs). The analysis is carried out through the pressure-driven unsteady flow modeling of an Italian WDN, in which a pressure control device is assumed to be installed in the pipe outgoing from the source. Scenarios are constructed considering alternatively a PRV or an RTC valve, as pressure control device, and two different sites for hydrant activation. The results highlight that, thanks to its capability of controlling the service pressure at the critical node, the RTC valve performs better than the PRV, which is regulated based on its outlet pressure. In fact, the adoption of the RTC valve attenuates pressure deficits in the network, above all when the control time step is suitably small to attenuate pressure head oscillations at the controlled node. An additional benefit of RTC lies in increased outflows from the hydrant. The benefits of the RTC valve are smaller when the hydrant is activated in more redundant parts of the network, where pipe water discharge variations put the system to a less severe test.

An optimal control strategy for hybrid actuator systems: Application to an artificial muscle with electric motor assist

Humans use multiple muscles to generate such joint movements as an elbow motion. With multiple lightweight and compliant actuators, joint movements can also be efficiently generated. Similarly, robots can use multiple actuators to efficiently generate a one degree of freedom movement. For this movement, the desired joint torque must be properly distributed to each actuator. One approach to cope with this torque distribution problem is an optimal control method. However, solving the optimal control problem at each control time step has not been deemed a practical approach due to its large computational burden. In this paper, we propose a computationally efficient method to derive an optimal control strategy for a hybrid actuation system composed of multiple actuators, where each actuator has different dynamical properties. We investigated a singularly perturbed system of the hybrid actuator model that subdivided the original large-scale control problem into smaller subproblems so that the optimal control outputs for each actuator can be derived at each control time step and applied our proposed method to our pneumatic–electric hybrid actuator system. Our method derived a torque distribution strategy for the hybrid actuator by dealing with the difficulty of solving real-time optimal control problems.

Efficient multi-scenario Model Predictive Control for water resources management with ensemble streamflow forecasts

Abstract Model Predictive Control (MPC) is one of the most advanced real-time control techniques that has been widely applied to Water Resources Management (WRM). MPC can manage the water system in a holistic manner and has a flexible structure to incorporate specific elements, such as setpoints and constraints. Therefore, MPC has shown its versatile performance in many branches of WRM. Nonetheless, with the in-depth understanding of stochastic hydrology in recent studies, MPC also faces the challenge of how to cope with hydrological uncertainty in its decision-making process. A possible way to embed the uncertainty is to generate an Ensemble Forecast (EF) of hydrological variables, rather than a deterministic one. The combination of MPC and EF results in a more comprehensive approach: Multi-scenario MPC (MS-MPC). In this study, we will first assess the model performance of MS-MPC, considering an ensemble streamflow forecast. Noticeably, the computational inefficiency may be a critical obstacle that hinders applicability of MS-MPC. In fact, with more scenarios taken into account, the computational burden of solving an optimization problem in MS-MPC accordingly increases. To deal with this challenge, we propose the Adaptive Control Resolution (ACR) approach as a computationally efficient scheme to practically reduce the number of control variables in MS-MPC. In brief, the ACR approach uses a mixed-resolution control time step from the near future to the distant future. The ACR-MPC approach is tested on a real-world case study: an integrated flood control and navigation problem in the North Sea Canal of the Netherlands. Such an approach reduces the computation time by 18% and up in our case study. At the same time, the model performance of ACR-MPC remains close to that of conventional MPC.

A new semi-active control based on nonlinear inhomogeneous optimal control for mixed base isolation

This paper presents a control algorithm for seismic mixed base isolation, combining passive isolators and semi-active viscous dampers. The objective is to limit base displacement while avoiding undesirable amplification of the response of the non-isolated modes. To this end, the proposed algorithm takes into account the constraints on the damping coefficient of the semi-active damper and information on the excitation. It is based on the approximate iterative solution, at each control time step, of a nonlinear inhomogeneous constrained optimal control problem. An autoregressive model is used to obtain, at each control time step, a prediction of the upcoming excitation in a short time interval ahead. Numerical simulation results demonstrate the efficacy of the above method, especially in improving floor response spectra, and its superiority with respect to clipped-optimal algorithms.