Practical Nonlinear Model Research Articles

Practical Nonlinear Model Predictive Control for Improving Two-Wheel Vehicle Energy Consumption

Increasing the range of electric vehicles (EVs) is possible with the help of eco-driving techniques, which are algorithms that consider internal and external factors, like performance limits and environmental conditions, such as weather. However, these constraints must include critical variables in energy consumption, such as driver preferences and external vehicle conditions. In this article, a reasonable energy-efficient non-linear model predictive control (NMPC) is built for an electric two-wheeler vehicle, considering the Paris-Brussels route with different driving profiles and driver preferences. Here, NMPC is successfully implemented in a test bed, showing how to obtain the different parameters of the optimization problem and the estimation of the energy for the closed-loop system from a practical point of view. The efficiency of the brushless DC motor (BLCD) is also included for this test bed. In addition, this document shows that the proposal increases the chance of traveling the given route with a distance accuracy of approximately 1.5% while simultaneously boosting the vehicle autonomy by almost 20%. The practical result indicates that the strategy based on an NMPC algorithm can significantly boost the driver’s chance of completing the journey. If the vehicle energy is insufficient to succeed in the trip, the algorithm can guide the minimal State of Charge (SOC) required to complete the journey to reduce the driver energy-related uncertainty to a minimum.

Data-driven Model Predictive Control for pH regulation in Raceway Reactors*

The industrial production of microalgae is a highly sustainable and attractive process due to its variety of applications, especially when it is combined with wastewater treatment. From a control point of view, the optimization of the process requires a considerable effort regarding the culture conditions. The biological nature of the process renders its characterization considerably difficult, as well as the acquisition of models describing its dynamics. In this work, a complete methodology for pH control in raceway photobioreactors based on the Practical Nonlinear Model Predictive Control (PNMPC) approach is proposed. Models based on artificial Neural Networks (ANN) of the system have been obtained and validated, and a PNMPC controller based on these data-driven models has been developed and tested in a real raceway reactor. The results demonstrate the reliability of this type of models, and justify the possibility of combining them with predictive control algorithms in highly nonlinear systems.

Optimal User Cooperation in IRS Assisted WPCN for Practical Non-Linear Phase-Shift Model

This letter is a novel attempt to consider intelligent reflecting surfaces (IRS) assisted user cooperation adopting the practical non-linear phase-shift model in a wireless-powered communication network (WPCN). Specifically, we aim to maximize both max-min fairness and sum throughput among the energy harvesting users while adopting the practical IRS model. We propose an alternating optimization (AO) algorithm exploiting convex relaxation and semidefinite programming to optimize the phase-shift matrices at IRS along with time and power allocation at the hybrid access point serving the users. Simulation results corroborate key analytical claims and show that the proposed jointly-optimal design provides better performance gain for max-min and sum-rate maximization over the existing benchmark schemes.

Nonlinear model predictive control algorithm with iterative nonlinear prediction and linearization for long short-term memory network models

In this paper, a practical nonlinear model predictive control with iterative nonlinear prediction and linearization is proposed, considering a long short-term memory (LSTM) artificial neural network (PNMPCi-LSTM) as process model for making the predictions. The prediction model is divided into two portions, the base output prediction, obtained with the LSTM nonlinear model, and the incremental output prediction, obtained using a linearized version of the LSTM model. The base response and the dynamic matrix of the system, which is obtained using the linearized version, are used to find an optimal control effort by solving a quadratic programming problem. This procedure is performed iteratively by updating the base input with the candidate control effort until the incremental response term is small enough compared with the base response term. The advantages of the proposed method in terms of performance and computing times are illustrated using the control of a simulated nonlinear neutralization reactor. For the evaluated case study, the results show that by using the proposed iterative procedure the closed-loop performance measured using the integral absolute error is improved by 8% for a setpoint tracking scenario while keeping the computation times within reasonable levels. In addition, the results support the idea that the proposed PNMPCi-LSTM is an alternative to implement a nonlinear MPC with reasonable computation times.

Nonlinear model predictive control-based guidance law for path following of unmanned surface vehicles

This work proposes a nonlinear model predictive control-based guidance strategy for unmanned surface vehicles, focused on path following. The application of this strategy, in addition to overcome drawbacks of previous line-of-sight-based guidance laws, intends to enable the application of predictive strategies also to the low-level control, responsible for tracking the references provided by the guidance strategy. The stability and robustness of the proposed strategy are theoretically discussed. Furthermore, given the non-negligible computational cost of such nonlinear predictive guidance strategy, a practical nonlinear model predictive control strategy is also applied in order to reduce the computational cost to a great extent. The effectiveness and advantages of both proposed strategies over other nonlinear guidance laws are illustrated through a complete set of simulations.

New Practical Nonlinear Energy-Harvesting Models for Wireless-Powered Communications

As a massive number of nodes are expected to be connected to each other in next-generation wireless networks, the power supply of such multiple-antenna nodes is a challenge and requires new and sustainable solutions. Radio frequency energy harvesting (EH) is among the promising approaches to solve this issue. In this paper, two new mathematically tractable nonlinear EH (NL-EH) models are proposed, for which the system performance is evaluated in terms of average harvested power, throughput, and bit error probability. The system consists of one multiantenna power-constraint source harvesting its power from a dedicated power beacon and transmitting its signal to a destination equipped with multiple antennas. For a comprehensive analysis of the system, closed-form expressions are derived for Nakagami- m fading channels and the special case of Rayleigh channels. For comparison purposes, the performance derivations in Nakagami- m fading channels are provided for linear and piece-wise linear EH models given in the literature. Besides, the simulation results are obtained by applying the Monte-Carlo method for NL-EH models existing in the literature. The results provide a broadening view of EH systems and thoroughly compare the proposed NL-EH models with linear, piece-wise linear, and NL-EH models available in the literature. Hence, these provide better insights towards the analyses and design of EH systems.

Adaptive Practical Nonlinear Model Predictive Control for Echo State Network Models.

This article proposes an adaptive practical nonlinear model predictive (NMPC) control algorithm which uses an echo state network (ESN) estimated online as a process model. In the proposed control algorithm, the ESN readout parameters are estimated online using a recursive least-squares method that considers an adaptive directional forgetting factor. The ESN model is used to obtain online a nonlinear prediction of the system free response, and a linearized version of the neural model is obtained at each sampling time to get a local approximation of the system step response, which is used to build the dynamic matrix of the system. The proposed controller was evaluated in a benchmark conical tank level control problem, and the results were compared with three baseline controllers. The proposed approach achieved similar results as the ones obtained by its nonadaptive baseline version in a scenario with the process operating with the nominal parameters, and outperformed all baseline algorithms in a scenario with process parameter changes. Additionally, the computational time required by the proposed algorithm was one-tenth of that required by the baseline NMPC, which shows that the proposed algorithm is suitable to implement state-of-the-art adaptive NMPC in a computationally affordable manner.

Performance of SWIPT in Cooperative Networks With Direct Link and Nonlinear Energy Harvesting at the Battery-Assisted Relay

This paper investigates the performance of time-switching (TS) and power-splitting (PS) energy harvesting (EH) protocols in a two-hop cooperative network with a battery-assisted EH relay. Assuming the presence of the direct link and optimal combining at the destination, and practical nonlinear model for EH, expressions are derived for throughput with selective decode-and-forward (DF) relaying with the direct link (SDFDL) as well incremental relaying (IR). Augmenting the harvested energy with a small amount of battery energy significantly enhances the throughput. Combining direct and relayed signals significantly enhances throughput and decreases the energy consumption at the battery for any desired throughput as compared to the case when no direct link (NDL) from source to destination is used. The IR scheme achieves the highest throughput with very small energy consumption. We demonstrate that, unlike linear EH, the use of nonlinear EH results in loss of diversity, which makes use of the direct link even very important. Also, the use of the linear EH model gives unrealistically low energy consumption figures for any target throughput, making use of nonlinear EH models important. We elaborate on the choice of EH parameters and target rate on throughput and battery energy consumption. Monte Carlo simulations confirm the accuracy of the derived expressions.

Echo State Networks for Practical Nonlinear Model Predictive Control of Unknown Dynamic Systems.

Nonlinear model predictive control (NMPC) of industrial processes is changeling in part because the model of the plant may not be completely known but also for being computationally demanding. This work proposes an extremely efficient reservoir computing (RC)-based control framework that speeds up the NMPC of processes. In this framework, while an echo state network (ESN) serves as the dynamic RC-based system model of a process, the practical nonlinear model predictive controller (PNMPC) simplifies NMPC by splitting the forced and the free responses of the trained ESN, yielding the so-called ESN-PNMPC architecture. While the free response is generated by the forward simulation of the ESN model, the forced response is obtained by a fast and recursive calculation of the input-output sensitivities from the ESN. The efficiency not only results from the fast training inherited by RC but also from a computationally cheap control action given by the aforementioned novel recursive formulation and the computation in the reduced dimension space of input and output signals. The resulting architecture, equipped with a correction filter, is robust to unforeseen disturbances. The potential of the ESN-PNMPC is shown by application to the control of the four-tank system and an oil production platform, outperforming the predictive approach with a long-short term memory (LSTM) model, two standard linear control algorithms, and approximate predictive control.

Practical Nonlinear Model Predictive Controller Design for Trajectory Tracking of Unmanned Vehicles

The trajectory tracking issue of unmanned vehicles has attracted much attention recently, with the rapid development and implementation of sensing, communication, and computing technologies. This paper proposes a nonlinear model predictive controller (NMPC) for the trajectory tracking application of an unmanned vehicle (UV). First, a two-degree-of-freedom (2-DOF) kinematics model of this UV is used to derive the desirable controller with two control variables as forward velocity and yaw angle. Next, the one-step Euler method is employed to establish the nonlinear prediction model, then a nonlinear optimization objective function is formulated to minimize the tracking errors of forward velocity and yaw angle from a preset time-varying reference road. Finally, the effectiveness of the proposed NMPC scheme is assessed under two different driving scenarios via MATLAB simulations. The simulation results confirm that the proposed NMPC scheme reveals better control accuracy and computational efficiency than the standard MPC controller under two different prescribed roads. Moreover, an outdoor field test is conducted to verify the performance of the proposed NMPC scheme, and the results show that the proposed NMPC can be applied to the real vehicle and can improve the tracking accuracy and the driving stability of trajectory tracking.

Nonlinear Model Predictive Control of Electrical Submersible Pumps based on Echo State Networks

Employed for artificial lifting in oil well production, Electrical Submersible Pumps (ESP) can be operated with Model Predictive Control (MPC) to drive an optimal production, while ensuring a safe operation and respecting system constraints. Due to the nonlinear dynamics of ESPs, Echo State Networks (ESNs), a recurrent neural network with fast training, are employed for efficient system identification of unknown dynamic systems. Besides the synthesis of highly accurate prediction models, this work contributes by designing two Nonlinear MPC (NMPC) strategies for the control of an ESP-lifted oil well: a standard Single-Shooting NMPC that embeds the ESN model completely, and the Practical Nonlinear Model Predictive Controller (PNMPC) that approximates the NMPC through fast trajectory-linearization of the ESN model. Another contribution is the implementation of an error correction filter to reject disturbances and counter modeling errors in both NMPC strategies. Finally, in computational experiments, both ESN-based NMPC strategies performed well in controlling simulated ESP-lifted oil wells when the model of the plant is unknown. However, PNMPC was more efficient and induced a similar performance to standard NMPC.

Cost reduction of heat pump assisted membrane distillation by using variable electricity prices

Heat pump assisted membrane distillation (MD) has recently been proposed as a new method for simultaneous heating and cooling of membrane distillation. In this work, the cost of water (COW) of such a system is analysed by simulations. The COW can be reduced by using variability in electricity prices and an optimal control method e.g., electricity consumption can be reduced at high price moments and vice versa. Here, practical nonlinear model predictive control (PNMPC) was chosen as an optimal control method, and a validated model was used for the simulations of the MD system. The results indicate that using the variability in electricity prices reduced the COW of the heat pump driven system by 0.05 USD/m3, to a value of 4.93 USD/m3. In addition, simulations with resistive heating were done as it has a lower capital cost. Results show that the COW is higher with resistive heating due to the higher electricity consumption. The COW of resistive heating was found to be 10.49 USD/m3. The use of local cooling instead of evaporative cooling can reduce the COW by 0.05 USD/m3. Overall, the use of heat pumps is a promising method.

Energy Efficient Thermal Comfort Control for Residential Building Based on Nonlinear EMPC

For purpose of achieving the desired thermal comfort level and reducing the economic cost of maintaining the thermal comfort of green residential building, an energy efficient thermal comfort control strategy based on economic model predictive control (EMPC) for green residential buildings which adopts household heat metering is presented. Firstly, the nonlinear thermal comfort model of heating room is analyzed and obtained. A practical nonlinear thermal comfort prediction model is obtained by using an approximation method. Then, the economic cost function and optimization problem of energy-saving under the necessary thermal comfort requirements are constructed to realize the optimal economic performance of the dynamic process. The energy efficient thermal comfort MPC (EETCMPC) is designed. Finally, the comparison and analysis between EETCMPC and Double-layer Model Predictive Control (DMPC) is simulated. The simulation results reveal that when the clothing insulation is typical, the energy efficiency of EETCMPC is 8.9% and 11.6%, respectively, in the two simulation scenarios. When the clothing insulation varies with temperature, the energy efficiency of EETCMPC is 7.29% and 9.15%, respectively, and the total energy consumption is reduced by about 1.65% and 14.6%, respectively, compared with the typical clothing insulation. The economic performance is improved in the thermal comfort dynamic process of heating room.

Practical Non-Linear Responsivity Model and Outage Analysis for SLIPT/RF Networks

Simultaneous lightwave information and power transfer (SLIPT) is considered as an effective method of transferring information and energy via illuminated lightwaves. In this paper, we investigate the effect of non-linear responsivity on the SLIPT/radio frequency (RF) performance. We develop a tractable mathematical model for the non-linearity of responsivity and use it to study the end-to-end signal-to-interference-plus-noise ratio (SINR). Based on that, we derive the closed-form expressions for the probability density function and cumulative distribution function of the output SINR at the receiver. These statistical distributions are then used to derive the closed-form expressions of the outage probability of SLIPT/RF system over Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula> fading channels. Numerical results indicate that the simplified model used in previous studies leads to inaccurate performance evaluation results, and that our model provides more accurate evaluation. We also verify the analytical findings by simulation.

Practical nonlinear constitutive model for rockfill materials with application to rockfill dam

In this paper, a nonlinear constitutive model for rockfill materials is proposed to account for the coupling influence of the mean effective stress p and the deviatoric stress q on the deformation of rockfill materials. In the model, the stress-dilatancy relationship derived from the microstructural changes of granular materials is adopted, and the strength nonlinearity of rockfill materials is considered by using a logarithmic relationship between the peak friction angle and the mean effective stress. The SMP criterion is incorporated into the model to consider the influence of the intermediate principal stress. The good performance of the proposed model is demonstrated through modelling triaxial tests on rockfill materials from a rockfill dam. In addition, the FEM simulated deformation of a real CFRD using the proposed model agrees well with the monitored data.

Specific Absorption Rate-Aware Beamforming in MISO Downlink SWIPT Systems

This paper investigates the optimal transmit beamforming design of simultaneous wireless information and power transfer (SWIPT) in the multiuser multiple-input-single-output (MISO) downlink with specific absorption rate (SAR) constraints. We consider the power splitting technique for SWIPT, where each receiver divides the received signal into two parts: one for information decoding and the other for energy harvesting with a practical non-linear rectification model. The problem of interest is to maximize as much as possible the received signal-to-interference-plus-noise ratio (SINR) and the energy harvested for all receivers, while satisfying the transmit power and the SAR constraints by optimizing the transmit beamforming at the transmitter and the power splitting ratios at different receivers. The optimal beamforming and power splitting solutions are obtained with the aid of semidefinite programming and bisection search. Low-complexity fixed beamforming and hybrid beamforming techniques are also studied. Furthermore, we study the effect of imperfect channel information and radiation matrices, and design robust beamforming to guarantee the worst-case performance. Simulation results demonstrate that our proposed algorithms can effectively deal with the radio exposure constraints and significantly outperform the conventional transmission scheme with power backoff.

Mixed Logical Dynamical Nonlinear Model Predictive Controller for Large‐Scale Solar Fields

AbstractThis paper presents a control algorithm for reducing heat losses caused by clouds in large solar fields. The formulation is based on a Mixed Logical Dynamical (MLD) representation of the solar field plus the application of a Practical Nonlinear Model Predictive Controller (PNMPC) for calculating the optimal control action. The main purpose of the controller is to deactivate fields with inlet temperature greater than outlet temperature and to manipulate the oil flow rate of the activated fields for tracking the reference of the outlet temperature. A simplified lumped parameters model is used for prediction and simulation of the solar fields.

UAV-Aided Wireless Powered Communication Networks: Trajectory Optimization and Resource Allocation for Minimum Throughput Maximization

This paper investigates wireless powered communication network (WPCN) systems aided by unmanned aerial vehicle (UAV) where a UAV-mounted access point (AP) serves multiple energy-constrained ground terminals (GTs). Specifically, the UAVs first transmit the wireless energy transfer (WET) signals to charge the GTs in the downlink. Then, by utilizing the harvested energy, the GTs send their wireless information transmission (WIT) signals to the UAVs in the uplink. In this paper, depending on the operations of the UAVs, we consider two different scenarios, namely integrated and separated UAV WPCNs. First, in the integrated system, a UAV acts as a hybrid AP in which both energy transfer and information reception are performed at a single UAV. In contrast, for the separated UAV WPCN, we consider two UAVs each of which behaves as an information AP and an energy AP independently, and thus the information decoding and the energy transfer are separately processed at two different UAVs. In each system, we formulate two optimization problems taking into account a linear energy harvesting (EH) model and a practical non-linear model. To maximize the minimum throughput of the GTs, we jointly optimize the trajectories of the UAVs, the uplink power control, and the time resource allocation for the WET and the WIT. Since the formulated problems are non-convex, in the linear EH model-based system, we apply the concave-convex procedure by deriving appropriate convex bounds for non-convex constraints and identify the suboptimal solution for the problem by a proposed iterative algorithm. In the non-linear model-based system, we propose another algorithm to obtain an efficient solution by adopting the successive convex approximation method with the alternating optimization framework. Simulation results demonstrate the efficiency and the performance of the proposed algorithms compared to conventional schemes.

Hybrid NMPC Applied to a Solar-powered Membrane Distillation System

This work proposes a hybrid control strategy for the optimal operation of a solar membrane distillation facility This kind of plants presents a hybrid nature allowing their operation in several modes, which must be properly selected according to the operating conditions. Thus, the control algorithm is based on a mixed logical dynamical characterization of the solar membrane distillation facility, combined with the application of a practical nonlinear model predictive control strategy for calculating the optimal control actions. The main objectives of the control system are to increase the operating temperature and the distillate production of the membrane distillation module, as well as the number of operational hours. For these goals, the control algorithm has to select the most appropriate operating mode and the optimal operating points in terms of water flow rate at each sampling time. Simulation results are presented for evidencing the benefits of the proposed control approach.

Practical Nonlinear Model Predictive Control Algorithm for Long Short-Term Memory Networks

Abstract This paper presents a practical nonlinear model predictive control algorithm using Long Short-Term Memory (LSTM) artificial neural networks as process model. The controller is based on the Practical Nonlinear Predictive Controller (PNMPC) algorithm, a general framework which can be used for the implementation of nonlinear model predictive controllers using nonlinear models of almost any class. LSTM has gained attention during the last years for its ability to build high fidelity models in data-driven problems, such as system identification. In the proposed control algorithm, the LSTM model is used to obtain on-line a nonlinear prediction of the system free response and a linearized version of the neural model is used to obtain a local approximation of the system step response, which is used to build the dynamic matrix of the system at each sampling instant. The proposed controller was tested in a benchmark neutralization reactor control problem. The process was identified using the LSTM approach and the identification and closed-loop results are compared with linear and Hammerstein nonlinear models. The LSTM approach outperformed the other alternatives in both identification and control problems. The results obtained in this study show that the proposed control algorithm is an option to use a state-of-the-art nonlinear MPC in a computationally affordable way.