Practical Nonlinear Model Predictive Control Research Articles

Tracking Control of Unforced and Forced Equilibrium Positions of the Pendubot System: A Nonlinear MHE and MPC Approach

This paper presents a unified control scheme of the Pendubot based on nonlinear model predictive control (NMPC) and nonlinear moving horizon estimation (NMHE) with the objective of point-to-point tracking its unstable unforced and ultimately forced equilibrium positions. In order to implement it on this fast, underactuated mechatronic system, we employ the Gauss–Newton real-time iteration scheme tailored to obtain the efficient solution of the underlying nonlinear optimization problems via sequential quadratic programming. The control performance is experimentally assessed on a real-world laboratory setup featuring an execution timing analysis and hints how to further improve the computational efficiency of the proposed nonlinear estimation control scheme. Even nowadays, the number of practical NMPC applications in the millisecond range is still rather limited, and the presented NMHE-based NMPC of the Pendubot thus also represents a unique case study for control practitioners.

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.

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.

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.

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.

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.

Nonlinear Model Predictive Control of an Oil Well with Echo State Networks

In oil production platforms, processes are nonlinear and prone to modeling errors, as the flow regime and components are not entirely known and can bring about structural uncertainties, making the design of predictive control algorithms a challenge. In this work, an efficient data-driven framework for Model Predictive Control (MPC) using Echo State Networks (ESN) as the prediction model is proposed. Unlike previous works, the ESN model for MPC is only linearized partially: while the free response of the system is kept fully nonlinear, only the forced response is linearized. This MPC framework is known in the literature as the Practical Nonlinear Model Predictive Controller (PNMPC). In this work, by using the analytically computed gradient from the ESN model, a finite difference method is not needed to compute derivatives as in PNMPC. The proposed method, called PNMPC-ESN, is applied to control a simplified model of a gas-lifted oil well, managing to successfully control the plant, obeying the established constraints while maintaining setpoint tracking.

Hierarchical Non-linear Control of a Tubular Photobioreactor

This work presents the development of a hierarchical control strategy for microalgal production. The proposed control scheme is composed of two layers. A lower layer focused on pH set-point tracking and where two different control algorithms were evaluated, a PI plus feedforward compensator and a Practical Non-linear Model Predictive Controller. The upper layer is in charge of calculating optimal pH set-points based on economic criteria to maximize profits, computed as the difference between the incomes obtained from the final production sale and the associated production costs (including the environmental impact of the exhausted CO2 losses). Two types of models have been used depending on the requirements of each layer. Simulated results of the proposed hierarchical control architecture are presented.

A practical NMPC with robustness of stability applied to distributed solar power plants

This paper presents the application of a Nonlinear Model Predictive Controller (NMPC) to a distributed solar collector field. The control technique is basically similar to Dynamic Matrix Control (DMC) but in the proposed approach a nonlinear model of the process is directly used without linearization of the process model involved in the control strategy. Moreover, a modified Practical Nonlinear Model Predictive Controller (PNMPC) algorithm adapted to solar plant is developed in this work. To include robustness of stability against uncertainties in the NMPC algorithm, a candidate Lyapunov function is included in the cost function. The main purpose of the controller is to manipulate the oil flow rate to maintain the field outlet temperature in the desired reference value and attenuate the disturbances effects. The simulated process used is a distributed parameter model, while for the prediction a lumped parameter model with time delay was considered.

Disturbance Estimator based NonLinear MPC of a Three Phase Separator

This paper presents a nonlinear predictive controller with a feed-forward action applied to a three-phase separator used in the petroleum industry. Two tools are used in order to include the feed-forward action in the NMPC, a disturbance estimator and a disturbance predictor. Moreover, a supervisory control changes the objective function characteristics of the NMPC depending on the type of disturbances acting on the process. The separator advanced controller, which is capable to maintain all process variables in pre-defined zones, uses a practical nonlinear model predictive controller (PNMPC) developed in the Department of Automation and Systems (Federal University of Santa Catarina). The performance of the proposed strategy is compared to a traditional PI Zone controller used in industry and to a different NMPC based on a Hammerstein model. All the case study simulations are developed with a complete phenomenological nonlinear model of the separator. The obtained comparative results show that the proposed strategy gives the best results, allowing good oscillation attenuation under slug perturbations.

Dynamic modelling and nonlinear model predictive control of a Fluid Catalytic Cracking Unit

The paper presents the application of two nonlinear model predictive control (NMPC) approaches: quasi-infinite-horizon nonlinear MPC (QIHNMPC) and moving horizon estimator nonlinear MPC (MHE-NMPC) to the Fluid Catalytic Cracking Unit (FCCU). A complex dynamic model of the reactor–regenerator–fractionator system is developed and subsequently used in the controller. The novelty of the model consists in that besides the complex dynamics of the reactor–regenerator system, it also includes the dynamic model of the fractionator, as well as a five lumps kinetic model for the riser. Tight control is achieved using the QIHNMPC approach. The MHE-NMPC considers important features of a real-time control algorithm, resulting in a framework for practical NMPC implementation, such as: state and parameter estimation and efficient solution of the optimisation problem. In the NMPC approach, only measurements available in practice are considered, whereas the rest of the states are estimated together with uncertain model parameters, via MHE technique. Using an efficient numerical implementation based on the multiple shooting algorithm real-time feasibility of the approach is achieved. The incentives of the proposed approaches are assessed on the simulated industrial FCCU.