Economic Nonlinear Model Predictive Control Research Articles

Two‐layer dynamic economic nonlinear model predictive control for a Lithium‐ion battery charge process with random disturbances

AbstractThe charging process of lithium‐ion batteries is necessary for normal operation, and improper lithium‐ion battery charging strategy can cause side reactions, significant temperature rise, performance degradation, and safety concerns. This paper proposes a two‐layer dynamic economic nonlinear model predictive control economic model predictive control (EMPC) method for lithium‐ion battery charge management in which the non‐Gaussian random noise of voltage and current signal are taken into account. In the two‐layer EMPC, the upper layer finds the optimal reference trajectory, and the power in the future prediction horizon is chosen as an economic indicator to optimize the upper layer. The lower layer tracks the optimal trajectory, and model predictive control based on generalized correntropy is used. The economic cost of the system and the dynamic changes of the process are considered to greatly reduce the computational complexity and realize rapid battery charge management. Finally, the simulation results show that the tracking error of the two‐layer EMPC method based on generalized correntropy is stable around 0, while the tracking error of the two‐layer EMPC method based on MSE is stable around 0.003. The average control action times of the proposed two‐layer EMPC and single‐layer EMPC are 0.0052 and 0.0267 s, respectively. It is verified that the proposed method performs better for the lithium‐ion battery charging process with random disturbances.

Fast two-layer nonlinear economic predictive control using machine learning for ORC systems with non-Gaussian disturbances

This study proposes a machine learning-based generalized correntropy two-layer nonlinear economic model predictive control (ML-GC-TL-NEMPC) algorithm to improve the computational speed for Organic Rankine Cycle (ORC) systems with non-Gaussian disturbances. In the upper layer, the ratio of the net output power to the total heat transfer area is used as the economic performance index to optimize the optimal reference trajectory. In the lower layer, the generalized correntropy-based MPC (GC-MPC) is used to track the optimal trajectory. To quickly obtain an optimal solution, a Deep Neural Network (DNN) neural network controller is combined with kernel support vector machine (SVM). It learns the possible optimal solution via off-line training. Then it can be quickly implemented on on-line applications, so it can save the optimal calculation time. The proposed ML-GC-TL-NEMPC is applied to ORC. Its computation and performance are faster and better than the traditional two-layer EMPC and single-layer EMPC.

Self-stabilizing economic model predictive control without pre-calculated steady-state optima: Stability and robustness

We propose a new economic nonlinear model predictive control (eNMPC) formulation that tracks the optimality conditions of the real-time optimization problem rather than any specific steady states. The proposed formulation maintains its nature of optimizing economic performance and assured stability properties with the Lyapunov inequality constraint for the closed-loop control. Under general assumptions, we prove that the proposed controller is asymptotically stable without process disturbances and is input-to-state stable when there is a process disturbance. The proposed eNMPC is demonstrated on two case studies and compared against setpoint-tracking NMPC with setpoints determined by the steady-state real-time optimizer to show improved dynamic performance. We also highlight the capability of self-stabilization of the new eNMPC with parameter updates in the process model.

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”

Robustness of an Economic Nonlinear Model Predictive Control for Wind Turbines Under Changing Environmental and Wear Conditions

In this letter, the authors have assessed the robustness of an Economic Nonlinear Model-Predictive Controller (ENMPC) aimed at maximizing the power production of wind turbines. The scope of this letter is to quantify the sensitivity of this type of controller concerning wind conditions, climate, wind speed prediction unavailability, and aerodynamic performance degradation. A power production controller’s robustness is crucial for the wind turbine industry due to the extreme variability of external conditions and the wear caused by long-term continuous operativity. Model-Predictive controllers are, in principle, more prone to robustness issues concerning standard controllers, a fact that limits their adoption on actual wind turbines. The analysis is performed with the fully-aeroelastic solver OpenFAST considering a wide set of realistic load cases. It is demonstrated that the ENMPC previously developed is robust to wind prediction unavailability and change in wind turbulence intensity. Conversely, it is not robust to the modelling error due to aerodynamic degradation. Indeed, a reduction in generated power concerning the reference controller is observed, especially for operating region two and end-life blades. Finally, a significant increase in power production is achieved considering the external temperature variation thanks to the ENMPC’s direct handling of the generator temperature constraint.

Optimal Control for Wind Turbine Wake Mixing on Floating Platforms

Dynamic induction control is a wind farm flow control strategy that utilises wind turbine thrust variations to accelerate breakdown of the aerodynamic wake and improve downstream turbine performance. However, when floating wind turbines are considered, additional dynamics and challenges appear that make optimal control difficult. In this work, we propose an adjoint optimisation framework for non-linear economic model-predictive control, which utilises a novel coupling of an existing aerodynamic wake model to floating platform hydrodynamics. Analysis of the frequency response for the coupled model shows that it is possible to achieve wind turbine thrust variations without inducing large motion of the rotor. Using economic model-predictive control, we find dynamic induction results that lead to an improvement of 7% over static induction control, where the dynamic controller stimulates wake breakdown with only small variations in rotor displacement. This novel model formulation provides a starting point for the adaptation of dynamic wind farm flow control strategies for floating wind turbines.

A novel Economic Nonlinear Model Predictive Controller for power maximisation on wind turbines

Reducing the Levelized Cost of Energy (LCoE) is one of the main objectives of the wind turbine industry. There are several ways to achieve this goal: reducing construction and installation costs, reducing Operating&Maintenance costs, or increasing the power output. In this work, an Economic Nonlinear Model Predictive Control strategy is developed to maximise the power production of wind turbines. A novel three-states, non-linear Reduced Order Model is developed to predict aerodynamic power, rotor thrust and generator temperature with suitable accuracy. The control action is obtained from a constrained optimisation problem that uses the developed model, where the objective is the maximisation of the integral of the aerodynamic power. A set of constraints (including a bound on the generator temperature and the rotor thrust) are imposed. First, the turbine model is validated against high-fidelity simulations, then the controller performance and robustness are assessed in the entire wind range of operation, obtaining a significant increase of average power. Apart from the assessment of the controller performance in OpenFAST, the controller robustness is verified, introducing errors in the estimation of incoming wind, up to the case of a complete lack of information. The controller (freely downloadable from a dedicated repository) is effective in all the operating regions without the need for logical switches. Moreover, thanks to the optimised numerical solver adopted, it can be applied to actual wind turbines (which require real-time algorithmic performance).

Q-learning of the storage function in Economic Nonlinear Model Predictive Control

The closed-loop stability of an optimal policy provided by an Economic Nonlinear Model Predictive Control (ENMPC) scheme requires the existence of a storage function satisfying dissipativity conditions. Unfortunately, finding such a storage function is difficult in general. In contrast, tracking NMPC scheme uses a stage cost that is lower-bounded by a class-K∞ function and the closed-loop stability is fairly straightforward to establish. Under the dissipativity conditions, ENMPC has an equivalent tracking MPC that delivers the same optimal policy. In this paper, we use this idea and parameterize the stage cost and terminal cost of a tracking MPC with an additional parameterized storage function. We show that, if the parameterization of the tracking MPC scheme is rich enough to capture the exact optimal action-value function of the ENMPC scheme, then the parameterized storage function for the optimal parameters satisfies the dissipativity conditions for both discounted and undiscounted ENMPC schemes. In fact, we show that these conditions are met for dissipative problems. We propose to use Q-learning as a practical way of adjusting the parameters of the tracking MPC. Different numerical examples are provided to illustrate the efficiency of the proposed method, including LQR, non-dissipative, non-polynomial and a nonlinear chemical case studies. For instance, in the provided non-polynomial case study, the learning method can improve the storage function estimation by about 60% and 99.5% after 10 and 50 learning steps, respectively, compared with the Sum-of-Square method.

Economic nonlinear model predictive control of fatigue for a hybrid wind-battery generation system

An economic nonlinear model predictive controller (ENMPC) is formulated for a wind turbine-battery hybrid generation system. The controller aims to maximize the operational profit of the generator by balancing between generated wind power and turbine tower fatigue as well as battery cyclic fatigue. Other than the tower fore-aft fatigue, tower side-side fatigue is also considered to assess impact on overall economic performance. A moving horizon estimator (MHE) is formulated to provide meaningful initialization to the ENMPC in presence of plant model mismatch.The formulated controller utilizes the parametric online rainflow counting (PORFC) approach for direct cyclic fatigue cost minimization within ENMPC. The closed-loop simulation shows significantly higher profit compared to a realistic base-case scenario and relatively higher profit compared to another economic controller.

A novel Nonlinear Model Predictive Controller for Power Maximization on Floating Offshore Wind Turbines

Reducing the Levelized Cost of Energy is the main objective of wind turbine industry, in particular for the emerging sector of floating offshore turbines. In this work, a novel Economic Nonlinear Model Predictive Control (ENMPC) strategy is developed to maximize the power production of floating offshore wind turbines. The control problem is solved through an indirect method, which achieves the computational efficiency required to apply it in real world cases. A non-linear Reduced Order Model of the floating turbine predicts aerodynamic power, generator temperature and platform motions inside the controller. A set of constraints, including a bound on the generator temperature, the thrust and platform velocities are imposed. Simulations using the open-source engineering tool OpenFAST on the 5MW NREL wind turbine supported by the OC3 spar buoy platform [1] are performed to validate the turbine model and then to assess the controller performances in realistic wind and sea state conditions. With respect to the standard controller, a 4.3% increase of generated power in rated conditions is achieved with a more stable generator temperature.

Economic nonlinear model predictive control of fatigue—Formulation and application to wind turbine control

AbstractIn this article, the estimation of fatigue is implemented in the cost function of a gradient‐based model predictive controller (MPC). This is a challenging problem, because calculating fatigue leads to a non‐standard and discontinuous cost function. Based on a brief previous publication, in the present work the method is derived, explained, and assessed in detail. The key enablers of the proposed method are a sequential implementation of MPC, the periodic substitution of discontinuous aspects of the cost function by linear functions, and the assumption of a sufficiently infrequent switching of this substitution. Fatigue cost gradients are obtained efficiently by automatic differentiation. The method is implemented in an economic nonlinear model predictive controller (ENMPC), which optimally balances revenue and fatigue cost. This novel formulation is applicable to a very wide range of domains, and it is demonstrated here on the control of a wind turbine. The proposed ENMPC is fully parameterized by physical and monetary variables, and outperforms a conventional ENMPC based on the literature. The method is assessed by considering various metrics, including frequency spectra, damage estimation, switching, and gradient dynamics, which together provide useful insight into its main characteristics and an initial assessment of its performance.

Hierarchical nonlinear model predictive control of offshore hybrid power systems

This paper presents an approach for controlling ofshore hybrid power systems consisting of gas turbines, offshore wind, and batteries for satisfying an exogenous power demand. A hierarchical controller is developed comprising a high-level economic nonlinear model predictive controller that distributes the power demand according to some economic objective, a low-level nonlinear tracking model predictive controller that actuates on the hybrid power system, and a nonlinear moving horizon estimator to estimate the system state. Simulation results and concluding remarks reveal the advantage of such a hierarchical approach for a simple simulation study.

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.

Artificial Intelligence-oriented economic non-linear model predictive control applied to a pressure swing adsorption unit: Syngas purification as a case study

• An MPC controller is applied to the syngas purification by pressure swing adsorption. • The proposed Economic MPC (EMPC) makes use of a Deep Neural Network (DNN) model. • The EMPC control law is solved by a modified Particle Swarm Optimization technique. • The plant-model mismatch is evaluated by phenomenological and DNN surrogate models. • CO2 recovery and purity and H2/CO are controlled while productivity is maximized. A novel Artificial Intelligence-oriented Economic nonlinear model predictive control (EMPC) strategy is proposed herein. It was applied to a Pressure Swing Adsorption (PSA) unit where syngas is purified by porous amino-functionalized titanium terephthalate MIL-125. This study addresses the open research problem of simultaneous economic optimization and advanced control in PSA units. A surrogate model based on a Deep Learning Neural Network (DNN) architecture is built to capture the process dynamics with high fidelity. The deployment of these DNN models into the EMPC control law allows obtaining solutions at a low computational cost, making it feasible to be applied in practice, even if using a particle swarm optimization technique. The robustness of the proposed EMPC controller is evaluated under a realistic plant-model mismatch in a software-in-the-loop approach. An experimentally validated phenomenological nonlinear model of the PSA unit for syngas purification was used to represent the plant and to train the DNN models. While EMPC maximizes the unit productivity in all zone/output tracking scenarios for CO 2 recovery and CO 2 purity, it can successfully fulfill the key operating endpoint constraint related to the H 2 /CO ratio, including the unmeasured perturbation scenarios.

Energy‐efficient cabin climate control of electric vehicles using linear time‐varying model predictive control

AbstractA cabin climate control system, often referred to as a heating, ventilation, and air conditioning (HVAC) system, is one of the largest auxiliary loads of an electric vehicle (EV), and the real‐time optimal control of HVAC brings a significant energy‐saving potential. In this article, a linear‐time‐varying (LTV) model predictive control (MPC)‐based approach is presented for energy‐efficient cabin climate control of EVs. A modification is made to the cost function in the considered MPC problem to simplify the Hessian matrix in utilizing quadratic programming for real‐time computation. A rigorous parametric study is conducted to determine optimal weighting factors that work robustly under various operating conditions. Then, the performance of the proposed LTV‐MPC controller is compared against a rule‐based (RB) controller and a nonlinear economic MPC (NEMPC) benchmark. Compared with the RB controller benchmark, the LTV‐MPC reaches the target cabin temperature at least 69 s faster with 3.2% to 15% less HVAC system energy consumption, and the averaged cabin temperature difference is 0.7°C at most. Compared with the NEMPC, the LTV‐MPC controller can achieve comparable performance in temperature regulation and energy consumption with fast computation time: the maximum differences in temperature and energy consumption are 0.4°C and 2.6%, respectively, and the computational time is reduced 72.4% on average with the LTV‐MPC.

Adaptive Sampling of Dynamic Systems for Generation of Fast and Accurate Surrogate Models

AbstractFor economic nonlinear model predictive control and dynamic real‐time optimization fast and accurate models are necessary. Consequently, the use of dynamic surrogate models to mimic complex rigorous models is increasingly coming into focus. For dynamic systems, the focus so far had been on identifying a system's behavior surrounding a steady‐state operation point. In this contribution, we propose a novel methodology to adaptively sample rigorous dynamic process models to generate a dataset for building dynamic surrogate models. The goal of the developed algorithm is to cover an as large as possible area of the feasible region of the original model. To demonstrate the performance of the presented framework it is applied on a dynamic model of a chlor‐alkali electrolysis.

Budget-constrained economic model predictive control: A user-friendly proposal for HVAC

Cost optimization of heating, ventilation and air conditioning systems (HVAC) in buildings has been approached by using sophisticated methodologies such as model predictive control (MPC) and real-time optimization. However, such techniques are not usually user-friendly to individuals without a process control background. Namely, it can be very difficult for building managers to estimate the economic impact of set point changes. For this reason, it is proposed an economic nonlinear model predictive control (eMPC) using a budget constraint. Using this concept, building managers will be able to balance the trade-off between operational cost and thermal comfort. To demonstrate the proposed approach, a first-principles model of a HVAC system is extended from a previous authors contribution to consider two new features: (1) thermal lag due to energy accumulation in the building envelope; (2) energy consumption by the fans. Then, the implemented HVAC system is tested in open- and closed-loop conditions. The closed-loop simulations showed the advantage for building managers of using the budget-constrained eMPC over the classical approach and On–Off control when using two different budget strategies. This approach ensures an user-friendly interface between building managers (i.e., non-expert users) and eMPC.

TH22. IDENTIFICATION OF IMMUNE-RELATED SERUM PROTEINS ASSOCIATED WITH GENETIC RISK OF BIPOLAR DISORDER

The goal of this work is an efficient control scheme for the robust satisfaction of constraints for batch processes under parametric uncertainties. The multi-stage economic nonlinear model-predictive controller (eNMPC) [S. Lucia, et al. J. Process Control, 2013] is combined with two different methods for robust dynamic optimization. The multi-stage NMPC considers a scenario tree, branching at each sampling interval. In this work, the scenarios for the branches are generated with two previously investigated methods of detecting worst-case scenarios. One method is based on discretization of the uncertain parameter set (J. Puschke, et al. Comput. Chem. Eng., Vol. 98, 2017a). With this approach, all worst-case models are considered, including points not lying at the boundary of the uncertainty set. The other method is a heuristic approach (J. Puschke, et al. Comput. Chem. Eng., 2017b), which considers only values at the boundary with a high sensitivity. These methods for robust control are evaluated on the basis of an illustrative case study. The results show that, in contrast to the nominal eNMPC, less or even no constraint violations occur.

Optimal management of energy sharing in a community of buildings using a model predictive control

Exporting generated electricity by on-site renewable energy systems from buildings to the grid is only slightly profitable in many countries. Therefore, it is required to investigate the benefits of sharing generated energy in a microgrid within a community of buildings. Exploiting the benefits of peer-to-peer energy exchange between prosumers in a community can make the best use of the on-site generation while reducing their bills. This study elaborates the potential of energy management to minimize the electricity cost of a community consisted of multiple buildings and connected to a microgrid. To implement this, an energy management system is designed based on non-linear economic model predictive control and successive linear programming for sharing the on-site surplus generated electricity between the buildings in the community. Four buildings are simulated and studied as an example of a small community. These buildings are dissimilar in their age, thermal mass, insulation, heating system and on-site renewable energy systems. It is shown that considering the community of buildings as a single entity, the novel model predictive control can be efficiently used for minimizing the energy cost of the community that has various sources of energy generation, conversion and storage, including significant non-linear interactions. Three different scenarios of the energy management system for the studied community are investigated, and the results indicate that the annual electricity energy cost for single buildings can be reduced by 3.0% to 87.9%, depending on the building and its systems, and by 5.4% to 7.7% on the community level.

Closed-loop in-silico control of a two-stage emulsion polymerization to obtain desired particle morphologies

Particle morphology strongly affects the performance of waterborne polymer dispersions, which are products-by-process materials produced by emulsion polymerization, a process prone to suffer run-to-run irreproducibility. Therefore, on-line control of particle morphology would be tremendously beneficial, but this is an unsolved issue because particle morphology is neither on-line measurable nor observable from available online monitoring techniques. This article explores in-silico the possibility to overcome this problem by using a mathematical model able to calculate the particle morphology from the monomer conversion and reactor temperature as a “soft sensor”. These estimates are used in combination with an economic nonlinear model predictive controller. It is shown that this controller is able to achieve a good control of the particle morphology even in the presence of serious disturbances such as the presence of a strong inhibition or the failure of the reactor cooling system. Under these circumstances, neither open-loop control nor tracking of off-line optimized reaction trajectories are able to control the particle morphology tightly. The limits of the soft sensor are investigated by considering non-detectable disturbances such as the use of a seed of unknown glass transition temperature and the benefits of a hypothetical online morphology measurement available for control is explored.