Multi-objective Model Predictive Control Research Articles

A novel two-stage multi-objective dispatch model for a distributed hybrid CCHP system considering source-load fluctuations mitigation

Small-scale distributed energy systems with combined cooling, heating, and power (DES-CCHP) production have attracted international interest. However, fluctuating loads and renewable energies continuously disturb the real-time operation of DES-CCHP and even the connected grid, hindering the broad application of grid-connected DES-CCHP. In this paper, a novel model predictive control (MPC) based two-stage strategy is developed for DES-CCHP, with multiple timescales consideration. In the first stage, a multi-objective MPC is built with inheritance and fusion mechanisms of multi-step scheduling instructions, simultaneously minimizing operation costs and power fluctuations. The second stage performs intelligent decision-making on the results of the first stage, which allows appropriate state-switching instructions to ensure economy. Meanwhile, the decision-making rejects the unnecessary one and triggers a second-round flexibility-based interventional optimization to revise scheduling planning. The case studies show that compared to dispatch without MPC, the economic single-objective MPC, single-stage multi-objective MPC (only applies the first-stage models), and two-stage multi-objective MPC save costs by 5.31 %, 4.80 %, and 4.57 %, respectively. As for fluctuations mitigation, the single-stage and two-stage models significantly smooth power fluctuations by 51.66 % and 69.93 %, respectively. The proposed strategy operates DES-CCHP economically, stably, and grid-friendly under a rugged operating environment.

A flexible and deep peak shaving scheme for combined heat and power plant under full operating conditions

Improving the flexible and deep peak shaving capacity of combined heat and power (CHP) plant under full operating conditions to facilitate renewable energy consumption is the main choice of novel power system. Accordingly, a dry/wet state automatic conversion control scheme fuses the precise mechanism structure, reinforcement learning and multi-objective model predictive control (MPC) algorithms is designed to promote the deep peak shaving ability of CHP plant in this paper. Firstly, the detailed mechanism models of once-through boiler at dry and wet state are presented by analyzing the dynamic characteristics of steam-water flow. Secondly, the large-scale unknown parameters in mechanism models are identified via the Takagi-Sugeno fuzzy modeling, reinforcement learning algorithms and actual dry/wet state conversion data. Thanks to the proposed hybrid modeling strategy, the high-precision boiler-steam unit models at dry and wet state are rapid obtained. Then, to meet different peak shaving demands, the multi-objective MPC algorithm is respectively constructed under dry and wet state with the comprehensive consideration of operational constraints, load tracking error, algorithm stability, power generation cost, CO2 and NOx emission costs. Aiming at maximizing the peak shaving efficiency and flexible operation ability of plant, a dry/wet automatic control scheme combined the designed multi-objective MPC algorithms and identified dry/wet state models is proposed. Finally, the load variation rate of 5 % and 2 % RCM/min is respectively achieved in the dry/wet state conversion tests on a 350 MW CHP plant based on the proposed control scheme. Thus, the rapid and thorough dry/wet state conversion performance of once-through boiler has successfully improved the operational flexibility of CHP plant under full operating conditions.

Multi-Objective Integrated Robust Optimal Control for Wastewater Treatment Processes

Multi-objective optimal control is widely applied in wastewater treatment processes (WWTPs) to ensure the security and stability of the operation processes. However, for the existing stepwise multi-objective optimal control (SMOC) algorithms, the unknown disturbances will further influence the obtain of set-points and the design of control laws, which may degrade the control performance and operation performance of WWTPs. Aim at the above-mentioned problem, this study presents a multi-objective integrated robust optimal control (MIROC) method for WWTPs. The merits of MIROC are three folds. First, a model approximator is designed to capture the nonlinear dynamics of WWTPs. Second, a disturbance observer is utilized to describe the disturbances of WWTPs. Then, based on the model approximator and disturbance observer, a more accurate prediction model of WWTPs with disturbances is established. Third, under the framework of multi-objective model predictive control (MMPC), a MIROC structure with a cooperative cost function (CCF) and a gradient-based multi-objective optimization algorithm (GMOA) is developed to coordinate optimization and control solution of WWTPs with unknown disturbances. Finally, the stability analysis of MIROC is provided in theory. Meanwhile, the results on the benchmark simulation platform demonstrate that MIROC can improve the performance of WWTPs. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The SMOC algorithms may degrade the performance of WWTPs with the unknown disturbances. In the paper, a MIROC scheme is presented for WWTPs with the unknown disturbances. Three key parts are contained, the model approximator, the disturbance observer and the MIROC structure. A prediction model of WWTPs with disturbances is established with the model approximator and the disturbance observer. Then, the model approximator and the disturbance observer are applied to improve modeling accuracy of MIROC. Based on the prediction model of WWTPs, a MIROC structure is designed to comprehensively analyze the optimization process and control process of WWTPs with the unknown disturbances. Then, MIROC structure is composed of a CCF and a GMOA. Finally, the results on an industrial application of WWTPs demonstrate that MIROC can achieve optimal operation of WWTPs.

A Frequency Control Strategy for EV Stations Based on MPC-VSG in Islanded Microgrids

The inertia level of microgrids decreases with the access of inverter-based distributed generations. Uncertainty of source loads in islanded microgrids can lead to frequency instability. Considering electric vehicles (EVs) as a typical regulable load, a charging station (CS) virtual synchronous generator (VSG) frequency control (FC) strategy that considers the user charging and grid FC demand is proposed. First, the control architecture of CS based on the VSG is designed. Second, considering the impact of VSG FC on EV user charging demand, the charging power response model considering the charging power FC cost is designed. Furthermore, multi-objective model predictive control (MPC) algorithm is designed to improve the VSG control strategy, and the FC strategy is obtained. Simulation results show that the proposed method can provide inertial support and frequency regulation capability by the CS with VSG control strategy while satisfying EV charging demand. In addition, the FC cost can be decreased.

Multi-criteria evaluation of novel multi-objective model predictive control method for indoor thermal comfort

We proposed a novel multi-objective model predictive control (MPC) approach based on a straightforward internal prediction model to achieve building energy efficiency and maintain the indoor temperature within a predetermined comfort range. Using the CARNOT Toolbox, we built a detailed room model based on a real room with water-circulated radiator heating. We developed an MPC controller using MATLAB and combined it with the room model in the CARNOT Toolbox to tune the controller parameters and evaluate its performance. Based on the co-simulations, a control step of 15 min and a prediction horizon of 90 min were found to be suitable for room level indoor thermal comfort control. The performance of the controller was evaluated in terms of multiple criteria, including control accuracy, hydrodynamic stability, and energy consumption. Compared with the traditional proportional-integral-derivative (PID) control, the MPC demonstrated a 16.4 % improvement in control accuracy, 2.8 % lower energy consumption, and a 50 % reduction in the hot water flow change rate, improving the system’s hydrodynamic stability. A significant advantage of the MPC is that it is possible to compute different efficient solutions by modifying the parameters, among which the decision-makers can choose their most preferred compromise solution considering multiple criteria.

Multiobjective Integrated Optimal Control for Nonlinear Systems.

The multiobjective optimal control method optimizes the performance indexes of nonlinear systems to obtain setpoints, and designs a controller to track the setpoints. However, the stepwise optimal control method that independently analyzes the optimization process may obtain unfeasible and difficult to track setpoints, which will reduce the operation and control performance of the systems. To solve this problem, a multiobjective integrated optimal control (MIOC) strategy is proposed for nonlinear systems in this article. The main contributions of MIOC are threefold. First, in the framework of multiobjective model predictive control, an integrated control structure with a comprehensive cost function and a collaborative optimization algorithm is designed to achieve the coordinate optimal control. Second, for the time inconformity of setpoints and control laws caused by the characteristic of tracking control, the different prediction horizons are designed for the comprehensive cost function. Then, the collaborative optimization algorithm is proposed for the comprehensive cost function to achieve the integrated solution of setpoints and control laws to enhance the operation and control performance of nonlinear systems. Third, the stability and control performance analysis of MIOC is provided. Finally, the proposed MIOC method is applied for a nonlinear system to demonstrate its effectiveness.

Lexicographic optimization for economic model predictive control with zone tracking

Tracking model predictive control (MPC) and economic model predictive control (EMPC) are essential techniques in process control. Economic model predictive control with zone tracking offers an effective means of concurrently addressing both tracking MPC and EMPC objectives. However, the aggregated conflicting objectives do not always align with the prioritization of critical tasks, such as safety, stability, quality, and economy. To address this issue, this study introduces a lexicographic approach for EMPC with zone tracking, which aims at balancing the competing zone tracking and economic objectives. The work also explores a generalized lexicographic multi-objective MPC (MoMPC) formulation and presents lexicographic zone economic model predictive control to accommodate multiple tracking and economic objectives. The advantages, disadvantages, and effectiveness of the proposed approach are validated and showcased through extensive simulation experiments.

Backup Plan Constrained Model Predictive Control with Guaranteed Stability

This paper proposes and evaluates a new safety concept called backup plan safety for path planning of autonomous vehicles under mission uncertainty using model predictive control (MPC). Backup plan safety is defined as the ability to complete an alternative mission when the primary mission is aborted. To include this new safety concept in control problems, we formulate a feasibility maximization problem aiming to maximize the feasibility of the primary and alternative missions. The feasibility maximization problem is based on multi-objective MPC, where each objective (cost function) is associated with a different mission and balanced by a weight vector. Furthermore, the feasibility maximization problem incorporates additional control input horizons toward the alternative missions on top of the control input horizon toward the primary mission, denoted as multihorizon inputs, to evaluate the cost for each mission. We develop the backup plan constrained MPC algorithm, which designs the weight vector that ensures asymptotic stability of the closed-loop system, and generates the optimal control input by solving the feasibility maximization problem with computational efficiency. The performance of the proposed algorithm is validated through simulations of an unmanned aerial vehicle path planning problem.

Robust multi‐objective model predictive control for constrained nonlinear systems with disturbances

AbstractThis work develops a new robust multi‐objective model predictive control (MoMPC) strategy for constrained non‐linear systems with bounded disturbances. The multiple objectives are always contradictory, and the presence of disturbances may result in the violation of state constraints and instability of the controlled system. Firstly, the conflict between multiple objectives is reconciled by minimizing the distance of the cost function vector to the vector of independently minimised objectives obtained by solving a set of steady‐state optimisation problems. Then the contractive state set, which takes into account the effect of disturbances on system states, is constructed to guarantee the robust satisfaction of state constraints. Finally, a stability constraint updated online by solving an auxiliary optimization problem is established to ensure the robust stability of the system under MoMPC. An isothermal chemical reactor system is employed to verify the effectiveness of the controller proposed here.

Multi-objective model predictive control for microgrid applications

Integration of microgrids may introduce significant power quality challenges to the power distribution networks that may necessitate additional enforcement such as installing new Power Quality Improvement Devices (PQID), which is costly and not always possible option. This paper proposes a control approach that enables the existing power electronics devices within the microgrid to perform multiple functions to address the resultant power quality problems. The proposed method introduces flexibility in harmonic and fundamental power sharing and controlling switching frequency through an improved cost function. Grid connected operation-mode, harmonic compensation capabilities as well as improved dynamic response of controller to fast reference changes have been studied and experimentally verified on a microgrid prototype. Finally, the experimental results of the proposed control method are compared with the results from most recent relevant research activities in the field, evidencing its superiority as compared to the existing control methods presented in the literature.

Multi-Objective Adaptive Optimization Model Predictive Control: Decreasing Carbon Emissions from a Zinc Oxide Rotary Kiln

The zinc oxide rotary kiln, as an essential piece of equipment in the zinc smelting industrial process, is presenting new challenges in process control. China’s strategy of achieving a carbon peak and carbon neutrality is putting new demands on the industry, including green production and the use of fewer resources; thus, traditional stability control is no longer suitable for multi-objective control tasks. Although researchers have revealed the principle of the rotary kiln and set up computational fluid dynamics (CFD) simulation models to study its dynamics, these models cannot be directly applied to process control due to their high computational complexity. To address these issues, this paper proposes a multi-objective adaptive optimization model predictive control (MAO-MPC) method based on sparse identification. More specifically, with a large amount of data collected from a CFD model, a sparse regression problem is first formulated and solved to obtain a reduction model. Then, a two-layered control framework including real-time optimization (RTO) and model predictive control (MPC) is designed. In the RTO layer, an optimization problem with the goal of achieving optimal operation performance and the lowest possible resource consumption is set up. By solving the optimization problem in real time, a suitable setting value is sent to the MPC layer to ensure that the zinc oxide rotary kiln always functions in an optimal state. Our experiments show the strength and reliability of the proposed method, which reduces the usage of coal while maintaining high profits.

Multi Objective Nonlinear Model Predictive Control of Diabetes Models Considering the Effects of Insulin and Exercise

Rigorous multiobjective nonlinear model predictive control on the diabetes model incorporating single and multiple control strategies. The amount of glucose is minimized with the Bergman model considering the effects of insulin and exercise. The optimization language pyomo is used in conjunction with the state-of-the-art global optimization solvers IPOPT and Baron. Pareto surfaces are generated. When some optimal control profiles were found to exhibit sharp spikes, an activation factor involving the hyperbolic tangent function was used. It is observed that a greater amount of glucose minimization is achieved when more control procedures were incorporated. This demonstrates that it is more beneficial to use multiple control strategies

A dynamic weight multi-objective model predictive controller for adaptive cruise control system

Adaptive cruise control (ACC) is recognized as an effective method to improve vehicle safety and reduce driver workload. This paper proposes a whole hierarchical multi-level state ACC system. According to the function of ACC system, the three-level state ACC system is designed and the conversion mechanism between different states is put forward. As for the complex car-following mode, considering the variable headway safety distance and the road adhesion coefficient, the expected safety distance model is established, using the distance error and the speed error as fuzzy input, based on the fuzzy control algorithm, the following mode is obtained; considering vehicle safety, tracking capability and ride comfort, the control objectives are formulated into the model predictive control algorithm. A dynamic weight strategy is proposed to solve time-varying multi-objective control problems, where the weight can be adjusted with respect to different following conditions. The simulation results demonstrate that the car following performance of ACC with the proposed dynamic weighted MPC can provide better performance than that using constant weight MPC, and the multi-level state ACC system can display the control mode more intuitively.

Hybrid power system with adaptive adjustment of weight coefficients multi-objective model predictive control

Considering the complex flight conditions of aircraft and the difficulty of the oil-electric hybrid system to rationally allocate the energy power and give full play to the various energy advantages under different flight conditions, an energy management strategy of the hybrid system based on multi-objective model prediction is proposed to optimize the engine working area, minimize the engine dynamic characteristics, and optimally manage the charge state of the energy storage battery. First, the fuel consumption efficiency curve identification based on the maximum likelihood method is proposed to obtain the optimal working power area of the engine. The real-time estimation of load power is realized by designing two load power filters. Then, combined with the working characteristics of the engine and energy storage battery, an optimal energy management strategy based on multi-objective model predictive control is designed. The fuzzy control method is adopted to dynamically adjust the weight coefficients of each constraint term according to the flight conditions to achieve the global optimization. Finally, the effectiveness of the proposed algorithm is verified by simulation experiments. The results show that in the proposed optimization management strategy, the engine works in the optimal fuel consumption area, which is more economical than the pure fuel drive, avoids the overcharging and discharging of the energy storage battery and the severe fluctuation of the engine power, and greatly improves the economic security and smoothness of the system.

Energy Management Strategies for Series-Parallel Hybrid Electric Vehicles Considering Fuel Efficiency and Degradation of Lithium-Ion Batteries

&lt;div&gt;Lithium-ion batteries are the most crucial component of hybrid electric vehicles (HEVs) with respect to cost and performance. In this article, a new energy management strategy (EMS) is developed that improves fuel efficiency (FE) and suppresses the degradation of the battery. A hybridized two-layer algorithm that combines multi-objective nonlinear model predictive control (NMPC) with a rule-based (RB) algorithm is proposed as a new EMS that is called RB-NMPC. The RB-NMPC is designed to optimize the torque split between the engine and electric motors while maintaining the maximum and minimum constraints of each component. The proposed EMS is incorporated into control-oriented vehicle models, and their performances are analyzed for different driving cycles by comparing with RB, dynamic programming (DP), and NMPC. In addition, the RB-NMPC algorithm is applied for two different powertrain configurations of HEV, P0P2 and P1P2 configurations for both an Urban Dynamometer Driving Schedule (UDDS) and a Highway Fuel Economy Test (HWFET). For P0P2, the results show that RB-NMPC outperforms other methods for UDDS with an FE that is 4.7% higher than that of RB and is the closest to that of DP, which is an optimal standard that is limited for real-time application due to its complexity among others. The capacity loss of the battery using RB-NMPC is 19.1% less than that using DP when applied to the UDDS. The FE of P1P2 is higher than that of P0P2, but the similar capacity fade is comparable. RB-NMPC shows the lowest capacity loss for both P0P2 and P1P2 configurations. Parallel comparisons are performed for the HWFET. For the HWFET, the FEs of P0P2 and P1P2 are similar. However, the capacity fades by RB-NMPC are 16.3% and 67.0% reduced compared to that by DP for P0P2 and P1P2, respectively. Finally, to verify the effectiveness of the RB-NMPC in reducing battery aging, the currents from DP and RB-NMPC EMSs are applied to pouch-type lithium-ion batteries and tested for multiple UDDSs using a battery test station. The results demonstrate that the RB-NMPC can effectively reduce battery aging.&lt;/div&gt;

Multi-objective real-time energy management for series–parallel hybrid electric vehicles considering battery life

The real-time control of energy management strategy (EMS) is becoming increasingly challenging as the complexity of the model and control strategy increases. To address this issue while ensuring the accuracy of the EMS, a multi-objective real-time EMS based on model predictive control (MPC) that considers battery life is proposed in this paper. Firstly, to balance the accuracy and efficiency of the prediction module, a kernel extreme learning machine based on the whale optimization algorithm is proposed as a short-term speed prediction model. Secondly, an adaptive state of charge (SOC) trajectory planning method is established to plan MPC reference trajectory. Next, to optimize fuel efficiency, electrical energy consumption, and battery aging in real-time, a multi-objective real-time MPC (MOR-MPC) algorithm is proposed. Finally, the effectiveness, real-time performance, and robustness of the proposed strategy are verified. Simulation results demonstrate that the total cost of the strategy is reduced by 6.15% compared to the equivalent consumption minimization strategy (ECMS), with 98.17% of dynamic programming (DP) performance achieved. Real-time performance is improved by 97.89% compared to DP-MPC. Hardware-in-the-loop (HIL) testing is also carried out to evaluate the proposed strategy.

Multiobjective Nonlinear Model Predictive Control of the Microbial Process

A rigorous multiobjective nonlinear model predictive control is performed on the microbiome dynamic model that takes into account competition, amensalism, parasitism, neutralism, commensalism and cooperation. The optimization language pyomo is used in conjunction with the state of the art global optimization solver BARON. It is demonstrated that when the species that produces the required product is favorable to the other species there is an initial decrease in the required product before an increase happens.

An Effective Transformerless PUC7-Based Dynamic Voltage Restorer Using Model Predictive Control

This paper investigates the performance of a seven-level Packed U Cell (PUC7) inverter-based transformerless Dynamic Voltage Restorer (DVR) topology under short-time voltage variations (voltage sags and swells). Unlike the existing multilevel inverter (MLI)-based DVR solutions, the proposed structure requires only one DC voltage source (suitable for PV-based DVR systems), one capacitor, and six switching devices to generate seven-level output voltage. Moreover, the studied topology is characterized by reduced cost and size due to the elimination of the injection transformer. The PUC7 inverter is controlled using a multi-objective (filtering current, compensating voltage, and PUC capacitor voltage controls) Model Predictive Control (MPC) strategy. Simulation and implementation tests are carried out to demonstrate the high performance of the proposed DVR at steady-state and during transient conditions, while keeping the load voltage unaffected by the disturbances in the grid voltage.

Multiobjective economic model predictive control using utopia-tracking for the wet flue gas desulphurization system

Efficient control of the desulphurization system is challenging in maximizing the economic objective while reducing the SO2 emission concentration. The conventional optimization method is generally based on a hierarchical structure in which the upper optimization layer calculates the steady-state results and the lower control layer is responsible to drive the process to the target point. However, the conventional hierarchical structure does not take the economic performance of the dynamic tracking process into account. To this end, multi-objective economic model predictive control (MOEMPC) is introduced in this paper, which unifies the optimization and control layers in a single stage. The objective functions are formulated in terms of a dynamic horizon and to balance the stability and economic performance. In the MOEMPC scheme, economic performance and SO2 emission performance are guaranteed by tracking a set of utopia points during dynamic transitions. The terminal penalty function and stabilizing constraint conditions are designed to ensure the stability of the system. Finally, an optimized control method for the stable operation of the complex desulfurization system has been established. Simulation results demonstrate that MOEMPC is superior over another control strategy in terms of economic performance and emission reduction, especially when the desulphurization system suffers from frequent flue gas disturbances.

New design of a wind farm frequency control considering output uncertainty and fatigue suppression

Frequency response capability is necessary for wind farms (WFs) in the power system with a high proportion of renewable energy. In frequency control, WFs need to meet the grid’s power demand and avoid obvious additional damage to wind turbines (WTs) due to frequency control. In terms of meeting the grid power demand, the actual power characteristics of WTs need to be accurately described. An improved Gaussian Mixture Model (GMM) is used to model the actual measured output of WTs. The wind farm control center can accordingly issue achievable effective power commands to the WTs in the frequency response. In terms of avoiding the structural fatigue increase of WTs, a two-degree-of-freedom control strategy is designed, which simultaneously controls the generator torque and pitch angle and achieves fatigue suppression through multi-objective model predictive control (MOMPC). The simulation results show that the proposed control system can improve the frequency response capability of the WF and reduce the fatigue load of WTs, which has obvious application prospects.