Application Of Model Predictive Control Research Articles

Model Predictive Control Applied to Different Time-Scale Dynamics of Flexible Joint Robots

Modern Lightweight robots are constructed to be collaborative, which often results in a low structural stiffness compared to conventional rigid robots. Therefore, the controller must be able to handle the dynamic oscillatory effect mainly due to the intrinsic joint elasticity. Singular perturbation theory makes it possible to decompose the flexible joint dynamics into fast and slow subsystems. This model separation provides additional features to incorporate future knowledge of the joint-level dynamical behavior within the controller design using the Model Predictive Control (MPC) technique. In this study, different architectures are considered that combine the method of Singular Perturbation and MPC. For Singular Perturbation, the parameters that influence the validity of using this technique to control a flexible-joint robot are investigated. Furthermore, limits on the input constraints for the future trajectory are considered with MPC. The position control performance and robustness against external forces of each architecture are validated experimentally for a flexible joint robot. The experimental validation shows superior performance in practice for the presented MPC framework, especially respecting the actuator torque limits.

Model predictive control and moving horizon estimation for adaptive optimal bolus feeding in high-throughput cultivation of E. coli

We discuss the application of a nonlinear model predictive control (MPC) and moving horizon estimation (MHE) framework to achieve optimal operation of E. coli fed-batch cultivations with intermittent bolus feeding. 24 parallel experiments were considered in a high-throughput mini-bioreactor platform at a 10 mL scale. The robotic facility can run up to 48 fed-batch processes in parallel with automated liquid handling, online and at-line analytics. Three main challenges emerge in implementing the model-based monitoring and control framework: First, the inputs are given in an instantaneous pulsed form by bolus injections; second, online and at-line measurement frequencies are severely imbalanced; and third, optimization for the distinctive multiple reactors can be either parallelized or integrated. We address these challenges by incorporating the concept of impulsive control systems, formulating multi-rate MHE with identifiability analysis, and suggesting criteria for deciding the reactor configuration. In this study, we present the key elements and background theory of the implementation with in silico simulations for bacterial fed-batch cultivations.

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

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

Hybrid MPC-P controller for the core power control system at TRIGA reactor

The Training, Research, Isotopes, General Atomics (TRIGA) research nuclear reactor is utilized in a wide range nuclear applications and has three versions, Mark I, Mark II, and Mark III. The TRIGA reactor that is available in Malaysia is a Mark II type, Reaktor TRIGA PUSPATI (RTP). The core power control system in the RTP is designed based on many components including the Feedback Control Algorithm (FCA), and the control rod selection algorithm (CRSA). The CRSA is used in the RTP operation to provide external control to the reactor core reactivity. Even though the CRSA provide stability to the reactor operation, it has relatively complex software structure which produce delayed response time for the control rods selection. Thus, the Single Control Absorbing Rod (SCAR) algorithm is designed to improve the reactor performance by minimizing the time response for the rods selection. However, the SCAR yields a non-constant tracking performance due to the highly non-linear dynamic of the control rods. Thus, to compensate the drawbacks of the SCAR with the existing FCA controller, a hybrid controller is proposed based on the integration of a linear model predictive control (MPC) and Proportional (P) controller named as Hybrid MPC-P-SCAR. The MPC application in the SCAR enable the controller to handle multiple constraints through built-in prediction ability to select the best sequence of future control rod velocity during transient state. Whereas at the steady-state, the MPC is optimized by a scheduled P control switches within the allowable range of power variation. The performance of the proposed Hybrid MPC-P-SCAR, the MPC-SCAR and the existing Feedback Control Algorithm with SCAR (FCA-SCAR) is compared via simulation and evaluated in terms of tracking performance, workload of the control rod drive mechanism (CRDM), and the offset elimination in the unmeasured disturbance. Overall, the Hybrid MPC-P-SCAR controller reduces the settling time by 45% and the steady-state error by 61% of the nominal value compared to the FCA-SCAR.

Orthogonalization-Based Gain Conditioning for Linear Model Predictive Control

Industrial practitioners who develop linear model predictive control (MPC) applications want to prevent undesirable controller behavior caused by ill-conditioned gain matrices and model mismatch. Control practitioners currently use time-consuming iterative methods based on relative gain arrays and singular value decomposition to condition their gain matrices to prevent degraded controller performance. Here, we propose a more straightforward approach, which extends an orthogonalization-based parameter ranking algorithm originally developed to aid parameter estimation in fundamental models. The proposed method ranks manipulated variables (MVs) from most influential to least influential while accounting for correlated steady-state influences of MVs on controlled variables. Problematic MVs are identified, and a constrained linear optimization algorithm is used to find optimal adjustments to condition the gain matrix. The effectiveness of the proposed methodology is verified using a new industrial case study based on fluidized catalytic cracking.

Simplified Model Predictive Current Control of Four-Level Nested Neutral Point Clamped Converter

Model predictive control (MPC) is an efficient and growing approach to power converter control. This paper proposes an improved and simplified model predictive current control (MPCC) technique for a four-level nested neutral point clamped (4L-NNPC) converter. Conventional MPCC exhibits better performances as compared to the conventional linear control system such as fast dynamic response, consideration of the system constraints, and nonlinearities. However, the application of the conventional model predictive current control (MPCC) approach on complex systems provokes a significant number of calculations, which is the main hurdle to its practical implementation. To fix this flaw, this paper proposes an effective algorithm to shorten the execution time of the conventional MPCC. In this proposed technique, 216 current predictions of the conventional MPCC are skipped and converted into one required voltage vector (RVV) prediction. With this equivalent reference voltage transformation, the calculation burden of MPCC is significantly reduced, while the output performance is not influenced. The results of the simplified MPCC for the 4L-NNPC converter are analyzed and compared with the conventional MPCC. The computational time is reduced by 19.56% using the simplified MPCC, while keeping an approximately similar error of output currents. The switching frequency and total harmonic distortion (THD) of the proposed method are reduced by 8.16% and 0.07%, respectively, as compared to the conventional technique. These results demonstrate the fact that that the performance of a conventional MPCC is enhanced with the proposed MPCC. The proposed algorithm can be applied to several inverter topologies.

Application of model predictive control on metro train scheduling problems

Application of model predictive control on metro train scheduling problems

Model Predictive Control With Disturbance Observer for Marine Diesel Engine Speed Control

The application of model predictive control (MPC) algorithm in the fixed phase control of marine diesel engine speed is studied under the premise of considering model mismatch and external disturbance. Firstly, the steady-state error problem of conventional MPC controller is solved by changing nonlinear model to incremental form. Furthermore, discrete disturbance observer (DO) is introduced in the feedback correction, which can filter out the high-frequency disturbance and reduce the requirement of algorithm on the accuracy of model. Then, considering that nonlinear MPC based on DO (DONMPC) requires a large amount of online computation, the algorithm is simplified by preliminarily converting the nonlinear model to linear model. Through analysis, the controller performance of the two models is similar. Furthermore, considering that the speed of marine diesel engine is usually set to a few fixed reference values, a linear multi-model predictive controller based on DO (DOLMMPC) with less online calculation is proposed. Finally, the designed controllers are verified by experiments. The software simulations of the designed controllers and the PID controller are carried out on the cylinder-by-cylinder mean value engine model (MVEM). It is proved that the algorithm simplification method retains the control performance of the DONMPC algorithm, and the control performance of the designed two controllers is better than the PID controller. Moreover, the DOLMMPC controller and PID controller are tested on the semi-physical simulation platform. The results demonstrate that the DOLMMPC controller can meet the computational power limit of the microprocessor in practical engineering.

Algebraic Decomposition of Model Predictive Control Problems.

This paper is concerned with the application of model predictive control (MPC) to large-scale linear dynamical systems with linear inequality constraints. A decomposition is proposed of such problems into sets of independent MPCs of lower dimensions that preserves all information about the system, cost function, and constraints. Different from previous work, the constraints are incorporated in the decomposition procedure, which is attained by generalizing a previously developed technique to simultaneously block diagonalize a set of matrices. This approach is applied to practical examples involving large-scale systems with inequality constraints. It is shown that the computational complexity and the CPU time required to solve the transformed MPC problems are lower than those required by the solution of the original MPC problem.

Application of model predictive control to building design optimisation

Optimisation algorithms offer a valuable tool for enhancing the energy efficiency of buildings by fine-tuning specific design parameters. Model Predictive Control (MPC) emerges as a compelling technology to address the rising need for improved efficiency and adaptable operation within building energy systems. A simulation study using MATLAB and EnergyPlus was conducted to examine the influence of MPC and building design optimisation (BDO) on wall insulation thickness and internal mass area. The focus was on their impact on heating energy use and indoor thermal comfort in an office room located in Brussels, Belgium. The study revealed that the sole implementation of MPC led to a 7.6% decrease in heating energy use, while the application of BDO resulted in a more significant reduction of 12.8%. Remarkably, the fusion of MPC and BDO yielded the highest energy savings, cutting heating electricity usage by 23.4% compared to the baseline model. Moreover, MPC effectively maintained indoor temperature within the desired thermal comfort boundaries. The optimal wall insulation thickness and internal mass area were also ascertained through BDO, both of which exceeded the levels set by the baseline model. BDO, in conjunction with MPC, demanded the maximum permissible insulation thickness of 320 mm for the external north and south walls. Interestingly, when BDO was combined with MPC, the requirement for the internal mass area reduced by 11.7 m2 compared to utilising BDO alone. The study’s results underscore the potential of integrating MPC with BDO to elevate building energy efficiency. Furthermore, this strategy may be adaptable to optimising other building parameters at the early design stage, thereby augmenting overall building energy efficiency.

Application of model predictive control on metro train scheduling problems

The arrangement of the metro train scheduling problem aims to maintain headway regularity and the number of passengers; therefore, it does not exceed capacity. In this study, the metro train traffic model was developed without referring to the nominal schedule, then the running time model and the dwell time model were added to the metro train traffic model, and considering changes in the number of passengers. A model predictive control is applied to control the metro train scheduling problems. The control adjusts the dwell time and the running time of the train. The optimisation problem in this study is a quadratic programming problem consisting of a quadratic cost function and linear constraints related to the train scheduling problems. Based on the simulation results, the headway deviation and the deviation of the number of train passengers in the metro train scheduling problem can be minimised using the model predictive control.

Automated Loading Operation for Mass-Production Hydraulic Excavators by Nonlinear Model Predictive Control

This study deals with the control methods for automation of the loading operation of hydraulic excavators for mass production. In the loading operation, it is necessary to move the bucket to the target position without spilling soil from the bucket. Since the loading operation is a combined operation of the front equipment and the swing operation, it is not easy to generate the ideal trajectory. We apply Model Predictive Control (MPC) to this problem and investigate a method to realize ideal loading operation by giving only the coordinates of the loading position. When using MPC, the challenge is that a lot of worker-hours are spent on tuning the weights of the objective function. We also propose an efficient weight tuning method to solve this problem, with a view to adapting it to hydraulic excavators for mass production. We have confirmed the effectiveness of the proposed method through numerical simulations.

Model Predictive Control of water resources systems: A review and research agenda

Model Predictive Control (MPC) has recently gained increasing interest in the adaptive management of water resources systems due to its capability of incorporating disturbance forecasts into real-time optimal control problems. Yet, related literature is scattered with heterogeneous applications, case-specific problem settings, and results that are hardly generalized and transferable across systems. Here, we systematically review 149 peer-reviewed journal articles published over the last 25 years on MPC applied to water reservoirs, open channels, and urban water networks to identify common trends and open challenges in research and practice. The three water systems we consider are inter-connected, multi-purpose and multi-scale dynamical systems affected by multiple hydro-climatic uncertainties and evolving socioeconomic factors. Our review first identifies four main challenges currently limiting most MPC applications in the water domain: (i) lack of systematic benchmarking of MPC with respect to other control methods; (ii) lack of assessment of the impact of uncertainties on the model-based control; (iii) limited analysis of the impact of diverse forecast types, resolutions, and prediction horizons; (iv) under-consideration of the multi-objective nature of most water resources systems. We then argue that future MPC applications in water resources systems should focus on addressing these four challenges as key priorities for future developments.

Integration of Design and NMPC-Based Control under Uncertainty and Structural Decisions: An MPCC-Based Approach

In this work, we investigate the challenges and limitations of the application of nonlinear model predictive control (NMPC) for the integration of design and control for systems subject to structural decisions and model uncertainty. The problem involving discrete and continuous decisions is referred to as a mixed-integer bilevel programming model (MIBLP), which cannot be directly solved with conventional MINLP solvers. To address this issue, we implement a classical KKT transformation strategy to transform the original MIBLP into a single-level MINLP. The KKT conditions for the NMPC are determined and incorporated as constraints in the problem for process design. A regularization strategy is implemented to reformulate the complementarity constraints. Then, the single-level MINLP is directly solved with a branch and bound strategy. The proposed approach is tested in a reaction system network subject to uncertainty. The performance of a nominal- and a robust-NMPC control approaches are compared in the presence of process disturbances. Results indicate that the strategy with a robust-NMPC returns a more conservative process design with better control performance compared to results with a nominal-NMPC.

Reducing NOx Emissions and Optimizing Fuel Economy by Controlling Torque and Catalyst Warm-up in Mild HEVs

In this paper, hierarchical model predictive control is applied to mild HEVs (Hybrid Electric Vehicles) in order to improve fuel economy and reduce NOx emissions. There is a difference in the timescale between the temperature control (high-level) and the torque control (low-level), which are connected via the battery. In high-level of the hierarchical control, the optimal amount of heating from the battery to the catalyst in the exhaust gas after-treatment system is determined. The amount of heating must be determined in a way that the catalyst can optimally purify NOx emitted from the engine. At the low-level of the hierarchical control, the optimal torque distribution for the engine and motor is determined. The controller at both levels then applies model predictive control to consider the future behavior of the HEV's components. Fuel consumption, battery SoC and NOx emissions from the engine are taken into account. Finally, the effectiveness of our proposed method is demonstrated by simulations.

PANTR: A Proximal Algorithm With Trust-Region Updates for Nonconvex Constrained Optimization

This work presents PANTR, an efficient solver for nonconvex constrained optimization problems, that is well-suited as an inner solver for an augmented Lagrangian method. The proposed scheme combines forward-backward iterations with solutions to trust-region subproblems: the former ensures global convergence, whereas the latter enables fast update directions. We discuss how the algorithm is able to exploit exact Hessian information of the smooth objective term through a linear Newton approximation, while benefiting from the structure of box-constraints or ℓ1-regularization. An open-source C++ implementation of PANTR is made available as part of the NLP solver library ALPAQA. Finally, the effectiveness of the proposed method is demonstrated in nonlinear model predictive control applications.

Evaluating optimal control of active insulation and HVAC systems in residential buildings

Recently, active insulation systems (AIS) have been conceptualized in building envelopes to optimally modulate thermal resistance in response to changing environmental conditions. Building flexibility can further be improved if the building is also equipped with optimized heating, ventilating, and air conditioning (HVAC) control. In this work, we investigate the annual potential benefits of jointly optimizing AIS and HVAC system controls in both heating and cooling days over all climate zones (CZs) in the U.S. To reduce the computational complexity of applying model predictive control (MPC) to annual operations and detailed whole-building energy models, timeseries clustering was used to identify a set of representative days for optimizing in each climate zone. To isolate the increase in benefits from this joint optimization, we compare the performance to cases where the AIS and HVAC controls are optimized separately. Results indicate savings potential in all CZs, with the largest annual average savings of 9.02% and 4.02% observed in the cooling days with large daily temperature swings and heating days with cold sunny conditions, respectively. Savings patterns across climate zone, day types, and HVAC modes (i.e., heating or cooling) are also discussed along with the implications of important system design variables.

AVsIs: An Analytical-Solution-Based Solver for Model-Predictive Control With Hexagonal Constraints in Voltage-Source Inverter Applications

The theory of a new analytical-solution-based algorithm for calculating the optimal solution in model-predictive control applications with hexagonal constraints is discussed in this article. Three-phase voltage-source inverters for power electronic and electric motor drive applications are the target of the proposed method. The indirect model-predictive control requires a constrained quadratic programming (QP) solver to calculate the optimal solution. Most of the QP solvers use numerical algorithms, which may result in unbearable computational burdens. However, the optimal constrained solution can be calculated in an analytical way when the control horizon is limited to the first step. A computationally efficient algorithm with a certain maximum number of operations is proposed in this article. A thorough mathematical description of the solver in both the stationary and rotating reference frames is provided. Experimental results on real test rigs featuring either an electric motor or a resistive–inductive load are reported to demonstrate the feasibility of the proposed solver, thus smoothing the way for its implementation in industrial applications. The name of the proposed solver is <monospace xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">aVsIs</monospace> , which is released under Apache License 2.0 in GitHub, and a free example is available in Code Ocean.

Optimizing space cooling of a nearly zero energy building via model predictive control: Energy cost vs comfort

The space conditioning of buildings is liable for more than 10 % of World final energy uses and related CO2-eq emissions. Such share must be drastically reduced to pursue sustainability by optimizing both energy design and devices control. In this frame, space cooling is assuming an increasing weight owing to climate change. Accordingly, this study applies a simulation- and optimization-based framework for the model predictive control (MPC) of space cooling systems. The case study is a nearly zero energy building located in Benevento – Southern Italy, Mediterranean climate – featuring an efficient air-source multi-split system for cooling. The framework is envisioned to provide optimal values of setpoint temperatures on a day-ahead planning horizon to minimize energy cost and thermal discomfort, based on weather forecasts. Accordingly, a Pareto multi-objective approach is applied considering different discomfort indicators to compare the Fanger theory with the adaptive one of ASHRAE 55. The optimization problem is solved by running a genetic algorithm – variant of NSGA II – under MATLAB® environment. The objective functions are assessed via the coupling between MATLAB® and EnergyPlus, using a validated building energy model. The multi-criteria decision-making is performed by setting a limit to discomfort to pick an optimal Pareto solution. The framework is tested addressing a typical day of the cooling season and using monitored weather data to simulate weather forecasts. Different optimal solutions are provided to fit different comfort categories. Compared to a reference control at fixed setpoint – 26 °C – the proposed solutions with similar comfort performance ensure cost savings around 28 %. Besides the proposed hypothetical implementation, the framework can be integrated in automation systems for real-time MPC. The novel contributions of this study lie in the methodology to combine MPC with different thermal comfort models as well as in the results, which provide deeps insights about the application of MPC for the space cooling of nearly zero energy buildings in a balanced climate.

Applications of hybrid model predictive control with computational burden reduction for electric drives fed by 3-phase inverter

Model predictive control (MPC) is recently emerging as an efficient and promising technique for the control of power converters. In the conventional MPC algorithm, the control objectives are usually estimated and evaluated for a large/definite number of switching states. Since prediction and evaluation are done for all possible states, massive amounts of estimations are needed, moreover, the computational burden is more challenging with the increase of control objectives. In this paper, a computationally efficient version of the finite control set-MPC (FCS-MPC) is proposed to decrease the calculation effort of the MPC algorithm likewise minimizing its execution time to enforce its vast application for the control of three-phase power converters. The suggested procedure is to eliminate the current predictions as well as reduce the number of available switching states that need to be estimated by the algorithm which reduces considerably the amount of time consumed by these computations. The studied techniques achieved nearly the same performance with an interesting reduction in the algorithm execution time accomplished by the proposed modified FCS-MPC algorithms.