Model Predictive Control Configuration Research Articles

Model Predictive Control in buildings with thermal and visual comfort constraints

Model Predictive Control can cope with conflicting control objectives in building energy managements. In terms of user satisfaction, visual comfort has been proven in several studies to be a crucial factor, however thermal comfort is typically considered the only important aspect. Besides human well-being, visual comfort strongly impacts the productivity of the occupants in offices. Therefore, from an economic point of view, it is essential to include visual comfort in Model Predictive Control for buildings. In this paper semi-linear support vector machine is applied to learn suitable models for visual comfort measured by Daylight Glare Probability. The resulting model is incorporated into a Model Predictive Control framework, together with an autoregressive exogenous model accounting for the thermal dynamics of the building. The approach is validated through an extensive numerical case study, and the benefits of including visual comfort and blind control in the Model Predictive Control problem are evaluated. We observe that the proposed Model Predictive Control scheme ensures both the thermal and visual comfort constraints at the expense of 2.2% to 7.2% higher energy consumption compared to the benchmark Model Predictive Control configuration, which considers only the thermal comfort constraints.

Moment based model predictive control for linear systems: Additive perturbations case

AbstractIn this article, we present a novel linear model predictive control (MPC) strategy for controlling uncertain dynamical systems. The moment based MPC strategy is based on the (centralized) moments of the stochastic cost and constraint functions. We show that moment based MPC formulations yield computationally tractable predictive control problems, due to the explicit analytic expressions of the moments and linearity in the dynamics. This article considers (i) the output regulation MPC configuration, where the output is steered towards a reference and state vector is not correctly accessible to the controller at the decision instants; (ii) the moment based MPC formulation with uncertainties that are non‐Gaussian random variables, and (iii) bound and polytopic constraints in the uncertain MPC problem subject to either Gaussian disturbances or uncertainties with symmetric distributions. We demonstrate the effectiveness of the proposed MPC technique on simulation examples such as a double integrator system and a quadruple tank system.

Efficient Calibration of Embedded MPC

Model Predictive Control (MPC) is a powerful and flexible design tool of high-performance controllers for physical systems in the presence of input and output constraints. A challenge for the practitioner applying MPC is the need of tuning a large number of parameters such as prediction and control horizons, weight matrices of the MPC cost function, and observer gains, according to different trade-offs. The MPC design task is even more involved when the control law has to be deployed to an embedded hardware unit endowed with limited computational resources. In this case, real-time implementation requirements limit the complexity of the applicable MPC configuration, giving rise to additional design tradeoffs and requiring to tune further parameters, such as the sampling time and the tolerances of the on-line numerical solver. To take into account closed-loop performance and real-time requirements, in this paper we tackle the embedded MPC design problem using a global, data-driven optimization approach. We showcase the potential of this approach by tuning an MPC controller on two hardware platforms characterized by largely different computational capabilities.

Robust stability analysis for barrier-based equation-free multi-linear model predictive control

On-line optimization strategies such as model predictive control (MPC) have been widely used to compute control actions for a range of complex industrial systems. Barrier based MPC has recently been introduced, bringing together theory and algorithms for analysing the stability of linear models, however such models may not describe complex systems dynamics adequately. Multi-model linear MPC configurations can be used as a more reliable solution as piecewise affine (PWA) models can describe the underlying nonlinear dynamics more accurately. Additionally, model order reduction can be applied to large-scale distributed systems, to reduce their dimensionality, jeopardising however their closed-loop stability. As a result, there is a clear need for an input to output stability analysis for closed loop systems under unstructured uncertainty when multi-model barrier MPC is utilized. In this work, we combine equation-free model reduction with integral quadratic constraints (IQCs) for the stability analysis of large-scale closed-loop systems under unstructured uncertainties, including model approximation errors and nonlinearities, including MPC. An illustrative example is used to elucidate the proposed methodology.

Move Suppression Calculations for Well-Conditioned MPC

Several popular tuning strategies applicable to Model Predictive Control (MPC) schemes such as GPC and DMC have previously been developed. Many of these tuning strategies require an approximate model of the controlled process to be obtained, typically of the First Order Plus Dead Time type. One popular method uses such a model to analytically calculate an approximate value of the move suppression coefficient to achieve a desired condition number for the regularized system dynamic matrix; however it is not always accurate and tends to under-estimate the required value. In this paper an off-line method is presented to exactly calculate the move suppression coefficient required to achieve a desired condition number directly from the unregularized system dynamic matrix. This method involves an Eigendecomposition of the system dynamic matrix - which may be too unwieldy in some cases –and a simpler analytical expression is also derived. This analytical expression provides a guaranteed tight upper bound on the required move suppression coefficient yielding a tuning formula which is easy to apply, even in on-line situations. Both methods do not require the use of approximate or reduced order process models for their application. Simulation examples and perturbation studies illustrate the effectiveness of the methods in both off-line and on-line MPC configurations. It is shown that accurate conditioning and improved closed loop robustness can be achieved.

Polder Flushing: Model Predictive Control of Flushing Operations to Effective and Real Time Control of Salinity in Polders

More than 35% of the world's population live within 100km of the coast. Groundwater resources in these areas are the main source for domestic, industrial and agricultural use. Worldwide, deltaic areas are under stress due to climate change, sea level increase and decrease in fresh water availability. In addition, in deltaic coastal areas around mean sea level, the saline groundwater will move toward the ground surface and exflitrate to surface water. This saline surface water will not be appropriate for drinking water production, agricultural and industrial use, and therefore, freshwater diverted from rivers is used for flushing the canals and ditches in coastal areas. Due to decreasing fresh water availability and increasing surface water salinization, current saline-fresh water management strategies have to be reviewed, and new sustainable strategies must be developed. Using real time measurements to see the effect of disturbances to the system and updating the control actions in real time will decrease the use of fresh water for flushing operations. Real time control of salinity in polders will result in more effective water management. Control of surface water salinization in a polder is a multi-objective problem such that water quality and quantity have to be considered. Moreover, the constraints of the system and uncertainties must be taken into account. Model Predictive Control (MPC) is a state-of-the-art control technique showing the best performance for these kind of problems. In this study, a MPC configuration for combined water quantity and quality control is discussed on a polder flushing case study for a hypothetical test water course/canal. The exfiltration of saline groundwater to the surface water is also considered and the predictions of saline groundwater exfiltration are used to achieve better control of the local water system.

Fuzzy Control and Model Predictive Control Configurations for Effluent Violations Removal in Wastewater Treatment Plants

In this paper the following new control objectives for biological wastewater treatment plants (WWTPs) have been established: to eliminate violations of total nitrogen in the effluent (Ntot,e) or ammonium and ammonia nitrogen concentration (NH) in the effluent (NHe) and at the same time handle the customary requirements of improving effluent quality and reducing operational costs. The Benchmark Simulation Model No. 1 (BSM1) is used for evaluation, and the control is based on Model Predicitive Control (MPC) and fuzzy logic. To improve effluent quality and to reduce operational costs, a hierarchical control structure is implemented to regulate the dissolved oxygen (DO) on the three aerated tanks. The high level of this hierarchical structure is developed with a fuzzy controller that adapts the DO set points of the low level based on the NH concentration in the fifth tank (NH5). The low level is composed of three MPC controllers with feedforward control (MPC + FF). For avoiding violations of Ntot,e, a second fuzzy controller is used to manipulate the external carbon flow rate in the first tank (qEC1) based on nitrate nitrogen in the fifth tank (NO5) plus NH5. For avoiding violations of NHe, a third fuzzy controller is applied to manipulate the internal recirculation flow rate (Qrin) based on NH5 and NH in the influent. Simulation results show the benefit of the proposed approach.

Model Predictive Control for Nonlinear Distributed Parameter Systems based on LS‐SVM

AbstractThis paper presents a novel model predictive control configuration for nonlinear distributed parameter systems based on least squares support vector machine. First, a data‐based modeling methodology for an unknown nonlinear distributed parameter system is introduced. Subsequently, the model predictive control framework based on the aforementioned model is presented at the measured point. To verify the effectiveness and feasibility of the control arithmetic, simulation results from a tubular reactor with the controller designed by the presented procedure are given.

Demand reduction in building energy systems based on economic model predictive control

This paper proposes and demonstrates the effectiveness of an economic model predictive control (MPC) technique in reducing energy and demand costs for building heating, ventilating, and air conditioning (HVAC) systems. A simulated multi-zone commercial building equipped with of variable air volume (VAV) cooling system is built in Energyplus. With the introduced Building Controls Virtual Test Bed (BCVTB) as middleware, real-time data exchange between Energyplus and a Matlab controller is realized by sending and receiving sockets. System identification is performed to obtain zone temperature and power models, which are used in the MPC framework. The economic objective function in MPC accounts for the daily electricity costs, which include time-of-use (TOU) energy charge and demand charge. In each time step, a min–max optimization is formulated and converted into a linear programming problem and solved. In a weekly simulation, a pre-cooling effect during off-peak period and a cooling discharge from the building thermal mass during on-peak period can be observed. Cost savings by MPC are estimated by comparing with the baseline and other open-loop control strategies. The effect of several experimental factors in the MPC configuration is investigated and the best scenario is selected for future practical tests.

A Radial Basis Function network training algorithm using a non-symmetric partition of the input space – Application to a Model Predictive Control configuration

This work presents the non-symmetric fuzzy means algorithm which is a new methodology for training Radial Basis Function neural network models. The method is based on a non-symmetric fuzzy partition of the space of input variables which results to networks with smaller structures and better approximation capabilities compared to other state-of-the-art training procedures. The lower modeling error and the smaller size of the produced models become particularly important when they are used in online applications. This is demonstrated by integrating the model produced by the proposed algorithm in a Model Predictive Control configuration, resulting in better control performance and shorter computational times.

Use of Optimal Controls to Mitigate Competing Performance Objectives in a Polymer Electrolyte Membrane Fuel Cell System

This paper describes a model predictive control (MPC) scheme as implemented on a polymer electrolyte membrane fuel cell system. The goal of this work is to reduce parasitic power consumption of the system, improving net system efficiency. The MPC is capable of balancing this performance objective (reducing power loss) with the objective of maintaining oxygen excess ratio, a parameter identified as essential to reliable fuel cell operation. Two configurations of a MPC were implemented in SIMULINK and connected to a dynamic system model in EASY5 using the XML (extensible markup language) metadata interchange (XMI) interface. Substantial improvements were noted on one of the MPC configurations compared to the reference feedforward and proportional-integral-derivative (PID) controller.

An adaptive model predictive control configuration for production–inventory systems

In this paper, an adaptive model predictive control (MPC) configuration is proposed for the identification and control of production–inventory systems. The time-varying dynamic behavior of the production process is approximated by an adaptive Finite Impulse Response (FIR) model. The well-known recursive least-squares (RLS) method is used for the online identification of the model coefficients. The adapted model along with a smoothed estimation of the future customer demand are used to predict inventory levels over the optimization horizon. The efficiency of the proposed scheme is evaluated regarding its capability to eliminate the inventory drift. The performance of the method with respect to the bullwhip effect is also considered and studied in the paper. Comparison with non-adaptive control approaches illustrates the advantages of the proposed method.

A Simulated Annealing Algorithm for Prioritized Multiobjective Optimization—Implementation in an Adaptive Model Predictive Control Configuration

This paper presents a new stochastic algorithm for solving hierarchical multiobjective optimization problems. The algorithm is based on the simulated annealing concept and returns a single solution that corresponds to the lexicographic ordering approach. The algorithm optimizes simultaneously the multiple objectives by assigning a different initial temperature to each one, according to its position in the hierarchy. A major advantage of the proposed method is its low computational cost. This is very critical, particularly, for online applications, where the time that is available for decision making is limited. The method is tested in a number of benchmark problems, which illustrate its ability to find near-optimal solutions even in nonconvex multiobjective optimization problems. The results are comparable with those that are produced by state-of-the-art multiobjective evolutionary algorithms, such as the Nondominated Sorting Genetic Algorithm II. The algorithm is further applied to the solution of a large-scale problem that is formulated online, when a multiobjective adaptive model predictive control (MPC) configuration is adopted. This particular control scheme involves an adaptive discrete-time model of the system, which is developed using the radial-basis-function neural-network architecture. A key issue in the success of the adaptation strategy is the introduction of a persistent excitation constraint, which is transformed to a top-priority objective. The overall methodology is applied to the control problem of a pH reactor and proves to be superior to conventional MPC configurations.

Multiobjective constrained MPC with simultaneous closed-loop identification

Model predictive control (MPC) methodologies are commonly used techniques for constrained control problems. In this paper, the principle of prioritized multiobjective optimization is incorporated in an adaptive MPC framework in order to improve the closed-loop performance in the case of time-varying systems. Instead of weighting the different control goals, the proposed methodology creates a hierarchy according to the importance of each objective and optimizes each one separately. In each optimization step a constraint is added, so that previous in rank objective functions maintain their optimal values. Adaptive capabilities are introduced in the proposed MPC formulation, by considering the persistent excitation requirement as a top priority objective, which is optimized first. The efficiency of the proposed MPC configuration is evaluated through three dynamic processes and the expected advantages are confirmed. Copyright © 2006 John Wiley & Sons, Ltd.

Nonlinear adaptive model predictive control based on self‐correcting neural network models

AbstractTwo major issues in process control are the nonlinearities and variations with time that are observed in the dynamics of the processes. In most cases these problems are confronted by robust linear controllers, which are frequently retuned to take into account changes in the operating region or the system dynamics. Obviously, the performance of these controllers is limited by the degree of nonlinearities and the frequency of process variations. In this paper we present a new model predictive control (MPC) framework that can deal with both these issues. The proposed methodology is based on a nonlinear dynamic radial basis function (RBF) model of the process that is able to correct itself as new information about the process dynamics becomes available. The adaptive training algorithm that is used is able to update both the structure and the parameters of the RBF model. The typical formulation of the on‐line optimization problem is augmented by a persistent excitation condition that guarantees that enough perturbation is introduced to the system by the control moves. The proposed MPC framework is applied on the digester control problem and proves to be superior to other MPC configurations. © 2005 American Institute of Chemical Engineers AIChE J, 2005

A PRIORITIZED MULTIOBJECTIVE MPC CONFIGURATION USING ADAPTIVE RBF NETWORKS AND EVOLUTIONARY COMPUTATION

In this work a prioritized multiobjective model predictive control configuration for nonlinear processes is proposed. The process is modeled by an adaptive radial basis function neural network so that modifications through time can be identified. The different control targets are formulated in a multiobjective optimization problem which is solved using a prioritized evolutionary algorithm. The request for adequate information in order to adapt the dynamics of the model is considered as the top priority objective. The algorithm is tested through the control of a pH reactor and the results are in favor of the proposed methodology.

Nonlinear Model Predictive Control Experiments on a Laboratory Gas Turbine Installation

Results on the feasibility and benefits of model based predictive control applied to a gas turbine are presented. For a laboratory gas turbine installation, the required dynamic simulation model and the real-time (nonlinear) model predictive control (MPC) implementation are discussed. Results on both model validation and control performance are presented. We applied a nonlinear MPC configuration to control the laboratory gas turbine installation and succeeded in a real-time implementation. Although the available computation time for prediction and optimization of the model limits the sample time, the advantages of MPC, i.e. constraint handling, and anticipation to future (set-point) changes are fully reached, and the control performance is good. Special attention is paid to the performance of the applied filter that compensates for inevitable mismatches between model and process measurements. In general, the opportunities of model based control of turbomachinery are promising.