Performance Of Model Predictive Control Research Articles

Sparse identification of nonlinear dynamics for model predictive control in the low-data limit.

Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling and control efforts, providing a tremendous opportunity to extend the reach of model predictive control (MPC). However, many leading methods in machine learning, such as neural networks (NN), require large volumes of training data, may not be interpretable, do not easily include known constraints and symmetries, and may not generalize beyond the attractor where models are trained. These factors limit their use for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics. In this work, we extend the recent sparse identification of nonlinear dynamics (SINDY) modelling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of MPC, based on limited, noisy data. SINDY models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable and generalizable. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than NN models, making it viable for online training and execution in response to rapid system changes. SINDY-MPC also shows improved performance over linear data-driven models, although linear models may provide a stopgap until enough data is available for SINDY. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges, including the chaotic Lorenz system, a simple model for flight control of an F8 aircraft, and an HIV model incorporating drug treatment.

Model predictive control of indoor microclimate: Existing building stock comfort improvement

Home retrofitting provides a means to improve the basic energy and comfort characteristics of a building stock, which cannot be renewed because of prohibitive costs. We analyze how model predictive control (MPC) applied to indoor microclimate control can provide energy-efficient solutions to the problem of occupants’ comfort in a variety of situations principally imposed by external weather and room occupancy. For this purpose we define an objective function for the energy consumption, and we consider two illustrative cases: one building designed and built in recent times with modern HVAC equipment, and one designed and built several decades ago with poor thermal characteristics and no dedicated ventilation system. Our model includes various physical effects such as air infiltration and indoor thermal “inertia mass” (inner walls, floor, ceiling, and furniture), and also accounts for the impact of human presence essentially as heat and CO2 sources. The influence on the numerical results of forecast horizons and of uncertainties due to inaccuracies in the weather and room occupancy forecasts, are analyzed. As we solve non-convex optimization problems using a linear and a nonlinear optimizer, full MPC performance is compared to both linearized MPC and a standard on/off controller. The main advantage of MPC is its ability to provide satisfactory solutions for microclimate control at the least possible energy cost for both modern and old buildings. As old buildings are usually not properly ventilated, we see in light of our simulation results, that a supply ventilation system installation provides a solution for significant air quality improvement.

A Study about Performance and Robustness of Model Predictive Controllers in a WEC System

This work is located in a growing sector within the field of renewable energies, wave energy converters (WECs). Specifically, it focuses on one of the point absorber waves (PAWs) of the hybrid platform W2POWER. With the aim of maximizing the mechanical power extracted from the waves by these WECs and reducing their mechanical fatigue, the design of five different model predictive controllers (MPCs) with hard and soft constraints has been carried out. As a contribution of this paper, two of the MPCs have been designed with the addition of an embedded integrator. In order to analyze and compare the MPCs with conventional PI type control, an exhaustive study about performance and robustness is realized through the computer simulations carried out, in which uncertainties in the WEC dynamics and JONSWAP spectrum are considered. The results obtained show how the MPCs with embedded integrator improve power production of the WEC system studied in this work.

Consistent and Effective Nonlinearity Index and its Application on Model Predictive Controller Performance Deterioration

Many control-relevant systems present the challenges of nonlinearity, directionality and ill-conditioning for the control systems, and exhibit poor controller performance. This study proposes a Nonlinearity Index to quantify the extent of nonlinearity of such systems. A dynamic nonlinear model of a pilot-scale distillation column operating near the azeotropic region was simulated using Aspen Plus Dynamics. A comparison of the results is made with the Nonlinearity Measure proposed by Du et al. Results show that a significant increase is exhibited in the proposed Nonlinearity Index values of the system as the system moves toward the azeotropic region. Prediction errors of the linear models are also shown to be correlated to the proposed index. Therefore, the proposed Nonlinearity Index is consistent with the existing indicators of nonlinearity, and thus its measurements of system nonlinearity are reliable. Controller performance for the system at higher values of the proposed index further presents its effi...

Nowcasting, predictive control, and feedback control for temperature regulation in a novel hybrid solar-electric reactor for continuous solar-thermal chemical processing

A novel 15 kW reactor for the hybridization of concentrated solar and conventional electric heat was fabricated for renewable and continuous chemical processing at temperatures up to 1700 °C. Solar-electric controllers based on feedback or predictive linear models were used to regulate the device at 925 °C for the production of syngas via the gasification of carbon. The system was challenged with cloud transients programmed on a 45 kW high-flux solar simulator that approximated weather observed in the San Luis Valley (Colorado, USA). In experiment it was found that model predictive control with a 1 min ahead nowcast of incipient clouding best regulated solar-electric reactor temperatures, potentially averting thermal fatigue. Upon clouding, model predictive control with a nowcast yielded temperature disturbances of ±10 °C, whereas feedback control alone featured ±25 °C excursions. Overall, the performance of model predictive control with a nowcast was 75% better than feedback as indicated by the integral squared error of temperature excursion residuals. The importance of nowcast accuracy was explored, and although the model-based controller was robust to forecast amplitude inaccuracy, temporal forecast inaccuracy wholly negated the benefits of predictive control.

A Stochastic Model Predictive Control Framework for Stationary Battery Systems

A stochastic model predictive control (MPC) framework is presented to determine real-time commitments in energy and frequency regulation markets for a stationary battery while simultaneously mitigating long-term demand charges for an attached load. The control problem is multi-scale in nature and poses challenges on computational tractability of the stochastic program and of forecasting and uncertainty quantification (UQ) procedures. The framework deals with tractability of the stochastic program by using a discounting factor for long-term demand charges, while a Ledoit–Wolf covariance estimator is used to overcome UQ tractability issues. The performance of stochastic MPC is benchmarked against that of perfect information MPC and deterministic MPC for different prediction horizon lengths and demand charge discounting strategies. A case study using real load data for a typical university campus and price and regulation data from PJM is considered. It is found that stochastic MPC can recover 83% of the ideal value of the battery, which is defined as the expected savings obtained by operating the battery under perfect information MPC. In contrast, deterministic MPC can only recover 73% of this ideal value. It is also found that operating the battery under stochastic MPC improves the battery payback period by 12.1%, while operating it under perfect information improves it by 27.9%.

Adaptive model predictive control for a dual-hormone artificial pancreas

We report the closed-loop performance of adaptive model predictive control (MPC) algorithms for a dual-hormone artificial pancreas (AP) intended for patients with type 1 diabetes. The dual-hormone AP measures the interstitial glucose concentration using a subcutaneous continuous glucose monitor (CGM) and administers glucagon and rapid-acting insulin subcutaneously. The discrete-time transfer function models used in the insulin and glucagon MPCs comprise a deterministic part and a stochastic part. The deterministic part of the MPC model is individualized using patient-specific information and describes the glucose-insulin and glucose-glucagon dynamics. The stochastic part of the MPC model describes the uncertainties that are not included in the deterministic part of the MPC model. Using closed-loop simulation of the MPCs, we evaluate the performance obtained using the different deterministic and stochastic models for the MPC on three virtual patients. We simulate a scenario including meals and daily variations in the model parameters for two settings. In the first setting, we try five different models for the deterministic part of the MPC model and use a fixed model for the stochastic part of the MPC model. In the second setting, we use a second-order model for the deterministic part of the MPC model and estimate the stochastic part of the MPC model adaptively. The results show that the controller is robust to daily variations in the model parameters. The numerical results also suggest that the deterministic part of the MPC model does not play a major role in the closed-loop performance of MPC. This is ascribed to the availability of feedback and the poor prediction capability of the model, i.e. the large disturbances and model-patient mismatch. Moreover, a second order adaptive model for the stochastic part of the MPC model offers a marginally better performance in closed-loop, in particular if the model-patient mismatch is large.

Model predictive control with active learning under model uncertainty: Why, when, and how

Optimal control relies on a model, which is generally uncertain because of incomplete knowledge of the system and changes in the dynamics over time. Probing the system under closed‐loop control can reduce the model uncertainty through generating input‐output data that is more informative than the data generated from normal operation. This paper addresses the problem of model predictive control (MPC) with active learning, with a particular focus on how incorporating probing in the control action can reduce model uncertainty. We discuss some of the central theoretical questions in this problem, and demonstrate the potential of active learning for maintaining MPC performance in the presence of uncertainty in model parameters and structure. Simulation results show that active learning is particularly beneficial when a system undergoes abrupt changes (such as the sudden occurrence of a fault) that can compromise operational safety, reliability, and profitability. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3071–3081, 2018

Data‐Driven Performance Monitoring for Model Predictive Control Using a mahalanobis distance based overall index

AbstractThis paper proposes a data‐driven approach for model predictive control (MPC) performance monitoring. It explores the I/O data of the MPC system. First, to evaluate the MPC performance and capture the fluctuation of the process variables, we present an overall performance index based on Mahalanobis distance (MDBI) with its deduced benchmark. The Mahalanobis distance can better characterize the change of the process variable in both principal component space and residual space. As the proper vectors of the two spaces are orthogonal, the MDBI eliminates the correlation between the process variables while considering the variables’ characteristics in both spaces simultaneously, which helps evaluate the MPC performance more effectively with fewer monitoring parameters. Furthermore, for the MPC performance diagnosis, we use the MDBI as inputs and construct a support vector machine (SVM) pattern classifier. The classifier can achieve a higher accuracy when recognizing four common performance degradation patterns and determine the root cause of performance degradation. The results of simulations on the Wood‐Berry distillation column process and experiments on NIAT multifunctional experiment platform illustrate the effectiveness of the proposed performance assessment/diagnosis strategies.

Novel Multiagent Model-Predictive Control Performance Indices for Monitoring of a Large-Scale Distributed Water System

High-order, often distributed, dynamical systems composed of several interconnected subsystems are often referred to as large-scale systems (LSSs). LSSs are often hard to control with a single centralized controller due to the complexity imposed by the system's dimensionality and distributedness. As a result, decentralized or hierarchical control schemes are employed in controlling LSSs. Control performance assessment (CPA) is an important strategy to analyze the efficiency of controllers in LSSs. This paper presents CPA for the Rhine–Meuse Delta water system in The Netherlands. The water system consists of a large number of rivers and sea outlets with barriers and sluices. A flood in this area can damage the ecosystem and cities around it. Thus, it is essential to control this LSS in a way to protect the distributed water system against floods. For this purpose, a multiagent predictive control is developed to control the subsystems in the LSS. Further, two novel control performance indices (CPIs) based on the model-predictive control strategy are introduced to monitor the performance of the controllers and detect any changes in the system. Finally, the root cause of controller deficiencies is diagnosed. The suggested CPIs are compared with a historical performance index. Simulation results show the ability and effectiveness of the proposed CPIs in comparison with the performance measure used in the past.

Stochastic model predictive control: Insights and performance comparisons for linear systems

SummaryIn this paper, we define several instances of model predictive control (MPC) for linear systems, including both deterministic and stochastic formulations. We show by explicit computation of the associated control laws that, under certain conditions, different formulations lead to identical results. This paper provides insights into the performance of stochastic MPC. Amongst other things, it shows that stochastic MPC and traditional MPC can give identical results in special cases. In cases where the solutions are different, we show that the explicit formulation of the problem can give insight into the performance gap.

Approximate model predictive building control via machine learning

Many studies have proven that the building sector can significantly benefit from replacing the current practice rule-based controllers (RBC) by more advanced control strategies like model predictive control (MPC). However, the optimization-based control algorithms, like MPC, impose increasing hardware and software requirements, together with more complicated error handling capabilities required from the commissioning staff. In recent years, several studies introduced promising remedy for these problems by using machine learning algorithms. The idea is based on devising simplified control laws learned from MPC. The main advantage of the proposed methods stems from their easy implementation even on low-level hardware. However, most of the reported studies were dealing only with problems with a limited complexity of the parametric space, and devising laws only for a single control variable, which inevitably limits their applicability to more complex building control problems. In this paper, we introduce a versatile framework for synthesis of simple, yet well-performing control strategies that mimic the behavior of optimization-based controllers, also for large scale multiple-input-multiple-output (MIMO) control problems which are common in the building sector. The approach employs multivariate regression and dimensionality reduction algorithms. Particularly, deep time delay neural networks (TDNN) and regression trees (RT) are used to derive the dependency of multiple real-valued control inputs on parameters. The complexity of the problem, as well as implementation cost, are further reduced by selecting the most significant features from the set of parameters. This reduction is based on straightforward manual selection, principal component analysis (PCA) and dynamic analysis of the building model. The approach is demonstrated on a case study employing temperature control in a six-zone building, described by a linear model with 286 states and 42 disturbances, resulting in an MPC problem with more than thousand of parameters. The results show that simplified control laws retain most of the performance of the complex MPC, while significantly decreasing the complexity and implementation cost.

Application of model-based control strategy to hybrid free cooling system with latent heat thermal energy storage for TBSs

This paper explored the application of model predictive control (MPC) technology to the TBSs hybrid free cooling system with latent heat thermal energy storage (LHTES) unit for minimizing the building operational cost without sacrificing temperature requirements. First, the system was briefly introduced and the dynamic thermal process models of building structure and LHTES unit were developed. Then, a hierarchical control structure with dynamic multi-swarm particle swarm optimization was presented to address the dimensional challenge and discontinuities in control variables. Due to the considerable decrease of optimization variable space, the method presented in this paper enables long-term simulation and application in a real controller. Simulations were carried out based on a typical TBS building located in Beijing, China. The total energy consumption of the cooling system and the control quality of indoor air temperature were used as the criteria to evaluate the performance. Compared to a defined baseline case, the optimal control method can achieve significant energy saving, i.e. up to 18%. The impacts of the size of LHTES unit and the type of building structure were discussed, as well. The active and passive heat capacity both played a catalytic role in performance of MPC. Additionally, an uncertainty analysis demonstrated that the proposed approach has strong robustness and can handle quite high errors in forecasting building disturbances from energy consumption level. In summary, the knowledge and use of the plant system and future disturbances make MPC a powerful control tool for TBS buildings for maximizing the use of renewable energy sources.

System Behavior and Predictive Controller Performance Near the Azeotropic Region

AbstractHigh‐purity distillation columns present challenges of nonlinearity, interactions, directionality, and ill‐conditioning for the control systems and thus exhibit poor controller performance. Effects of these issues on the performance of model predictive control in operations in near‐azeotropic regions are investigated. A dynamic model of a pilot‐scale distillation column is simulated and controlled by a linear model predictive controller. As the system moves towards the azeotropic region, the nonlinearity, directionality, and interactions of the system increase. A significant decline is observed in the system control performance since the controller incurs overshoots and offsets for negative and positive setpoint changes. The integral time absolute errors are substantially higher near the azeotropic region. Only a small operating range is able to ensure sufficient controllability near the azeotropic region.

Adaptive-model predictive control of electronic expansion valves with adjustable setpoint for evaporator superheat minimization

In many refrigeration and air-conditioning systems, the automatic controller in electronic expansion valves have been employed as a component responsible for controlling the valve opening so that the superheat at the outlet of the evaporator remains within the desired limits. In some of these controllers, the control parameters are tuned once for a certain operating point and remain unaltered, even when the operating conditions change, unless the operator changes it manually. For a strongly nonlinear plant with a dramatically time varying characteristics, linear time invariant (LTI) prediction accuracy might degrade significantly that the performance of traditional Model Predictive Controller (MPC) becomes unacceptable. This work presents an Adaptive-Model Predictive Control (AMPC) mechanism to address this degradation where the parameters are tuned continuously through recursive estimation and update approaches, making the MPC insensitive to prediction errors and to achieve the optimal superheat response. Moreover, an adaptive setpoint hunting algorithm is implemented so that the system achieves stability and improves energy efficiency simultaneously.

Disturbances Attenuation of Permanent Magnet Synchronous Motor Drives Using Cascaded Predictive-Integral-Resonant Controllers

The performance of a standard model predictive controller (MPC) is directly related to its predictive model. If there are unmodeled periodic disturbances in the actual system, MPC will be difficult to suppress the disturbances, thus causing fluctuations of system output. To solve this problem, this paper proposes an improved MPC named predictive-integral-resonant control (PIRC). Compared with the standard MPC, the proposed PIRC could enhance the suppression ability for disturbances by embedding the internal model composing of the integral and resonant loop. Furthermore, this paper applies the proposed PIRC to PMSM drives, and proposes the PMSM control strategy based on the cascaded PIRC, which could suppress periodic disturbances caused by the dead time effects, current sampling errors, and so on. The experimental results show that the PIRC can suppress periodic disturbances in the drive system, thus ensuring good current and speed performance. Meanwhile, the PIRC could maintain the excellent dynamic performance as the standard MPC.

Hydraulic valve-based active-heave compensation using a model-predictive controller with non-linear valve compensations

This work showcases the development and results of a model-predictive controller (MPC) for a marine active-heave compensation (AHC) system. The system utilizes a common hydraulic 4-way, 3-position proportional valve where the hysteresis, dead-band and non-linear properties have been overcome to directly control a radial piston motor in the experimental test setup. The MPC controller, with a set-point prediction algorithm, is used to actuate the unloaded hydraulic test system and the results are compared to a tuned Proportional-Integral-Derivative (PID) controller operating the same experimental setup. The MPC controller is found to track a variety of test cases and references while outperforming the tuned PID controller for all experiments. Additionally, a MATLAB Simulink model of the experimental setup is created and validated. Within the simulator, a load is then applied to the winch to test how the MPC and PID performance compare under loaded operating conditions. Based on the results of these tests, simulations of an MPC controller running in parallel with a Proportional-Integral (PI) controller are carried out for both the unloaded and loaded scenarios. For the conditions tested in this research, the resulting simulations suggest that the MPC-PI controller is able to decouple up to 99.6% of the transmitted motion.

Methodology to determine the impact of simplified building models on model-predictive-control morning start optimization performance

The current article introduces a method of quantifying the losses in a model predictive control scheme for morning start optimization by using a simplified statistical building model compared to a detailed engineering building model. A new concept of “emulated” model predictive control is introduced using a detailed EnergyPlus model as a baseline for expected savings to which the simplified model predictive control results can be compared. The examples provided with the methodology shows that the simplified model predictive control captures a minimum 84% of the savings that are achieved using the detailed emulated model predictive control, with a minimal increase in the number of thermal comfort violations when the building has not reached set-point during the occupied period. A comparison between different building types and climates is also conducted to determine the influence these have on simplified model predictive control performance. It shows that both climate and building type do influence the level of performance for the simplified modeling employed in the current article. Other areas for the application of emulated model predictive control are also introduced, such as evaluating objective functions and other model predictive control parameters (horizon length, timestep, etc.).

Effective recursive parallelotopic bounding for robust output-feedback control

In this paper an approach is studied to guaranteed (set-membership) state estimation for robust output-feedback model predictive control (MPC) with hard input and state constraints. Uncertainties are assumed to arise in a dynamic system from unknown initial conditions of state variables and due to unknown-but-bounded measurement noise. The uncertainty in the state variables is represented as a parallelotopic set. The employed state-estimation algorithm recursively outbounds the feasible set that is given by an intersection of model predictions with obtained measurement information. Along with the well-known minimum-volume criterion for parallelotopic outbounding, three alternative criteria are proposed and studied. The aim is to identify the best outbounding approach for improving performance of the robust MPC.

Identification and estimation of valve stiction by the use of a smoothed model

Stiction in control valves is considered one of the most common causes of poor performance in control loops. Thus, non-invasive, reliable and efficient methods which can detect and quantify this malfunction are highly desirable in the process industry. Under the framework of Hammerstein model identification and nonlinear optimization, this paper proposes an approach to estimate stiction amount on the basis of a recently proposed smoothed model. One of the motivations of the work is to improve the performance of a stiction unaware model predictive controller which exhibits sustained oscillations in the presence of valve stiction. By augmenting process model with the identified valve dynamics, the controller is turn to a stiction embedding formulation which can actually remove fluctuations and then guarantees good set-point tracking. Applications to simulation case studies and industrial loops are used to demonstrate the validity of the proposed method. Results are compared with a standard grid-search approach and other identification techniques of the literature.