Model Predictive Control Formulation Research Articles

Calibrating models for MPC of energy systems in buildings using an adjoint-based sensitivity method

For several years, Model Predictive Control (MPC) is depicted in the literature as a promising way to increase buildings’ energy efficiency during operation. This model-based control technique uses the optimal control theory to provide a constraint compliant, anticipative control, maximizing performance criteria. However, building and calibrating a reliable model for a real application is difficult, costly and time-consuming. Indeed, it requires hard expert work to retrieve all the building’s data and tune the corresponding model. This prevents MPC to be widespread in Building Management Systems.In this paper, we propose a MPC formulation where all the optimization problems included in a MPC strategy (calibration, estimation, optimal control) are performed efficiently using gradient-based techniques and adjoint-based gradient computations. This formulation relies on an automated “white-box” modeling technique (with partial-differential equations) using Building Information Model (BIM - using gbXML standard here) files parsing. We also show that making extensive use of adjoint models in MPC opens opportunities for fast sensitivity analysis, which can, for instance, help to choose which parameters to calibrate.

Hierarchical Energy Management System for Microgrid Operation Based on Robust Model Predictive Control

This paper presents a two-level hierarchical energy management system (EMS) for microgrid operation that is based on a robust model predictive control (MPC) strategy. This EMS focuses on minimizing the cost of the energy drawn from the main grid and increasing self-consumption of local renewable energy resources, and brings benefits to the users of the microgrid as well as the distribution network operator (DNO). The higher level of the EMS comprises a robust MPC controller which optimizes energy usage and defines a power reference that is tracked by the lower-level real-time controller. The proposed EMS addresses the uncertainty of the predictions of the generation and end-user consumption profiles with the use of the robust MPC controller, which considers the optimization over a control policy where the uncertainty of the power predictions can be compensated either by the battery or main grid power consumption. Simulation results using data from a real urban community showed that when compared with an equivalent (non-robust) deterministic EMS (i.e., an EMS based on the same MPC formulation, but without the uncertainty handling), the proposed EMS based on robust MPC achieved reduced energy costs and obtained a more uniform grid power consumption, safer battery operation, and reduced peak loads.

Risk-Averse Model Predictive Operation Control of Islanded Microgrids

In this paper we present a risk-averse model predictive control (MPC) scheme for the operation of islanded microgrids with very high share of renewable energy sources. The proposed scheme mitigates the effect of errors in the determination of the probability distribution of renewable infeed and load. This allows to use less complex and less accurate forecasting methods and to formulate low-dimensional scenario-based optimisation problems which are suitable for control applications. Additionally, the designer may trade performance for safety by interpolating between the conventional stochastic and worst-case MPC formulations. The presented risk-averse MPC problem is formulated as a mixed-integer quadratically-constrained quadratic problem and its favourable characteristics are demonstrated in a case study. This includes a sensitivity analysis that illustrates the robustness to load and renewable power prediction errors.

Model Predictive Control of Linear Systems With Preview Information: Feasibility, Stability, and Inherent Robustness

The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is present in the model and on the system. We show how standard stabilizing terminal conditions may be modified to account for the use of disturbances in the prediction model. Robust stability and feasibility are established under the assumption that the disturbance change across sampling instances is limited.

Data-Driven Model Predictive Control for Trajectory Tracking With a Robotic Arm

High-precision trajectory tracking is fundamental in robotic manipulation. While industrial robots address this through stiffness and high-performance hardware, compliant and cost-effective robots require advanced control to achieve accurate position tracking. In this letter, we present a model-based control approach, which makes use of data gathered during operation to improve the model of the robotic arm and thereby the tracking performance. The proposed scheme is based on an inverse dynamics feedback linearization and a data-driven error model, which are integrated into a model predictive control formulation. In particular, we show how offset-free tracking can be achieved by augmenting a nominal model with both a Gaussian process, which makes use of offline data, and an additive disturbance model suitable for efficient online estimation of the residual disturbance via an extended Kalman filter. The performance of the proposed offset-free GPMPC scheme is demonstrated on a compliant 6 degrees of freedom robotic arm, showing significant performance improvements compared to other robot control algorithms.

Economic Optimal Control for Minimizing Fuel Consumption of Heavy-Duty Trucks in a Highway Environment

This paper provides a comparative assessment of three economic optimal control strategies, aimed at minimizing the fuel consumption of heavy-duty trucks in a highway environment, under a representative lead vehicle model informed by traffic data. These strategies fuse a global, off-line dynamic programming (DP) optimization with online model predictive control (MPC). We then show how two of the three strategies can be adapted to accommodate the presence of traffic and optimally navigate signalized intersections using infrastructure-to-vehicular (I2V) communication. The MPC optimization, which is local in nature, makes refinements to a coarsely (but globally, subject to grid resolution) optimized target velocity profile from the DP optimization. The three candidate economic MPC formulations that are evaluated include a nonlinear time-based formulation that directly penalizes the predicted fuel consumption, a nonlinear time-based formulation that penalizes the braking effort as a surrogate for fuel consumption, and a linear distance-based convex formulation that maintains a tradeoff between energy expenditure and tracking of the coarsely optimized velocity profile obtained from DP. Using a medium-fidelity Simulink model, based on a Volvo truck’s longitudinal and engine dynamics, we analyze the optimization’s performance on four highway routes under various traffic scenarios. Results demonstrate 3.7%–8.3% fuel economy improvement on highway routes without traffic and 6.5%–10% on the same routes with traffic included. Furthermore, we present a detailed analysis of energy usage by “type” (aerodynamic losses, braking losses, and comparison of brake-specific fuel consumption), under each candidate control strategy.

Feedback control design using model predictive control formulation and Carleman approximation method

AbstractModel predictive control (MPC) for nonlinear systems involves a nonlinear dynamic optimization (NDO) step, which is required to be solved repeatedly. This step is computationally demanding, specially in dealing with constrained and/or nonlinear large‐scale systems. This paper presents a method for accelerating the NDO in state‐feedback regulation problems. Exploiting Carleman approximation, this method represents the nonlinear dynamics in a bilinear form and discretizes the resulting system in the time domain. The gradient and Hessian of the cost function with respect to the feedback gains are also analytically derived. The Carleman approximation of the nonlinear system may introduce errors in the prediction and sensitivity analysis. The manuscript derives a criterion under which the input‐to‐state stability of the new design is guaranteed. The proposed MPC is implemented in a chemical reactor example. Simulation results show that replacing conventional MPC schemes by the presented method reduces the computation time by an order of magnitude.

Nonlinear Model Predictive Control Strategies for Optimal Charging of a Lithium-Ion Battery

Lithium-ion (Li-ion) batteries, due to their high energy/power density, good temperature range and long battery life, can be used in a wide range of applications from electric vehicles to smart phones and smart grids1 2. For an optimal and safe operation of a Li-ion battery, Battery Management Systems (BMS) are pivotal. BMS monitors voltage, current and temperature, predicts State of Charge (SOC), State of Health (SOH) and estimates time before complete charge/discharge3. BMS depends on the mathematical models of Li-ion batteries for managing and regulating their performance. Most of the current BMS deploy empirical or semi-empirical models which may lead to inaccurate predictions of internal states3. Comparatively, using first principles models based on electrochemical and thermodynamic principles help in accurately predicting the dynamic nature of the internal states3. Therefore, BMS based on physics-based models is imperative for an enhanced and efficient performance of a Li-ion battery. Model Predictive Control (MPC) can be used in the design of BMS due its efficiency in handling constraints in an explicit manner and its ability for performing multivariable control.4–6 In MPC, the controller uses an explicit process model to generate a sequence of manipulated variable moves over a control horizon by optimizing an objective over a prediction horizon in a receding horizon approach.7–9 Classical MPC algorithms use linear process models to predict the outputs over the prediction horizon4,5. But, the main limitation in such classical MPC schemes is the usage of the linear prediction models restricting their application only to mildly nonlinear processes9. Though linear approximations of the first principles models have been used in the past for determining optimal charging profiles for Li-ion batteries,4–6 these versions might not be well placed to accurately capture the dynamics of the system. Traditionally, high computational cost of online calculations has been often cited as one of the main reasons for restricted use of nonlinear MPC formulations for battery models4–6. To the best of our knowledge, non-linear model predictive control (NMPC) has not yet been applied on physics-based battery models. In the current work, we present a strategy to formulate an NMPC framework for the reformulated pseudo-2D model in real-time. Such a strategy will be extremely useful for BMS applications. The performance objective in NMPC is defined to minimize the error between the deviation of the desired controlled variable from its set point. Optimal current densities (manipulated variables), satisfying a set of different bounds for a defined performance criteria, are reported. The performance of the proposed strategy is illustrated by (i) servo and regulatory control problems with Voltage, SOC as output variables (ii) maximizing SOC, (iii)minimizing the capacity fade, while simultaneously having constraints on state variables such as temperature and anode over-potential to mitigate lithium plating. Acknowledgements The work presented herein was funded in part by the Advanced Research Projects Agency –Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275 along with the Clean Energy Institute (CEI) at the University of Washington (UW) and the Washington Research Foundation.

Plug-and-Play Model Predictive Control for Load Shaping and Voltage Control in Smart Grids

This paper presents a predictive controller for handling plug-and-play charging requests of flexible loads in a distribution system. Two types of flexible loads are defined: 1) deferrable loads that have a fixed power profile but can be deferred in time and 2) shapeable loads that have flexible power profiles but fixed energy requests, such as plug-in electric vehicles. The proposed method uses a hierarchical control scheme based on a model predictive control formulation for minimizing the global system cost. The first stage computes a reachable reference that trades off deviation from the nominal voltage with the required generation control. The second stage uses a price-based objective to aggregate flexible loads and provide load shaping services, while satisfying system constraints and users’ preferences at all times. It is shown that the proposed controller is recursively feasible under specific conditions, i.e., the flexible load demands are satisfied and bus voltages remain within the desired limits. Finally, the proposed scheme is illustrated on a 55 bus radial distribution network.

A modeling framework for optimization-based control of a residential building thermostat for time-of-use pricing

Heating, ventilation and air conditioning for residential and commercial buildings requires a substantial share of electric energy, and ultimately drives summer peak demand in the United States. Variable electric rates are becoming more common in the residential market, as utilities try to encourage users to shift their energy demand. Model predictive controls, one method of reducing energy usage, employ an optimization model to minimize peak demand, energy usage, or electricity costs. This paper details the development of a co-simulation framework to rapidly model and simulate building energy use and optimize cooling setpoint controls. The framework integrates commercially available software to: (i) simulate all energy interactions between the building, internal gains, outdoor environment, and heating and cooling systems via a building energy simulation program (EnergyPlus), (ii) algebraically formulate an optimization problem (with AMPL) using a black-box, reduced-order model for rapid calculations, (iii) employ Simulink as the environment that links calls to EnergyPlus and AMPL, and (iv) solve the optimization model (with CPLEX) to minimize electricity costs and user discomfort. Variable electric time-of-use rates are analyzed in the context of total cooling electricity costs, thermal comfort of users, and peak demand shedding. The framework uses a model predictive control formulation capable of reducing cooling electricity costs by up to 30%; however, cost savings and peak demand shedding are highly dependent on the time-of-use electricity rate schedule.

Humanoid walking pattern generation based on model predictive control approximated with basis functions

ABSTRACTThis paper proposes a real-time walking pattern generator (WPG) based on model predictive control (MPC). Since reducing the calculation time is a crucial problem in real-time WPG, we consider introducing basis functions to reduce the number of control input. The control inputs in the MPC are described by a series of basis functions. Compared with the standard discrete-time MPC formulation, the approach with basis functions requires fewer optimization variables at the cost of decreasing precision. In order to find an appropriate trade-off, two basis functions named Laguerre functions and Haar functions, are tested in this paper. MPC with Laguerre functions decreases more computational load while MPC with Haar functions offers a more accurate solution. The approach is not restricted to Laguerre functions or Haar functions, users can select their own basis functions for different applications and preferences.

Model predictive control of phthalic anhydride synthesis in a fixed-bed catalytic reactor via machine learning modeling

This work proposes a general framework for linking a state-of-the-art computational fluid dynamics (CFD) solver, ANSYS Fluent, and other computing platforms using the lock synchronization mechanism in an effort to extend the utilities of CFD solvers from strictly modeling and design to also control and optimization applications. To demonstrate the effectiveness of the proposed approach, a challenging control problem in chemical engineering, i.e., maximizing the product yield and suppressing the hot-spot temperature in a fixed-bed reactor (FBR) with a highly exothermic reaction, is considered. Specifically, phthalic anhydride (PA) synthesis is chosen for this investigation because of its industrial significance and its extreme high exothermicity. Initially, a high-fidelity two-dimensional axisymmetric heterogeneous CFD model for an industrial-scale FBR is developed in ANSYS Fluent. Next, the CFD model is used to explore a wide operating regime of the FBR to create a database, from which recurrent neural network and ensemble learning techniques are used to derive a homogeneous ensemble regression model using a state-of-the-art application program interface (API), i.e., Keras. Then, a model predictive control (MPC) formulation that is designed to drive the process output to the desired set-point and suppress the magnitude of the hot-spot temperature to avoid catalyst deactivation is developed using the ensemble regression model. Subsequently, the CFD model, the ensemble regression model and the MPC are combined to create a closed-loop system by linking ANSYS Fluent to SciPy (a Python library used for scientific computing) via a message-passing interface (MPI) with lock synchronization mechanism. Finally, the simulation data generated by the closed-loop system are used to demonstrate the robustness and effectiveness of the proposed approach.

Distributed fault-tolerant model predictive control for intermittent fault: A cooperative way

For intermittent actuator faults of large-scale system, a cooperative distributed fault-tolerant model predictive control (DFTMPC) is presented. The actuator plug and play strategy is adopted in the interconnected systems with physical coupling making fault estimation and controller redesign unnecessary. The actuator plug and play process is modeled as a distributed switching model, and there a theoretical stability analysis is provided with switching form of model predictive control (MPC) cost functions. The novel cooperative distributed fault-tolerant performance index is raised in a global view for distributed model predictive control. A simulation example is taken to show the e?ectiveness of the proposed method.

Improved predictions from measured disturbances in linear model predictive control

Measured disturbances are often included in model predictive control (MPC) formulations to obtain better predictions of the future behavior of the controlled system, and thus improve the control performance. In the prediction model, a measured disturbance is in many ways treated like a control input to the system. However, while control inputs change only once per sampling interval as new control inputs are calculated, measured disturbances are typically sampled from continuous variables. While this difference is usually neglected, it is shown in this paper that taking this difference into account may improve the control performance. This is demonstrated through two simulation studies, including a realistic multivariable control problem from the petroleum industry. The proposed method requires only a minor modification in the implementation of the prediction model, and may thus improve the control performance with a minimal effort.

Distributed model predictive control—Recursive feasibility under inexact dual optimization

We propose a novel model predictive control (MPC) formulation, that ensures recursive feasibility, stability and performance under inexact dual optimization. Dual optimization algorithms offer a scalable solution and can thus be applied to large distributed systems. Due to constraints on communication or limited computational power, most real-time applications of MPC have to deal with inexact minimization. We propose a modified optimization problem inspired by robust MPC which offers theoretical guarantees despite inexact dual minimization. The approach is not tied to any particular optimization algorithm, but assumes that the feasible optimization problem can be solved with a bounded suboptimality and constraint violation. In combination with a distributed dual gradient method, we obtain a priori upper bounds on the number of required online iterations. The design and practicality of this method are demonstrated with a benchmark numerical example.

Direct Design of Controllers Using Complementary State and State-Derivative Feedback

This paper is concerned with controllers design using complementary state and state-derivative feedback, as an extension of the work presented in Rossi et al. (in: Proceedings of XXI Congresso Brasileiro de Automatica, Vitoria, Brazil, pp 828–833, 2016). The novel approach is more general, in that it enables the direct design of an CSSDF controller, dispensing with the need for a preliminary state feedback design. For this purpose, a discrete-time design model is derived to describe the plant dynamics in terms of the state and state-derivative combinations available for feedback. The resulting model can be used with existing discrete-time state-space methods for the design of linear or nonlinear control laws. Simulation examples are presented to illustrate the proposed design method within a model predictive control formulation.

Machine Learning-Based Model Predictive Control of Distributed Chemical Processes

Abstract This work proposes a general framework for linking of a state-of-the-art computational fluid dynamics (CFD) solver, ANSYS Fluent, and other computing platforms using the lock synchronization mechanism in an effort to extend the utilities of CFD solvers from strictly modeling and design to also control and optimization applications. Specifically, phthalic anhydride (PA) synthesis is chosen for this investigation because of its industrial significance and its extreme high exothermicity. Initially, a high-fidelity two-dimensional axisymmetric heterogeneous CFD model for an industrial-scale FBR is developed in ANSYS Fluent. Next, the CFD model is used to explore a wide operating regime of the FBR to create a database, from which recurrent neural network and ensemble learning techniques are used to derive a homogeneous ensemble regression model using a state-of-the-art application program interface. Then, a model predictive control (MPC) formulation that is designed to drive the process performance to the desired set-point and to avoid catalyst deactivation is developed using the ensemble regression model. Subsequently, the CFD model, the ensemble regression model and the MPC are combined to create a closed-loop system by linking ANSYS Fluent to SciPy via a message-passing interface (MPI) with lock synchronization mechanism. Finally, the simulation data generated by the closed-loop system are used to demonstrate the robustness and effectiveness of the proposed approach.

Experimental Validation of a Kinematic Bicycle Model Predictive Control with Lateral Acceleration Consideration

Abstract Nowadays, Automated Driving has a growing interest in the scientific and industrial automotive community. The vehicle motion planning is an essential procedure to obtain safe and comfortable trajectories, adapting the longitudinal speed to the road legal limits and mainly to avoid the excessive lateral accelerations along the journey. Typically, the proper speed of the vehicle is intrinsically related to the curvature of the path, requiring a previous approximation of this parameter in the planning stage. In this work, a novel procedure to follow a route trajectory and speed limits considering the lateral acceleration parameter is presented. A lateral jerk equation was developed and introduced into a kinematic bicycle model predictive control formulation. An adaptive speed weight equation that depends on the lateral acceleration is presented to improve the lateral positioning. A vehicle motion control simulation, developed in Dynacar, is validated with some real tests. The results show the capabilities of the proposed approach. An accurate vehicle motion control considers the lateral acceleration to avoid unfeasibility in optimization problem.

Handling sensor faults in economic model predictive control of batch processes

The problem of sensor fault detection and isolation (FDI) and fault‐tolerant economic model predictive control (FT‐EMPC) for batch processes is addressed. To this end, we first model batch processes using subspace‐based system identification techniques. The analytical redundancy within the identified model is subsequently exploited to detect, isolate, and handle the faulty measurements. The reconciled fault‐free measurements are then incorporated in an economic model predictive controller formulation. Simulation case studies involving the application of the proposed data‐driven FDI and FT‐EMPC algorithms to the energy intensive electric arc furnace process illustrate the improvement in economic performance under various fault scenarios. © 2018 American Institute of Chemical Engineers AIChE J, 65: 617–628, 2019

An efficient offline implementation for output feedback min‐max MPC

SummaryPrevious works have presented the output feedback min‐max model predictive control (MPC) for the discrete‐time system with both polytopic uncertainty and bounded persistent disturbance, where the controller parameters are optimized at each sampling instant. This paper proposes the corresponding offline approach in order to reduce the online computational burden. Such offline MPC, when the state is measurable and there is no disturbance, has been constructed in the work of Wan and Kothare (An efficient off‐line formulation of robust model predictive control using linear matrix inequalities. Automatica. 2003;39(5):837‐846). Since this paper considers the case when the true state is unknown, the ellipsoidal regions of attraction (applying only to the estimated state) lose their asymptotic invariance property, and the estimation error set (EES) has a major effect on the control performance. This paper refreshes EES invoking the one‐step reachable set and guarantees that the signals being penalized in the performance cost function to converge to a neighborhood of the equilibrium point. Two examples are given to illustrate the effectiveness of the approach.