Real-time Model Predictive Control Research Articles

A real-time optimization framework for the time-varying economic environment

In this paper, we propose a conceptual framework for nonlinear systems to integrate real-time optimization (RTO) and model predictive control (MPC) under time-varying economic environments. In the RTO layer, we introduce a lookup table including a large number of steady-state points of the nonlinear system, which are predetermined offline. Once the parameters of the economic cost function are varied, we are able to take a quick online search on the lookup table to find a point for satisfied economic performance and then send it to the MPC layer as a temporary control target. The temporary target is also employed as the initial solution for solving the optimization of the RTO layer. When the optimal target is calculated by RTO, it will replace the temporary one as the new control target of MPC. Compared to the two-layer framework which suffers from long waiting time to get the optimal operating points, the lookup-table-based RTO (LT-RTO) framework provides a quick-produced suboptimal target for MPC. It avoids unnecessary economic losses if MPC is still tracking outdated target even parameters of the cost function have already changed. We demonstrate the effectiveness through a chemical process model that the LT-RTO framework makes an improvement of the economic performance.

Model Predictive Control for Distributed Microgrid Battery Energy Storage Systems

This paper proposes a new convex model predictive control strategy for dynamic optimal power flow between battery energy storage systems distributed in an AC microgrid. The proposed control strategy uses a new problem formulation, based on a linear d-q reference frame voltage-current model and linearised power flow approximations. This allows the optimal power flows to be solved as a convex optimisation problem, for which fast and robust solvers exist. The proposed method does not assume real and reactive power flows are decoupled, allowing line losses, voltage constraints and converter current constraints to be addressed. In addition, non-linear variations in the charge and discharge efficiencies of lithium ion batteries are analysed and included in the control strategy. Real-time digital simulations were carried out for an islanded microgrid based on the IEEE 13 bus prototypical feeder, with distributed battery energy storage systems and intermittent photovoltaic generation. It is shown that the proposed control strategy approaches the performance of a strategy based on non-convex optimisation, while reducing the required computation time by a factor of 1000, making it suitable for a real-time model predictive control implementation.

Enhancement of safety and comfort of cyclists at intersections

Cyclist safety is increasingly becoming a societal problem in Europe, as shown by road safety statistics. Frequent stops for red traffic lights at intersections are experienced by cyclists as a major inconvenience. This study introduces a green wave concept for cyclists, with focus on the traffic management and control aspects under cooperative intelligent transport systems applications. It especially addresses increasing stability of the adaptive control system, to overcome the drawbacks of both actuated and traditional adaptive control (which are too unpredictable for a green wave speed advice). In addition, solutions for avoiding increased delays for other traffic are investigated, as generally result from a classic green wave approach (with only fixed-time control) and traditional adaptive control. This study introduces an adaptive control algorithm for a real-time model-predictive controller and implements a plan-deviation cost function to address stabilisation. Simulation results show that the developed method increases stability of the adaptive control system, limits extra delays for other traffic and yields a high success rate for the green wave concept.

A Fast NMPC Approach based on Bounded-Variable Nonlinear Least Squares

Abstract In this paper, we present an approach for real-time nonlinear model predictive control (NMPC) of constrained multivariable dynamical systems described by nonlinear difference equations. The NMPC problem is formulated by means of a quadratic penalty function as an always feasible, sparse nonlinear least-squares problem subject to box constraints on the decision variables. This formulation is exploited by the proposed fast solution algorithm, which is based on the Gauss-Newton method and bounded-variable least squares (BVLS). Linear time-invariant and linear time-varying model predictive control based on BVLS are special cases of the proposed NMPC framework. The proposed approach and its benefits are demonstrated through a typical numerical example in simulation.

Advanced-step Multistage Nonlinear Model Predictive Control

We present a real-time implementable robust Nonlinear Model Predictive Control (NMPC) framework that simultaneously addresses model uncertainty and unmeasured disturbances based on a multistage scenario tree to describe the evolution of uncertainties. The multistage scenario tree computes a control action that hedges against all possible uncertainty realizations and optimizes expected performance. However, the scenario tree structure inevitably increases the optimization problem size, as robust horizons become longer. This presents a challenge to solve large-scale problems in real-time. We propose a parallelizable advanced-step multistage NMPC (as-msNMPC) that precomputes a set of solutions in background so that the online computation effort is negligible. We apply an as-msNMPC framework to a CSTR example to show the controller’s robustness and improved online performance over competing robust NMPC methods.

Real-time MPC Design Based on Machine Learning for a Diesel Engine Air Path System

This study investigated a control design method based on machine learning to achieve non-linear model predictive control (MPC) at a low computational load. In addition, we describe examples of the application of this method to a diesel engine air path system. The solution to the optimal control problem determined at each point in time by MPC depends on several parameters at that time. Thus, if the relationship between the solution and the parameters could be approximated in advance using machine learning, solving this problem online would become unnecessary, and the control computation time could be reduced. We designed a controller that operates the valves of the air path system using this method and used a simulation to verify that this resulted in a favorable tracking performance of the target values. The computation time of the approximated MPC controller was 0.022 ms.

Parallelizable Real-Time Algorithm for Integrated Experiment Design MPC

This paper proposes a parallelizable real-time algorithm for integrated experiment-design model predictive control (MPC). Integrated experiment design MPC is needed if a system is not observable at a tracking reference and needs to be excited on purpose in order to be able to estimate the system’s states and parameters. The contribution of this paper is a real-time MPC algorithm using two processors. On the first processor an extended Kalman filter (EKF) as well as a parametric certainty-equivalent MPC controller are implemented, which can provide immediate feedback at high sampling rates. On the second processor, optimal experiment design (OED) problems are solved in parallel in order to perturb the certainty-equivalent MPC control loop improving the accuracy of the state estimator at a lower sampling rate. We show that this framework can achieve optimal tradeoffs between OED and control objectives. The approach is applied to a biochemical process in order to illustrate that the proposed controller can achieve superior control performance when compared to certainty-equivalent MPC.

An Efficient Convex Formulation for Model-Predictive Control on Wave-Energy Converters1

Model-predictive control (MPC) has shown its strong potential in maximizing energy extraction for wave-energy converters (WECs) while handling hard constraints. However, the computational demand is known to be a primary concern for applying MPC in real time. In this work, we develop a cost function in which a penalty term on the slew rate of the machinery force is introduced and used to ensure the convexity of the cost function. Constraints on states and the input are incorporated. Such a constrained optimization problem is cast into a Quadratic Programming (QP) form and efficiently solved by a standard QP solver. The current MPC is found to have good energy-capture capability in both regular and irregular wave conditions, and is able to broaden favorably the bandwidth for capturing wave energy compared to other controllers in the literature. Reactive power required by the power-take-off (PTO) system is presented. The effects of the additional penalty term are discussed.

Day-Ahead Scheduling and Real-Time Economic MPC of CHP Unit in Microgrid With Smart Buildings

This paper presents a model for day-ahead scheduling of the combined heat production heat and electric energy production for a residential microgrid taking into account the economic factors in a liberalized electricity markets, the technical factors in the safety/quality of supply, and the consumer preferences. This day-ahead scheduling model is complemented with a real-time economic model predictive control (MPC) model for a subsequent control with respect to the outcomes of the day-ahead scheduling. This combined scheduling and economic MPC provides a general set-up capable of overcoming several major difficulties encountered with a typical scheduling + tracking MPC set-up, e.g., the problems of connecting the economic objectives with different temporal resolution and different requirements in terms of delivery.

Real-Time Nonlinear Model Predictive Control of a Battery–Supercapacitor Hybrid Energy Storage System in Electric Vehicles

A nonlinear model predictive control (NMPC) method has been presented as the energy management strategy of a battery–supercapacitor (SC) hybrid energy storage system (H-ESS) in a Toyota Rav4EV. For the first time, the NMPC has been shown to be real-time implementable for these fast systems. The performance of the proposed controller has been demonstrated against a linear model predictive control (LMPC) and a rule-based control (RBC) strategy. The NMPC shows to outperform the RBC even with no prior knowledge of the future trip available. The NMPC also shows performance improvement over the LMPC by compensating for the error accompanied by linearization in LMPCs. Hardware-in-the-loop (HiL) testing has been performed to demonstrate the NMPC capability for real-time implementation in a battery–SC H-ESS. Upon carefully choosing the prediction horizon and control horizon size, as well as the maximum number of iterations, the turn-around time for the control update is shown to fall far below the necessary sampling time of 10 ms in vehicle control.

Real-time algorithm for self-reflective model predictive control

This paper is about a real-time model predictive control (MPC) algorithm for a particular class of model based controllers, whose objective consists of a nominal tracking objective and an additional learning objective. Here, the construction of the learning term is based on an economic optimal experiment design criterion. It is added to the MPC objective in order to excite the system on purpose thereby improving the accuracy of the state and parameter estimates in the presence of incomplete or noise affected measurements. The focus of this paper is on so-called self-reflective model predictive control schemes, which have the property that the additional learning term can be interpreted as the expected loss of optimality of the controller in the presence of random measurement errors. The main contribution is a formulation-tailored algorithm, which exploits the particular structure of self-reflective MPC problems in order to speed-up the online computation. It is shown that the proposed algorithm can solve the self-reflective optimization problems with reasonable additional computational effort and in real-time.

An algorithm for gradient-based dynamic optimization of UV flash processes

This paper presents a novel single-shooting algorithm for gradient-based solution of optimal control problems with vapor–liquid equilibrium constraints. Such optimal control problems are important in several engineering applications, for instance in control of distillation columns, in certain two-phase flow problems, and in operation of oil reservoirs. The single-shooting algorithm uses an adjoint method for the computation of gradients. Furthermore, the algorithm uses either a simultaneous or a nested approach for the numerical solution of the dynamic vapor–liquid equilibrium model equations. Two numerical examples illustrate that the simultaneous approach is faster than the nested approach and that the efficiency of the underlying thermodynamic computations is important for the overall performance of the single-shooting algorithm. We compare the performance of different optimization software as well as the performance of different compilers in a Linux operating system. These tests indicate that real-time nonlinear model predictive control of UV flash processes is computationally feasible.

Thermal Management in Plug-In Hybrid Electric Vehicles: A Real-Time Nonlinear Model Predictive Control Implementation

A real-time nonlinear model predictive control (NMPC) for the thermal management (TM) of the electrical components cooling circuit in a Plug-In Hybrid Electric Vehicle (PHEV) is presented. The electrical components are highly temperature sensitive and, therefore, working out of the ranges recommended by the manufacturer can lead to their premature aging or even failure. Consequently, the goals for an accurate and efficient TM are to keep the main component, the Li-ion battery, within optimal working temperatures, and to consume the minimum possible electrical energy through the cooling circuit actuators. This multi-objective requirement is formulated as a finite-horizon optimal control problem (OCP) that includes a multi-objective cost function, several constraints, and a prediction model especially suitable for optimization. The associated NMPC is performed on real time by the optimization package MUSCOD-II and is validated in three different repeatable test-drives driven with a PHEV. Starting from identical conditions, each cycle is driven once being the cooling circuit controlled with NMPC and once with a conventional approach based on a finite-state machine. Compared to the conventional strategy, the NMPC proposed here results in a more accurate and healthier temperature performance, and at the same time, leads to reductions in the electrical consumption up to 8%.

Adaptive Energy Management System Based on a Real-Time Model Predictive Control With Nonuniform Sampling Time for Multiple Energy Storage Electric Vehicle

The performance of a dual energy storage electric vehicle system mainly depends on the quality of its power and energy managements. A real-time management strategy supported by a model predictive control (MPC) using the nonuniform sampling time concept is developed and fully addressed in this paper. First, the overall multiple energy storage powertrain model including its inner control layer is represented with the energetic macroscopic representation and used to introduce the energy strategy level. The model of the system with its inner control layer is translated into the state-space domain in order to develop an MPC approach. The management algorithm based on mixed short- and long-term predictions is compared to rule-based and constant sampling time MPC strategies in order to assess its performance and its ability to be used in a real vehicle. The real-time simulation results indicate that, compared to other strategies, the proposed MPC strategy can balance the power and the energy of the dual energy storage system more effectively, and reduce the stress on batteries. Moreover, battery and supercapacitor key variables are kept within safety limits, increasing the lifetime of the overall system.

Implicit Integrators for Linear Dynamics Coupled to a Nonlinear Static Feedback and Application to Wind Turbine Control

Efficient integration schemes with sensitivity propagation are crucial for deploying real-time Nonlinear Model Predictive Control on systems described by continuous time dynamics. Implicit integration schemes are preferred when stiff modes are present in the model equations, or when the equations are implicit. We consider here a class of models, where the dynamics are linear, but coupled to a general static nonlinear feedback function. We propose a collocation-based implicit integration scheme where a lifting-condensing approach is used to exploit this specific structure to reduce the size of the linear algebra underlying the integrator. This technique yields a significant reduction in the computational complexity of performing the system integration and sensitivity analysis, when the static nonlinearity is of much smaller dimensions than the complete dynamics. The proposed method is illustrated on a complex wind turbine model, resulting in a significant gain of computational time in the linear algebra, and an overall gain of computational time of a factor 2.

Parallel Explicit MPC for Hardware with Limited Memory

This paper proposes a real-time model predictive control (MPC) algorithm for problems with convex quadratic objectives, linear dynamic systems, as well as polytopic state-and control constraints. The method features, on the one hand, explicit model predictive control algorithms and parametric optimization, but, on the other hand, also uses ideas from iterative distributed optimization. This leads to an explicit real-time algorithm with constant and verifiable run-time bounds that scale linearly with the prediction horizon length of the MPC problem. Moreover, unlike standard explicit MPC algorithms, the memory requirements of the proposed algorithm do not dependent on the prediction horizon length. The practical advantages of the method are illustrated with a numerical example.

A State-Dependent Updating Period for Certified Real-Time Model Predictive Control

In this paper, a state-dependent control updating period strategy is proposed for use in interrupted implementation of real-time Model Predictive Control (MPC). The strategy can be used as soon as a certification bound is available for the underlying optimization algorithm. Moreover, a new fast-Gradient based certifiable algorithm is proposed with the associated certification bounds for convex generally constrained optimization problems.

Real-time economic nonlinear model predictive control for wind turbine control

ABSTRACTNonlinear model predictive control (NMPC) is a strong candidate to handle the control challenges emerging in the modern wind energy industry. Recent research suggested that wind turbine (WT) control based on economic NMPC (ENMPC) can improve the closed-loop performance and simplify the task of controller design when compared to a classical NMPC approach. This paper establishes a formal relationship between the ENMPC controller and the classic NMPC approach, and compares empirically their closed-loop nominal behaviour and performance. The robustness of the performance is assessed for an inaccurate modelling of the tower fore-aft main frequency. Additionally, though a perfect wind preview is assumed here, the effect of having a limited horizon of preview of the wind speed via the LIght Detection And Ranging (LIDAR) sensor is investigated. Finally, this paper provides new algorithmic solutions for deploying ENMPC for WT control, and report improved computational times.

Performance comparison of next generation controller and MPC in real time for a SISO process with low cost DAQ unit

In this paper, a brief overview of real time implementation of next generation Robust, Tracking, Disturbance rejecting, Aggressive (RTDA) controller and Model Predictive Control (MPC) is provided. The control algorithm is implemented through MATLAB. The plant model used in controller design is obtained using system identification tool and integral response method. The controller model is developed in Simulink using jMPC tool, which will be executed in real time. The outputs obtained are tested for various constraint values to obtain the desirable results. The implementation of Hardware in Loop is done by interfacing it with MATLAB using Arduino as data acquisition unit. The performance of RTDA is compared with those of MPC and Proportional Integral controller.

Real-Time Nonlinear Model Predictive Control of a Transport–Reaction System

Two real-time nonlinear model predictive control (NMPC) algorithms for a transport–reaction system are designed. The system is modeled by a hyperbolic partial differential equation and discretized by means of a two-time-level semi-implicit semi-Lagrangian scheme. For the resulting lumped-parameter system, a constrained optimal control problem is formulated and state constraints are implemented in the form of barrier functions. The NMPC algorithms perform a single step or several steps of an iterative solution routine of the optimal control problem at every sampling point. With this suboptimal solution strategy, a fixed maximum evaluation time and execution in real time are guaranteed. An analysis of the nominal stability is provided for one NMPC scheme. The robustness of the controllers is evaluated for an example problem, where a nonisothermal plug-flow reactor with irreversible exothermic reactions is considered. The control objectives are to limit the maximum reactor temperature (avoid hot spots) and to maximize the process output.