Finite Horizon Model Predictive Control Research Articles

Optimized energy management of a solar battery microgrid: An economic approach towards voltage stability

As the adoption of renewable energy sources (RESs) continues to surge, and the concept of microgrids (MGs) gains widespread recognition, the need for efficient battery energy storage system (BESS) management within MGs has become increasingly prominent. This paper introduces a novel Energy Management System (EMS) designed for grid-connected MGs, with the primary objectives of enhancing the energy economics of the MG, minimizing BESS degradation, and ensuring that the point of common coupling (PCC) voltage remains within prescribed limits. The proposed EMS utilizes a finite-horizon Model Predictive Control (MPC) framework to seamlessly coordinate BESS operations, encompassing charging, discharging, and reactive power provision. This coordination is done in conjunction with solar power generation, load demand, electricity pricing, and feed-in tariffs. Furthermore, the EMS accounts for uncertainties related to load and solar demand using a Monte Carlo simulation approach. The optimization goal of the proposed EMS is to minimize the expected total operational cost of the MG over a 24-hour prediction horizon. This cost encompasses both economic costs and battery degradation costs. The optimization process adheres to a set of constraints that consider BESS limitations, such as state of charge (SoC) constraints and charging/discharging limits, as well as inverter capacity limits and PCC voltage requirements. Conducting rigorous case studies on the MATLAB Simscape Electrical platform and validating them in real-time using the OPAL-RT simulator demonstrate the effectiveness of the proposed EMS across diverse operational scenarios and pricing models. The findings of these case studies provide valuable insights into the effectiveness of the EMS in real-world MG applications.

Modeling and Finite-Horizon MPC for a Boiler-Turbine System Using Minimal Realization State-Space Model

This paper aims to address a finite-horizon model predictive control (MPC) for non-linear drum-type boiler-turbine system using a system-identification method. Considering that the strong state coupling of a non-linear mechanism model, the subspace identification method is first utilized to obtain a linear state-space model, and transformed into an input–output model. By taking the inputs and outputs of the input–output model as system states, an augmented non-minimal state-space (NMSS) model of state measurable is constructed. In order to reduce the computation burden, the augmented NMSS model is further transformed into a canonical formulation by adopting a Kalman decomposition. Based on the minimal realization state-space model, the MPC controller is parameterized as a finite-horizon optimization problem. Finally, simulations are performed and evaluated the performance of the proposed method, and the simulation results show that: the linear model approximate the non-linear system accurately; the proposed MPC method can achieve a satisfactory stable control performance; and the computation time 18.388 s for the overall optimization problem also illustrates the real-time performance effectively.

Stability of finite horizon optimisation based control without terminal weight

This paper presents a stability analysis tool for model predictive control (MPC) where control action is generated by optimising a cost function over a finite horizon. Stability analysis of MPC with a limited horizon but without terminal weight is a well-known challenging problem. We define a new value function based on an auxiliary one-step optimisation related to stage cost, namely optimal one-step value function (OSVF). It is shown that a finite horizon MPC can be made to be asymptotically stable if OSVF is a (local) control Lyapunov function (CLF). More specifically, by exploiting the CLF property of OSFV to construct a contractive terminal set, a new stabilising MPC algorithm (CMPC) is proposed. We show that CMPC is recursively feasible and guarantees stability under the condition that OSVF is a CLF. Checking this condition and estimation of the maximal terminal set are discussed. Numerical examples are presented to demonstrate the effectiveness of the proposed stability condition and corresponding CMPC algorithm.

A fast equivalent scheme for robust constrained-input min–max finite horizon model predictive control via model-free critic-only Q-learning

A fast equivalent scheme for robust constrained-input min–max finite horizon model predictive control via model-free critic-only Q-learning

Finite-horizon, energy-efficient trajectories in unsteady flows.

Intelligent mobile sensors, such as uninhabited aerial or underwater vehicles, are becoming prevalent in environmental sensing and monitoring applications. These active sensing platforms operate in unsteady fluid flows, including windy urban environments, hurricanes and ocean currents. Often constrained in their actuation capabilities, the dynamics of these mobile sensors depend strongly on the background flow, making their deployment and control particularly challenging. Therefore, efficient trajectory planning with partial knowledge about the background flow is essential for teams of mobile sensors to adaptively sense and monitor their environments. In this work, we investigate the use of finite-horizon model predictive control (MPC) for the energy-efficient trajectory planning of an active mobile sensor in an unsteady fluid flow field. We uncover connections between trajectories optimized over a finite-time horizon and finite-time Lyapunov exponents of the background flow, confirming that energy-efficient trajectories exploit invariant coherent structures in the flow. We demonstrate our findings on the unsteady double gyre vector field, which is a canonical model for chaotic mixing in the ocean. We present an exhaustive search through critical MPC parameters including the prediction horizon, maximum sensor actuation, and relative penalty on the accumulated state error and actuation effort. We find that even relatively short prediction horizons can often yield energy-efficient trajectories. We also explore these connections on a three-dimensional flow and ocean flow data from the Gulf of Mexico. These results are promising for the adaptive planning of energy-efficient trajectories for swarms of mobile sensors in distributed sensing and monitoring.

Multi-Objective Model Predictive Control for Vehicle Active Suspension System

This paper puts forward a multi-objective model predictive control scheme in order to address the conflicting control objectives of a vehicle active suspension system. The key problem in designing an active suspension controller is that the controller has to realize a feasible control input that can satisfy the competing control requirements such as ride comfort, suspension travel and road handling. Hence, in this work, these constraints are integrated into an optimal control framework and a finite horizon model predictive controller is used to solve the multi-objective cost function. The key advantage of the proposed scheme is that the model predictive control design finds the optimal control input by solving the discrete time algebraic Riccati equation. This guarantees not only a robust closed loop system but also a realizable control effort, without violating the hard constraints of the active suspension system. The proposed model predictive control design is experimentally validated on a laboratory scale quarter car suspension system using hardware-in-loop testing. The performance of the model predictive control scheme is compared with the one of the unconstrained linear quadratic regulator and tested for four realistic road profiles. The experimental results substantiate that the suspension system controlled by the model predictive controller offers better ride comfort and road handling features when compared to the conventional linear quadratic regulator.

An implementable stabilizing model predictive controller applied to a rotary flexible link: An experimental case study

This work addresses the application of implementable stabilizing model predictive control (MPC) strategies to a rotary flexible link (RFL). Despite their practice usefulness and design simplicity, the implementation of these stable MPC controllers with guaranteed feasibility in a real experiment, and dedicated to dynamic features of RFL systems, have not yet been documented by the literature. In contrast to conventional finite-horizon MPC strategies, infinite-horizon MPC (IHMPC) techniques ensure nominal closed-loop stability irrespective of the cost function parameters. Also, if these IHMPC strategies have feasible-optimization problem based formulations, such as implementable ones investigated here, their applicability naturally becomes attractive to the industry. Simulation and experimental results illustrate the usefulness of the implementable stabilizing MPC controllers when compared to non-feasible in practice ones, such as a classical infinite-horizon MPC and a conventional finite-horizon generalized predictive controller, thus ensuring their benefits in terms of performance and computational burden in the context of constrained RFL mechatronic systems.

Dynamic path planning and trajectory tracking using MPC for satellite with collision avoidance

This paper proposes a dynamic path planning and trajectory tracking algorithm for an autonomous satellite, released from the space station, to get to the desired position for performing space tasks. The complex construction of the space station results in the presence of a geometric channel constraint for the obstacles avoidance. In addition, a three dimension B-spline template with minimizing the curvature of the path is designed, which could guarantee the continuity of the curvature to make the trajectory smooth and avoid the satellite from stopping at discontinuities waypoints. Then, the reference states and inputs are solved by a new projection method, which provides a foundation for the subsequent trajectory tracking. Subsequently, a finite horizon model predictive control method is constructed for the path tracking. The benefits of this approach are to take constraints into consideration, and to get optimal performance by minimizing the fuel consumption compared with other tracking controllers. The closed-loop stability is guaranteed by the feedback controller, terminal penalty, and a newly terminal constraint set. In simulation experiments, results illustrate the effectiveness and practicality of the algorithm.

Stability of Soft-Constrained Finite Horizon Model Predictive Control

This paper addresses the stability of soft-constrained model predictive control (MPC). It is shown that the infinite horizon soft-constrained MPC problem can be solved as a finite horizon soft-constrained MPC problem if the prediction horizon is greater than an upper bound. The contribution of this paper is a procedure to compute the prediction horizon upper bound, which guarantees the stability. The proposed technique is verified using two simulation examples. The second example (inverted pendulum) is verified through practical implementation.

Finite horizon model predictive control of electrowetting on dielectric with pinning

A time-discrete spatially-continuous electrowetting on dielectric (EWOD) model with contact line pinning is considered as the state system in an optimal control framework. The pinning model is based on a complementarity condition. In addition to the physical variables describing velocity, pressure, and voltage, the solid-liquid-air interface, i.e., the contact line, arises as a geometric variable that evolves in time. Due to the complementarity condition, the resulting optimal control of a free boundary problem is thus a mathematical program with equilibrium constraints (MPEC) in function space. In order to cope with the geometric variable, a finite horizon model predictive control approach is proposed. Dual stationarity conditions are derived by applying a regularization procedure, exploiting techniques from PDE-constrained optimization, and then passing to the limit in the regularization parameters. Moreover, a function-space-based numerical procedure is developed by following the theoretical limit argument used in the derivation of the dual stationarity conditions. The performance of the algorithm is demonstrated by several examples; including barycenter matching and trajectory tracking.

Stability of finite horizon model predictive control with incremental input constraints

Model predictive control of discrete-time nonlinear systems with incremental input constraints is proposed in this paper. Firstly, the existence of the terminal set and terminal penalty is proven on the assumption that the considered system is twice continuously differentiable. Secondly, properties of the optimal cost function are exploited. It shows that the optimal cost function is positive semi-definite, continuous at the equilibrium and monotonically decreasing along the predicted trajectory. The systems under control converge to the equilibrium since the optimal cost function is monotonically decreasing. Thirdly, stability of nonlinear systems is proven in terms of the classical Lyapunov Theorem, where an upper bound of the optimal cost function in the terminal set is chosen as a candidate Lyapuonv function. Finally, the system is asymptotically stable since the system state converges to the equilibrium and the system is stable.

A Modifier-Adaptation Strategy towards Offset-Free Economic MPC

We address in the paper the problem of designing an economic model predictive control (EMPC) algorithm that asymptotically achieves the optimal performance despite the presence of plant-model mismatch. To motivate the problem, we present an example of a continuous stirred tank reactor in which available EMPC and tracking model predictive control (MPC) algorithms do not reach the optimal steady state operation. We propose to use an offset-free disturbance model and to modify the target optimization problem with a correction term that is iteratively computed to enforce the necessary conditions of optimality in the presence of plant-model mismatch. Then, we show how the proposed formulation behaves on the motivating example, highlighting the role of the stage cost function used in the finite horizon MPC problem.

TUNING OF MODEL PREDICTIVE CONTROL WITH MULTI-OBJECTIVE OPTIMIZATION

Two multi-objective optimization based tuning methods for model predictive control are proposed. Both methods consider the minimization of the error between the closed-loop response and an output reference trajectory as tuning goals. The first approach is based on the ranking of the outputs according to their importance to the plant operation and it is solved by a lexicographic optimization algorithm. The second method solves a compromise optimization problem. The former is designed for systems in which the number of inputs is equal to the number of outputs, while the latter can also be applied to non-square systems. The main contribution is an automated tuning framework based on a straightforward goal definition. The proposed methods are tested on a finite horizon model predictive controller in closed-loop with a 3x3 subsystem of the Shell Heavy Oil Fractionator benchmark system. The simulation results show that the methods proposed here can be a useful tool to reduce the commissioning time of the controller. The methods are compared to an existing multi-objective optimization based tuning approach. The computational time required to run the proposed tuning algorithms is considerably reduced when compared to the existing approach and, moreover, it does not need an a posteriori decision to select a solution from a set of Pareto optimal solutions.

Model predictive control of P-time event graphs

ABSTRACTThis paper deals with model predictive control of discrete event systems modelled by P-time event graphs. First, the model is obtained by using the dater evolution model written in the standard algebra. Then, for the control law, we used the finite-horizon model predictive control. For the closed-loop control, we used the infinite-horizon model predictive control (IH-MPC). The latter is an approach that calculates static feedback gains which allows the stability of the closed-loop system while respecting the constraints on the control vector. The problem of IH-MPC is formulated as a linear convex programming subject to a linear matrix inequality problem. Finally, the proposed methodology is applied to a transportation system.

Simultaneous Tracking of Multiple Ground Targets from a Multirotor Unmanned Aerial Vehicle

An algorithm for simultaneous tracking of multiple ground targets by an unmanned aerial vehicle is presented. The algorithm is specifically tailored toward multirotor vehicles, and it consists of a particle filter to predict target motion, a reference trajectory generator, and a finite-horizon model predictive controller for trajectory tracking. Two versions of the algorithm are proposed: for a vehicle equipped with a gimbaled camera, and for a vehicle equipped with a fixed camera. Furthermore, a target rejection algorithm is included to prune targets that inhibit accurate tracking of the majority of the target set. The tracking algorithm and multirotor vehicle dynamic model are first described, followed by example simulations for both the gimbaled and fixed-camera cases. Trade studies are presented, analyzing the effects of controller tuning parameters and camera field of view, as well as performance of the target rejection algorithm. In simulation experiments, real-world target data are used to improve simulation fidelity. Overall, results show that the algorithm is effective in capturing a set of ground targets within the field of view simultaneously when using either gimbaled or fixed-camera configurations, but performance is somewhat degraded in the fixed-camera case when target dynamics occur on timescales similar to tracking vehicle dynamics.

Design and Comparison of Constrained MPC With PID Controller for Heave Disturbance Attenuation in Offshore Managed Pressure Drilling Systems

AbstractThis paper presents a constrained finite horizon model predictive control (MPC) scheme for regulation of the annular pressure in a well during managed pressure drilling from a floating vessel subject to heave motion. In addition to the robustness of a controller, how to deal with heave disturbances despite uncertainties in the friction factor and bulk modulus is investigated. The stochastic model describing sea waves in the North Sea is used to simulate the heave disturbances. The results show that the closed-loop simulation without disturbance has a fast regulation response, without any overshoot, and is better than a proportional-integral-derivative controller. The constrained MPC for managed pressure drilling shows further improved disturbance rejection capabilities with measured or predicted heave disturbance. Monte Carlo simulations show that the constrained MPC has a good performance to regulate set point and attenuate the effect of heave disturbance in case of significant uncertainties in the well parameter values.

Generalised polynomial chaos expansion approaches to approximate stochastic model predictive control†

This paper considers the model predictive control of dynamic systems subject to stochastic uncertainties due to parametric uncertainties and exogenous disturbance. The effects of uncertainties are quantified using generalised polynomial chaos expansions with an additive Gaussian random process as the exogenous disturbance. With Gaussian approximation of the resulting solution trajectory of a stochastic differential equation using generalised polynomial chaos expansion, convex finite-horizon model predictive control problems are solved that are amenable to online computation of a stochastically robust control policy over the time horizon. Using generalised polynomial chaos expansions combined with convex relaxation methods, the probabilistic constraints are replaced by convex deterministic constraints that approximate the probabilistic violations. This approach to chance-constrained model predictive control provides an explicit way to handle a stochastic system model in the presence of both model uncertainty and exogenous disturbances.

Finite horizon model predictive control with ellipsoid mapping of uncertain linear systems

A model predictive control scheme was proposed for discrete-time uncertain linear systems subject to input constraints. The cost functional to be minimised is a finite horizon quadratic cost, which describes the performance of the corresponding nominal system. The control action is specified in terms of both feedback and open-loop components. The open-loop part of the control action steers the centre of associated ellipsoids into a set around the origin, while the feedback component forces the actual system states to remain in those ellipsoids. Both feedback and open-loop control are determined online by repeatedly solving a convex optimisation problem. The predictive control scheme guarantees recursive feasibility and robust stability if the convex optimisation problem is feasible at the initial time instant. A numerical example illustrates the effectiveness of the proposed approach.

Stability analysis of classic finite horizon model predictive control

This paper revisits the stability issue of earlier model predictive control (MPC) algorithms where the performance index has a finite receding horizon and there is no terminal penalty in the performance index or other constraints added in online optimisation for the purpose of stability. Stability conditions are presented for MPC of constrained linear and nonlinear systems, and there is no restriction on the length of the horizon. These conditions can be used to test whether or not desired stability properties can be achieved under chosen state and control weightings.

IHMPC and POD to the control of a non-isothermal tubular reactor

This paper presents the result of applying POD (Proper Orthogonal Decomposition) and IHMPC (Infinite Horizon Model Predictive Control) to the control of a non-isothermal tubular reactor. This paper is based on a previous work of O.M. Agudelo, J.J. Espinosa, B. De Moor Control of a Tubular Chemical Reactor by means of POD and Predictive Control Techniques, in Proceedings of the European Control Conference 2007 (ECC 2007), pp. 1046–1053, Kos, Greece, 2007, where a finite horizon model predictive control and POD techniques are applied a non-isothermal tubular reactor. In this paper the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. POD and Galerkins method are used to derive the low order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. Two IHMPC formulations are constructed on the basis of the low order linear model and are demonstrated, through simulation, to achieve the control objectives.