Linear Model Predictive Control Research Articles

Optimization of liquid cooling heat dissipation control strategy for electric vehicle power batteries based on linear time-varying model predictive control

The heat dissipation performance of batteries is crucial for electric vehicles, and unreasonable thermal management strategies may lead to reduced battery efficiency and safety issues. Therefore, this paper proposed an optimization strategy for battery thermal management systems (BTMS) based on linear time-varying model predictive control (LTMPC). To begin, based on the results of three-dimensional thermal flow analysis, a reduced order substitution model for the battery cooling system was established. Next, to address the issue of high computational complexity caused by the nonlinear model in the controller, a linearization method based on staged control was designed. Furthermore, the control parameters were optimized using the particle swarm optimization algorithm. Finally, a BTMS physical model based on SIMSCAPE was established for performance simulation. The performance of the logic threshold controller (LTC), linear model predictive controller (LMPC), and nonlinear model predictive controller (NMPC) was compared and analyzed. LTMPC was found to reduce the average temperature of the battery by up to 2.33 °C and 1.90 °C, and the cumulative temperature difference is reduced by 13.9% and 16.6% compared to LTC and NMPC, respectively. Compared to LMPC, LTMPC reduces thermal management energy consumption by 21.2%.

Do-mpc: Towards FAIR nonlinear and robust model predictive control

Over the last decades, model predictive control (MPC) has shown outstanding performance for control tasks from various domains. This performance has further improved in recent years with advanced MPC schemes for nonlinear systems under uncertainty including economic control objectives. These recent improvements often fail to bridge the gap between MPC researchers and control practitioners in academia and industry, where classical control approaches and traditional linear MPC still dominate most applications. This is despite the fact that advanced MPC controllers can lead to significant energy savings, yield improvements, safer operation and other benefits.In this work, we identify four main obstacles hindering the widespread adoption of advanced MPC methods. These are the unavailability of models, the challenges associated with deploying complex controllers on physical systems, the scarcity of rapid prototyping tools for advanced methods and the limited reproducibility and reusability of advanced MPC controllers and their results. We find that the FAIR principles (findable, accessible, interoperable, reusable) for scientific data-management and research software can play an important role in tackling these obstacles. Following these guidelines, we discuss FAIR solutions and present the open-source software do-mpc as a concrete implementation. The presented solutions include interoperability with neural network toolboxes to simplify nonlinear system identification, interoperability with the OPC UA communication protocol for deployment, and a reproducible data-sampling framework for transparent controller validation, system identification and approximate MPC. The potential of the proposed solutions is illustrated with several simulation studies.

Efficiently Solving the Harmonic Model Predictive Control Formulation

Harmonic model predictive control (HMPC) is a model predictive control (MPC) formulation which displays several benefits over other MPC formulations, especially when using a small prediction horizon. These benefits, however, come at the expense of an optimization problem that is no longer the typical quadratic programming problem derived from most linear MPC formulations due to the inclusion of a particular class of second order cone constraints. This article presents a method for efficiently dealing with these constraints in operator splitting methods, leading to a computation time for solving HMPC in line with state of the art solvers for linear MPC. We show how to apply this result to the alternating direction method of multipliers algorithm, presenting a solver which we compare against other solvers from the literature, including solvers for other linear MPC formulations. The results show that the proposed solver, and by extension the HMPC formulation, is suitable for its implementation in embedded systems.

Linear and nonlinear Model Predictive Control (MPC) for regulating pedestrian flows with discrete speed instructions

Linear and nonlinear Model Predictive Control (MPC) for regulating pedestrian flows with discrete speed instructions

Model prediction controller for penetration mechanism of seabed cone penetration test system

The system of seabed Cone Penetration Test (CPT) is a kind of equipment for offshore investigations. Seabed CPT is used to assess multiple physical properties of marine sediments. Constant-rate penetration mechanism is the core part of seabed CPT, which adopts dual-cylinder drive to penetrate the probe rod into the seafloor sediments at a constant speed (2cm/s). At present, the domestic CPT and its penetration equipment almost all rely on imports. In the process of system design, we found that the traditional PID control of the hydraulic cylinder position control accuracy is low, so we need to study higher precision position tracking control method to achieve uniform penetration of the probe rod. In this paper, a Linear Time-Varying Model Predictive Controller (LTV-MPC) is introduced, which can control two hydraulic cylinders to penetrate probe rod into the seabed sediment with smaller penetration rate error under the condition of changing penetration resistance.

Heat exchanger networks: A predictive control approach

This work demonstrates the development of a practical predictive control approach to regulate the outputs of a network of heat exchangers. The full nonlinear continuous-time dynamic of the network is introduced to simulate the real process. Whereas a discrete linear and simpler version of this dynamic is employed to construct the predictive controller as well as an extended Kalman estimator. The presented algorithm is a time-varying model predictive control (MPC) where the simplified model is successively linearized on-line around the current available measurements. For the closed-stability of the introduced MPC scheme, a modified method is suggested to design terminal stabilizing weights where reference tracking problem, external disturbance dynamics, as well as the proper dynamics of a heat exchanger with bypass are all considered. The on-line updated extended Kalman estimator is utilized to estimate both the process states and unknown disturbances. Thanks to the successive linearization technique, the introduced predictive controller benefits from efficient online computations and online adaptations in operation points. Nonetheless, an accurate model of the heat exchanger is essential. Compared with a typical linear MPC, it is concluded that the presented predictive algorithm produces satisfactory results for disturbance rejection and switched operation points circumstances.

Closed-Loop Stability of a Non-Minimum Phase Quadruple Tank System Using a Nonlinear Model Predictive Controller with EKF

The dynamics of a quadruple tank system (QTS) represent an extensive class of multivariate nonlinear uncertain systems found in the industry. It has been established that changes in split fractions affect the transmission zero location, thereby altering the operating conditions between the minimum and non-minimum phase regions. The latter is difficult to control as more fluid flows into the two upper tanks than into the two bottom tanks, resulting in competing effects between the initial and final system responses. This attribute, alongside nonlinearity, uncertainties, constraints, and a multivariate nature, can degrade closed-loop system performance, leading to instability. In this study, we addressed the aforementioned challenges by designing controllers for the regulation of the water flow in the two bottom tanks of the QTS. For comparative analysis, three controller algorithms—a nonlinear model predictive controller (NMPC), NMPC augmented with an extended Kalman filter (i.e., NMPC-EKF) and linear model predictive controller (LMPC)—were considered in the analysis and design of the control mechanism for the quadruple water level system in a non-minimum phase condition via the Matrix Laboratory (MATLAB) simulation package environment. The simulated and real-time results in the closed loop were analyzed, and the controller performances were considered based on faster setpoint responses, less oscillation, settling time, overshoot, and smaller integral absolute error (IAE) and integral square error (ISE) under various operational conditions. The study showed that the NMPC, when augmented with an EKF, is effective for the control of a QTS in the non-minimum phase and could be designed for more complex, nonlinear, and multivariable dynamics systems, even in the presence of constraints.

L1 Adaptive Control for Marine Structures

Nowadays, many maritime structures require precise dynamic positioning (DP) of the constructive elements that compose them. In addition, the use of preconstructed elements that are later moved to the final location has become widespread. These operations have not been automated with the risks involved in carrying out the complex operations required. To minimize these operational risks and to perform a correct DP of floating structures, a new approach based on the L1 adaptive control technique is proposed. As an example of application, a proposed L1 adaptive controller was implemented in the dynamic positioning of a floating caisson. Several simulations of the system with wave disturbances were carried out, and the results were compared with those obtained by applying other classical and advanced control techniques, such as linear quadratic Gaussian control (LQG) and model predictive control (MPC). It was concluded that the proposed L1 adaptive controller performs correct dynamic positioning and reduces the tension generated on the lines concerning the other advanced control techniques with which it was compared. This reduction in line tension leads to an important improvement due to the possibility of reducing the size of the actuators or reducing their number, with the important economic and safety repercussions that these actions entail.

Deep learning-based model predictive control for real-time supply chain optimization

This paper presents a deep learning-based model predictive control (MPC) method for operational supply chain optimization in real time. The method follows an offline-online procedure. In the offline phase, the state-space model of a supply chain system is developed and the MPC problem for supply chain operation is formulated. Then, the MPC problem is solved for a set of initial states to obtain the corresponding optimal inputs. A deep neural network (DNN) is built and trained by using the optimal state-input pairs as training data to approximate the optimal MPC law. In the online phase, the DNN controller is employed to provide real-time decisions. In this paper, the MPC problem for supply chain operation is formulated as a mixed-integer linear program. A deep learning-based MPC method is proposed to accommodate time delays in the system. Moreover, a heuristic method is proposed for feasibility recovery with the binary decision variables taken into account. The training set for the DNN controller contains two subsets, one formed from MPC solutions corresponding to random initial states, and the other formed from optimal state-input pairs in closed-loop simulations. The deep learning-based MPC is validated via two case studies through closed-loop simulation. The first case study involves a linear MPC, and the second case study involves a more complicated mixed-integer linear MPC. Results show that deep learning-based MPC can achieve a high accuracy in approximating the MPC decisions and a significant reduction in the online computation time. Compared with MPC, the average performance loss of using deep learning-based MPC in the two cases is 0.43% and 1.8%, respectively.

Model Predictive Control With Wind Preview for Aircraft Forced Landing

Autonomous emergency landing capability of fixed-wing aircraft is essential for opening airspace for civil unmanned aviation. This paper proposes a goal-oriented control scheme to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">exploit</i> wind information for the benefit of forced landing. Different from general disturbances in a classic control system, a favorable wind would help aircraft to glide to a selected landing site more easily so increase the level of safety, while an adverse wind may render a selected landing site infeasible. We formulate the forced landing problem with wind preview information in the framework of Economic Model Predictive Control (EMPC) which aims to maximize the aircraft's final altitude when reaching a target region. A double-layer MPC scheme is adopted to lessen the computational burden and to increase the prediction time window for practical implementation, where a piecewise-constant disturbance preview based EMPC (DP-EMPC) maximizes the altitude at the upper-level, and a linear MPC is employed at the lower-level to track the reference signal optimized by the upper-level planner. Moreover, the effectiveness of the goal-oriented optimal control scheme is illustrated by several case studies, where an unmanned aircraft is gliding towards potential landing sites under various conditions.

A Terminal Set Feasibility Governor for Linear Model Predictive Control

The Feasibility Governor (FG) is an add-on unit for Model Predictive Controllers (MPC) that increases the closed-loop region of attraction by manipulating the applied reference to ensure the underlying optimal control problem is always feasible. The FG requires an estimate of the feasible set of the optimal control problem that underlies the MPC; obtaining this estimate can be computationally intractable for high-dimensional systems. This paper proposes a modified FG that bypasses the need for an explicit estimate, instead relying entirely on the MPC terminal set. The proposed FG formulation is proven to be asymptotically stable, exhibits zero-offset tracking, satisfies constraints, and achieves finite-time convergence of the reference. Numerical comparisons featuring an MPC with a long prediction horizon show that the FG+MPC system can achieve comparable closed-loop performance to long-horizon MPC at a significantly reduced computational cost by suitably detuning the terminal controller to enlarge the terminal set.

Cautious Bayesian MPC: Regret Analysis and Bounds on the Number of Unsafe Learning Episodes

This paper investigates the combination of model predictive control (MPC) concepts and posterior sampling techniques and proposes a simple constraint tightening technique to introduce cautiousness during explorative learning episodes. The provided theoretical analysis in terms of cumulative regret focuses on previously stated sufficient conditions of the resulting ‘Cautious Bayesian MPC’ algorithm and shows Lipschitz continuity of the future reward function in the case of linear MPC problems. In the case of nonlinear MPC problems, it is shown that commonly required assumptions for nonlinear MPC optimization techniques provide sufficient criteria for model-based RL using posterior sampling. Furthermore, it is shown that the proposed constraint tightening implies a bound on the expected number of unsafe learning episodes in the linear and nonlinear case using a soft-constrained MPC formulation. The efficiency of the method is illustrated using numerical examples.

Multiple-Input-Single-Output prediction models of crowd dynamics for Model Predictive Control (MPC) of crowd evacuations

Predicting crowd dynamics in real-time may allow the design of adaptive pedestrian flow control mechanisms that prioritize attendees’ safety and overall experience. Single-Input-Single-Output (SISO) AutoRegresive eXogenous (ARX) prediction models of crowd dynamics have been effectively used in Linear Model Predictive Controllers (MPC) that adaptively regulate the movement of people to avoid overcrowding. However, an open research question is whether Multiple-Input, State-space, and Nonlinear modeling approaches may improve MPC control performance through better prediction capabilities. This paper considers a simulated controlled evacuation scenario, where evacuees in a long corridor dynamically receive speed instructions to modulate congestion at the exits. We aim to investigate Multiple-Input-Single-Output (MISO) prediction models such that the inputs are the control action (speed recommendation) and pedestrian flow measurement, and the output is the local density of the pedestrian outflow. State-space and Input–output MISO models, linear and neural, are identified using a data-driven approach in which input–output datasets are generated from strategically designed microscopic evacuation simulations. Different estimation algorithms, including the subspace method, prediction error minimization, and regularized AutoRegressive eXogenous (ARX) model reduction, are evaluated and compared. Finally, to investigate the importance of measuring and modeling the pedestrian inflow, the case in which the models’ structure is defined as a Single-Input-Single-Output (SISO) system has been explored, where the pedestrian inflow is considered an unmeasured input disturbance. This study has important implications for the design of more effective MPC controllers for regulating pedestrian flows. We found that the prediction error minimization algorithm performs best and that nonlinear state-space modeling does not improve prediction performance. The study suggests that modeling the inner state of the evacuation process through a state-space model positively influences predicting system dynamics. Also, modeling pedestrian inflow improves prediction performance from a predefined prediction horizon value. Overall, linear state-space models have been deemed the most suitable option in corridor-type scenarios.

Controlled synchronization of coupled pendulums by Koopman Model Predictive Control

We propose a method to solve a class of control problems arising from a system of coupled pendulums. The system considered in this work is a one-dimensional array of pendulums pivoting around a single axis with adjacent pendulums coupled through torsion springs. Only a single torque motor attached to one of the two boundary pendulums actuates the system. This setup of coupled pendulums is a mechanical realization of the Frenkel–Kontorova (FK) model – a spatially discrete version of the sine-Gordon equation describing (nonlinear) waves. The main challenges of controlling this system are high order (the number of pendulums can be high), nonlinear and oscillatory dynamics, and only one actuator. The proposed class of problems can be characterized as controlled synchronization – designing a closed-loop controller that synchronizes the motion of the pendulums. Controlled synchronization is a special case of reference tracking, where all pendulums reach a common point or a trajectory. One can formulate many practically motivated problems within this class; here, we identify three problems: a vibration control of a flexible structure, swing-up control of all pendulums in the array, and low-friction sliding of an atomic-scale structure. We show that the presented problems can be dealt with by the Koopman Model Predictive Control (KMPC). The KMPC allows for controlling nonlinear systems by combining the classical linear model predictive control (MPC) with the Koopman operator approach for nonlinear dynamical systems. The main idea of the method is to construct a linear predictor of a nonlinear system in a higher-dimensional, lifted space and use the predictor within the linear MPC. The optimization problem formulation within the KMPC can then be tailored to a specific problem in the class. Simulations and experiments on a hardware platform realizing the FK model show the effectiveness of the method.

Linear Model Predictive Control of Olefin Metathesis Process

The applicability of linear model predictive control to the 2-butene metathesis process is studied. Similarly to industrial practice, the model predictive controller is configured on a supervisory level, providing set points to basic process controllers. The development of the process model is based on open-loop identification from input–output data extracted from dynamic simulation performed in Aspen Plus Dynamics. The model predictive controller, designed using MATLAB tools, supervises a system consisting of two inputs (feed rate and reaction temperature) and two outputs (ethylene and propylene production rates). The performance of the model-based control strategy is assessed by Aspen Plus Dynamics-Simulink co-simulation and compared to regulatory control through several indexes (mean square error, integral square error, peak error, and integral absolute error). The model predictive controller outperforms the feedback controller. Considerations regarding the workflow for the implementation of model predictive control in an industrial environment are provided.

Tractable robust MPC for tracking piecewise constant references based on nominal predictions

This paper proposes two tractable linear MPC strategies for robust piecewise constant reference tracking in the presence of bounded disturbances. The definition of the stabilizing ingredients are simplified so that the offline computational burden of the robust MPC for tracking becomes similar to the non-robust MPC version. An implicit characterization of the Maximal Robust Positively Invariant (MRPI) set for tracking is used in the first robust MPC algorithm. Alternatively, a terminal equilibrium constraint with a slack variable is proposed to provide a further terminal set simplification in the second MPC approach. It is shown that recursive feasibility and Input-to-State Stability are preserved despite the proposed simplifications. A numerical case study that simulates a multivariable chemical process and a double integrator benchmark problem are presented to illustrate the offset-free tracking properties of the proposed approaches.

A feedback linearization approach for coordinated traffic flow management in highway systems

In this paper, a control solution to reduce congestion in highway traffic systems is presented. The aim is to produce a control strategy characterized by low computational cost, so that real-time implementation can be attained. The adopted model to describe traffic dynamics is the METANET model. A particular spatio-temporal derivative relationship, describing how control signals (ramp metering and variable speed limits) and disturbances effects propagate along the highway system, is highlighted in the paper. This relationship is the basis of a proposition providing the essential tool for relative degree calculation in generic highway systems. Utilizing this proposition, a feedback linearization-based control law is developed. The control design is completed by employing a linear MPC, which allows for complying with the physical constraints. The performance of the proposed method is evaluated by conducting comprehensive simulation studies, also considering a real-world traffic system. The computational costs are analyzed by comparing the developed methodology with a nonlinear MPC-based approach. Simulation evidence confirms that the proposed method can provide satisfactory solutions for coordinating RM and VSL in highway systems. Such solutions are compatible with real-time implementation.

Evaluation of two model predictive control schemes with different error compensation strategies for power management in fuel cell hybrid electric buses

Fuel cell hybrid electric buses (FCHEBs) employing hydrogen fuel cells as the main power source and supercapacitors as the energy buffer could be a feasible electrified transportation technology. This paper evaluates two model predictive control (MPC) schemes with different error compensation strategies for power management in FCHEBs: MPC scheme with Adaptive Compensation (denoted as AC-MPC) and MPC scheme with Gaussian Process Regression Compensation (denoted as GPRC-MPC). AC-MPC introduces adaptive weights based on the supercapacitor state of charge (SOC) and compensates for the errors associated with the linearization of the nonlinear fuel cell/supercapacitor hybrid energy storage system. GPRC-MPC utilizes Gaussian process regression to predict and compensate for the load disturbance error and the residual error. AC-MPC and GPRC-MPC are evaluated using the New York Bus (NYBus) drive cycle and a drive cycle collected along the GBG17 bus route in Sweden. Simulation results demonstrate the effectiveness of AC-MPC and GPRC-MPC in improving the hydrogen system performance by reducing the hydrogen consumption and the maximum fuel cell current change rate compared to the linear MPC scheme without any compensation while ensuring that the supercapacitor SOC is bounded.

Modelling and Control Tank Testing Validation for Attenuator Type Wave Energy Converter - Part I: Experiment Setup and Control-Oriented Modelling

Advanced non-causal optimal control strategies have been demonstrated to significantly improve the energy output of a scale physical model of an attenuator type wave energy converter (WEC) by tank testing experiments using FloWave tank facilities in Edinburgh supported by Wave Energy Scotland's control project. The results are reported in a series of three papers, summarizing the tank testing setup, dynamic modelling, and validation of both linear non-causal optimal control (LNOC) and model predictive control (MPC) in regular and irregular waves. Compared with an optimally tuned passive damping control, both LNOC and MPC can significantly improve the energy output, by between 10% to 460%, using irregular waves with low to medium magnitude and peak periods ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1.7~\mathrm{s}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2.8~\mathrm{s}$</tex-math></inline-formula> at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1/20^{th}$</tex-math></inline-formula> scale, as shown in Part II and Part III papers. These controllers also show robust performance in spread waves and side waves which are normally encountered in real sea conditions. Furthermore, the control technologies can be transferred to other types of WECs. The results pave the way for the sea trial testing and full control system validation involving the electricity generation stage and power conditioning stage. This Part I paper will focus on the tank testing setup, the passive damping control experimental results, and the control-oriented models for the WEC. Two state-space models derived respectively from the hydrodynamic model and system identification of experimental data, are validated and compared for use on the controller designs to be presented in Part II and Part III.

Observer-Based Approximate Affine Nonlinear Model Predictive Controller for Hydraulic Robotic Excavators with Constraints

Given the highly nonlinear and strongly constrained nature of the electro-hydraulic system, we proposed an observer-based approximate nonlinear model predictive controller (ANMPC) for the trajectory tracking control of robotic excavators. A nonlinear non-affine state space equation with identified parameters is employed to describe the dynamics of the electro-hydraulic system. Then, to mitigate the plant-model mismatch caused by the first-order linearization, an approximate affine nonlinear state space model is utilized to represent the explicit relationship between the output and input and an ANMPC is designed based on the approximate nonlinear model. Meanwhile, the Extended Kalman Filter was introduced for state observation to deal with the unmeasurable velocity information and heavy measurement noises. Comparative experiments are conducted on a 1.7-ton hydraulic robotic excavator, where ANMPC and linear model predictive control are used to track a typical excavation trajectory. The experimental results provide evidence of convincing trajectory tracking performance.