Proposed Model Predictive Control Strategy Research Articles

Dynamic safety control of offshore wind turbine based on model predictive control

Offshore wind power is a clean energy source with excellent development prospects that are conducive to realising China's goal of carbon neutrality. However, offshore wind turbines (WTs) are prone to failure and damage owing to their long-term operation in marine environments with high humidity, high wind speeds, and frequent extreme weather. To ensure the safe operation of offshore WTs, a modified dynamic model predictive control (MPC) method was proposed in this study. First, a dynamic model of an offshore WT was established and its nonlinear state-space equations were obtained. These state-space equations were subsequently linearised and discretised, then fast trajectory tracking of the state variables was performed according to the conventional MPC principle. Finally, a control strategy was designed to realise the safe operational control of offshore WT using the safety index as a constraint condition in the MPC. Simulation results confirmed that the proposed MPC strategy using the safety index-based constraint exhibited superior tracking of the set trajectory and achieved the minimum energy loss under varying wind speeds.

Model Predictive Control in buildings with thermal and visual comfort constraints

Model Predictive Control can cope with conflicting control objectives in building energy managements. In terms of user satisfaction, visual comfort has been proven in several studies to be a crucial factor, however thermal comfort is typically considered the only important aspect. Besides human well-being, visual comfort strongly impacts the productivity of the occupants in offices. Therefore, from an economic point of view, it is essential to include visual comfort in Model Predictive Control for buildings. In this paper semi-linear support vector machine is applied to learn suitable models for visual comfort measured by Daylight Glare Probability. The resulting model is incorporated into a Model Predictive Control framework, together with an autoregressive exogenous model accounting for the thermal dynamics of the building. The approach is validated through an extensive numerical case study, and the benefits of including visual comfort and blind control in the Model Predictive Control problem are evaluated. We observe that the proposed Model Predictive Control scheme ensures both the thermal and visual comfort constraints at the expense of 2.2% to 7.2% higher energy consumption compared to the benchmark Model Predictive Control configuration, which considers only the thermal comfort constraints.

Model predictive control of an electrically-heated steam methane reformer

Steam methane reforming (SMR) is one of the most widely used hydrogen (H2) production processes. In addition to its extensive utilization in industrial sectors, hydrogen is expanding it share as a clean energy carrier, and more sustainable and efficient H2 production methods are continuously being explored and developed. One method replaces conventional fossil fuel-based heating with electrical heating through the flow of electrons across the reformer. At UCLA, an experimental setup was built of an electrically heated steam methane reforming process. This paper describes the system components, explains the digitalization of the experimental setup and introduces methods for building a first-principles-based dynamic process model using parameters estimated via data-driven methods from process experimental data. The modeling approach uses a lumped parameter approximation and employs algebraic equations to solve for gas-phase variables. The reaction parameters are calculated from steady-state experimental data, and the temperature change is modeled with respect to change in electric current using a first-order dynamic model. The overall dynamic process model is then used in a computational model predictive control (MPC) scheme to drive the process to a new H2 production set-point under unperturbed and steam flowrate disturbance cases. The performance and robustness of the proposed MPC scheme are compared to the ones of a classical proportional–integral (PI) controller and are demonstrated to be superior in terms of closed-loop response, robustness, and constraint handling.

Model Predictive Control for Automatic Transmission Upshift Inertia Phase

This article deals with model predictive control (MPC) design for automatic transmission (AT) upshift inertia phase, which aims to optimally coordinate the actions of oncoming (ONC) and off-going (OFG) clutches and engine and to facilitate calibration. The designed MPC strategy accounts for clutch actuation dynamics and constraints, while setting the tradeoff between three key and conflicting shift quality criteria: comfort; duration; and efficiency. The shift comfort and duration are ensured by minimizing output shaft torque and ONC clutch slip speed tracking errors, and the shift efficiency is reflected in clutch energy loss minimization on a prediction horizon. This allows for the calibration of the MPC performance through setting the inertia phase duration, the output shaft torque reference, cost function weighting coefficients, and constraints, rather than optimizing the shift control profiles themselves. The MPC problem is formulated as a constrained quadratic programming problem and efficiently solved online by an interior-point solver. The proposed MPC strategy is applicable to other transmissions with multiple actuators, such as parallel hybrid transmissions. The MPC system is examined through nonlinear powertrain model simulations for one to three shift and its performance is compared with an offline, multiobjective optimization-based control strategy. The MPC design flexibility and ease of calibration are demonstrated for different shift comfort and duration targets, as well as cost function tuning, and robustness with respect to clutch actuation parameter uncertainties is examined.

Risk-averse receding horizon motion planning for obstacle avoidance using coherent risk measures

This paper studies the problem of risk-averse receding horizon motion planning for agents with uncertain dynamics, in the presence of stochastic, dynamic obstacles. We propose a model predictive control (MPC) scheme that formulates the obstacle avoidance constraint using coherent risk measures. To handle disturbances, or process noise, in the state dynamics, the state constraints are tightened in a risk-aware manner to provide a disturbance feedback policy. We also propose a waypoint following algorithm that uses the proposed MPC scheme for discrete distributions and prove its risk-sensitive recursive feasibility while guaranteeing finite-time task completion. We further investigate some commonly used coherent risk metrics, namely, conditional value-at-risk (CVaR), entropic value-at-risk (EVaR), and g-entropic risk measures, and propose a tractable incorporation within MPC. We illustrate our framework via simulation studies.

Dynamic output-feedback model predictive control for polytopic uncertain systems with amplify-and-forward relays

In this paper, the dynamic output-feedback model predictive control (MPC) problem is investigated for systems with polytopic uncertainties and amplify-and-forward (AF) relays, where the signal transmission with random power is adopted to facilitate the remote transmission with the limited transmission capacity of sensors. With respect to the parameter uncertainties of the system and the randomness of AF relays, a new objective function is constructed, which is defined by the mathematical expectation of the conventional quadratic function over the infinite time horizon. Then, the singular value decomposition technique is applied to handle the inherent couplings of variables to formulate a solvable optimization problem. Furthermore, sufficient conditions are provided to guarantee the recursive feasibility of the proposed MPC algorithm, meanwhile the underlying system can be stabilized in the mean-square sense by the designed controllers. Finally, two simulation examples are used to show the effectiveness of the proposed MPC strategy.

Machine learning-based predictive control using on-line model linearization: Application to an experimental electrochemical reactor

The electrochemical reaction-based process, a new type of chemical process that can generate valuable products using renewable electricity, is a sustainable alternative to the traditional chemical manufacturing processes. One promising research area of electrochemical reaction processing is to reduce carbon dioxide (CO2) into carbon-based products, which can contribute to closing the carbon cycle if CO2 is directly captured from the atmosphere. In this work, we demonstrate a model predictive control (MPC) scheme that uses a neural network (NN) model as the process model to implement real-time multi-input-multi-output (MIMO) control in an electrochemical reactor for CO2 reduction. Specifically, a long short-term memory network (LSTM) model is developed using historical experimental data of the electrochemical reactor to capture the nonlinear input-output relationship as an alternative to the complex, first principles-based model. Furthermore, the Koopman operator method is used to linearize the LSTM model to reduce the nonlinear optimization step in the MPC to a well-understood and easy-to-solve quadratic programming (QP) problem. The performance of the LSTM model, Koopman-based optimization, and MPC using the linearization of the LSTM model are evaluated with various simulations as well as open-loop and closed-loop experiments. As the results, the proposed MPC scheme can drive the two output states, that are concentrations of the products (C2H4 and CO), to their desired setpoints by computing optimal input variables (surface potential and electrode rotation speed) in real-time in closed-loop experiments. Furthermore, a transfer learning-based method is utilized to update the NN model to handle process variability.

An integrated thermal management strategy for cabin and battery heating in range-extended electric vehicles under low-temperature conditions

The integrated thermal management strategy under low-temperature conditions can effectively alleviate mileage anxiety associated with electric vehicles and improve the thermal comfort of the cabin. In this study, an integrated thermal management topology for range-extended electric vehicles is proposed, which recovers the waste heat from the range extender and the electric drive system for the heating of the battery and the cabin to improve energy utilization. Considering the driving modes and heating demands, the working modes and switching rules are designed. Especially, a control-oriented coupling system model is established for pure-electric mode. Taking cabin heat load demand, battery heat generation, and electric drive system heat generation as disturbances, a model predictive controller is designed for the heating power of the heater. An integrated thermal management system model verified by experiments is established in AMEsim. The initial temperature of the environment and vehicle is −20 °C, and the target temperatures of the cabin and the battery are set at 20 °C and 25 °C respectively. The feasibility of the strategy is verified by the co-simulation of Simulink and AMEsim under 4 WLTC cycles. The results show that in the range-extended mode, the integrated system shortens the battery heating time and reduces fuel consumption by more than 10.2 % compared with the independent system. In pure-electric mode, the heating speed of the proposed model predictive control strategy is slightly faster than that of the on–off strategy, the heating energy consumption is reduced by 20.95 %, and the total energy consumption for propulsion and thermal management decreased by 2.84 %.

Model Predictive Control of Parabolic PDE Systems under Chance Constraints

Model predictive control (MPC) heavily relies on the accuracy of the system model. Nevertheless, process models naturally contain random parameters. To derive a reliable solution, it is necessary to design a stochastic MPC. This work studies the chance constrained MPC of systems described by parabolic partial differential equations (PDEs) with random parameters. Inequality constraints on time- and space-dependent state variables are defined in terms of chance constraints. Using a discretization scheme, the resulting high-dimensional chance constrained optimization problem is solved by our recently developed inner–outer approximation which renders the problem computationally amenable. The proposed MPC scheme automatically generates probability tubes significantly simplifying the derivation of feasible solutions. We demonstrate the viability and versatility of the approach through a case study of tumor hyperthermia cancer treatment control, where the randomness arises from the thermal conductivity coefficient characterizing heat flux in human tissue.

Error-Summation Enhanced Newton Algorithm for Model Predictive Control of Redundant Manipulators

Redundant manipulators have been investigated and employed in various fields, and its trajectory tracking is of much importance in the field of robotic control. In this article, a model predictive control (MPC) scheme for the trajectory tracking of redundant manipulators is constructed, which minimizes the tracking error, velocity norm, and acceleration norm simultaneously. The commonly used trajectory tracking schemes for redundant manipulators, such as the minimum-velocity-norm scheme and minimum-acceleration-norm scheme, handle joint limits at different levels by introducing additional parameters, which reduces the feasible region of decision variables. In contrast, the proposed scheme directly considers these limits at three different levels, without reducing the feasible region of decision variables. In addition, to compensate for the deficiencies of most existing algorithms in noise environments, an error-summation enhanced Newton (ESEN) algorithm is proposed for solving the MPC scheme. Through theoretical analysis, it is determined that the proposed ESEN algorithm has a small steady-state error under noise conditions. Finally, in contrast with the comparative trajectory tracking schemes, as determined through computer simulations and experiments, the proposed MPC scheme solved by the ESEN algorithm not only enables the redundant manipulator to perform the trajectory tracking task in excellent fashion, but also offers advantages of high efficiency, fast responsiveness, and strong noise tolerance.

Prior-knowledge-embedded model predictive control for blood glucose regulation: Towards efficient and safe artificial pancreas

Objective:The artificial pancreas (AP) system based on model predictive control (MPC) has the potential to provide effective and reliable regulation of blood glucose concentration (BGC) for people with type 1 diabetes by utilizing glucose prediction models and appropriate safety constraints. Methods:In this work, a MPC strategy with novel model and safety constraints is proposed for BGC regularization. A prior-knowledge-embedded glucose prediction model based on kernel-regularized latent variables (LV) regression method is developed where the prediction power of the model is improved by integrating the prior knowledge of glycemic dynamics and balancing model complexity and flexibility by tuning the hyper-parameters of the kernel. Based on the prior-knowledge-embedded model, MPC strategy is formulated and BGC constraints that are not dependent on the announcement of meals and physical activity are proposed and incorporated into the MPC to reduce the risk of hypoglycemia. The benefits of the proposed model and MPC approach were evaluated through in-silico studies. Results:The proposed model achieves comparable or improved prediction accuracy with a root mean squared error of 14.08 mg/dL, 18.47 mg/dL, and 21.23 mg/dL for 30-min, 60-min, and 120-min-ahead prediction, respectively. And simulation results showed significant improvement in the time in the safe range (70–180 mg/dL) from 58.04% to 71.27% and from 78.81% to 82.31% without causing hypoglycemia. Conclusions:The proposed MPC strategy can provide safe and effective regulation of BGC without requiring manual announcements of meals and physical activity. Significance:This work is a step forward towards a fully-automated AP system.

Nonlinear model predictive trajectory following control with feedback compensation for autonomous four-wheel independent drive electric vehicles

Trajectory following is an important function of autonomous vehicles. To enable a four-wheel independent drive electric vehicle to precisely follow a predefined or real-time generated trajectory with good lateral stability and ride comfort at high velocity, a model predictive control (MPC) scheme with feedback compensation considering model mismatch is proposed in this paper to coordinate the direct yaw-moment control and active front steering. The system input signal computed by model predictive control is corrected by the feedback compensation to cope with the model mismatch existing between the controlled vehicle and the nominal model. Moreover, co-simulation is carried out between the software MATLAB/Simulink and Carsim to verify the proposed method. In comparison, the integration of the direct yaw-moment control and active front steering through model predictive control can overcome the non-smooth problem of vehicle dynamics while implementing the active front steering only. However, the value of the external yaw moment computed by the model predictive controller might be too large due to the predictive error in extreme situations, which could endanger the vehicle. The results reveal that the proposed model predictive control scheme with feedback compensation can effectively compensate the front steering angle and enhance the control effect. Therefore, it can significantly improve the trajectory following accuracy and yaw stability.

Tracking of Uncertain Robotic Manipulators Using Event-Triggered Model Predictive Control With Learning Terminal Cost

This paper presents an event-triggered model predictive control (MPC) strategy with learning terminal cost for robotic manipulators containing model uncertainty and input constraints. In the proposed MPC structure, an adaptive predictive model for the robotic system is established by radial basis function neural networks (RBFNNs) firstly. Then, a terminal cost adjusted by the global learning mechanism is constructed. Both global steady-state optimization and transient fast convergence are achieved by adding the learning terminal cost to the MPC scheme. After that, a triggering condition of the MPC solving is developed based on the predictive model’s weights and the predictive tracking error. Besides, the condition to avoid Zeno behavior is obtained. The recursive feasibility of the proposed MPC strategy is verified, and the ultimately uniformly boundedness (UUB) of all variables is proved according to the Lyapunov theorem. Finally, experiments based on an xMate7 Pro robot are conducted to demonstrate the effectiveness of the presented method. Note to Practitioners—The tracking control of robotic manipulators is a common and important problem in industrial applications, such as grasping, loading, unloading, et al. There exist some limitations in existing control methods. For example, general control strategies such as adaptive control, sliding mode control neglect the balance between control costs and expected performance; existing optimal control approaches rarely consider global steady-state optimization and transient fast convergence under the influence of model uncertainty. This paper is motivated by these limitations of robotic control design and inspired by model predictive control and optimal control theory. It develops a novel strategy for tracking control of robotic manipulators, which includes three following items: (1) adopt an approximation model constructed by neural networks as the predictive model for estimating the robotic system; (2) introduce a critic network into the terminal cost of the objective function of MPC for learning global optimal solution; (3) establish an event-triggered mechanism for solving of the optimization problem. The proposed method is verified by experimental results. In our future work, the proposed control strategy will be applied to more industrial processes.

Linear Tracking MPC for Nonlinear Systems—Part I: The Model-Based Case

We develop a tracking model predictive control (MPC) scheme for nonlinear systems using the linearized dynamics at the current state as a prediction model. Under reasonable assumptions on the linearized dynamics, we prove that the proposed MPC scheme exponentially stabilizes the optimal reachable equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on the fact that, close to the steady-state manifold, the prediction error of the linearization is small and hence, we can slide along the steady-state manifold towards the optimal reachable equilibrium. The closed-loop stability properties mainly depend on a cost matrix which allows us to trade off performance, robustness, and the size of the region of attraction. In an application to a nonlinear continuous stirred tank reactor, we show that the scheme, which only requires solving a convex quadratic program online, has comparable performance to a nonlinear MPC scheme while being computationally significantly more efficient. Further, our results provide the basis for controlling nonlinear systems based on data-dependent linear prediction models, which we explore in our companion paper.

From Walking to Running: 3D Humanoid Gait Generation via MPC.

We present a real time algorithm for humanoid 3D walking and/or running based on a Model Predictive Control (MPC) approach. The objective is to generate a stable gait that replicates a footstep plan as closely as possible, that is, a sequence of candidate footstep positions and orientations with associated timings. For each footstep, the plan also specifies an associated reference height for the Center of Mass (CoM) and whether the robot should reach the footstep by walking or running. The scheme makes use of the Variable-Height Inverted Pendulum (VH-IP) as a prediction model, generating in real time both a CoM trajectory and adapted footsteps. The VH-IP model relates the position of the CoM to that of the Zero Moment Point (ZMP); to avoid falling, the ZMP must be inside a properly defined support region (a 3D extension of the 2D support polygon) whenever the robot is in contact with the ground. The nonlinearity of the VH-IP is handled by splitting the gait generation into two consecutive stages, both requiring to solve a quadratic program. Thanks to a particular triangular structure of the VH-IP dynamics, the first stage deals with the vertical dynamics using the Ground Reaction Force (GRF) as a decision variable. Using the prediction given by the first stage, the horizontal dynamics become linear time-varying. During the flight phases, the VH-IP collapses to a free-falling mass model. The proposed formulation incorporates constraints in order to maintain physically meaningful values of the GRF, keep the ZMP in the support region during contact phases, and ensure that the adapted footsteps are kinematically realizable. Most importantly, a stability constraint is enforced on the time-varying horizontal dynamics to guarantee a bounded evolution of the CoM with respect to the ZMP. Furthermore, we show how to extend the technique in order to perform running on tilted surfaces. We also describe a simple technique that receives input high-level velocity commands and generates a footstep plan in the form required by the proposed MPC scheme. The algorithm is validated via dynamic simulations on the full-scale humanoid robot HRP-4, as well as experiments on the small-sized robot OP3.

A Model Predictive Controlled Bidirectional Four Quadrant Flying Capacitor DC/DC Converter Applied in Energy Storage System

Energy storage system (ESS) has been widely used in photovoltaic system to ensure stable power generation. This article proposes a flying capacitor bidirectional buck–boost converter (FCBBC), aiming at making the ESS work with bidirectional four quadrant in the wide dc+bus voltage variation condition. With the symmetrical modulation strategy, the proposed FCBBC can achieve seamless switching between buck and boost mode to match the voltage changes at energy storage and dc bus side. Meanwhile, considering the ESS application requirements, a fixed frequency model predictive control (MPC) strategy based on binary search algorithm is proposed to achieve the control purpose. The decoupling relationship between flying capacitor (FC) and output voltage is derived so that the proposed MPC strategy can control the voltage of two FCs simultaneously. In addition, the adoption of binary search algorithm effectively reduces the computation load of the proposed MPC strategy. Finally, the effectiveness of the proposed converter and MPC strategy are verified with a downscaled ESS experimental platform.

An integrated model predictive control scheme with disturbance preview

This article proposes an integrated model predictive control (MPC) framework with disturbance preview information for nonlinear systems. It is assumed that the disturbance can be previewed within the prediction horizon but unknown outside the horizon. First an integrated terminal control law consisting of both feedback and feedforward is considered. Based on that, a procedure is presented to calculate the associated terminal constraints and terminal cost. A new MPC formulation is then presented with these terminal elements and it is shown that stability and recursive feasibility can be guaranteed under the proposed design using the input-to-state stability tool. Another distinctive feature of the proposed MPC scheme is that the disturbance and the reference information in the horizon is integrated in online optimization, rather than treating disturbance rejection and trajectory following separately, which makes it possible to make full use of the predictable disturbance if it is beneficial to the control task. Numerical examples show that this integrated MPC yields a larger stability region and better performance under prescribed disturbance in comparison with the existing MPC algorithms with disturbance preview.

Capacity Configuration Method of Hybrid Energy Storage Participating in AGC Based on Improved Meta-Model Optimization Algorithm

To improve the performance and economy of the hybrid energy storage system (HESS) coordinating thermal generators to participate in automatic generation control (AGC), a HESS bi-layer capacity configuration model that considers the control strategy and net benefits of HESS is proposed. In addition, an improved mode-pursuing sampling (MPS) optimization algorithm based on meta-model is presented to improve the accuracy of model solving. In the lower layer, to improve the performance of HESS participating in AGC, a model predictive control (MPC) strategy is presented to distribute HESS power reasonably. Based on this, the upper layer develops a life-cycle net benefit model of HESS participating in AGC to improve its economy. The bi-layer model realizes iterative optimization of HESS capacity and operation through parameter transmission. Furthermore, to improve the solution accuracy of the bi-layer model, the convergence speed of the MPS algorithm is improved, so that the global search and local convergence speed can be taken into account. The case study results show that the bi-layer model can comprehensively consider the interaction between the economy and operating strategy of HESS. The proposed MPC strategy has better frequency regulation performance and the improved MPS algorithm has better solution performance.

A model predictive control approach for highly automated vehicles in urban environments

AbstractIn this paper, a model predictive control (MPC) approach for the lateral and longitudinal control of a highly automated electric vehicle with all-wheel drive and dual-axis steering is presented. For the prediction of state trajectories a two-track vehicle model is used. The MPC problem for trajectory tracking is formulated by controlling the front and rear steering angle as well as the individual drive torques with respect to actuator and design constraints. Beside the steering angles, the MPC controller computes the individual drive torques to not only match the reference velocity but also to support the lateral dynamics of the vehicle using torque vectoring. The MPC problem is solved using ACADOS, a software package for efficiently solving optimal control problems. The effectiveness of the proposed MPC scheme is demonstrated via simulation.

Model predictive control for a data centre waste heat-based heat prosumer in Norway

Waste heat from a data centre (DC) is a promising heat source because of the evenly distributed load profile and intensive waste heat generation. Many studies have proven the substantial financial benefits for the district heating (DH) operators by integrating DC waste heat with DH systems. However, there is a scarcity of research focusing on the optimal control of the DH system after integrating DC waste heat to further improve the system’s economic performance. Therefore, this study aimed to further improve the economic performance of a DH system with DC waste heat by utilizing a model predictive control (MPC) scheme. This MPC scheme employed an economic-related objective function and formulated technical operational constraints. The proposed MPC scheme was tested on a campus DH system in Norway by simulation. Compared to a traditional rule-based control approach, the MPC scheme reduced the monthly energy cost by 1.8% while providing more stable chilled water for the DC cooling system.