Nonlinear Model Predictive Control Approach Research Articles

Cooperative path and trajectory planning for autonomous vehicles on roads without lanes: A laboratory experimental demonstration

Autonomous vehicles that travel without considering the lane marks and utilizing all road width have an opportunity to maximize the use of vehicles’ performance. By taking advantage of the entire width of curvy roads and the cooperative behavior of connected autonomous vehicles, new options for path planning can be implemented while utilizing the existing infrastructure. The proposed cooperative controller uses a nonlinear model predictive control (NMPC) approach for dozens of autonomous vehicles without considering lane marks. This controller maximizes vehicles’ progress on the road with minimal control efforts while complying with design constraints imposed by road geometry, distances between vehicles, and vehicle dynamics. The controller is tested in two simulation case studies. The first examines the performance under two different plant (reality) models. The second considers dozens of vehicles and compares the traffic flow characteristics between the lane-free concept and the lane-based concept within different vehicle densities. The simulation results show that the lane-free concept can improve the traffic flow performance compared with the lane-based road concept, i.e. reducing passengers’ time on the road, reducing energy consumption, and increasing road capacity. These improvements depend on the road density and track layout. In order to demonstrate the proposed controller, three laboratory experiments with several homogeneous and heterogeneous robots were conducted.

On nonlinear model predictive direct yaw moment control for trailer sway mitigation

In car–trailer combinations, the hitch angle is the relative yaw angle between towing car and trailer. The literature has shown that the inclusion of the hitch angle measurement for the feedback control of trailer oscillations can bring safety benefits, compared with conventional trailer sway mitigation algorithms based on the yaw rate of the car. Given the nonlinearity of the vehicle system in the typical conditions requiring the hitch angle control function intervention, nonlinear model-based controllers could be an effective solution. This paper presents four real-time implementable nonlinear model predictive control (NMPC) formulations, using the hitch angle measurement for the torque-vectoring (TV) control of an electric front-wheel drive car towing a trailer. The simulation results show that: (i) the active safety is enhanced by the proposed NMPC TV formulations, with respect to a benchmarking NMPC TV controller only based on the control of the towing car; (ii) the NMPC formulations that directly constrain the hitch angle error, or perform continuous hitch angle tracking, outperform those that modify the reference yaw rate or yaw rate error based on the hitch angle error; and (iii) the NMPC approaches including a dynamic model of the trailer are robust with respect to variations of trailer parameters.

Discrete‐time contraction constrained nonlinear model predictive control using graph‐based geodesic computation

AbstractModern chemical processes need to operate around time‐varying operating conditions to optimize plant economy, in response to dynamic supply chains (e.g., time‐varying specifications of product and energy costs). As such, the process control system needs to handle a wide range of operating conditions whilst optimizing system performance and ensuring stability during transitions. This article presents a reference‐flexible nonlinear model predictive control approach using contraction based constraints. Firstly, a contraction condition that ensures convergence to any feasible state trajectories or setpoints is constructed. This condition is then imposed as a constraint on the optimization problem for model predictive control with a general (typically economic) cost function, utilizing Riemannian weighted graphs and shortest path techniques. The result is a reference flexible and fast optimal controller that can trade‐off between the rate of target trajectory convergence and economic benefit (away from the desired process objective). The proposed approach is illustrated by a simulation study on a CSTR control problem.

Nonlinear Hybrid Model Predictive Control for building energy systems

This paper presents a nonlinear hybrid Model Predictive Control (MPC) approach for building energy systems based on Modelica. The MPC approach takes into account two characteristics that are very common for building energy systems: nonlinearities (inherent in the building envelope and Heating, Ventilation and Air Conditioning (HVAC) systems) and discontinuities (in the form of on/ off operation, discrete operation states and operation modes). The hybrid MPC approach integrates both continuous and discrete optimization variables into the control concept and thus is capable of controlling building energy systems with binary or integer decision variables, switching dynamics or logic if-then-else constraints. By employing a time-variant linearization approach, nonlinear Modelica optimization problems are approximated with high accuracy and transformed into a linearized state-space representation. Based on the linearization output, a linearized optimization problem is generated automatically in every MPC iteration, which is extensible by various integer characteristics and is accessible for a wide range of mixed-integer solvers. A simulation study on a nonlinear Modelica building energy system demonstrates the control quality of the proposed toolchain revealing a small linearization error and successful integration of multiple integer characteristics. The benefits of the approach are manifested by comparing its performance with different reference control strategies.

Acceleration slip regulation by electric motor torque of battery electric vehicle with nonlinear model predictive control approach

Step increase of electric motor torque results in wheel slip during the acceleration of battery electric vehicle (BEV), making vehicle body instability paramount. This is particularly challenging for regulating the torque of electric motor to keep stability in the process of acceleration, for which regulating the wheel slip to an ideal set-point is difficult for the central driving powertrain that adopts one electric motor to drive both left and right wheels by a differential. While much of the research on acceleration slip regulation has focused on solving the wheel anti-slip of internal combustion powertrain by electronic stability programme, comparatively little is known about the wheel slip control by electric motor torque of the central driving powertrain that is the most common style of driveline in the market of BEV currently. Here we discuss a series of studies on the acceleration slip regulation by electric motor torque that, collectively, design an approach of how the nonlinear model predictive controller based on a novel driving dynamics model regulates the wheel slip to an ideal set-point from the ideal slip ratio curve. Testing and validating this approach embedded into vehicle control unit are carried out in a BEV to fully realise the wheel slip control by electric motor torque during the acceleration.

Nonlinear model predictive control of USC boiler-turbine power units in flexible operations via input convex neural network

Coordinated control of an ultra-supercritical (USC) boiler-turbine unit in the flexible-operation mode is challenging because of internal nonlinearity, various unknown disturbances, and the strong-coupled multivariable behavior of the unit. A novel nonlinear model predictive control (NMPC) approach is proposed to improve the flexibility of the USC unit, which introduces an input convex neural network (ICNN) to model the dynamics of the USC unit, and then computes the optimal control decisions by solving a convex model predictive control problem. Simulations are conducted on a 1000 MW USC boiler-turbine unit. The results demonstrate that the ICNN exhibits equivalent performance to a conventional neural network in learning the system dynamics. The root mean square errors of the throttle steam pressure, the separator steam enthalpy, and the power are 0.003 MPa, 0.162 kJ/kg, and 0.513 MW, respectively. In load tracking and disturbance rejection simulations, the proposed ICNN-based NMPC outperforms the linear model predictive control and conventional neural network-based NMPC. The ICNN-based NMPC provides a fast and stable load tracking capacity at a ramp rate of 10.8% MCR/min. Moreover, the superiority of the proposed approach is further confirmed by comparison with the internal-model robust adaptive control method, which is a state-of-the-art method. The proposed approach has good potential to improve the operational flexibility of USC power units.

Efficiency-aware nonlinear model-predictive control with real-time iteration scheme for wave energy converters

ABSTRACT Several solutions have been proposed in the literature to maximise the harvested ocean energy, but only a few consider the overall efficiency of the power take-off system. The fundamental problem of incorporating the power take-off system efficiency is that it leads to a nonlinear and non-convex optimal control problem. The main disadvantage of the available solutions is that none solve the optimal control problem in real-time. This paper presents a nonlinear model predictive control (NMPC) approach based on the real-time iteration (RTI) scheme to incorporate the power take-off system's efficiency when solving the optimal control problem at each time step in a control law aimed at maximising the energy extracted. The second contribution of this paper is the derivation of a condensing algorithm for ‘output-only’ cost functions required to improve computational efficiency. Finally, the RTI-NMPC approach is tested using a scaled model of the Wavestar design, demonstrating the benefit of this new control formulation.

A Predictive Control Approach for Cooperative Transportation by Multiple Underwater Vehicle Manipulator Systems

This article addresses the problem of cooperative object transportation for multiple underwater vehicle manipulator systems (UVMSs) in a constrained workspace involving static obstacles. We propose a nonlinear model predictive control (NMPC) approach for a team of UVMSs in order to transport an object while avoiding significant constraints and limitations, such as kinematic and representation singularities, obstacles within the workspace, joint limits, and control input saturation. More precisely, by exploiting the coupled dynamics between the robots and the object and using certain load sharing coefficients, we design a predictive controller for each UVMS in order to cooperatively transport the object within the workspace’s feasible region. Moreover, the control scheme adopts load sharing among the UVMSs according to their specific payload capabilities. In addition, the feedback relies on each UVMS’s onboard measurements and no explicit data are exchanged online among the robots, thus reducing the required communication bandwidth. Finally, realistic simulation results conducted in the UwSim dynamic simulator running in robot operating system (ROS) environment as well as real-time experiments employing two small UVMSs and demonstrated the effectiveness of the proposed control strategy.

Nonpharmaceutical Stochastic Optimal Control Strategies to Mitigate the COVID-19 Spread

This article proposes a stochastic nonlinear model predictive controller to support policymakers in determining robust optimal nonpharmaceutical strategies to tackle the COVID-19 pandemic waves. First, a time-varying SIRCQTHE epidemiological model is defined to get predictions on the pandemic dynamics. A stochastic model predictive control problem is then formulated to select the necessary control actions (i.e., restrictions on the mobility for different socioeconomic categories) to minimize the socioeconomic costs. In particular, considering the uncertainty characterizing this decision-making process, we ensure that the capacity of the healthcare system is not violated in accordance with a chance constraint approach. The effectiveness of the presented method in properly supporting the definition of diversified nonpharmaceutical strategies for tackling the COVID-19 spread is tested on the network of Italian regions using real data. The proposed approach can be easily extended to cope with other countries’ characteristics and different levels of the spatial scale. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article is motivated by the emerging need for developing effective methods to support policymakers in mitigating the effects of the COVID-19 pandemic. The proposed feedback control strategy—combining a multiregion epidemiological model with a nonlinear stochastic model predictive control approach—allows the robust identification of the most effective restrictive measures considering the corresponding effects on the healthcare and socioeconomic systems. The proposed framework is a general and flexible method that can be applied to various real scenarios, leveraging mobility data, available from the Google mobility service, to recognize patterns and predict future behaviors of individuals.

Predictive hierarchical harmonic emotional neuro-cognitive control of nonlinear systems

Emotion enables biological organisms to respond quickly and reasonably to uncertain and unpredictable events. This basic survival instinct is remarkably in line with the theory of model predictive control (MPC) that predicts the future occurrences of events to determine a present appropriate action. Specifically, here we propose to resolve the basic challenge of nonlinear MPC in keeping low computational cost by using a modified computational model of the limbic brain. For this purpose, we modify the thalamus–amygdala expansion link by a harmonic function to reach a differentiable and smooth mathematical model. The proposed harmonic emotion-based neuro-cognitive network (HENN) avoids the typical hidden layers in neural networks, leading to a lower computational cost. We then extend this architecture to a hierarchical HENN (H2ENN) to reach higher modeling accuracy. Theoretical analysis proves the training algorithm’s convergence for the general case of brain emotional learning (BEL). Specifically, the learning rules are shown to converge in a finite number of iterations if a solution exists. These theoretical results are general and equally applicable to HENN and hierarchical harmonic emotional neuro-cognitive network (H2ENN). Predictive control based on H2ENN is then applied to control a 3-Prismatic-Spherical-Prismatic (3-PSP) nonlinear parallel robot manipulator and compared with the same general structure that uses a conventional neural network instead. Results indicate the proposed H2ENN-based nonlinear MPC approach offers better accuracy. At the same time, its computational cost is twenty times less than the competing method.

Improving the NOx reduction performance of an Euro VI d SCR System in real-world condition via nonlinear model predictive control

This paper deals with the possibility of improving the urea dosage control for the Selective Catalytic Reduction Systems (SCR) of an Euro VI d diesel light commercial vehicle in order to increase [Formula: see text] after-treatment reduction performance. To this aim, first, we assess the effective emissions abatement performance for the appraised diesel vehicle via real-world experimental campaign, carried out according to the Real Driving Emissions (RDE) tests on urban, extra-urban and motorway road sections in Naples, Italy. Based on these real-world data, we derive a parameterized control-oriented model for the SCR system which is, then, exploited for the designing of an alternative urea injection logic which could be able to maximize the [Formula: see text] reduction efficiency while minimizing tailpipe ammonia slip. Specifically, the optimal AdBlue injection rate is designed according to a Nonlinear Model Predictive Control Approach which allows obtaining a proper trade-off between the [Formula: see text] abatement and the urea overdosing problem. The effectiveness of the proposed controller is evaluated by comparing the performance assessed for the appraised SCR system during the experimental tests with the ones achievable if the Euro VI diesel would be equipped with the proposed control strategy. Numerical simulation discloses the effectiveness of the NMPC controller in ensuring improved [Formula: see text] reduction with performance complying with the emissions norms, main in avoiding excessive ammonia slip and in guaranteeing a reduced feed ratio w.r.t. to the standard industrial SCR controller mounted on the vehicle.

Simulating Human Upper and Lower Limb Balance Recovery Responses Using Nonlinear Model Predictive Control.

The ability to generate predictive dynamic simulations of human movement using optimal control has been a growing point of interest in the design of medical/assistive devices, e.g. robotic exoskeletons. Despite this, many disseminated simulations of whole-body tasks, such as balance recovery, neglect the role of the upper body instead focusing on postural joints, e.g. ankle, knees, hips. Thus, the purpose of the current study was to use a novel nonlinear model predictive control (NMPC) approach to assess how actuated upper limbs, as well as different individual performance (optimality) criteria, can shape simulated reactive balance recovery responses. A sagittal biomechanical model of a young adult standing was designed and actuated via nonlinear muscle torque generators (rotational single-muscle equivalents). Forward dynamic simulations of balance recovery (NMPCdriven) following an unexpected support-surface perturbation were generated for each unique combination of selected performance criteria (6 total), perturbation direction (forward and backward), and arm joints free/locked. The observed joint trajectories provide insight into the emergence of human elements of postural control from individual optimality criteria, e.g. hip-ankle strategies emerge from single-joint regulation. Quantitative analysis of performance improvements with the arms free suggest that whether arm responses emerge in the simulations may be dependent on the problem's initial guess. Future work should focus on testing further performance criteria and improving NMPC as a model of the nervous system.

Nonlinear Model Predictive Control of Mild Hybrid Powertrains With Electric Supercharging

Energy management plays a decisive role in the design of efficient 48V mild hybrid drives owing to the limited amounts of energy and power. In particular, strong nonlinearities of an electrified engine air path and the high interaction between the 48V mild hybrid powertrain and the electrical system pose a major challenge. Current research results show the fundamental potential of optimization-based energy management strategies. However there is a lack of optimization-based solutions that allow online direct control of the electrified air path and the electric motor. In this context, this study presents a nonlinear model predictive control (NMPC) approach for a 48V mild hybrid powertrain with an electric supercharger, which is able to simultaneously improve the response behavior and energy consumption. The control concept is developed on the basis of a detailed system description. The special features of optimization-based control for the degrees of freedom of the powertrain, i.e., the belt starter generator (BSG) and the electrified air path through a throttle, waste gate, and electric supercharger (eC), are addressed. After an analysis and verification of the control properties, the NMPC is evaluated in dynamic driving cycle simulations through a comparison with a state-of-the-art rule-based control strategy. The investigations show that the NMPC is able to control the system well even under transient situations with a high influence of disturbance variables. In addition, the NMPC allows a specific and fuel saving use of the 48V system while improving the driving dynamics at the same time.

Safety-Aware Nonlinear Model Predictive Control for Physical Human-Robot Interaction

This letter proposes a nonlinear model predictive control (NMPC) approach for real-time planning of point-to-point motions of serial robot manipulators that share their workspace with a human. The NMPC law solves a nonlinear program online, based on a kinematic model, and guarantees safety by constraining the robot speed within the time-varying bounds determined by the speed-and-separation-monitoring (SSM) principle. Closed-loop stability is proven in detail, and the performance (in terms of productivity) of the proposed method is tested against standard SSM schemes via experiments on a Kinova Gen3 robot.

Adaptive model predictive control design using multiple model second level adaptation for parameter estimation of two‐degree freedom of helicopter model

AbstractThis paper proposed an adaptive nonlinear model predictive control approach for a 2‐DoF helicopter model with both parametric uncertainties and input–output constraints. In the proposed control technique, the nonlinear helicopter model is linearized along the prediction horizon using a state and parameter‐dependent state‐space model. Furthermore, a linear quadratic objective function with constraints is carried out using the developed linearized model. Here, the multiple estimation model and the concept of second‐level adaptation are used to handle the parametric uncertainty of the nonlinear system. To ensure the boundedness of the estimated parameter within a predefined compact region, a projection based adaptive law is used. The adaptive tuning laws for the unknown parameters are derived by Lyapunov stability analysis. An ensemble Kalman filter has been used to observe the unavailable states of the 2‐DoF helicopter model. The effectiveness of the proposed control algorithm has been verified successfully in simulation as well as real‐time experimental setup of 2‐DoF of helicopter model and results are documented in tabular form to show superiority with an existing approach.

Nonlinear Model Predictive Control for a Simulated Reconfigurable Battery Pack

Abstract Cells within the same battery pack age unequally fast due to the non-uniform manufacturing process, and inhomogeneous operating conditions, and environment. This paper proposes a nonlinear Model Predictive Control approach for optimal pack balancing while taking pack and cell limitations into account. The control is designed for a sophisticated battery pack, which is a pack augmented by semiconductor switches to vary the number of cells connected in series. This pack is usually composed of more cells than a conventional battery pack. Each serial cell in the pack can be activated or deactivated while keeping the serial connection. Simulation results based on a realistic mission profile illustrate the effectiveness of the proposed approach by optimizing the overall performance and degradation of the battery architecture.

Modeling and temperature control of a moving substrate

Abstract This paper describes the development of a control system for an industrial heating application. In this process a moving substrate is passing through a heating zone with variable speed. Heat is applied by hot air to the substrate with the air flow rate being the manipulated variable. The aim is to control the substrate’s temperature at a specific location after passing the heating zone. First, a model is derived for a point attached to the moving substrate. This is modified to reflect the temperature of the moving substrate at the specified location. In order to regulate the temperature a nonlinear model predictive control approach is applied using an implicit Euler scheme to integrate the model and an augmented gradient based optimization approach. The performance of the controller has been validated both by simulations and experiments on the physical plant. The respective results are presented in this paper.

Advanced Coolant Temperature Control Study With Integrated Thermal Management System Valve

Abstract Objective of the vehicle thermal management system is to achieve precise coolant temperature control that ensures operation of the combustion engine in the region with the maximum thermal efficiency. In this study it is achieved by a combined effect of coolant temperature control algorithm that is operating an advanced electronic valve with one input and three outputs that balances distribution of the coolant flow between the heat source and sink components. The objective is to present an application of a nonlinear model predictive control (NMPC) approach for coolant temperature control. It is a simulation study to quantify benefits of precise coolant temperature control with the possible inclusion of preview information.

A Real-Time Nonlinear CRPE Predictive PHEV Energy Management System Design and HIL Evaluation

The explicit nonlinear model predictive control (eNMPC) approach is a challenging yet encouraging prospective to design model-based and real-time controllers for complicated automotive applications. The precision of the nonlinear control-oriented model may contribute to the superior performance of the controller but adversely affect the real-time capability and even the convergence of optimization solution involved in such an approach. To address this challenge, control-relevant parameter estimation (CRPE) is used to ameliorate the capability of the nonlinear control-oriented model to exploit the cardinal dynamics of a complex plug-in hybrid powertrain. As such, an eNMPC energy management system is developed to be implemented in to an experimental hardware with fettered memory and computational capabilities. Hardware-in-the-Loop (HIL) simulation, which is conducted on a dSPACE MicroAutoBox unit along with sophisticated high-fidelity Autonomie model shows a superior performance of the proposed control scheme for various driving scenarios while maintaining real-time capability.

Stability of Optimal Closed-Loop Cleaning Scheduling and Control with Application to Heat Exchanger Networks under Fouling

Heat exchanger networks subject to fouling are an important example of dynamic systems where performance deteriorates over time. To mitigate fouling and recover performance, cleanings of the exchangers are scheduled and control actions applied. Because of inaccuracy in the models, as well as uncertainty and variability in the operations, both schedule and controls often have to be revised to improve operations or just to ensure feasibility. A closed-loop nonlinear model predictive control (NMPC) approach had been previously developed to simultaneously optimize the cleaning schedule and the flow distribution for refinery preheat trains under fouling, considering their variability. However, the closed-loop scheduling stability of the scheme has not been analyzed. For practical closed-loop (online) scheduling applications, a balance is usually desired between reactivity (ensuring a rapid response to changes in conditions) and stability (avoiding too many large or frequent schedule changes). In this paper, metrics to quantify closed-loop scheduling stability (e.g., changes in task allocation or starting time) are developed and then included in the online optimization procedure. Three alternative formulations to directly include stability considerations in the closed-loop optimization are proposed and applied to two case studies, an illustrative one and an industrial one based on a refinery preheat train. Results demonstrate the applicability of the stability metrics developed and the ability of the closed-loop optimization to exploit trade-offs between stability and performance. For the heat exchanger networks under fouling considered, it is shown that the approach proposed can improve closed-loop schedule stability without significantly compromising the operating cost. The approach presented offers the blueprint for a more general application to closed-loop, model-based optimization of scheduling and control in other processes.