Novel Nonlinear Model Predictive Control Research Articles

A robust nonlinear tracking MPC using qLPV embedding and zonotopic uncertainty propagation

In this paper, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for tracking for piece-wise constant reference signals. The main novelty is the use of quasi-Linear Parameter Varying (qLPV) embeddings in order to describe the nonlinear dynamics. Furthermore, these embeddings are exploited by an extrapolation mechanism, which provides the future behaviour of the scheduling parameters with bounded estimation error. Therefore, the resulting NMPC becomes computationally efficient (comparable to a Quadratic Programming algorithm), since, at each sampling period, the predictions are linear. Benefiting from artificial target variables, the method is also able to avoid feasibility losses due to large set-point variations. Robust constraint satisfaction, closed-loop stability, and recursive feasibility certificates are provided, thanks to uncertainty propagation zonotopes and parameter-dependent terminal ingredients. A benchmark example is used to illustrate the effectiveness of the method, which is compared to state-of-the-art techniques.

Nonlinear Model Predictive Control for a Dynamic Positioning Ship Based on the Laguerre Function

In this paper, we present a novel nonlinear model predictive control (NMPC) algorithm based on the Laguerre function for dynamic positioning ships to solve the problems of input saturation, unknown time-varying disturbances, and heavy computation. The nonlinear model of a dynamic positioning ship is presented as a linear model, transformed from a standard affine nonlinear state-space model by precise feedback linearization. The environmental disturbance is overcome using an integrator. The time cost of the proposed nonlinear control algorithm is decreased by inducing the Laguerre function to describe the feedback-linearization system input increments. The Laguerre function reduces the matrix dimensions of the nonlinear optimization problem. The simulation results for a DP supply vessel showed that the novel algorithm maintained the effective control performance of the original nonlinear model predictive control algorithm and had a reduced computation load to satisfy the requirements of real-time operation.

Intelligent frequency stabilization of low-inertia islanded power grids-based redox battery

Renewable energy sources (RES)-generated electricity is increasing at a fast pace and is becoming more prevalent in microgrids (MGs). System inertia is much decreased due to the fact that MGs are mostly powered by RES rather than synchronous generators. As a result, system stability suffers, which is especially problematic with MGs. A suitable solution for this problem is an energy storage system and an appropriate inertial control technique. Redox flow batteries (RFBs) have an unusually long charge-discharge life cycle and a fast reaction time, which allows them to reduce oscillations in the power system when there is a sudden disturbance in the power system. This paper suggests a unique concept for VIC based on RFB in an isolated MG, which emulates the primary frequency control, virtual inertia, and damping all at once. In addition to the VIC concept, we suggest a novel nonlinear model predictive control (NMPC) method for MG secondary control. The NMPC utilizes non-integer order calculus and interval type-3 (IT3) fuzzy logic systems (FLSs). Finally, OPAL-RT-based real-time hardware-in-the-loop (HIL) simulation results are used to examine the validity and applicability of the suggested techniques in low inertia islanded MG.

Fuel consumption optimization for a plug-in hybrid electric bus during the vehicle-following scenario

In this paper, a robust SOC (state of charge of battery) trajectory planning method is proposed for a plug-in hybrid electric bus (PHEB) in the vehicle-following scenario. Firstly, the trajectory areas of SOC are planned based on the Taguchi robust design (TRD) considering the noises of the vehicle mass and driving cycles. Moreover, the reliability of the result of TRD is verified based on the Monte Carlo simulation (MCS). Then, the longitudinal driving control of PHEB is transformed into a multi-objective optimal problem that incorporates driving safety, fuel economy and ride comfort in the vehicle-following scenario. Finally, based on a novel nonlinear model predictive control (NMPC), the electric motor, engine and brake system are collaboratively optimized to comprehensively adjust the dynamic and economy of PHEB. The results show that the planning trajectory areas of SOC effectively improved the fuel economy compared with the pre-planning. Furthermore, based on the novel NMPC, the fuel consumption of the proposed method is lower than the method that just adds an energy management strategy to adaptive cruise control (ACC + EMS). The hardware-in-loop test results show that the proposed method can be implemented into the vehicle controller, and the results between the HIL and offline simulations are largely coincident.

NMPC-Based Path Tracking Control Strategy for Autonomous Vehicles With Stable Limit Handling

A novel nonlinear model predictive control (NMPC) strategy for path tracking of autonomous vehicles with stable limit handling is proposed in this article. To improve the path tracking performance under complex driving maneuvers, a tire lateral force model, which treats road adhesion coefficient and vertical load as variable parameters, is discussed first. It has the advantage that the dynamics model can be applied under different driving conditions. In addition, the stability properties of the dynamics system with the front tire lateral force as the virtual control input are analyzed. The global asymptotical stability with zero input and local input-to-state stability with nonzero input of the dynamics system are proved respectively. To perform path tracking within the handling limits, both constraints of front tire lateral force and rear tire slip angle are included in the NMPC controller. The constraint of front tire lateral force is considered as peak limits related to load transfer and adhesion coefficient. And for the rear tire slip angle, a combining constraint scheme is proposed, where the indirect constraint is implemented by a penalty term that predicts the saturation of rear tire lateral force, while the direct constraint is implemented by a dead-zone exponential penalty function. The Continuation/Generalized Minimum Residual (C/GMRES) algorithm is applied to improve the computation efficiency of the NMPC. The performance of the controller is evaluated in simulations and hardware-in-the-loop (HIL) tests, and the results show that the controller is able to track the reference path with high precision in real-time.

Sustainable building climate control with renewable energy sources using nonlinear model predictive control

Sustainable energy sources are promising solutions for reducing carbon footprint and environmental impacts within the building sectors. Reducing energy consumption while ensuring thermal comfort for occupants is now an essential task in building climate control. Two possible ways to cut down building energy consumption are implementing renewable and sustainable energy sources, such as solar energy and geothermal energy, and adopting the model predictive control method. In this study, we develop a novel nonlinear model predictive control (NMPC) framework for climate control of buildings with renewable energy systems to minimize electricity costs. A nonlinear dynamic model of the building climate and renewable energy systems, including temperature, humidity, thermal comfort, geothermal heat pump, and solar panels, is first constructed based on mass and energy balance equations. The nonlinear dynamic model is then integrated into the proposed NMPC framework, which iteratively solves a nonlinear programming problem to generate the optimal control inputs which minimize energy consumption and carbon footprints for sustainability. A simulation case study on controlling a building located on the Cornell University campus is conducted to demonstrate the capability of renewable energy sources to reduce building energy consumption using the proposed NMPC framework. The results show the NMPC framework could efficiently minimize total electricity cost and constraint violation for thermal comfort to 12.9% with no more than 0.2 of violation on predicted mean value index in different seasons. Implementing an electricity storage component could reduce the electricity cost by 19%. The results indicate better sustainability for the smart building using sustainable energy sources and the NMPC framework.

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.

Intelligent control and energy optimization in controlled environment agriculture via nonlinear model predictive control of semi-closed greenhouse

Greenhouse climate is a highly complex system that contains nonlinearity and dependencies between each system state. This paper proposes a novel nonlinear model predictive control (NMPC) framework for greenhouse climate control to minimize the total control cost mainly coming from energy use. A nonlinear dynamic model of the greenhouse climate, including temperature, humidity, CO2 level, and light intensity, is first constructed based on developed mass balances and energy transport phenomena. Real-world greenhouse climate data and outdoor weather data are gathered to systematically identify the system parameters for the nonlinear greenhouse climate model. The nonlinear dynamic model is then integrated into the proposed NMPC framework which iteratively solves a nonlinear programming problem to obtain the optimal control inputs of fan airflow rate, pad cooling air velocity, heating pipe flow rate, CO2 injection rate, fogging rate, supplemental light intensity, and shade curtain coverage. The stability and feasibility issues of the proposed NMPC framework on a semi-closed greenhouse are explicitly discussed in this work. Case studies on controlling a greenhouse located in Cornell University campus are simulated to demonstrate the performance of the proposed NMPC framework. The results show the NMPC framework could efficiently minimize total control cost and constraint violation. Humidity, CO2 level, and light intensity can be controlled with nearly no violation on the predetermined constraints over different seasons and climate conditions. As for temperature, it is almost always maintained within the acceptable region in winter and spring. On extreme days of summer, there are some temperature violations due to the limited cooling capacity.

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 for robust bipedal locomotion: exploring angular momentum and CoM height changes

Human beings can utilize multiple balance strategies, e.g. step location adjustment and angular momentum adaptation, to maintain balance when walking under dynamic disturbances. In this work, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for robust gait pattern generation, with the capabilities of step location adjustment, Center of Mass (CoM) height variation, and angular momentum adaptation. These features are realized by constraining the Zero Moment Point within the support polygon. By employing the nonlinear inverted pendulum plus flywheel model, the effects of upper-body rotation and vertical height motion are considered. As a result, the NMPC is formulated as a quadratically constrained quadratic program problem, which is solved fast by sequential quadratic programming. Consequently, robust walking patterns that exploit reactive stepping, body inclination, and CoM height variation are generated. Adaptable walking in multiple scenarios has been demonstrated through simulation studies.

Modal-Based Nonlinear Model Predictive Control for 3-D Very Flexible Structures

In this article a novel nonlinear model predictive control (NMPC) scheme is derived, which is tailored to the underlying structure of the intrinsic description of geometrically exact nonlinear beams (in which velocities and strains are primary variables). This is an important class of partial differential equation (PDE) models whose behavior is fundamental to the performance of flexible structural systems (e.g., wind turbines, high-altitude long-endurance aircraft). Furthermore, this class contains the much-studied Euler–Bernoulli and Timoshenko beam models, but has significant additional complexity (to capture 3-D effects and arbitrarily large displacements) and requires explicit computation of rotations in the PDE dynamics to account for orientation-dependent forces. A challenge presented by this formulation is that uncontrollable modes necessarily appear in any finite dimensional approximation to the PDE dynamics. We show, however, that an NMPC scheme can be constructed in which the error introduced by the uncontrollable modes can be explicitly controlled. It is demonstrated that the asymptotic error can be made insignificant (from a practical perspective) using our NMPC scheme and excellent performance is obtained even when applied to a highly resolved numerical simulation of the PDEs. We also present a generalization of Kelvin–Voigt damping to the intrinsic description of geometrically exact beams. Finally, special emphasis is placed on constructing a framework suitable for real-time NMPC control, where the particular structure of the underlying PDEs is exploited to obtain both efficient finite-dimensional models and numerical schemes.

Nonlinear MPC for Collision Avoidance and Control of UAVs With Dynamic Obstacles

This article proposes a Novel Nonlinear Model Predictive Control (NMPC) for navigation and obstacle avoidance of an Unmanned Aerial Vehicle (UAV). The proposed NMPC formulation allows for a fully parametric obstacle trajectory, while in this article we apply a classification scheme to differentiate between different kinds of trajectories to predict future obstacle positions. The trajectory calculation is done from an initial condition, and fed to the NMPC as an additional input. The solver used is the nonlinear, non-convex solver Proximal Averaged Newton for Optimal Control (PANOC) and its associated software OpEn (Optimization Engine), in which we apply a penalty method to properly consider the obstacles and other constraints during navigation. The proposed NMPC scheme allows for real-time solutions using a sampling time of 50 ms and a two second prediction of both the obstacle trajectory and the NMPC problem, which implies that the scheme can be considered as a local path-planner. This paper will present the NMPC cost function and constraint formulation, as well as the methodology of dealing with the dynamic obstacles. We include multiple laboratory experiments to demonstrate the efficacy of the proposed control architecture, and to show that the proposed method delivers fast and computationally stable solutions to the dynamic obstacle avoidance scenarios.

A Unified NMPC Scheme for MAVs Navigation With 3D Collision Avoidance Under Position Uncertainty

This article proposes a novel Nonlinear Model Predictive Control (NMPC) framework for Micro Aerial Vehicle (MAV) autonomous navigation in constrained environments. The introduced framework allows us to consider the nonlinear dynamics of MAVs and guarantees real-time performance. Our first contribution is to design a computationally efficient subspace clustering method to reveal from geometrical constraints to underlying constraint planes within a 3D point cloud, obtained from a 3D lidar scanner. The second contribution of our work is to incorporate the extracted information into the nonlinear constraints of NMPC for avoiding collisions. Our third contribution focuses on making the controller robust by considering the uncertainty of localization and NMPC using the Shannon entropy. This step enables us to track either the position or velocity references, or none of them if necessary. As a result, the collision avoidance constraints are defined in the local coordinates of MAVs and it remains active and guarantees collision avoidance, despite localization uncertainties, e.g., position estimation drifts. Additionally, as the platform continues the mission, this will result in less uncertain position estimations, due to the feature extraction and loop closure. The efficacy of the suggested framework has been evaluated using various simulations in the Gazebo environment.

Microsecond nonlinear model predictive control for DC‐DC converters

SummaryIn this paper, we present a novel nonlinear model predictive control (NMPC) formulation for the transient control of a DC‐DC converter. We demonstrate that a real‐time implementation of the proposed NMPC scheme using the PANOC solver can be efficiently applied to control DC‐DC converters in the microsecond range. Moreover, an embedded, code‐generated version of PANOC can be implemented using microcontrollers or digital signal processors. The algorithm is incorporated in the transient simulator of PWM DC‐DC converters, and the operation of the simulator on the boost converter's example is presented, comparing the performance of our NMPC‐controller with that of a classical PID controller. The operation of the boost converter controlled using the proposed NMPC algorithm is validated experimentally.

A Study on Aero-Engine Direct Thrust Control with Nonlinear Model Predictive Control Based on Deep Neural Network

For enhancing engine response ability, a novel nonlinear model predictive control (NMPC) method for aero-engine direct thrust control is proposed. The control objective of the proposed method is the thrust instead of the measurable parameters. The online-sliding window deep neural network (OL-SW-DNN) is proposed as predictive model. The OL-SW-DNN adopts deep-learning structure to increase the model accuracy and selects the nearest point data of certain length as training data which will reduce the sensitivity for the noise of training data. The direct thrust simulations of the popular NMPC based on extended Kalman filler (EKF) and the proposed one are conducted, respectively. The simulations demonstrate that compared with the popular NMPC, the proposed NMPC decreases the acceleration time by 0.425 s and increases response speed about 1.14 times.

Optimal Control of Human Muscle‐Actuated Motion

AbstractThe question how the brain controls locomotion is a highly treated one. This topic is taken up in this study by means of human computational models, simulating the human musculoskeletal system actuated by advanced Hill‐type muscle models. A forward dynamic approach is considered allowing to simulate human motion independently from pre‐measured trajectories and enabling to resemble the control of the central nervous system – the motor command selection. It is suggested that movement paths arise implicitly through optimisation [1,4]. Hence, stimulation patterns passing through activation dynamics are determined by means of constrained optimal control problems with physiologically motivated objective functions. One advantage concerning the implementation within Neweul‐M2 is the possibility to apply well‐elaborated and tested optimisation algorithms available with Matlab to solve optimal control problems, enabling to employ the novel non‐linear model predictive control (NMPC). The introduced framework is applied to treat different biomechanical movement scenarios including reaching scenarios of the arm which are validated against experimental data from [2–4]. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Optimum Energy Management of PEM Fuel Cell Systems Based on Model Predictive Control

This work presents an optimum energy management framework, which is developed for integrated Polymer Electrolyte Membrane (PEM) fuel cell systems. The objective is to address in a centralized manner the control issues that arise during the operation of the fuel cell (FC) system and to monitor and evaluate the system’s performance at real time. More specifically the operation objectives are to deliver the demanded power while operating at a safe region, avoiding starvation, and concurrently minimize the fuel consumption at stable temperature conditions. To achieve these objectives a novel Model Predictive Control (MPC) strategy is developed and demonstrated. A semiempirical experimentally validated model is used which is able to capture the dynamic behaviour of the PEMFC. Furthermore, the MPC strategy was integrated in an industrial-grade automation system to demonstrate its applicability in realistic environment. The proposed framework relies on a novel nonlinear MPC (NMPC) formulation that uses a dynamic optimization method that recasts the multivariable control problem into a nonlinear programming problem using a warm-start initialization method and a search space reduction technique which is based on a piecewise affine approximation of the variable’s feasible space.The behaviour of the MPC framework is experimentally verified through the online deployment to a small-scale fully automated PEMFC unit. During the experimental scenarios the PEMFC system demonstrated excellent response in terms of computational effort and accuracy with respect to the control objectives.

Constrained Spectrum Control

A novel Nonlinear Model Predictive Control (NMPC) scheme is proposed in order to shape the harmonic response of constrained nonlinear systems. The salient ingredient is the short-time Fourier transform (STFT) of the system's output signal, which is constrained in an NMPC problem, leading to the novel formulation of so-called spectrum constraints. Recursive feasibility and asymptotic stability of the proposed NMPC scheme with such spectrum constraints are guaranteed by means of an appropriate ellipsoidal terminal invariant set. The efficacy of the proposed approach is demonstrated on a nonlinear vibration damping problem.

Nonlinear Model Predictive Control for Heterogeneous Process Models in Water Resources

AbstractThis paper introduces a novel Non-linear Model Predictive Control (NMPC) algorithm for the real-time control of heterogeneous, large-scale water resources systems. The algorithm is based on the idea of defining a Lagrangian function in which the system state transition equations are defined as separate equality constraints of the optimization problem. This enables the derivation of an adjoint of the state transition equations and provides the objective function gradient. The optimization problem can then be solved by any numerical solver, under the consideration of the constraints and the gradient. The main advantage of the proposed approach is the possibility of easily dealing with the process-based models commonly adopted in the environmental literature, under the assumption of both explicit and implicit time-stepping schemes. The proposed procedure computes the gradient of a cost function by computational costs comparable to a model simulation itself, thus enabling the management of large-scale systems. The capabilities of the NMPC algorithm are first evaluated on a test case study, and then demonstrated for the control of six hydraulic structures and two major flood detention basins along the bifurcation points of the Rhine River in The Netherlands.

State estimation and nonlinear predictive control of autonomous hybrid system using derivative free state estimators

In this work, we develop a state estimation scheme for nonlinear autonomous hybrid systems, which are subjected to stochastic state disturbances and measurement noise, using derivative free state estimators. In particular, we propose the use of ensemble Kalman filters (EnKF), which belong to the class of particle filters, and unscented Kalman filters (UKF) to carry out estimation of state variables of autonomous hybrid system. We then proceed to develop novel nonlinear model predictive control (NMPC) schemes using these derivative free estimators for better control of autonomous hybrid systems. A salient feature of the proposed NMPC schemes is that the future trajectory predictions are based on stochastic simulations, which explicitly account for the uncertainty in predictions arising from the uncertainties in the initial state and the unmeasured disturbances. The efficacy of the proposed state estimation based control scheme is demonstrated by conducting simulation studies on a benchmark three-tank hybrid system. Analysis of the simulation results reveals that EnKF and UKF based NMPC strategies is well suited for effective control of nonlinear autonomous three-tank hybrid system.