Application Of Nonlinear Control Research Articles

Autonomous Lunar rendezvous trajectory planning and control using nonlinear MPC and Pontryagin’s principle

This paper explores the application of Nonlinear Model Predictive Control (NMPC) techniques, based on the Pontryagin Minimum Principle, for a minimum-propellant autonomous rendezvous maneuver in non-Keplerian Lunar orbits. The relative motion between the chaser and the target is described by the nonlinear dynamics of the circular restricted three body-problem, posing unique challenges due to the complex and unstable dynamics of near-rectilinear halo orbits. Key aspects of the proposed NMPC include trajectory optimization, maneuver planning, and real-time control, leveraging on its ability to satisfy complex mission requirements while ensuring safe and efficient spacecraft operations and in the presence of input and nonlinear/non-convex state constraints. The proposed formulation allows the design of a minimum-propellant controller, whose optimal control signal results to be bang–bang in time. A case study based on the Artemis III mission - where the docking of the Orion spacecraft to the Gateway station is planned - is illustrated in order to demonstrate the efficiency of the proposed approach, showcasing its potential for enhancing target tracking accuracy, while reducing propellant consumption.

A wave forecasting method based on probabilistic diffusion LSTM network for model predictive control of wave energy converters

Accurate long-term prediction of wave excitation forces is critical for optimizing wave energy converters, enabling enhanced control, and improving energy absorption efficiency. Traditional prediction models often employ deterministic conservative approaches, overlooking uncertainties. This paper introduces a novel prediction method based on the probabilistic diffusion model, offering a more precise prediction while accounting for uncertainty. Notably, our approach goes beyond previous works by simultaneously achieving control objectives for maximizing energy absorption, contrasting with methodologies solely focused on prediction and control tasks. The proposed method utilizes long short-time memory to extract temporal information from historical wave excitation observation. The hidden features are then processed through a diffused probabilistic-based unit. Subsequently, a time-scale neural network is developed for wave excitation moment prediction, followed by the application of nonlinear model predictive control to maximize the energy absorption. The methodology is validated on the 1:20 Wavestar prototype devices through numerical simulations. Results indicate that the predicted excitation moment closely align with measured values. In cases 4, 5, 6, the proposed method yields a substantial improvement in maximum control energy absorption–22%, 16%, and 31%, respectively–compared to traditional prediction methods. The proposed approach not only achieves a more accurate wave excitation moment prediction with uncertainty consideration but also introduces advanced control strategies in a full-scale plant application. This work contributes significantly to the field by bridging the gap between precise prediction and effective control in wave energy conversion systems.

Nonlinear model-based predictive control of a yeast fermentation bioreactor using new bee colony-WNN modelling structure

This paper concentrates on the application of a newly developed model for the nonlinear control of a yeast fermentation bioreactor. The primary control objectives are the maintenance of temperature and product concentration within the desired range. So, having an accurate model in control strategy is not ignorable and this model influences on close-loop controllability. In the context of online control, the parameters are changed (the system is time varying) and precision of extracted model is more important. Moreover, there is a demand for a computationally efficient model, and the convergence speed during the training of the neural network is significant. To overcome the challenges associated with slow convergence, the risk of being trapped in local minima, and the imperative of achieving computational efficiency, this study introduces a novel combination of a pruned Bee Colony Wavelet Neural Network for the online modeling of the bioreactor. The method's superiority lies in its ability to conduct searches in multiple sections independently, thereby avoiding local minima. The hybrid model controllability is further investigated using Dynamic Matrix Control (DMC) and Generalized Matrix Control (GPC) techniques. Subsequently, the paper explores the application of Nonlinear Model Predictive Control (NMPC) by solving a Gauss-Newton quadratic programming problem online, followed by a comparative analysis of the results. It is demonstrated that the precision of the model closely influences profitability and enhances product yields.

Performance improvement through nonlinear control design and power management of a grid-connected wind-battery hybrid energy storage system

This paper presents a study on the application of nonlinear control and optimal power management techniques in a grid-connected wind energy conversion system with battery storage. The objective is to efficiently supply power to a load while considering performance constraints. The energy system under investigation comprises a wind turbine, battery, AC-grid, and load. Power is delivered to the load through various converters and a DC-link. However, the intermittent nature of wind energy and frequent load fluctuations can negatively impact the battery's lifetime and charging performance. To address these challenges, a nonlinear controller and a novel energy management system are designed. The energy management system generates multiple energy flow scenarios to achieve equilibrium in energy distribution between the load and energy sources. This equilibrium aims to minimize overall system costs, ensure DC-grid stability, and enhance power quality. Two distinct operation modes are identified: i) MPPT mode, which utilizes an optimizer to maximize power extraction, and ii) adaptive power point tracking (APPT) mode, which considers demand-driven production and the state of charge (SOC) of the storage system. The convergence of the closed-loop control is formally analyzed, and simulation results confirm the improved performance of the proposed multi-criteria design for energy management.

Cloud-Based Computational Model Predictive Control Using a Parallel Multiblock ADMM Approach

Heavy computational load for solving nonconvex problems for large-scale systems or systems with real-time demands at each sample step has been recognized as one of the reasons for preventing a wider application of nonlinear model predictive control (NMPC). To improve the real-time feasibility of NMPC with input nonlinearity, we devise an innovative scheme called cloud-based computational model predictive control (MPC) by using an elaborately designed parallel multi-block alternating direction method of multipliers (ADMM) algorithm. This novel parallel multi-block ADMM algorithm is tailored to tackle the computational issue of solving a nonconvex problem with nonlinear constraints. It is ensured that the designed algorithm converges to a locally optimal solution of the optimization problem under reasonable assumptions by using the Kurdyka–Łojasiewicz property. With the help of this distributed optimization algorithm, a computational MPC scheme is developed, which can transform the NMPC optimization problem into a set of subproblems only associated with the decision variables at one prediction step. Through the parallel computing algorithm, the computational MPC can deal with large computational loads caused by high dimensional optimization problems, and improve computational efficiency. Furthermore, to allow for a more efficient implementation of the developed computational MPC and alleviate local calculation loads, a cloud-based computational MPC architecture is devised, which makes significantly better use of computational resources provided by a cloud server. An important advantage of this architecture with Docker (https://www.docker.com/) container to implement parallelization is that it does not lead to large increases in the solution time regardless of how long the prediction horizon is set. Finally, the developed cloud-based computational MPC architecture is trialed on a group of plug-in hybrid electric vehicles (PHEVs).

Closed-loop operation of a simulated recirculating aquaculture system with an integrated application of nonlinear model predictive control and moving horizon estimation

High water recirculation combined with a low rate of water exchange can deteriorate water quality and affect fish welfare in recirculating aquaculture systems (RAS). A nonlinear model predictive controller (NMPC) integrated with moving horizon estimation (MHE) was implemented in this work to maintain water quality parameters (e.g., oxygen, ammonia, and nitrate concentration) in RAS. The performance of the proposed control scheme was then evaluated in the presence of process uncertainty and measurement noise with full and partial accessibility to the system’s states under several common scenarios that can arise during the operation of RAS. In all scenarios, the proposed framework showed acceptable performance in keeping the water quality parameters close to their setpoints, demonstrating the high potential of this strategy in closed-loop operation of RAS.

Application of Nonlinear PID Active Disturbance Rejection Control in the Temperature Control System of Fast Steering Mirror

Application of Nonlinear PID Active Disturbance Rejection Control in the Temperature Control System of Fast Steering Mirror

Integration of Design and NMPC-Based Control under Uncertainty and Structural Decisions: An MPCC-Based Approach

In this work, we investigate the challenges and limitations of the application of nonlinear model predictive control (NMPC) for the integration of design and control for systems subject to structural decisions and model uncertainty. The problem involving discrete and continuous decisions is referred to as a mixed-integer bilevel programming model (MIBLP), which cannot be directly solved with conventional MINLP solvers. To address this issue, we implement a classical KKT transformation strategy to transform the original MIBLP into a single-level MINLP. The KKT conditions for the NMPC are determined and incorporated as constraints in the problem for process design. A regularization strategy is implemented to reformulate the complementarity constraints. Then, the single-level MINLP is directly solved with a branch and bound strategy. The proposed approach is tested in a reaction system network subject to uncertainty. The performance of a nominal- and a robust-NMPC control approaches are compared in the presence of process disturbances. Results indicate that the strategy with a robust-NMPC returns a more conservative process design with better control performance compared to results with a nominal-NMPC.

Energy Management of a Parallel Hybrid Electric Vehicle using Model Predictive Static Programming

Energy management of Parallel Hybrid Electric Vehicles (PHEVs) involves computation of energy efficient torque-speed set-points for the engine and the motor. Application of Nonlinear Model Predictive Control (NMPC) for this problem has been reported in the recent literature. In this work, a fast iterative implementation of the NMPC, known as Model Predictive Static Programming (MPSP) is deployed for the first time for energy management of PHEVs, with an appropriate multi-objective cost function and the applicable equality and inequality constraints. Additionally, a systematic approach based on the Theory of Dominance is used to tune parameters of the controller efficiently. Performance is evaluated with a validated PHEV model on the ADVISOR simulation environment, in terms of various performance metrics on standard drive cycles. The results show that the performance of the MPSP-based technique is close to the ideal performance achieved with Dynamic Programming (DP) and improved over a standard implementation using the Linear Time-Varying MPC (LTV-MPC) and Sequential Quadratic Programming MPC (SQP-MPC) algorithm. Moreover, its execution time on an industry standard micro-controller board is seen to be significantly less than that of LTV-MPC and SQP-MPC. This algorithm therefore appears to be one of the best candidates for on-board vehicle implementation of an optimal energy management strategy for a PHEV.

A Study on Application of Nonlinear Model Predictive Control to Crawler Type Stair Climbing Robot

A Study on Application of Nonlinear Model Predictive Control to Crawler Type Stair Climbing Robot

Application of Nonlinear Stabilization Control to Multicopters

Application of Nonlinear Stabilization Control to Multicopters

Fuzzy Logic Based Metaheuristic Algorithm for Optimization of Type-1 Fuzzy Controller: Fault-Tolerant Control for Nonlinear System with Actuator Fault

This research offers a fuzzy-based harmonic search (HS) metaheuristic technique for optimizing type-1 fuzzy controller for Fault-Tolerant Control (FTC) for nonlinear level control application subject to two uncertainties (i.e. actuator fault and external process disturbances), using type-1 and interval type-2 fuzzy-based HS algorithms. The effectiveness of a fuzzy logic-based adaptive HS algorithm in a nonlinear two-tank level control process with the primary actuator has dwindled (LOE). The work key contribution is the discovery of the best technique for constructing an optimal vector of values for the fuzzy controller’s membership functions (MFs) optimization. This is made to improve dynamic response by bringing the process value of the two-tank level control process close to the target process value (set-point). It’s worth noting that the type-1 fuzzy controller’s optimized MFs use an interval type-2 fuzzy system for parameter adaptation of the HS algorithm, which can handle greater uncertainty than a type-1 fuzzy system. In this case, the limiting MFs of interval type-2 fuzzy sets are type-1 fuzzy sets, which defne the footprint of uncertainty (FOU). Simulation results show that FHSO using an interval type-2 fuzzy system outperforms FHSO using a type-1 fuzzy system in the optimal design of a type-1 fuzzy controller.

Nonlinear substructuring control for simultaneous control of acceleration and displacement in shake table substructuring experiments

This paper reports the first application of nonlinear substructuring control (NLSC) to shake table experiments in which the table dynamics is significantly affected by the specimen. Substructuring experiments using a shake table require simultaneous control of acceleration and displacement of the table because it functions as both an actuation system and a part of the substructure in the experiments. NLSC was developed as an enhanced version of linear substructuring control (LSC), the basic method for the control of dynamically substructured system. This paper first describes the formulation of substructures for shake table experiments using a multiple-degree-of-freedom structure and NLSC design for the substructures. The stability analysis of NLSC, which has three controllers, becomes much more complicated, more frequently showing conditional stability than is observed in conventional experiments. To assess various conditionally stable systems, this paper proposes an equivalent approach that can systematically count encirclements of the critical point in Nyquist plots. In the stability analysis using the proposed approach, NLSC is more robust against parameter variations in the substructures than LSC. In addition, the error feedback controller in both LSC and NLSC enhances the robustness against the variations. This study numerically and experimentally examined control performances for shake table substructuring experiments involving nonlinear characteristics. In the examinations, NLSC achieved the expected displacement and acceleration control with stability and reasonable accuracy, whereas LSC could not. The error feedback controller design of NLSC was found to be essential for performing shake table substructuring experiments with severe nonlinear characteristics.

Applications of optimal nonlinear control to a whole-brain network of FitzHugh-Nagumo oscillators.

We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and the internode coupling strengths are derived from diffusion tensor imaging data of the connectome of the human brain. Nodes are coupled using an additive scheme without delays and are driven by background inputs with fixed mean and additive Gaussian noise. Optimal control inputs to nodes are determined by minimizing a cost functional that penalizes the deviations from a desired network dynamic, the control energy, and spatially nonsparse control inputs. Using the strength of the background input and the overall coupling strength as order parameters, the network's state-space decomposes into regions of low- and high-activity fixed points separated by a high-amplitude limit cycle, all of which qualitatively correspond to the states of an isolated network node. Along the borders, however, additional limit cycles, asynchronous states, and multistability can be observed. Optimal control is applied to several state-switching and network synchronization tasks, and the results are compared to controllability measures from linear control theory for the same connectome. We find that intuitions from the latter about the roles of nodes in steering the network dynamics, which are solely based on connectome features, do not generally carry over to nonlinear systems, as had been previously implied. Instead, the role of nodes under optimal nonlinear control critically depends on the specified task and the system's location in state space. Our results shed new light on the controllability of brain network states and may serve as an inspiration for the design of new paradigms for noninvasive brain stimulation.

Real-Time Nonlinear Model Predictive Controller for Multiple Degrees of Freedom Wave Energy Converters with Non-Ideal Power Take-Off

An increase in wave energy converter (WEC) efficiency requires not only consideration of the nonlinear effects in the WEC dynamics and the power take-off (PTO) mechanisms, but also more integrated treatment of the whole system, i.e., the buoy dynamics, the PTO system, and the control strategy. It results in an optimization formulation that has a nonquadratic and nonstandard cost functional. This article presents the application of real-time nonlinear model predictive controller (NMPC) to two degrees of freedom point absorber type WEC with highly nonlinear PTO characteristics. The nonlinear effects, such as the fluid viscous drag, are also included in the plant dynamics. The controller is implemented on a real-time target machine, and the WEC device is emulated in real-time using the WECSIM toolbox. The results for the successful performance of the design are presented for irregular waves under linear and nonlinear hydrodynamic conditions.

Application of Nonlinear Adaptive Control in Temperature of Chinese Solar Greenhouses

The system of a greenhouse is required to ensure a suitable environment for crops growth. In China, the Chinese solar greenhouse plays a crucial role in maintaining a proper microclimate environment. However, the greenhouse system is described with complex dynamic characteristics, such as multi-disturbance, parameter uncertainty, and strong nonlinearity. It is difficult for the conventional control method to deal with the above problems. To address these problems, a dynamic model of Chinese solar greenhouses was developed based on energy conservation laws, and a nonlinear adaptive control strategy combined with a Radial Basis Function neural network was presented to deal with temperature control. In this approach, nonlinear adaptive controller parameters were determined through the generalized minimum variance laws, while unmodeled dynamics were estimated by a Radial Basis Function neural network. The control strategy consisted of a linear adaptive controller, a neural network nonlinear adaptive controller, and a switching mechanism. The research results show that the mean errors were 0.8460 and 0.2967, corresponding to a conventional PID method and the presented nonlinear adaptive scheme, respectively. The standard errors of the conventional PID method and the nonlinear adaptive control strategy were 1.8480 and 1.3342, respectively. The experimental results fully prove that the presented control scheme achieves better control performance, which meets the actual requirements.

Crystal phases of charged interlayer excitons in van der Waals heterostructures

Throughout the years, strongly correlated coherent states of excitons have been the subject of intense theoretical and experimental studies. This topic has recently boomed due to new emerging quantum materials such as van der Waals (vdW) bound atomically thin layers of transition metal dichalcogenides (TMDs). We analyze the collective properties of charged interlayer excitons observed recently in bilayer TMD heterostructures. We predict strongly correlated phases—crystal and Wigner crystal—that can be selectively realized with TMD bilayers of properly chosen electron-hole effective masses by just varying their interlayer separation distance. Our results can be used for nonlinear coherent control, charge transport and spinoptronics application development with quantum vdW heterostuctures.

Model Predictive Control of the Vertical Gradient Freeze Crystal Growth Process

Abstract This contribution presents the application of nonlinear model predictive control to the Vertical Gradient Freeze crystal growth process. Due to the time-varying spatial extent of the crystal and melt during growth, this process is characterised by two coupled free boundary problems that form a so called two-phase Stefan problem which is of nonlinear nature. To apply model predictive control to this process, a simplified, spatially distributed representation of the system is derived and transferred into a spatially lumped form by means of the finite element method. For this model, a nonlinear control problem is formulated, that takes process limitations into account and tries to satisfy different quality objectives by formulating demands on the systems spatiotemproal temperature distribution. This provides the foundation for the presented predictive control design. Finally, the approximated model and the controller are verified for different real-world scenarios that include model errors and parameter uncertainties.

A New Hyperchaotic Map for a Secure Communication Scheme with an Experimental Realization

Using different chaotic systems in secure communication, nonlinear control, and many other applications has revealed that these systems have several drawbacks in different aspects. This can cause unfavorable effects to chaos-based applications. Therefore, presenting a chaotic map with complex behaviors is considered important. In this paper, we introduce a new 2D chaotic map, namely, the 2D infinite-collapse-Sine model (2D-ICSM). Various metrics including Lyapunov exponents and bifurcation diagrams are used to demonstrate the complex dynamics and robust hyperchaotic behavior of the 2D-ICSM. Furthermore, the cross-correlation coefficient, phase space diagram, and Sample Entropy algorithm prove that the 2D-ICSM has a high sensitivity to initial values and parameters, extreme complexity performance, and a much larger hyperchaotic range than existing maps. To empirically verify the efficiency and simplicity of the 2D-ICSM in practical applications, we propose a symmetric secure communication system using the 2D-ICSM. Experimental results are presented to demonstrate the validity of the proposed system.

A Robust Self-Adaptive Interval Type-2 TS Fuzzy Logic for Controlling Multi-Input–Multi-Output Nonlinear Uncertain Dynamical Systems

Recently, Type-2 fuzzy systems have become increasingly prominent as they have been applied to various nonlinear control applications. This article presents an adaptive fuzzy controller based on the sliding-mode control theory. The proposed self-adaptive interval Type-2 fuzzy controller (SAF2C) is based on the Takagi–Sugeno (TS) fuzzy model and it accommodates the “enhanced iterative algorithm with stop condition” type-reducer, which is more computationally efficient than the “Kernel–Mendel” type-reduction algorithm. We developed an integrated multi-input–multi-output (MIMO) SAF2C-controller to reduce the computation time so that we can expedite the learning process of our control algorithm by 80% compared to separate single-input–single-output (SISO) controllers. The stability of our controller is proven using the Lyapunov technique. To ensure the applicability of the presented control scheme, we implemented our controller on various nonlinear systems, including a hexacopter unmanned aerial vehicle (UAV). We also compare the accuracy of our controller with a conventional proportional–integral–derivative autopilot system. Our research indicates around 20% improvement in its transient response, in addition to achieving a better noise rejection capability with respect to a Type-1 fuzzy counterpart.