Robustly stable adaptive horizon nonlinear model predictive control

In this article, we present a quasi-infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi-infinite horizon terminal cost. As a result, we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. The practicality of this approach is demonstrated with a benchmark example.

A magnetic levitation system (Maglev) is a sensitive, multi-parameter, nonlinear, and unstable system that is utilized to levitate a ferromagnetic object in free space. Due to its vast applications, various research studies in the field of control strategy have become extremely important and challenging. This work proposes the design of a nonlinear model predictive (NMPC) control scheme for the object position control against the nonlinearities and uncertainties of a Maglev system. A novel bio-inspired Artificial Protozoa Optimization (APO) algorithm is used to fine-tune the NMPC parameters, which include best weighting matrices ( ), shorter prediction horizons ( ), and shorter time steps ( ) to minimize the objective cost function. The effective performance of the NMPC is verified using simulation-based results in MATLAB. The CasADi toolbox is utilized to solve nonlinear optimization problems and handle the nonlinearity of the Maglev system model. Simulations are implemented for three trajectories tracking (step, sine, and square) with 20% and without Maglev parameters perturbations. To prove the superiority of the proposed controller, comparisons are made with the conventional Linear Quadratic Regulator (LQR) and proportional-integral-derivative (PID) controllers. Two performance indices are introduced, Integral of Squared Error (ISE) and Integral of Absolute Error (IAE), to examine the tracking performances of the NMPC, LQR, and PID controller. The NMPC controller has shown more efficient performance and accurate results than other controllers. The contributions of this work include a new optimization technique of APO, a new engineering application of the APO integrated with NMPC to control a Maglev system, consideration of inherent nonlinearities and system constraints, and robustness improvement under perturbation.

In this paper a novel controller for stable and precise operation of multi-rotors with heavy slung loads is introduced. First, simplified equations of motions for the multi-rotor and slung load are derived. The model is then used to design a Nonlinear Model Predictive Controller (NMPC) that can manage the highly nonlinear dynamics whilst accounting for system constraints. The controller is shown to simultaneously track specified waypoints whilst actively damping large slung load oscillations. A Linear-quadratic regulator (LQR) controller is also derived, and control performance is compared in simulation. Results show the improved performance of the Nonlinear Model Predictive Control (NMPC) controller over a larger flight envelope, including aggressive maneuvers and large slung load displacements. Computational cost remains relatively small, amenable to practical implementation. Such systems for small Unmanned Aerial Vehicles (UAVs) may provide significant benefit to several applications in agriculture, law enforcement and construction.

Robust model predictive control for continuous nonlinear systems with the quasi-infinite adaptive horizon algorithm

In this paper, the parameterized dynamical model of the diesel engine intake and exhaust system using a data-based method, namely a Gain-Scheduled model is proposed and designed based on the data from a virtual engine test bench under normal load conditions. In the first step, the Multiple Input Multiple Output model structure is defined with five inputs and two outputs. Using the constructed model, it is possible to establish the relations between intake Manifold Pressure, Air Mass Flow, the control signals, and changes of the load. Then, the model is further used to design a Nonlinear Model Predictive Control controller, aimed at optimizing the efficiency of the combustion system in terms of the control reference value tracking with respect to emission reduction. This paper follows a model-based design approach to construct the Nonlinear Model Predictive Control objective function for the engine intake Manifold Pressure and Air Mass Flow nonlinear control problem. The proposed data-based dynamical modeling method is shown to increase the flexibility for the modeling of nonlinear plant at a low cost in computational requirements. The experimental results illustrate that the optimized nonlinear control approach significantly improve the control reference tracking performance and the exhaust emissions against the standard decentralized Single Input Single Output control in the standard production Engine Control Unit.

SUMMARY A worldwide accident survey of manned and unmanned aircraft shows in-flight loss of control remains a major contributor to aircraft accidents. Operation outside the normal fight envelope is usually subject to failure of components, inappropriate crew response, and environmental conditions. The aerodynamic model of aircraft associated with hazardous weather and abnormal conditions is inherently nonlinear and unsteady. A novel adaptive nonlinear model predictive controller is proposed and conceptually proven to ensure safe control of the Meridian unmanned aerial system in off-nominal conditions. Nonlinear model predictive controllers are capable of handling input and output constraints that directly satisfy safety and performance requirements in off-nominal conditions. The performance of a nonlinear model predictive controller relies heavily on the physics-based model. Controller performance is improved by updating the physics-based model by using real-time nonlinear estimation of aerodynamic forces. Real-time nonlinear estimation of aerodynamic forces is obtained utilizing artificial neural networks with time-varying adaptive parameters. The adaptive nonlinear model predictive controller, coupled with real-time parameter identification, is shown to exhibit robust characteristics and to successfully mitigate the impact of nonlinear and unsteady aerodynamics while preventing loss of control. Copyright © 2013 John Wiley & Sons, Ltd.

Air-Handling or Air-handler Units (AHUs) as a section of a Heating, Ventilating, and Air-Conditioning (HVAC) system are used for refrigerating and filtering the environment. AHU provides comfortable conditions by adjusting the control actuators of the air and water in a field-level of industrial automation. This device has strong interacting nonlinearities characteristics with complicated coupling between states and variable parameters. Thus, designing a controller has been always a challenging issue. In this work, a multivariable Nonlinear Model Predictive Controller (NMPC) centered on fmincon algorithm for AHU with a single zone in a Variable Air Volume (VAV) is pro-posed. The NMPC structure is focused on iterative optimization (online) of a cost function with a finite horizon of operating performance and using the future behavior of air-handler to generate the control effort without considering the past error. Simulation results indicate good efficiency of the NMPC approach in estimation and tracking the desired set-point compared to Linear Quadratic Regulator (LQR).

Current research predominantly focuses on enhancing vehicle driving stability when tires operate in the linear region. Thus, the effect of cornering stiffness on vehicle driving stability under nonlinear region remains an unresolved challenge. To address this issue, this paper proposes a novel nonlinear model predictive control (NMPC)-based four-wheel steering trajectory tracking controller that incorporates time-varying cornering stiffness. First, the longitudinal and lateral axle forces are estimated using a strong tracking unscented Kalman filter (STUKF); these estimated forces are then applied to a cornering stiffness estimator based on the unscented Kalman filter (UKF). Simulation tests under various scenarios are conducted using CarSim and Simulink, with comparisons made against the linear quadratic regulator (LQR) and conventional model predictive control (MPC) strategies. Finally, hardware-in-the-loop (HIL) experimental results verify that the proposed NMPC controller exhibits satisfactory trajectory tracking performance, stability, and real-time performance.

The article studies the trajectory tracking control problem of underactuated marine vehicles via the nonlinear model predictive control (NMPC) strategy, where practical control and state constraints present. It is a well-known challenging issue that the conventional NMPC is not applicable for underactuated marine vehicles, due to the fact that there does not exist a local static continuous state-feedback controller to stabilize the underactuated dynamics. To resolve this issue, this article proposes to construct an auxiliary time-varying tracking controller to aid terminal constraint design in the NMPC framework, where the time-varying tracking controller borrows the ideas from Lyapunov's direct method and backstepping approach. Based on this, a novel NMPC algorithm is designed to ensure trajectory tracking control of underactuated marine vehicles. Furthermore, a systematic parameter design approach is developed. Under the designed parameters, we show that the tracking error system is input-to-state stable (ISS). Finally, the effectiveness of the designed algorithm is verified by thorough simulation and hardware experiments.

Managed Pressure Drilling (MPD) is an advanced drilling technique that enhances safety and efficiency by maintaining precise control over bottomhole pressure. Nonlinear Model Predictive Control (NMPC) has proven effective in MPD due to its ability to handle constraints and nonlinearities. However, NMPC performance depends on the accuracy of the underlying system model. Traditionally, low-fidelity first-principle models have been used for MPD control system design, but recent advances in data-driven modeling offer alternatives. This study presents a comparative analysis of two predictive controllers using Machine Learning (ML)-based NMPC frameworks—Long Short-Term Memory (LSTM) networks and Transformer-based self-attention mechanisms—for automatic MPD. The machine learning models were trained using the input-output data collected from the simulated model of the MPD. The ability of the trained models in making predictions of bottomhole pressure was tested using the validation dataset. The r2 score of the LSTM model on the validation dataset is 0.8747 and that of the transformer model is 0.8639 while the RMSE value is 116820 for the LSTM model and 113130 for the transformer model. The RMSE values are considered low given that bottomhole pressures in the system are of the order of 10 million (~107 Pa). These trained models were employed as the prediction models in the NMPC formulation. The ML-based NMPC were evaluated on their ability to track bottomhole pressure setpoints during normal drilling operation and to reject bottomhole pressure disturbances which can be caused by measurement error or plant model mismatch. The LSTM-based NMPC demonstrated slightly better setpoint tracking and faster disturbance rejection as a result of its shorter rise time. For the servo simulation, the Integral Absolute Error (IAE) was 3.2544×107 for LSTM-based NMPC and 3.9345×107 for Transformer-based NMPC. Under regulatory conditions involving disturbances in bottomhole pressure measurements, the LSTM-based controller had an IAE of 6.15×106, compared to 9.5733×106 for the Transformer-based NMPC. In terms of computational efficiency, transformer-based NMPC with an average computational time of 0.5862s outperformed LSTM-NMPC with 2.1768s for setpoint tracking over a simulation time of 750s. Overall, while LSTM-based NMPC exhibited slightly better control accuracy performance, Transformer-based NMPC exhibits better potential for applications in a real-time automatic MPD operation given its very low computational time.

Nonlinear model predictive control of PEMFC anode hydrogen circulation system based on dynamic coupling analysis

This paper intends to compare controllers used for non-isolated (transformer less) interleaved double dual boost (IDDB) converter which provide high voltage gain and can be used for high-power applications. A control subsystem is required to improve dynamic behaviour of converter and to have a better output response. In most cases small signal model of converter is obtained which are linearized at an operating point to derive a controller which cannot take uncertainties into consideration. Robust control and Nonlinear control methods are probably areas which can handle uncertainties and non-linearities effectively. Conventional linear quadratic regulator (LQR) controller cannot assure stability if system is highly uncertain. A convex model of converter dynamics is obtained taking uncertainties into account. To apply LQR control in uncertain converter case linear matrix inequalities(LMIs) are used to optimize the performance index. A comparative study of LMI-LQR control, LQR Controller and PID controller is done.

The linear quadratic regulator (LQR) is a classical optimal control approach that can regulate gait dynamics about target kinematic trajectories. Exoskeletons to restore gait function have conventionally utilized time-varying proportional-derivative (PD) control of leg joints. But, these PD parameters are not uniquely optimized for whole-body (full-state) performance. The objective of this study was to investigate the effectiveness of LQR full-state feedback compared to PD control to maintain bipedal walking of a sagittal-plane computational model against force disturbances. Several LQR controllers were uniquely solved with feedback gains optimized for different levels of tracking capability versus control effort. The main implications to future exoskeleton control systems include (1) which LQR controllers out-perform PD controllers in walking maintenance and effort, (2) verifying that LQR desirably produces joint torques that oppose rapidly growing joint state errors, and (3) potentially equipping accurate sensing systems for nonjoint states such as hip-position and torso orientation. The LQR controllers capable of longer walk times than respective PD controllers also required less control effort. During sudden leg collapse, LQR desirably behaved like PD by generating feedback torques that opposed the direction of leg-joint errors. Feedback from nonjoint states contributed to over 50% of the LQR joint torques and appear critical for whole-body LQR control. While LQR control poses implementation challenges, such as more sensors for full-state feedback and operation near the desired trajectories, it offers significant performance advantages over PD control.

For omnidirectional mobile robot (OMR), it is difficult to achieve adequate tracking flexibility and accuracy with nonlinear model predictive control (NMPC) in a fixed horizon due to the dynamic change of system variables. This paper proposed a strategy of NMPC with self-turned prediction horizon, which can adapt to the change of system variables and perform a stable tracking control. Firstly, we construct a kinematics model for the Ackerman mode of the OMR. Secondly, the NMPC strategy is adapted to trajectory tracking. Moreover, a method to select the appropriate prediction of horizon is proposed by considering the influence of velocity and road curvature on the system. And the switch problem of the self-turned prediction horizon is solved through the division of the terminal region. Theoretical analysis reveals that the NMPC method is stable, and the convergence of the state errors can be guaranteed. Finally, simulation experiments on a four-wheeled OMR validate the effectiveness and superiority of the self-turned prediction horizon control method comparing with the fixed horizon NMPC method or other variable prediction horizon NMPC methods.

Designing non-linear model predictive control (NMPC) laws for controlling multiple autonomous surface vessels in arbitrary formations in environments containing obstacles are reported in this paper. Two leader-follower decentralized geometrical control schemes that are required for defining a unique two-dimensional formation are considered. A three-degree-of-freedom dynamic model of surface vessels has been used for the controller design. It is assumed that the surface vessels are under-actuated and obstacles are present in the vessels' work environment. The real-time optimization abilities of the NMPC method has been used to improve the response of the unactuated DOF of the vessels and to directly incorporate the local obstacle avoidance into the formation control eliminating the need for an external local obstacle avoidance algorithm. This leads to more effective obstacle avoidance decisions based on the dynamics of the vehicle. The effectiveness the developed control law, even in the presence of model uncertainty and external disturbances are demonstrated via computer simulations.