Nonlinear Model Predictive Control Controller Research Articles

Design of the predictive management and control system for combined propulsion complex

The object of this researching is the process of maneuvering a sea-based vehicle under compressed conditions, which requires one hundred percent reserve of thrusters (THRs) of various modifications and locations. The main problem is the provision of energy-efficient control over the ship's motion at low speed in the horizontal plane using a high-level predictive controller. The hierarchy of the motion control system (MCS) is usually divided into several levels with the help of a high-level motion controller and the THR motor control distribution algorithm. This allows for a modular software structure where a high-level controller (HLC) can be designed without using comprehensive information about the THR motors. However, for a certain reference of THR configurations, such a decoupling can lead to reduced control performance due to the limitations of HLC regarding the physical constraints of the vessel and the behavior of MCS. The main results of the researching are methods to improve control performance using a nonlinear model predictive control (MPC) as a basis for the designed motion controllers due to its optimized solution and ability to consider constraints. A decoupled system was implemented for two simple motor tasks showing dissociation problems. The shortcomings were eliminated through the development of a nonlinear MPC controller, which combines the motion controller and the distribution of control over THR motors. To preserve the discrete modularity of the control system and achieve adequate performance, a nonlinear MPC controller with time-varying constraints was designed. This has made it possible to take into account the current limitations of the THR control system, increase the accuracy of control, and reduce the response time of the system by 10 %.

Efficient Nonlinear Model Predictive Path Tracking Control for Autonomous Vehicle: Investigating the Effects of Vehicle Dynamics Stiffness

Motion control is one of the three core modules of autonomous driving, and nonlinear model predictive control (NMPC) has recently attracted widespread attention in the field of motion control. Vehicle dynamics equations, as a widely used model, have a significant impact on the solution efficiency of NMPC due to their stiffness. This paper first theoretically analyzes the limitations on the discretized time step caused by the stiffness of the vehicle dynamics model equations when using existing common numerical methods to solve NMPC, thereby revealing the reasons for the low computational efficiency of NMPC. Then, an A-stable controller based on the finite element orthogonal collocation method is proposed, which greatly expands the stable domain range of the numerical solution process of NMPC, thus achieving the purpose of relaxing the discretized time step restrictions and improving the real-time performance of NMPC. Finally, through CarSim 8.0/Simulink 2021a co-simulation, it is verified that the vehicle dynamics model equations are with great stiffness when the vehicle speed is low, and the proposed controller can enhance the real-time performance of NMPC. As the vehicle speed increases, the stiffness of the vehicle dynamics model equation decreases. In addition to the superior capability in addressing the integration stability issues arising from the stiffness nature of the vehicle dynamics equations, the proposed NMPC controller also demonstrates higher accuracy across a broad range of vehicle speeds.

Optimized Trajectory Tracking for ROVs Using DNN + ENMPC Strategy

This study introduces an innovative double closed-loop 3D trajectory tracking approach, integrating deep neural networks (DNN) with event-triggered nonlinear model predictive control (ENMPC), specifically designed for remotely operated vehicles (ROVs) under external disturbance conditions. In contrast to single-loop model predictive control, the proposed double closed-loop control system operates in two distinct phases: (1) The outer loop controller uses a DNN controller to replace the LMPC controller, overcoming the uncertainties in the kinematic model while reducing the computational burden. (2) The inner loop velocity controller is designed using a nonlinear model predictive control (NMPC) algorithm with its closed-loop stability proven. A DNN + ENMPC 3D trajectory tracking method is proposed, integrating a velocity threshold-triggered mechanism into the inner-loop NMPC controller to reduce computational iterations while sacrificing only a small amount of tracking control performance. Finally, simulation results indicate that compared with the ENMPC algorithm, NMPC + ENMPC can better track the desired trajectory, reduce thruster oscillations, and further minimize the computational load.

Study of parabolic trough collector with crucial analysis on controller and estimator with variable mirror efficiency

Solar Thermal Power (STP) plants are a crucial technology for converting solar energy into electricity. Among the STP, the Parabolic Trough Collector (PTC) is one of the integral parts of STP systems for electrical power generation. Maximizing PTC performance is a challenge due to dynamic and unpredictable solar radiation and environmental disturbances, such as cloud cover and dust accumulation. The optical efficiency parameter of the PTC is critical for calculating the desired heat gain, which is difficult to measure in real-time, necessitating sophisticated control and estimation strategies for optimal heat regulation. This study introduces two control mechanisms for the PTC system and comparing their efficacy. A classical PI controller supplemented by Static Feed-Forward (SFF) control demonstrates improved performance with an optimal transfer function model. In contrast, Nonlinear Model Predictive Control (NMPC) excels in disturbance rejection and setpoint tracking, considering operational constraints. The NMPC controller notably outperforms the PI controller with SFF in performance metrics, with the Integral Time Squared Error (ITSE) decreasing by approximately 99% across case studies. Also, in the case of heat gain, NMPC controller exhibits percentage increases when compared to the PI controller. Furthermore, since the measurement of optical efficiency is essential, but due to difficulty in the measurement for various reasons, the estimator is used as a virtual sensor to estimate those optical efficiency. The unmeasured states and parameters, including optical efficiencies of the PTC, are estimated using Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) techniques, with UKF exhibiting superior accuracy. However, considering the average computation time, EKF is preferred for real-time applications.

A nonlinear model predictive control method for ship path following in waves

ABSTRACT With the development of intelligent ships, the problem of ship path following has attracted much attention in recent years. Ship motion is inevitably affected by an external environment and thus the design of the ship control system in currents or waves, etc. has always been a challenging work. In the present work, a Nonlinear Model Predictive Control (NMPC) method is proposed for ship path following in waves. The NMPC controller can obtain the desired rudder angle of nonlinear ship system by solving an open-loop optimisation problem. The NMPC controller integrated with a Line-of-Sight (LOS) guidance is proposed and applied for a container ship which is controlled to follow two desired paths in both calm water and waves. The simulation results demonstrate the more effectiveness and greater anti-interference of the proposed NMPC method, compared with that the results by using a traditional Proportional-Derivative (PD) control method.

An Advanced Control Method for Aircraft Carrier Landing of UAV Based on CAPF–NMPC

This paper investigates a carrier landing controller for unmanned aerial vehicles (UAVs), and a nonlinear model predictive control (NMPC) approach is proposed considering a precise motion control required under dynamic landing platform and environment disturbances. The NMPC controller adopts constraint aware particle filtering (CAPF) to predict deck positions for disturbance compensation and to solve the nonlinear optimization problem, based on a model establishment of carrier motion and wind field. CAPF leverages Monte Carlo sampling to optimally estimate control variables for improved optimization, while utilizing constraint barrier functions to keep particles within a feasible domain. The controller considers constraints such as fuel optimization, control saturation, and flight safety to achieve trajectory control. The advanced control method enhances the solution, estimating optimal control sequences of UAV and forecasting deck positions within a moving visual field, with effective trajectory tracing and higher control accuracy than traditional methods, while significantly reducing single-step computation time. The simulation is carried out using UAV “Silver Fox”, considering several scenarios of different wind scales compared with traditional CAPF–NMPC and the nlmpc method. The results show that the proposed NMPC approach can effectively reduce control chattering, with a landing error in rough marine environments of around 0.08 m, and demonstrate improvements in trajectory tracking capability, constraint performance and computational efficiency.

Set Membership identification for NMPC complexity reduction

A Set Membership (SM) approach is proposed to reduce the computational burden of Nonlinear Model Predictive Control (NMPC) algorithms. In particular, a SM identification method is applied to derive an approximation and tight bounds of the NMPC control law, using a set of its values computed offline. These quantities are used online to reduce the dimension and the volume of the search domain of the NMPC optimization algorithm, and to perform a warm start, allowing a significant shortening of the computational time. The developed NMPC methodology is tested in simulation, considering an obstacle avoidance application in a realistic autonomous vehicle scenario. The obtained results demonstrate the effectiveness of the proposed approach in terms of computation time, without affecting the solution quality.

Time-certified Input-constrained NMPC via Koopman Operator

Determining solving-time certificates of nonlinear model predictive control (NMPC) implementations is a pressing requirement when deploying NMPC in production environments. Such a certificate guarantees that the NMPC controller returns a solution before the next sampling time. However, NMPC formulations produce nonlinear programs (NLPs) for which it is very difficult to derive their solving-time certificates. Our previous work, Wu and Braatz (2023), challenged this limitation with a proposed input-constrained MPC algorithm having exact iteration complexity but was restricted to linear MPC formulations. This work extends the algorithm to solve input-constrained NMPC problems, by using the Koopman operator and a condensing MPC technique. We illustrate the algorithm performance on a high-dimensional, nonlinear partial differential equation (PDE) control case study, in which we theoretically and numerically certify the solving time to be less than the sampling time.

Trajectory Tracking Control of a Skid-Steer Mobile Robot Based on Nonlinear Model Predictive Control with a Hydraulic Motor Velocity Mapping

In this study, we address the trajectory tracking control problem of a hydraulic-driven skid-steer mobile robot. A hierarchical control strategy is proposed to simultaneously consider the robot’s position control and the velocity control of the hydraulic motors. At the upper level, a nonlinear model predictive control (NMPC) method is employed to control the position and heading of the mobile robot. The NMPC controller takes into account the robot’s physical constraints and generates the desired robot motion velocity. Then, to control the hydraulic drive system, a current–velocity mapping-based control method is introduced. By establishing the mapping relationship between the control current applied to the hydraulic motor and its corresponding output velocity, the dynamics of the hydraulic motors are characterized. Consequently, the lower-level controller can directly obtain the control signal for the hydraulic actuator through lookup mappings. Additionally, PID controllers are adopted to compensate for velocity tracking errors. The proposed hierarchical control strategy decouples the robot’s position control and the hydraulic system control, simplifying the overall controller design, leading to improved control performance. To validate the effectiveness of the proposed control strategy, several experiments were conducted on a hydraulic-driven skid-steer mobile robot, and the results demonstrate the effectiveness of the proposed approach.

Robust tube-based NMPC for dynamic systems with discrete degrees of freedom

We present a robust nonlinear model predictive control (NMPC) algorithm for dynamic systems with mixed degrees of freedom, i.e., continuous and discrete manipulated variables. The discrete variables are often excluded from the NMPC layer and determined at a supervisory layer, which typically leads to suboptimal solutions. In contrast, the proposed controller optimizes both classes of degrees of freedom within the NMPC layer, thereby enhancing the closed-loop performance. Our approach relies on a computationally efficient relaxation and integrality restoration strategy. Initially, a nominal controller computes relaxed central reference trajectories for the states and the input variables. These trajectories are then tracked by an ancillary NMPC controller before the integrality of the discrete variables is restored. The role of the ancillary controller is to ensure robustness against the integer restoration error as well as other disturbances based on a nonlinear Tube MPC approach. Furthermore, we provide sufficient conditions to establish recursive feasibility and guarantee robust closed-loop stability. Finally, the effectiveness of the approach is demonstrated through two nonlinear simulation examples, affirming its viability and robustness.

Robust adaptive three-dimensional trajectory tracking control for unmanned underwater vehicles with disturbances and uncertain dynamics

Aiming at the three-dimensional (3-D) trajectory tracking problem of UUV with uncertain dynamics in an unknown and bounded external disturbance environment, a new dual closed-loop controller based on nonlinear model predictive control (NMPC) and adaptive integral sliding mode control (AISMC) is designed. The outer-loop NMPC controller designed based on position and attitude tracking errors generates a virtual desired velocity command and transmits it to the inner-loop controller. The inner-loop adaptive integral sliding mode controller based on speed tracking error design combines adaptive radial basis (RBF) neural network controller and disturbance observer to approximate the uncertainty of system model parameters and environmental disturbances, and then generates the actual control input to the UUV system. Different from other cascaded control systems, the designed controller combines the advantages of display processing constraints of MPC and robustness of SMC, which can improve the robustness of the control system, it effectively considers the actual constraints of the system input and state, and avoids the saturation of the actuator. In addition, the stability of the closed-loop system with and without disturbances is proved respectively based on the Lyapunov method. Finally, simulation results verify the effectiveness of the proposed controller: Under the perturbation of 10% model parameters, the UUV can accurately track the desired trajectory.

Trajectory Tracking and Obstacle Avoidance of Robotic Fish Based on Nonlinear Model Predictive Control.

The attainment of accurate motion control for robotic fish inside intricate underwater environments continues to be a substantial obstacle within the realm of underwater robotics. This paper presents a proposed algorithm for trajectory tracking and obstacle avoidance planning in robotic fish, utilizing nonlinear model predictive control (NMPC). This methodology facilitates the implementation of optimization-based control in real-time, utilizing the present state and environmental data to effectively regulate the movements of the robotic fish with a high degree of agility. To begin with, a dynamic model of the robotic fish, incorporating accelerations, is formulated inside the framework of the world coordinate system. The last step involves providing a detailed explanation of the NMPC algorithm and developing obstacle avoidance and objective functions for the fish in water. This will enable the design of an NMPC controller that incorporates control restrictions. In order to assess the efficacy of the proposed approach, a comparative analysis is conducted between the NMPC algorithm and the pure pursuit (PP) algorithm in terms of trajectory tracking. This comparison serves to affirm the accuracy of the NMPC algorithm in effectively tracking trajectories. Moreover, a comparative analysis between the NMPC algorithm and the dynamic window approach (DWA) method in the context of obstacle avoidance planning highlights the superior resilience of the NMPC algorithm in this domain. The proposed strategy, which utilizes NMPC, demonstrates a viable alternative for achieving precise trajectory tracking and efficient obstacle avoidance planning in the context of robotic fish motion control within intricate surroundings. This method exhibits considerable potential for practical implementation and future application.

Energy Efficiency and Optimization Strategies in a Building to Minimize Airborne Infection Risks

Heating, ventilation, and air conditioning (HVAC) systems play a crucial role in either increasing or decreasing the risk of airborne disease transmission. High ventilation, for instance, is a common method used to control and reduce the infection risk of airborne diseases such as COVID-19. On the other hand, high ventilation will increase energy consumption and cost. This paper proposes an optimal HVAC controller to assess the trade-off between energy consumption and indoor infection risk of COVID-19. To achieve this goal, a nonlinear model predictive controller (NMPC) is designed to control the HVAC systems of a university building to minimize the risk of COVID-19 transmission while reducing building energy consumption. The NMPC controller uses dynamic models to predict future outputs while meeting system constraints. To this end, a set of dynamic physics-based models are created to capture heat transfer and conservation of mass, which are used in the NMPC controller. Then, the developed models are experimentally validated by conducting experiments in the ETLC building at the University of Alberta, Canada. A classroom in the building is equipped with a number of sensors to measure indoor and outdoor environmental parameters such as temperature, relative humidity, and CO2 concentration. The validation results show that the model can predict room temperature and CO2 concentration by 0.8%, and 2.4% mean absolute average errors, respectively. Based on the validated models, the NMPC controller is designed to calculate the optimal airflow and supply air temperature for every 15 min. The results for real case studies show that the NMPC controller can reduce the infection risk of COVID-19 transmission below 1% while reducing energy consumption by 55% when compared to the existing building controller.

Trajectory planning and control for autonomous vehicles: a “fast” data-aided NMPC approach

A huge research effort is being spent worldwide by automotive companies and academic institutions for developing vehicles with high levels of autonomy, ranging from advanced driving-assisted systems to fully automated vehicles. Nonlinear Model Predictive Control (NMPC) has the potential to become a key technology in this context, thanks to its capability to deal with linear and nonlinear systems, manage physical constraints and satisfy multi-objective performance criteria. However, NMPC is based on the on-line solution of a nonconvex optimization problem and this operation may require a high computational cost, compromising its real-time implementation. In this paper, a “fast” data-aided NMPC approach is developed, aimed at trajectory planning and control for autonomous vehicles. In particular, a Set Membership approximation method is used to derive from data tight bounds on the optimal NMPC control law. These bounds are used to restrict the search domain of the underlying NMPC optimization process, allowing a significant reduction of the computation time. The proposed NMPC trajectory planning and control approach is tested in simulation and compared with other state-of-the-art methods, considering different road scenarios.

Energy Management of P2 Hybrid Electric Vehicle Based on Event-Triggered Nonlinear Model Predictive Control and Deep Q Network

Hybrid electric vehicles (HEVs) are used as a bridge during the transition to battery electric vehicles (BEVs) and to make energy consumption more efficient. The main problem in improving the efficiency of HEV energy consumption is torque management. In this study, a novel approach based on a nonlinear model predictive controller to solve the reference tracking and torque distribution problem is proposed. That is to say, in order to increase the efficiency of torque distribution, the weights of nonlinear model predictive control (NMPC) are trained with a Deep Q Network (DQN), and an event-triggered mechanism is designed with DQN to reduce the computational cost of MPC. The considered torque distribution problem varies according to the type and structure of the HEV. In this study, a parallel type 2 hybrid electric vehicle (P2 HEV) is considered and modeled via publicly shared passenger vehicle data of the engine, motor, high-voltage battery, transmission, clutch, differential, and wheel characteristics. NMPC is formulated so that the torque values remain within the physical limits of the engine, and the battery also operates at its physical limits. Namely, it is guaranteed that the battery works according to a certain state of charge (SOC) window and current limits. The state of health (SOH) of the battery is also considered in the optimization. The motor and engine efficiencies increase by 3.61% and 2.86%, respectively, with the proposed control structure, while the computational cost is reduced by 52.01% when utilizing the proposed event-triggering mechanism in the NMPC controller.

A novel engine and battery coupled thermal management strategy for connected HEVs based on switched model predictive control under low temperature

Under a low-temperature environment, electric vehicles face serious environmental adaptability problems, and efficient vehicle thermal management strategies are urgently needed. This paper presents a novel engine–battery coupled thermal management strategy for connected hybrid electric vehicles (HEVs). An improved system structure for an engine–battery coupled thermal management system (engine–battery CTMS) is designed to avoid unnecessary heat loss. The control requirements of the engine–battery CTMS include minimum engine fuel consumption, minimum power battery aging damage and minimum system energy consumption, which constitutes a multi-objective optimal control problem in a finite time domain. Based on model predictive control (MPC) theory, a switched nonlinear MPC (NMPC) control strategy is proposed to solve the optimal control problem of the complex coupled multi-input multi-output system. To verify the effectiveness of the proposed strategy, three comparative experiments of the centralized NMPC-based and rule-based methods combined with the improved system structure and the unimproved system structure are designed. The results of the cosimulation experiment between MATLAB/Simulink and AMEsim under various driving cycles and different ambient temperatures show that the improved structure and switched control strategy confer great advantages in reducing the controller computation burden, engine fuel consumption, and power battery aging damage.

Embedded MPC Strategies for ESP-Lifted Oil Wells: Hardware-in-the-Loop Performance Analysis of Nonlinear and Robust Techniques

This paper proposes embedded model predictive control strategies for oil-production processes equipped with electric submersible pump (ESP) installations. The novelty of this paper is the robustness and computational performance analysis of the Robust Infinite-Horizon Model Predictive Controller (RIHMPC) and Nonlinear Model Predictive Controller (NMPC) strategies, which have not yet been documented by the oil and gas exploration and production literature. The proposed method to embed the control laws is flexible with different hardware and is based on automatic code generation, which facilitates the project workflow. Hardware-in-the-loop simulation cases were used to compare the performance of both control strategies embedded in the Teensy 4.1 microcontroller, using key indices for real applications. The results showed that the RIHMPC strategy is a very promising alternative for real-time operation in ESP-lifted oil wells, with overall performance similar to the NMPC controller, even in noisy and plant–model mismatch scenarios, and using only linear models in its formulation.

Design and Control of the “TransBoat”: A Transformable Unmanned Surface Vehicle for Overwater Construction

This article presents the TransBoat, a novel omnidirectional unmanned surface vehicle (USV) with a magnet-based docking system for overwater construction with wave disturbances. This is the first such USV that can build overwater structures by transporting modules. The TransBoat incorporates two features designed to reject wave disturbances. First, the TransBoat's expandable body structure can actively transform from a mono-hull into a multihull for stabilization in turbulent environments by extending its four outrigger hulls. Second, a real-time nonlinear model predictive control (NMPC) scheme is proposed for all shapes of the TransBoat to enhance its maneuverability and resist disturbance to its movement, based on a nonlinear dynamic model. An experimental approach is proposed to identify the parameters of the dynamic model, and a subsequent trajectory tracking test validates the dynamics, NMPC controller, and system mobility. Further, docking experiments identify improved performance in the expanded form of the TransBoat compared with the contracted form, including an increased success rate (of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\sim } 10\%$</tex-math></inline-formula> ) and reduced docking time (of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\sim } 40$</tex-math></inline-formula> s on average). Finally, a bridge construction test verifies our system design and the NMPC control method.

Path tracking control of unmanned ground vehicles considering the signal time delay

Research on path tracking control of unmanned ground vehicles based on control methods such as model predictive control (MPC) is gradually prosperous. However, the problem caused by the signal time delay has not been taken seriously. It is found that the iterative mechanism of MPC is beneficial for solving this problem, and proposed a solution based on this mechanism. The principle of this solution is to use the control inputs of previous control periods as the inputs of the iteration periods of the prediction model corresponding to the signal time delay. So that the start moment of the iteration period where the first value of the control input sequence of the current control period is located can correspond to the moment when the control input arrives at the vehicle precisely. Based on this solution, a nonlinear MPC (NMPC) controller is designed and verified by co-simulation with MATLAB and Carsim. The simulation results show that the proposed controller can complete the path tracking control in the system with the signal time delay which the traditional NMPC controller and Stanley controller fail, and has high accuracy and real-time performance. In all simulation results, the absolute value of the displacement error does not exceed 0.2622 m, the absolute value of the heading error does not exceed 0.0909 rad, and the solution cost in each control period does not exceed 13 ms. Furthermore, it is also confirmed that the performance of this solution is superior to other solutions dealing with signal time delay.

A Comparative Study between NMPC and Baseline Feedback Controllers for UAV Trajectory Tracking

Transport, rescue, search, surveillance, and disaster relief tasks are some applications that can be developed with unmanned aerial vehicles (UAVs), where accurate trajectory tracking is a crucial property to operate in a cluttered environment or under uncertainties. However, this is challenging due to high nonlinear dynamics, system constraints, and uncertainties presented in cluttered environments. Hence, uncertainties in the form of unmodeled dynamics, aerodynamic effects, and external disturbances such as wind can produce unstable feedback control schemes, introducing significant positional tracking errors. This work presents a detailed comparative study between controllers such as nonlinear model predictive control (NMPC) and non-predictive baseline feedback controllers, with particular attention to tracking accuracy and computational efficiency. The development of the non-predictive feedback controller schemes was divided into inverse differential kinematics and inverse dynamic compensation of the aerial vehicle. The design of the two controllers uses the mathematical model of UAV and nonlinear control theory, guaranteeing a low computational cost and an asymptotically stable algorithm. The NMPC formulation was developed considering system constraints, where the simplified dynamic model was included; additionally, the boundaries in control actions and a candidate Lyapunov function guarantees the stability of the control structure. Finally, this work uses the commercial simulator DJI brand and DJI Matrice 100 UAV in real-world experiments, where the NMPC shows a reduction in tracking error, indicating the advantages of this formulation.