Time-varying Model Predictive Control Research Articles

Steering control for handling and stability and wear resistance of multi-axle vehicles

The steering performance of a vehicle directly affects its handling and stability, and tire wear during steering. For multi-axle vehicles equipped with a mechanical hydraulic steering system (MHS), this paper describes a steering-by-wire hydraulic system (SHS) for a third axle that can reduce the steering wear of third-axle tires while improving the handling and stability. A hydraulic steering system based on a reliable self-locking alignment cylinder was designed in this study, and a nonlinear dynamics model of a multi-axle vehicle was developed. In terms of the control strategy, the upper controller was a decision selector with a lateral acceleration threshold of 0.3 g , at which point the system entered the nonlinear kinematic state as a criterion for decision-making. The suboptimal linear time-varying model predictive control (S-LTV-MPC) method or Ackermann steering theory was used to calculate the target steering angle of the third axle. The lower controller was a fuzzy proportional–integral–derivative controller for tracking the steering angle of the third axle. The simulation and test results showed that the S-LTV-MPC method can meet the requirements of real-time control and accuracy. The designed SHS exhibited good handling and stability, and anti-wear properties during steering.

Real-time time-varying economic nonlinear model predictive control for wind turbines

Economic nonlinear model predictive control is a great choice to tackle the control issues appearing in the current wind energy industry. In this paper, instead of generator power, aerodynamic power is employed in the economic cost function to establish the required conditions of stability and convergence of the economic performance, such as turnpike and problem convexity. However, since aerodynamic power depends on time-varying wind speed, conventional time-invariant economic nonlinear model predictive controllers cannot guarantee the stability and convergence of economic performance. This paper proposes a new time-varying economic nonlinear model predictive controller for wind turbine control that considers an economic trajectory, instead of a steady-state, in its optimization problem. The proposed time-varying economic cost function directly considers aerodynamic power, the activity of pitch angle and generator torque, and fatigue loads on the shaft and tower. Therefore, this controller can maximize power extraction and reduce fatigue load on the tower, drivetrain, and actuators. Furthermore, a fast-parallel Newton-type method is used to implement the proposed controller in actual wind turbines. An accurate aeroelastic model is used to validate the performance of the proposed control scheme. The proposed controller is also compared with two tracking nonlinear model predictive controllers, the baseline controller, and a newly developed method, under fatigue and extreme load scenarios in the presence and absence of uncertainty. The simulation results show the superior economic performance of the proposed approach. Moreover, the real-time results verify the computational speed that the proposed controller requires to deploy actual wind turbines.

A novel collision avoidance strategy for highway overtaking considering the driver’s steering intent

Intelligent driving has been prevailing worldwide and is also challenging, which can be complicated by the factors of human drivers. In this paper, a novel collision avoidance strategy is proposed to enhance driving safety in highway overtaking by comprehensively considering the driver’s steering intent. First, in order to capture the driver’s operational characteristics from the driving data, we formulate the prediction of the driver’s steering intent and the ego vehicle’s states as a multivariate time series (MTS) forecasting problem, which is then handled by deep learning with a time pattern attention mechanism (DL-Attn). Second, a predictive risk field (PRF) model is proposed to quantify the real-time overtaking risk based on the above prediction results. Then, the overtaking is evaluated via a personalized risk threshold which can be set for a specific driver via experiments. Next, a linear time-varying model predictive control (LTV-MPC) -based assistance controller is designed so as to interfere in the risky overtaking and take over the ego vehicle from the driver to avoid possible collisions. And the feasibility and stability of the closed system are ensured theoretically. Finally, experiments are carried out in three typical cases. The results demonstrate that the proposed strategy can not only effectively improve driving safety for highway overtaking, but also identify safe overtaking to avoid unnecessary interference.

A time-varying driving style oriented model predictive control for smoothing mixed traffic flow

Connected and automated vehicles (CAVs) have great potential to smooth mixed traffic flow. To focus on the fact that the driving styles of HDVs are time-varying, a new control framework based on time-varying model predictive control (MPC) is proposed for mixed traffic flow in longitudinal control. Firstly, a genetic algorithm can be employed to calibrate the parameters of the car-following model based on offline trajectory data, representing the long-term driving style of HDVs. Secondly, the short-term driving style is recognized through modifying the long-term driving style based on real-time trajectory data within a sliding window. Then, this paper seeks to design a time-varying MPC control framework to realize a smoother mixed traffic flow. Finally, compared to the baseline model, the method we proposed achieves the high-performance both in fuel consumption and driving comfort under various scenarios, and maintains fast online calculations. Besides, it also displays the significant potential of saving fuel consumption in a large-scale traffic system, reducing by over 11.28% with 17∼33% penetration rates of CAVs.

Coordinated control of path tracking and yaw stability for distributed drive electric vehicle based on AMPC and DYC

Maintaining both path-tracking accuracy and yaw stability of distributed drive electric vehicles (DDEVs) under various driving conditions presents a significant challenge in the field of vehicle control. To address this limitation, a coordinated control strategy that integrates adaptive model predictive control (AMPC) path-tracking control and direct yaw moment control (DYC) is proposed for DDEVs. The proposed strategy, inspired by a hierarchical framework, is coordinated by the upper layer of path-tracking control and the lower layer of direct yaw moment control. Based on the linear time-varying model predictive control (LTV MPC) algorithm, the effects of prediction horizon and weight coefficients on the path-tracking accuracy and yaw stability of the vehicle are compared and analyzed first. According to the aforementioned analysis, an AMPC path-tracking controller with variable prediction horizon and weight coefficients is designed considering the change of vehicle speed in the upper layer. The lower layer involves DYC based on the linear quadratic regulator (LQR) technique. Specifically, the intervention rule of DYC is determined by the threshold of the yaw rate error and the phase diagram of the sideslip angle. Extensive simulation experiments are conducted to evaluate the proposed coordinated control strategy under different driving conditions. The results show that, under variable speed and low adhesion conditions, the vehicle yaw stability and path-tracking accuracy have been improved by 21.58% and 14.43%, respectively, compared to AMPC. Similarly, under high speed and low adhesion conditions, the vehicle yaw stability and path-tracking accuracy have been improved by 44.30% and 14.25%, respectively, compared to the coordination of LTV MPC and DYC. The results indicate that the proposed adaptive path-tracking controller is effective across different speeds. Furthermore, the proposed coordinated control strategy successfully enhances the vehicle stability while maintaining good path-tracking accuracy even under extreme conditions.

Linear time-varying fractional-order model predictive attitude control for satellite using two reaction wheels

Achieving precise attitude control in satellites equipped with two reaction wheels remains a significant challenge. During the last decade, model predictive control has emerged as a promising technique for satellite attitude control. However, this paper takes a step by introducing the novel concept of linear time-varying fractional-order model predictive control specifically tailored for satellites with dual reaction wheels, enabling them to achieve desired orientations more effectively. This study begins by elucidating the nonlinear dynamics and kinematic equations governing the satellite's behavior. To facilitate control design, the satellite linear time-varying model is derived by linearizing the nonlinear equations around the operating point. Leveraging this linearized representation, a linear time-varying fractional-order model predictive control method is designed, leveraging the benefits of fractional-order cost functions. Finally, the simulation results show the remarkable performance of the linear time-varying fractional-order model predictive control approach, particularly when confronted with input constraints. Notably, the proposed method outperforms the traditional linear time-varying model predictive control method by achieving an 80% improvement in tracking speed, while simultaneously reducing the applied torque by 67%. Additionally, the proposed approach decreases the mean absolute error of the satellite attitude angles by over 80% compared to the conventional linear time-varying model predictive control method. This research not only addresses the pressing challenge of attitude control in satellites with dual reaction wheels but also presents a novel and highly effective approach that surpasses existing methods in terms of performance and efficiency. As such, it holds immense potential for the field of satellite attitude control, making it an indispensable read for engineers and researchers working in the domain of aerospace engineering and control systems.

Obstacle avoidance decision and trajectory tracking control of intelligent vehicle considering surrounding vehicles

To enhance the obstacle avoidance performance and trajectory tracking control stability of vehicles in emergency scenarios, and to solve the problem that the existing decision-making methods based on the minimum safe distance model cannot effectively make decisions in some scenarios, a novel lane-changing obstacle avoidance decision-making and control method is proposed. Initially, when emergency braking cannot avoid obstacles safely, the lane-changing trajectory is planned by quintic polynomial, and the minimum distance and collision detection (MDCD) algorithm is then employed to ascertain whether the lane-changing trajectory meets the safety conditions. Subsequently, a Linear Time-Varying Model Predictive Control (LTV MPC) trajectory tracking controller is designed based on the 7-DOF vehicle dynamics model. Finally, the effectiveness of the proposed method is verified through two representative scenarios. The simulation results indicate that the MDCD algorithm can ensure the safety and effectiveness of obstacle avoidance decisions in all emergency obstacle avoidance scenarios, and when tracking the emergency lane-changing trajectory in different typical scenarios, compared with the LTV MPC controller based on the single-track vehicle dynamics model (STVDM), the maximum tracking error can be reduced by 50.7% and 60.1%, respectively, while ensuring near-equivalent real-time performance operation.

Energy management of hybrid electric vehicle based on linear time-varying model predictive control

Energy management of hybrid electric vehicle based on linear time-varying model predictive control

Risk-informed decision-making and control strategies for autonomous vehicles in emergency situations

This paper proposes risk-informed decision-making and control methods for autonomous vehicles (AVs) under severe driving conditions, where many vehicle interactions occur on slippery roads. We assume that the AV should approach a specific safe zone in case of vehicle malfunctioning. In normal situations, the driving behavior of the AV is based on the deterministic finite-state machine (FSM) that makes an appropriate real-time decision depending on the driving condition, which is efficient when compared with some conventional decision-making algorithms; alternatively, in emergency situations, the AV first has to be prevented the rear-end conflicts while the specific safe zone is simultaneously determined by evaluating the level of risk via two safety level indicators, i.e., Time-To-Collision (TTC) and Deceleration Rate to Avoid the Crash (DRAC). The safe path that guides the AV to avoid car crashes is generated based on the trajectory optimization theory (i.e., Pontryagin maximum principle), and the AV follows it based on the linear time-varying model predictive control (LTV-MPC), which ensures the AV’s lateral stability. We verify the effectiveness of the proposed decision-making and control strategies in various test scenarios, and the results show that the AV behaves appropriately according to the behaviors of surrounding vehicles and road condition.

Optimization of liquid cooling heat dissipation control strategy for electric vehicle power batteries based on linear time-varying model predictive control

The heat dissipation performance of batteries is crucial for electric vehicles, and unreasonable thermal management strategies may lead to reduced battery efficiency and safety issues. Therefore, this paper proposed an optimization strategy for battery thermal management systems (BTMS) based on linear time-varying model predictive control (LTMPC). To begin, based on the results of three-dimensional thermal flow analysis, a reduced order substitution model for the battery cooling system was established. Next, to address the issue of high computational complexity caused by the nonlinear model in the controller, a linearization method based on staged control was designed. Furthermore, the control parameters were optimized using the particle swarm optimization algorithm. Finally, a BTMS physical model based on SIMSCAPE was established for performance simulation. The performance of the logic threshold controller (LTC), linear model predictive controller (LMPC), and nonlinear model predictive controller (NMPC) was compared and analyzed. LTMPC was found to reduce the average temperature of the battery by up to 2.33 °C and 1.90 °C, and the cumulative temperature difference is reduced by 13.9% and 16.6% compared to LTC and NMPC, respectively. Compared to LMPC, LTMPC reduces thermal management energy consumption by 21.2%.

Model prediction controller for penetration mechanism of seabed cone penetration test system

The system of seabed Cone Penetration Test (CPT) is a kind of equipment for offshore investigations. Seabed CPT is used to assess multiple physical properties of marine sediments. Constant-rate penetration mechanism is the core part of seabed CPT, which adopts dual-cylinder drive to penetrate the probe rod into the seafloor sediments at a constant speed (2cm/s). At present, the domestic CPT and its penetration equipment almost all rely on imports. In the process of system design, we found that the traditional PID control of the hydraulic cylinder position control accuracy is low, so we need to study higher precision position tracking control method to achieve uniform penetration of the probe rod. In this paper, a Linear Time-Varying Model Predictive Controller (LTV-MPC) is introduced, which can control two hydraulic cylinders to penetrate probe rod into the seabed sediment with smaller penetration rate error under the condition of changing penetration resistance.

Heat exchanger networks: A predictive control approach

This work demonstrates the development of a practical predictive control approach to regulate the outputs of a network of heat exchangers. The full nonlinear continuous-time dynamic of the network is introduced to simulate the real process. Whereas a discrete linear and simpler version of this dynamic is employed to construct the predictive controller as well as an extended Kalman estimator. The presented algorithm is a time-varying model predictive control (MPC) where the simplified model is successively linearized on-line around the current available measurements. For the closed-stability of the introduced MPC scheme, a modified method is suggested to design terminal stabilizing weights where reference tracking problem, external disturbance dynamics, as well as the proper dynamics of a heat exchanger with bypass are all considered. The on-line updated extended Kalman estimator is utilized to estimate both the process states and unknown disturbances. Thanks to the successive linearization technique, the introduced predictive controller benefits from efficient online computations and online adaptations in operation points. Nonetheless, an accurate model of the heat exchanger is essential. Compared with a typical linear MPC, it is concluded that the presented predictive algorithm produces satisfactory results for disturbance rejection and switched operation points circumstances.

Model predictive real-time architecture for secondary voltage control of microgrids

The integration of new elements and technologies to the power grid, driven by the expansion of electric microgrids, brings various challenges requiring a suitable control architecture for systems to operate ensuring economic and reliable access to electricity. This paper presents the development of a time-varying constraint real-time model predictive secondary voltage control (MPVC) strategy for microgrids built up in a multi-class Python environment with InfluxDB and SQLExpress databases storing the controller and microgrid data, and its experimental implementation with Modbus communication to physical devices at the Universidad Pontificia Bolivariana (UPB) campus microgrid. The microgrid characteristics are described and the experimental setup is presented. The mathematical model of the resource used as case study is obtained through experimental identification, and it is integrated to the MPVC scheme. Polytopic invariant sets are used as terminal sets in the MPVC scheme to ensure stability of the solution, and time-varying constraints of reactive power availability are considered. Validation studies of the proposed control system in computational simulation are presented prior to real application in the UPB campus microgrid. Controller performance results are described for three different implementation scenarios of low, medium and high variability of external disturbances, presenting adequate voltage regulation around the reference value and considerable dependence on the meteorological forecast quality. The model predictive voltage controller is finally benchmarked against a commercial microgrid controller to evaluate its performance, standing out as a more comprehensive and tailor-made solution.

Game Theory-Based Decision-Making and Iterative Predictive Lateral Control for Cooperative Obstacle Avoidance of Guided Vehicle Platoon

This paper presents a systematic decision-making and lateral control framework to realize cooperative obstacle avoidance (OA) of the guided vehicle platoons safely and integrally in multiple scenarios. In the control framework, a centralized decision-making strategy is developed to determine optimal overtaking maneuver (i.e., OA) in the dynamic driving environment, and a distributed lateral controller with a safe driving corridor planner is designed for lateral reference trajectories tracking. The proposed decision-making strategy formulates the influence mechanism between the controlled platoon and potential surrounding vehicles based on an interactive behavior model. Moreover, a game theory-based algorithm is applied to calculate safe timing of overtaking and select efficient overtaking mode while avoiding the negative impact on the surrounding vehicles. For the distributed lateral control strategy, the control problem is solved by a linear time-varying model predictive control (LTV-MPC) algorithm so as to reduce the computational burden. Furthermore, to improve the accuracy of LTV-MPC algorithm in varying scenarios, a tailored iterative control logic is presented. The performance of the proposed framework is evaluated on the dSPACE hardware-in-loop platform. The results show that the proposed framework works well under various test scenarios involving multiple static and moving obstacles.

Integrated Decision Making and Motion Control for Autonomous Emergency Avoidance Based on Driving Primitives Transition

Emergency avoidance is an aggressive maneuver with high collision risk. This paper presents an integrated decision making and motion control framework to achieve emergency avoidance in complex driving scenarios. This is realized by combining reasonable decision making based on driving primitives transition and efficient motion control under critical driving conditions. For decision making, the driving primitives including braking, lane changing, and accelerating are generalized to perform a complete emergency avoidance maneuver through the Minimum Safety Spacing analysis, which is numerically executed as a mapping function of the host vehicle's speed and road adhesion coefficient. For motion control, the quintic polynomial-based path planning is formulated as solving a minimum lane changing duration problem. Moreover, the Linear Time-Varying Model Predictive Control combined with the Direct Yaw-moment Control is put forward to realize accurate path tracking control for emergency avoidance. The effectiveness of the proposed scheme is examined under various scenarios based on comprehensive Hardware-in-Loop tests. The results show that the proposed framework can realize timely emergency avoidance with guaranteed vehicle dynamics stability based on proper decision-making and accurate path tracking control.

Research on control strategy of vehicle stability based on dynamic stable region regression analysis.

The intervention time of stability control system is determined by stability judgment, which is the basis of vehicle stability control. According to the different working conditions of the vehicle, we construct the phase plane of the vehicle's sideslip angle and sideslip angular velocity, and establish the sample dataset of the stable region of the different phase planes. To reduce the complexity of phase plane stable region division and avoid large amount of data, we established the support vector regression (SVR) model, and realized the automatic regression of dynamic stable region. The testing of the test set shows that the model established in this paper has strong generalization ability. We designed a direct yaw-moment control (DYC) stability controller based on linear time-varying model predictive control (LTV-MPC). The influence of key factors such as centroid position and road adhesion coefficient on the stable region is analyzed through phase diagram. The effectiveness of the stability judgment and control algorithm is verified by simulation tests.

Optimal coordinated control of active steering and direct yaw moment for distributed-driven electric vehicles

This paper considers the problem of optimal coordination of active steering and direct yaw moment for general electric vehicles equipped with in-wheel motors and steer-by-wire devices. As a typical over-actuated system, vehicle planar motion shows flexible control performance under different wheel actuations, thus achieving the optimal integration among them is of critical significance. Based on the modeling from wheel actuations of motor torques and wheel angles to vehicle planar motion states, this paper proposes an optimal hierarchical control framework composed of a reference state generator, a linear time-varying model predictive controller (LTV-MPC), and an optimal control allocator. Motor torques and wheel angles are decoupled as equivalent distributed variables by linearization technique. Then an optimal allocation framework is formed towards the trade-off between driving security and power saving, and a compensation module based on the back-propagation neural network (BPNN) is designed to guarantee the control allocation accuracy. Holistic multi-objective optimization is demonstrated through Co-simulations with Matlab/Simulink and TruckSim. Results verify the effectiveness of the proposed control strategy.

Design and Comparative Analysis of Several Model Predictive Control Strategies for Autonomous Vehicle Approaching a Traffic Light Crossing

Recent advancements in automated driving technology and vehicle connectivity are associated with the development of advanced predictive control systems for improved performance, energy efficiency, safety, and comfort. This paper designs and compares different linear and nonlinear model predictive control strategies for a typical scenario of urban driving, in which the vehicle is approaching a traffic light crossing. In the linear model predictive control (MPC) case, the vehicle acceleration is optimized at every time instant on a prediction horizon to minimize the root-mean-square error of velocity tracking and RMS acceleration as a comfort metric, thus resulting in a quadratic program (QP). To tackle the vehicle-distance-related traffic light constraint, a linear time-varying MPC approach is used. The nonlinear MPC formulation is based on the first-order lag description of the vehicle velocity profile on the prediction horizon, where only two parameters are optimized: the time constant and the target velocity. To improve the computational efficiency of the nonlinear MPC formulation, multiple linear MPCs, i.e., a parallel MPC, are designed for different fixed-lag time constants, which can efficiently be solved by fast QP solvers. The performance of the three MPC approaches is compared in terms of vehicle velocity tracking error, root-mean-square acceleration, traveled distance, and computational time. The proposed control systems can readily be implemented in future automated driving systems, as well as within advanced driver assist systems such as adaptive cruise control or automated emergency braking systems.

Trajectory-following and off-tracking minimisation of long combination vehicles: a comparison between nonlinear and linear model predictive control

In this paper, we compared the linear and nonlinear motion prediction models of a long combination vehicle (LCV). We designed a nonlinear model predictive control (NMPC) for trajectory-following and off-tracking minimisation of the LCV. The used prediction model allowed coupled longitudinal and lateral dynamics together with the possibility of a combined steering, propulsion and braking control of those vehicles in long prediction horizons and in all ranges of forward velocity. For LCVs where the vehicle model is highly nonlinear, we showed that the control actions calculated by a linear time-varying model predictive control (LTV-MPC) are relatively close to those obtained by the NMPC if the guess linearisation trajectory is sufficiently close to the nonlinear solution, in contrast to linearising for specific operating conditions that limit the generality of the designed function. We discussed how those guess trajectories can be obtained allowing off-line fixed time-varying model linearisation that is beneficial for real-time implementation of MPC in LCVs with long prediction horizons. The long prediction horizons are necessary for motion planning and trajectory-following of LCVs to maintain stability and tracking quality, e.g. by optimally reducing the speed prior to reaching a curve, and by generating control actions within the actuators limits.

Nonlinear hierarchical control for four-wheel-independent-drive electric vehicle

As under-constrained systems, four-wheel-independent-drive (4WID) electric vehicles have more driving degrees of freedom. In this context, reasonable control and distribution of driving or braking torque to each wheel is extremely important from the vehicle safety perspective. However, it is difficult to provide the optimal wheel torque because of the time-varying characteristics and typical over-actuated nature of the system. In light of these challenges, a novel hierarchical control scheme comprising a top- and bottom-level controller is proposed herein. First, for the top-level controller, a time-varying model-predictive-control (TV-MPC) controller is designed based on an extended 3-degree-of-freedom (3-DOF) reference vehicle model. The total driving force and additional yaw moment can be obtained using the TV-MPC. Second, for the bottom-level controller, the torque expression of each wheel is determined using the equal-adhesion-rate-rule -based algorithm. The co-simulation results obtained herein indicate that the proposed control scheme can effectively improve vehicle safety.