Model Predictive Control Structure Research Articles

Offset-Free Koopman Model Predictive Control of Thermal Comfort Regulation for a Variable Refrigerant Flow-Dedicated Outdoor Air System-Combined System

Abstract Variable refrigerant flow (VRF) system has been an appealing solution of air conditioning for residential and commercial buildings, due to its flexibility and cost effectiveness, while lack of ventilation capability is a major drawback. Incorporation of dedicated outdoor air system (DOAS) is a typical practice. However, good coordination between DOAS and VRF is critical for achieving desired thermal comfort is challenging due to the possible complexity of mixed sensible and latent heat exchanges. In this paper, to handle the nonlinear dynamic characteristics of VRF-DOAS system, we propose an offset-free Koopman model predictive control (MPC) strategy for thermal comfort regulation, in which the MPC design is computationally more efficient due to the convex problem formulation and the use of reduced-order Koopman models, and the offset-free MPC structure enhances the robustness to model uncertainties and unmeasured disturbances. A control-oriented model is obtained by hybridizing the first-principle and data-driven modeling approach. The proposed controls strategy is evaluated with a Modelica simulation model of a VRF-DOAS system. A Dymola-Python cosimulation platform is developed via the functional mockup interface (FMI), for which the MPC algorithms are implemented in Python. Simulation results show significantly better performance of the offset-free Koopman MPC in thermal comfort regulation.

A Model Predictive Control Scheme with Minimum Common-Mode Voltage for PMSM Drive System Fed by VSI

Common-mode voltage (CMV) brings shaft voltage and shaft current, and corrodes the bearings of the permanent-magnet synchronous machine (PMSM), which affects the reliability of the whole PMSM drive system. Since the CMV applied by the zero voltage vectors (ZVVs) is three times that applied by the active voltage vectors (AVVs), a modulation scheme achieving minimum CMV without ZVV is proposed and introduced into the model predictive control structure for the PMSM drive system. Firstly, the whole modulation range is divided into three regions, including the low voltage modulation region (LVMR), high voltage modulation region (HVMR), and over-voltage modulation region (OVMR). Meanwhile, the regional boundary expression is derived. Then, the active zero-state pulse width modulation (AZSPWM) is adopted in LVMR. To improve the steady-state performance, near-state pulse width modulation (NSPWM) without opposite ZVVs is applied to the HVMR. Furthermore, when the reference voltage vector (VV) is located in OVMR, an optimal scheme is proposed to improve the dynamic response. Under the premise of no ZVV existing in the whole modulation region, simulation and experimental results show that the proposed hybrid modulation method can improve the steady-state and dynamic performance of the PMSM drive system.

Modeling and economic model predictive control of constrained cutterhead system with disturbance in tunnel boring machines

Tunnel boring machines (TBMs) are usually the first choice for tunneling construction with its advantages on high safety, time saving, and less operators. Cutterhead system is an important component for TBMs since it is used to excavate rocks and soil. It is difficult to guarantee both the boring efficiency and energy saving under the excavating rock disturbances and the constraints on the driving motors in TBMs by manual operation. To deal with this problem, it is necessary to develop advanced control algorithms for the cutterhead system. Thus, we investigate an economic model predictive control (EMPC) structure for cutterhead system in TBMs. A generalized nonlinear dynamic model of TBM cutterhead system is built based on the first principle method. An economic cost is constructed with the boring efficiency and energy cost to evaluate the tunnel construction quality. EMPC algorithms are designed to optimize the constructed economic cost for a cutterhead system to guarantee good economic performance. It is shown that EMPC can improve the economic performance of the cutterhead system.

An optimal hybrid quadcopter control technique with MPC-based backstepping

Quadcopter unmanned aerial vehicle is a multivariable, coupled, unstable, and underactuated system with inherent nonlinearity. It is gaining popularity in various applications and has been the subject of numerous research studies. However, modelling and controlling a quadcopter to follow a trajectory is a challenging issue for which there is no unique solution. This study proposes an optimal hybrid quadcopter control with MPC-based backstepping control for following a reference trajectory. The outer-loop controller (backstepping controller) regulates the quadcopter’s position, whereas the inner-loop controller (Model Predictive Control) regulates its attitude. The translational and rotational dynamics of the quadcopter are analyzed utilizing the Newton-Euler method. After that, the backstepping controller (BC) is created, which is a recurrent control method according to Lyapunov’s theory that utilizes a genetic algorithm (GA) to choose the controller parameters automatically. In order to apply a linear control technique in the presence of nonlinearities in the quadcopter dynamics, Linear Parameter Varying (LPV) Model Predictive Control (MPC) structure is developed. Simulation validated the dynamic performance of the proposed optimal hybrid MPC-based backstepping controller of the quadcopter in following a given reference trajectory. The simulations demonstrate the fact that using a command control input in trajectory tracking, the proposed control algorithm offers suitable tracking over the assigned position references with maximum appropriate tracking errors of 0.1 m for the �� and �� positions and 0.15 m for the �� position.

Internal Model-Based Robust Path-Following Control for Autonomous Vehicles

The paper presents a new internal model control (IMC) based control technique for lateral trajectory tracking of autonomous vehicles. The controller’s proposed structure employs a robust, fault-tolerant nonlinear internal servo control with optimal reference generation concerning vehicle yaw stability and physical limitations. The presented inscription of the reference generation creates a convex optimization task that can be used in real-time applications. Improvements in yaw-rate stability of vehicle motion control are first shown through simulation results performed in a Simulink environment. The controller structure was also implemented in a real-time model and was examined in a Mercedes C-Class vehicle. In this article, the simulation results and the real-time measurements are presented. The results show that the proposed controller has high efficiency in disturbance rejection and lower sensitivity towards parameter changes compared to a model predictive control (MPC) structure.

The impact of model predictive control structures and constraints on a wave energy converter with hydraulic power take off system

Ocean waves present a promising renewable energy source, but are challenging to harness given their irregular nature. In order to maximize energy capture on wave energy converters (WECs), power take off (PTO) systems are typically used to effectively adjust the device’s resonant frequency. Optimal control techniques can oversee the PTO operation to maximize overall power output, but optimization in real-time poses difficulties given the wave variability and underlying constraints of the system. This study compares two different model predictive control approaches. One method uses only a model of the hydrodynamics of the WEC while the second has a state space model that includes the WEC hydrodynamics as the dynamics of a hydraulic PTO system. The impact of the PTO constraints, control structure and control prediction horizon on the wave energy converter control performance was explored and quantified for irregular wave conditions. Results show that utilizing a model that includes both the hydrodynamics and PTO dynamics can increase power output by 23% compared to an approach that uses the hydrodynamics only.

Proportional-Integral Control and ARX-based Model Predictive Control for Extractive Dividing Wall Column

Extractive dividing wall column (EDWC) is a typical process intensification technology and possesses significant energy-saving prospects, while the poor dynamic controllability hinders its industrialization goal. In this work, taking the benzene and cyclohexene azeotrope separation as an example, a proportional-integral (PI) control structure based on four-point temperature control loops is proposed for EDWC by considering temperature difference as the discriminant criterion. Subsequently, to improve the control performance of EDWC, two model predictive control (MPC) structures based on auto-regressive with external input (ARX) model obtained from closed-loop identification and linear time-invariant state-space (LTI-SS) model, respectively, are studied for EDWC. The performance of three control structures is tested by ±20 % feed flow rate and composition disturbances, and further quantitatively evaluated by integral absolute error (IAE). The dynamic responses demonstrate that the ARX-based MPC structure achieves the best control performance in the presence of feed flow rate and composition disturbances, which can be attributed to the capability of the identified ARX model to track the dynamic features of EDWC accurately.

Model Predictive Controller Approach for Automated Vehicle's Path Tracking.

In this paper, a model predictive control (MPC) approach for controlling automated vehicle steering during path tracking is presented. A (linear parameter-varying) LPV vehicle plant model including steering dynamics is proposed to determine the system evolution matrices. The steering dynamics are modeled in two different ways by using first-order lag and a second-order lag; the application of the first-order system resulted in a slightly more accurate path-following. Additionally, a cascade MPC structure is applied in which two MPCs are used; the second-order steering dynamics are separated from the path-following controller in a second MPC. Both steering system models and the cascade MPC are evaluated in simulation and on a test vehicle. The reference trajectory is calculated based on a fixed predefined path by transforming the necessary path segment to the vehicle ego coordinate system, thereby describing the reference for the path-following task in a novel way. The MPC method computes the optimal steering angle vector at each time step for following the path. The longitudinal dynamics is controlled separately by a PI controller. After simulation evaluation, experimental tests were conducted on a test vehicle on an asphalt surface. Both simulation and experimental results prove the effectiveness of the proposed reference definition method. The effect of the applied steering system models is evaluated. The inclusion of the steering dynamics in the prediction model resulted in a significant increase in controller performance. Finally, the computational requirements of the proposed control and modeling methods are also discussed.

Data-driven torque and pitch control of wind turbines via reinforcement learning

This paper addresses the torque and pitch control problems of wind turbines. The main contribution of this work is the development of an innovative reinforcement learning (RL)-based control method targeting wind turbine applications. Our RL-based control framework synergistically combines the advantages of deep neural networks (DNNs) and model predictive control (MPC) technologies. The proposed control strategy is data-driven, adapting to real-time changes in system dynamics and enhancing control performance and robustness. Additionally, the incorporation of an MPC structure within our design improves learning efficiency and reduces the high computational complexity typically found in deep RL algorithms. Specifically, a DNN is designed to approximate the wind turbine dynamics based on a continuously updated dataset composed of state and action measurements taken at specified sampling intervals. The real-time control policy is generated by integrating the online trained DNN into an MPC architecture. The proposed method iteratively updates the DNN and control policy in real-time to optimize performance. As a primary result of this work, the proposed method demonstrates superior robustness and control performance compared to commonly-employed MPC and other baseline wind turbine controllers in the presence of uncertainties and unexpected actuator faults. This effectiveness is showcased through simulations with a high-fidelity wind turbine simulator.

Enhancing sustainability of acid gas treatment in a Waste-to-Energy plant via Model Predictive Control

The municipal solid waste fed to waste-to-energy (WtE) plants produces acid flue gas with a wide and volatile range of composition, a scenario which implies significant process disturbances for traditional control schemes. In this paper, a two-stage dry sorbent system in an Italian treatment plant is used as a case study. The focus was on the first stage of abatement, where calcium hydroxide is injected into a reactor to reduce the hydrogen chloride (HCl) content in the acid flue gas. A state-space model, identified and tested in a previous work, was here implemented in a model predictive control (MPC) structure. In particular, four different MPC solutions were derived and tested on routine data in order to increase the process performance. Three suitable key performance indicators were used to assess the quantitative comparison between the proposed advanced control approaches and the simulated architecture of the one implemented in the WtE plant. The analysis evidenced the benefits obtained by MPC structures with respect to the current sub-optimal control architecture. Controller tuning and the possibility to include the online HCl concentration in the model have been also tested to highlight the best solution. Overall, the advanced controllers allowed one to achieve a solid profit-safety trade-off, by strictly tracking set-point on outlet HCl concentration and, at the same time, by requiring minimal sorbent doses and then minimal solid residues, with limited stress on the actuation system.

Constrained nonlinear high-efficiency model predictive technics for test mass capture

This paper presents a nonlinear high-efficiency model predictive control (NHMPC) with constraints designed for the test mass (TM) capture phase of the drag-free satellite about gravitational wave observatory. To avoid collisions between test mass and satellite cavity, TM capture is the essential technology for drag-free satellite. Test mass is located inside an electrostatic suspension and locked by a clamp mechanism initially. The test masses are released with high initial offsets and velocities when the mechanism is retracted. The purpose of this phase is to guarantee the TM to be positioned at the cage center and attitude aligned with the local cage frame. Due to the low actuation authority of electrostatic suspension along with critical initial offsets and velocities, it is a challenging task to design the attitude and translation control schemes with simultaneous consideration of system performance and energy consumption. For the problem given above, the TM capture can be reformulated into a nonlinear quadratic optimal control problem with the state and input constraints. A nonlinear model predictive control (NMPC) structure is also designed to handle the noises by forming a closed loop. This control framework can realize optimality and robustness in a compromise. To improve the speed of solving high-dimensional nonlinear optimal control online for MPC, the indirect Chebyshev pseudospectral method with constraints is employed. The convergence and stability of the control loop are analyzed. Simulation examples show that the feasibility and performance of the designed control loop are verified compared with the existing methods and computation times in the millisecond range can be achieved.

A Model Predictive Control of Electronic Limited Slip Differential and Differential Braking for Improving Vehicle Yaw Stability

This article presents a model predictive control design for improving the yaw stability of a rear-wheel-drive vehicle equipped with an electronic limited slip differential (ELSD) and differential braking capability. It first develops a model for an ELSD system for predicting its torque distribution dynamics, then uses the model in designing an intelligent ELSD control that prevents unwanted oversteering yaw moments through direct control of the ELSD clutch pressure. Since differential braking degrades the vehicle’s longitudinal motion and driver comfort, two control actuations are prioritized: 1) ELSD clutch pressure and 2) differential braking. An appropriate stability limit is defined for the vehicle yaw rate, and two control objectives: 1) enforcing the yaw rate stability limit and 2) tracking the desired yaw rate are defined and prioritized. The actuation priorities and the objective priorities are combined within a model predictive control structure with particular soft constraints such that the low priority actuation is activated when the high priority objective demands it. Additionally, optimum corner braking forces are calculated by geometrically analyzing tire force vectors. The performance of the proposed controller, implemented in a Cadillac CTS vehicle, is experimentally evaluated for a variety of driving maneuvers.

Low Computational Burden Predictive Direct Power Control of Quasi Z-Source Inverter for Grid-Tied PV Applications

This paper proposes a simplified predictive direct power control for the grid-tied quasi Z-source inverter. The proposed control implements a model predictive control structure to achieve the maximum obtainable power from the collected PV source. The power delivered to the grid is managed to compensate for the reactive power and, as needed, to ensure the grid’s stability. A predictive power model for a quasi Z-source inverter is developed in which the proposed control can operate with a fixed switching frequency without a weighting factor. The simplified space vector modulation uses the three appropriate switching vectors that are selected and applied using precalculated switching times during each switching period, in which the required switching vectors are determined only from one sector in the space vector diagram, taking all of the information of the other sectors, which leads to reducing the computational burden. Simulation results and comparative study are used to confirm the proposed control performance for the grid-tied quasi Z-source inverter capable of tracking and generating the maximum power from PV with fast-tracking dynamics, ensuring the ac voltage desired, and better tracking of the active and reactive power reference with the lowest power ripple. The grid current harmonics were tested and conformed to the IEEE-519 standard. Additionally, the proposed simplified PDPC is experimentally validated using the Hardware-in-the-Loop emulator and the C2000TM-microcontroller-LaunchPadXL TMS320F28379D kit, establishing the usability and good result of our proposed control approach in terms of requirements.

Model predictive control of power plant cycling using Industry 4.0 infrastructure

This work involves the Industry 4.0 infrastructure developed at West Virginia University (WVU) for process systems applications. This infrastructure emulates an interconnected environment, enabling communication and data sharing among different components for use in academic and industrial settings. The current infrastructure encompasses a power plant model interacting with online load demand, distributed control systems, and data analytics components. The developed model of a sub-critical coal-fired power plant is employed to evaluate classical and advanced control strategies using this infrastructure under different operating conditions. Specifically, the control strategies evaluated include classical proportional–integral–derivative (PID) and advanced model predictive control (MPC) structures, focusing on the dynamic matrix control (DMC) approach with an in-house modified sequential quadratic programming (SQP) solver. The MPC approach is developed and simulated in closed loop to address setpoint tracking and load-following scenarios under power plant cycling conditions. In this infrastructure, the PI System centralizes all the information received from the power plant model and the online power demand and sends the control actions calculated by the MPC back to the power plant model for implementation. Results of the implementation of these control strategies are discussed focusing on power plant operating regions associated with cycling.

Economic and resilient operation of hydrogen-based microgrids: An improved MPC-based optimal scheduling scheme considering security constraints of hydrogen facilities

Optimally scheduling alkaline electrolyzers (AELs) in a hydrogen-based microgrid (HBM) can greatly unleash the operational flexibility of the HBM. However, existing scheduling strategies of AELs mostly utilize a simplified AEL model, which ignores the nonlinear coupling of electric-hydrogen-thermal sectors, violating the AEL’s security constraints thereby making the scheduling scheme infeasible. This paper proposes an improved model predictive control (MPC) based optimal scheduling framework which incorporates a scheduling correction algorithm into the basic MPC structure. This framework is utilized for implementing economic and resilient scheduling of an HBM under normal and emergency conditions, respectively. With the scheduling correction algorithm, this framework can be formulated into a computationally efficient mixed-integer linear programming, meanwhile guaranteeing the solutions strictly satisfy the security constraints of hydrogen facilities (i.e. AEL and hydrogen tank). Case studies are conducted based on real operating data of a Danish energy island Bornholm. The results demonstrate that the proposed scheduling scheme under normal conditions can contribute to significant comprehensive benefits from the daily operation cost saving of 68%, computational time saving of 98%, and satisfying the security constraints of hydrogen facilities, compared to previous scheduling strategies. Besides, it sharply reduces load shedding under emergency conditions by proactively allocating distributed energy sources in the HBM.

Hierarchical model predictive control for an off-highway diesel engine with SCR catalyst

Diesel engines become more and more complex systems, especially due to increasingly restrictive emission laws. The selective catalytic reduction (SCR) is a promising way to lower nitrogen oxide emissions. The slow dynamics of the catalyst, however, have to be compensated by the engine, for example to comply with emission laws during transients. This work presents a bi-level nonlinear model predictive control (MPC) concept for a diesel engine with an upper MPC layer to account for the SCR catalyst and a lower MPC layer to control the engine. The resulting hierarchical MPC structure is able to solve the overall control problem in real-time on ECU level using suitable MPC formulations as well as interconnecting variables. The numerical solution is based on an augmented Lagrangian MPC algorithm and control-oriented models. Simulation results against a detailed reference model of the overall system demonstrate the high performance of the hierarchical MPC concept.

Toward Learning Human-Like, Safe and Comfortable Car-Following Policies With a Novel Deep Reinforcement Learning Approach

In this paper, we present an advanced adaptive cruise control (ACC) concept powered by Deep Reinforcement Learning (DRL) that generates safe, human-like, and comfortable car-following policies. Unlike the current trend in developing DRL-based ACC systems, we propose defining the action space of the DRL agent with discrete actions rather than continuous ones, since human drivers never set the throttle/brake pedal level to be actuated, but rather the required change of the current pedal levels. Through this human-like throttle-brake manipulation representation, we also define explicit actions for holding (keeping the last action) and coasting (no action), which are usually omitted as actions in ACC systems. Moreover, based on the investigation of a real-world driving dataset, we cast a novel reward function that is easy to interpret and personalized. The proposed reward enforces the agent to learn stable and safe actions, while also encouraging the holding and coasting actions, just like a human driver would. The proposed discrete action DRL agent is trained with action masking, and the reward terms are completely derived from the real-world dataset collected from a human driver. We present exhaustive comparative results to show the advantages of the proposed DRL approach in both simulation and scenarios extracted from real-world driving. We clearly show that the proposed policy imitates human driving significantly better and handles complex driving situations, such as cut-ins and cut-outs, implicitly, in comparison with a DRL agent trained with a widely-used reward function proposed for ACC, a model predictive control structure, and traditional car-following approaches.

HAVOK Model Predictive Control for Time-Delay Systems with Applications to District Heating

A computationally efficient Model-Predictive Control (MPC) approach is proposed for systems with unknown delay using only input/output data. We use the Koopman operator framework and the related Hankel Alternative View of Koopman (HAVOK) algorithm to identify a model in a basis of projected time-delay coordinates and demonstrate a novel MPC structure that reduces and bounds the computational complexity. The proposed HAVOK-MPC approach is validated experimentally on a laboratory-scale District Heating System (DHS), demonstrating excellent prediction and tracking performance while only requiring knowledge of a conservative upper bound on the system delay.

Cascaded Model Predictive Control of a Tandem-Rotor Helicopter

This letter considers cascaded model predictive control (MPC) as a computationally lightweight method for controlling a tandem-rotor helicopter. A traditional single MPC structure is split into separate outer and inner-loops. The outer-loop MPC uses an SE2(3) error to linearize the translational dynamics about a reference trajectory. The inner-loop MPC uses the optimal angular velocity sequence of the outer-loop MPC to linearize the rotational dynamics. The outer-loop MPC is run at a slower rate than the inner-loop allowing for longer prediction time and improved performance. Monte-Carlo simulations demonstrate robustness to model uncertainty and environmental disturbances. The proposed control structure is benchmarked against a single MPC algorithm where it shows significant improvements in position and velocity tracking while using significantly less computational resources.

Optimal Sub-References for Setpoint Tracking: A Multi-level MPC Approach

We propose a novel method to improve the convergence performance of model predictive control (MPC) for setpoint tracking, by introducing sub-references within a multilevel MPC structure. In some cases, MPC is implemented with a short prediction horizon due to limited on-line computation capacity, which could lead to deteriorated dynamic performance. The introduced multi-level optimization method can generate proper sub-references for the MPC setpoint tracking problem, and efficiently improve the dynamic performance. In the higher level a specific performance criterion is taken as the objective, while explicit MPC is utilized in the lower level to represent the control input. The generated sub-references are then used in MPC for the real system with prediction horizon restrictions. Setpoint-tracking MPC for linear systems is used to illustrate the approach throughout the paper. Numerical simulations show that MPC with sub-references significantly improves the convergence performance compared with regular MPC with the same prediction horizon. Thus, it can be concluded that MPC with sub-references has a high potential to tackle more complicated control problems with limited computation capacity.