Fast gradient‐based distributed optimisation approach for model predictive control and application in four‐tank benchmark

In this paper two model predictive control (MPC) approaches, an on-line and an off-line MPC approach, for constrained uncertain continuous-time systems with piecewise constant control input are presented. Both MPC approaches guarantee robust asymptotic stability by taking into account the hybrid dynamics of the closed-loop system, resulting from the continuous-time system dynamics and the discrete-time model predictive controller dynamics. Examples are presented to demonstrate the applicability of the proposed MPC approaches.

To improve the load frequency control (LFC) performance of power systems incorporating virtual power plants (VPPs) while reducing network resource consumption, a model predictive control (MPC) method based on a mixed time/event-triggered mechanism (MTETM) is proposed. This mechanism integrates an event-triggered mechanism (ETM) with a time-triggered mechanism (TTM), where ETM avoids unnecessary signal transmission and TTM ensures fundamental control performance. Subsequently, for the LFC system incorporating VPPs, a state hard constrained MPC problem is formulated and transformed into a “min-max” optimisation problem. Through linear matrix inequalities, the original optimisation problem is equivalently transformed into an auxiliary optimisation problem, with the optimal control law solved via rolling optimisation. Theoretical analysis demonstrates that the proposed auxiliary optimisation problem possesses recursive feasibility, whilst the closed-loop system satisfies input-to-state stability. Finally, validation through case studies of two regional power systems demonstrates that the MPC approach based on MTETM outperforms the ETM-based MPC approach in terms of control performance while maintaining a triggering rate of 33.3%. Compared with the TTM-based MPC algorithm, the MTETM-based MPC method reduces the triggering rate by 66.7%, while maintaining nearly equivalent control performance. Consequently, the results validate the effectiveness of the MTETM-based MPC approach in conserving network resources while maintaining control performance.

A linear Lagrangian model predictive controller of macro- and micro- variable speed limits to eliminate freeway jam waves

The problem of path following for marine surface vessels using the rudder control is addressed in this paper. The need to enforce the roll constraints and the fact that the rudder actuation is limited in both amplitude and rate make the model predictive control (MPC) approach a natural choice. The MPC design is based on a linearized model for computational and implementation considerations, while the evaluation of the performance of MPC controller is performed on a nonlinear 4 degree of freedom surface vessel model. The simulation results are presented to verify the effectiveness of the resulting controller and a simulation based tuning process for the controller is also presented. Furthermore, the performance of the path following MPC control in wave fields is evaluated using an integrated maneuvering and seakeeping model, and the simulation confirms its robustness.

This paper presents a model predictive control (MPC) approach to control the steering angle in an autonomous vehicle. In designing a highly automated driving control algorithm, one of the research issues is to cope with probable risky situations for enhancement of safety. While human drivers maneuver the vehicle, they determine the appropriate steering angle and acceleration based on the predictable trajectories of surrounding vehicles. Likewise, it is required that the automated driving control algorithm should determine the desired steering angle and acceleration with the consideration of not only the current states of surrounding vehicles but also their predictable behaviors. Then, in order to guarantee safety to the possible change of traffic situation surrounding the subject vehicle during a finite time-horizon, we define a safe driving envelope with the consideration of probable risky behaviors among the predicted probable behaviors of surrounding vehicles over a finite prediction horizon. For the control of the vehicle while satisfying the safe driving envelope and system constraints over a finite prediction horizon, a MPC approach is used in this research. At each time step, MPC based controller computes the desired steering angle to keep the subject vehicle in the safe driving envelope over a finite prediction horizon. Simulation and experimental tests show the effectiveness of the proposed algorithm.

Model-based network-wide optimizations in real-time emergency control of power systems are largely bottlenecked by the fast computational requirements. Furthermore, the operational aspects of modern power and energy systems are going through transformative changes to tackle global renewable energy expansion-related issues. Decentralized operations in power systems are becoming essential with the influx of distributed energy resources (DERs), dynamic loads, and electric vehicles (EVs). This research considers a well-known model-based strategy, Model Predictive Control (MPC), for real-time operation and controls of power systems and proposes novel methods utilizing machine learning, data-driven methods, and operator theory to solve computational challenges by making those real-time for the first time. Additionally, we develop a distributed MPC framework to address the recent needs of power systems' operation and control. In Part I, we first present a machine learning (ML)-accelerated MPC implementation in emergency voltage control problems. This method computes an optimal control strategy for the nominal system model offline and performs successive online control corrections at each control instant to adapt the offline computed controls for real-time scenarios. In the online phase, the required voltage trajectory prediction and its sensitivity computation to control inputs are achieved by machine learning-based approaches, thereby accelerating the overall control computation multiple times. Next, we present an alternative data-learned linear Koopman embedding approach for model predictive emergency voltage control in a power grid. This approach involves a "basis-dictionary free" method to lift the nonlinear power system dynamics to a higher dimensional linear space where MPC is exercised in a real-time fashion. We propose a novel data-driven encoder-decoder architecture, Koopman-inspired deep neural network (KDNN), which supports end-to-end learning from trajectory data. The MPC optimization in linear space makes the problem scalable and rapid for real-time implementations. Part II of this research focuses on distributed MPC design for quasi-static power flow-based voltage control problems under short-term (15-minute) variations of load and generation profiles. To realize the proposed distributed control, first, a centralized voltage control problem assuming grid observability is formulated and next transferred to the distributed versions based on both bus-wise and area-wise decomposition of the network. Distributed versions are solved via the alternating direction method of multipliers (ADMM), utilizing only neighbor-to-neighbor communications to attain optimal solutions. The implementation, efficacy, performance, and robustness of proposed research approaches are validated with IEEE test system benchmarks.

Model predictive control (MPC) is an efficient and growing approach to power converter control. This paper proposes an improved and simplified model predictive current control (MPCC) technique for a four-level nested neutral point clamped (4L-NNPC) converter. Conventional MPCC exhibits better performances as compared to the conventional linear control system such as fast dynamic response, consideration of the system constraints, and nonlinearities. However, the application of the conventional model predictive current control (MPCC) approach on complex systems provokes a significant number of calculations, which is the main hurdle to its practical implementation. To fix this flaw, this paper proposes an effective algorithm to shorten the execution time of the conventional MPCC. In this proposed technique, 216 current predictions of the conventional MPCC are skipped and converted into one required voltage vector (RVV) prediction. With this equivalent reference voltage transformation, the calculation burden of MPCC is significantly reduced, while the output performance is not influenced. The results of the simplified MPCC for the 4L-NNPC converter are analyzed and compared with the conventional MPCC. The computational time is reduced by 19.56% using the simplified MPCC, while keeping an approximately similar error of output currents. The switching frequency and total harmonic distortion (THD) of the proposed method are reduced by 8.16% and 0.07%, respectively, as compared to the conventional technique. These results demonstrate the fact that that the performance of a conventional MPCC is enhanced with the proposed MPCC. The proposed algorithm can be applied to several inverter topologies.

Preliminary study for motion sickness reduction in autonomous vehicles: an MPC approach

Part I of the thesis investigates novel urban traffic state estimation methods utilizing probe vehicle data. Chapter 2 proposes a method to integrate the collective effect of dispersed probe data with traffic kinematic wave theory and data mining techniques to model the spatial and temporal dynamics of queue formation and dissipation in arterials. The queue estimation method captures interdependencies in queue evolutions of successive intersections, and moreover, the method is applicable in oversaturated conditions and includes a queue spillover statistical inference procedure. Chapter 3 develops a travel time reliability model to estimate arterial route travel times distribution (TTD) considering spatial and temporal correlations between traffic states in consecutive links. The model uses link-level travel time data and a heuristic grid clustering method to estimate the state structure and transition probabilities of a Markov chain. By applying the Markov chain procedure, the correlation between states of successive links is integrated and the route-level TTD is estimated. The methods in Part I are tested with various probe vehicle penetration rates on case studies with field measurements and simulated data. The methods are straightforward in implementation and have demonstrated promising performance and accuracy through numerous experiments. Part II studies network-level modeling and control of large-scale urban networks. Chapter 4 is the pioneer that introduces the urban perimeter control for two-region urban cities as an elegant control strategy to decrease delays in urban networks. Perimeter controllers operate on the border between the two regions, and manipulate the percentages of transfer flows between the two regions, such that the number of trips reaching their destinations is maximized. The optimal perimeter control problem is solved by the model predictive control (MPC) scheme, where the prediction model and the plant (reality) are formulated by macroscopic fundamental diagrams (MFD). Chapter 5 extends the perimeter control strategy and MFD modeling to mixed urban-freeway networks to provide a holistic approach for large-scale integrated corridor management (ICM). The network consists of two urban regions, each one with a well-defined MFD, and a freeway, modeled by the asymmetric cell transmission model, that is an alternative commuting route which has one on-ramp and one off-ramp within each urban region. The optimal traffic control problem is solved by the MPC approach to minimize total delay in the entire network considering several control policies with different levels of urban-freeway control coordination. Chapter 6 integrates traffic heterogeneity dynamics in large-scale urban modeling and control to develop a hierarchical control strategy for heterogeneously congested cities. Two aggregated models, region- and subregion-based MFDs, are introduced to study the effect of link density heterogeneity on the scatter and hysteresis of MFD. A hierarchical perimeter flow control problem is proposed to minimize the network delay and to homogenize the distribution of congestion. The first level of the hierarchical control problem is solved by the MPC approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant is the subregion-based MFD, which is a more detailed model. At the lower level, a feedback controller tries to maximize the network outflow, by increasing regional homogeneity.

This paper presents a novel motion control strategy based on model predictive control (MPC) for distributed drive electric vehicles (DDEVs), aiming to simultaneously control the longitudinal and lateral motion while considering efficiency and the driving feeling. Initially, we analyze the vehicle's dynamic model, considering the vehicle body and in-wheel motors, to establish the foundation for model predictive control. Subsequently, we propose a model predictive direct motion control (MPDMC) approach that utilizes a single CPU to directly follow the driver's commands by generating voltage references with a minimum cost function. The cost function of MPDMC is constructed, incorporating factors such as the longitudinal velocity, yaw rate, lateral displacement, and efficiency. We extensively analyze the weighting parameters of the cost function and introduce an optimization algorithm based on particle swarm optimization (PSO). This algorithm takes into account the aforementioned factors as well as the driving feeling, which is evaluated using a trained long short-term memory (LSTM) neural network. The LSTM network labels the response under different weighting parameters in various working conditions, i.e., "Nor", "Eco", and "Spt". Finally, we evaluate the performance of the optimized MPDMC through simulations conducted using MATLAB and CarSim software. Four typical scenarios are considered, and the results demonstrate that the optimized MPDMC outperforms the baseline methods, achieving the best performance.

A novel Model Predictive Control (MPC) approach for Permanent Magnet Synchronous Machines (PMSMs) is proposed in this paper. It consists of choosing a number of MPC cost functions appropriately, in accordance with PMSM control strategy and torque requirements. These are then minimized following an appropriate order of priority, thus enabling enhanced MPC performances and flexibility compared to those achievable by employing weighting factors. Such a good result is achieved also by suitably managing PMSM operating constraints, over both dynamic and steady state operation. The effectiveness of the proposed MPC approach is validated through an experimental study, which refers to a Surface-Mounted Permanent Magnet Synchronous Machine (SPM) driven by means of a suitable control board. This consists mainly of Field Programmable Gate Arrays (FPGA), whose computational performances enable the real-time implementation of the proposed MPC algorithm.

A microgrid with an advanced energy management approach is a feasible solution for accommodating the development of distributed generators (DGs) and electric vehicles (EVs). At the primary stage of development, the total number of EVs in a microgrid is fairly small but increases promptly. Thus, it makes most prediction models for EV charging demand difficult to apply at present. To overcome the inadaptability, a novel robust approach is proposed to handle EV charging demand predictions along with demand-side management (DSM) on the condition of satisfying each EV user’s demand. Variables with stochastic forecast models join the objective function in the form of probability-constrained scenarios. This paper proposes a scenario-based model predictive control (MPC) approach combining both robust and stochastic models to minimize the total operational cost for energy management. To overcome the concern about the convergence time increasing from the combination of scenarios, the Benders decomposition (BD) technique is further adopted to improve computational efficiency. Simulation results on a combined heat and power microgrid indicate that the proposed scenario-based MPC approach achieves a better economic performance than a traditional deterministic MPC (DMPC) approach, while ensuring EV charging demands, as well as minimizing the trade-off between optimal solutions and computing times.

In this study, a supervisory controller for an ASU (Air Separations Unit) has been designed based on a MPC (Model Predictive Control) approach. This has been applied to a detailed pressure-driven Aspen Plus/Aspen Dynamics model to understand the performance of a multivariable MPC when adopted for such a complex process with critical targets. In addition, an effective PI-based secondary-layered controller design has been proposed for open-loop stability and maximizing oxygen yield. The rigorous Aspen model is interfaced with Matlab/Simulink and has been used as a “real plant” when performing the step tests for the identification of the simplified linear model and application of supervisory control. The effectiveness of the designed controller has been proved through the comparison between the linear MPC approach, that handles absolute and rate-of-change constraints, and a more conventional control configuration. The results show a significant reduction in overshoots and settling time during load variations. The paper clearly shows how the MPC approach for a supervisory control layer is reliable, easy to design and of real value for practical purposes.

THIS dissertation addresses the technical challenges associated with the operation and control of high-power modular multilevel converters. To improve the performance of modular multilevel converter (MMC), a generalized three-phase mathematical model with common-mode voltage (CMV) is proposed. By using the proposed mathematical model, the magnitude of circulating currents, capacitors voltage ripple, and the ripple in DC-link current during balanced and unbalanced operating conditions can be minimized. The modulation scheme and switching frequency are directly affected the output power quality and the performance of the converter and control method. In this dissertation, a novel sampled average and space vector modulation scheme is proposed. These modulation schemes are suitable to control the MMC with any number of submodules (without modifications), operates at low switching frequency, minimizes the ripple in output current and voltage harmonic distortion, and reduces the output filter size. For reliable operation of MMC, the voltage balancing among submodules is mandatory. This dissertation proposes a generalized single-stage balancing approach with reduced current sensors to control the MMC. The proposed balancing approach is suitable to implement with both phase-shifted and level-shifted pulse width modulation schemes. With the proposed approach, it is also possible to control the MMC with half-bridge and three level flying capacitor submodules. Also, an improved balancing approach often referred as the dual-stage balancing approach is proposed to minimize the voltage harmonic distortion and device power losses. This dissertation also proposes a direct model predictive control (D-MPC) approach to minimize the ripple in submodule capacitors voltage. To implement D-MPC approach, a discrete-time model of MMC with CMV is proposed. With the use of proposed model, the D-MPC approach does not require a cost function to minimize the circulating currents. The computational complexity is one of the major issues in the implementation of D-MPC approach for MMC. In this dissertation, a novel reduced computational MPC approaches named as dual-stage D-MPC and indirect model predictive control (I-MPC) approach are proposed. These approaches significantly minimize the computational complexity and, improve the voltage and current waveform quality while operating at the low switching frequency. Finally, the simulation and experimental studies are presented to validate the dynamic and steady-state performance of proposed methodologies. Index Terms • Modular Multilevel Converters. • Capacitors Voltage Balancing. • Pulse Width Modulation Schemes. • Circulating Currents. • Capacitors Voltage Ripple • Direct Model Predictive Control. • Dual-Stage Direct Model Predictive Control. • Indirect Model Predictive Control. • Total Harmonic Distortion.

An improved model predictive control approach for fuel efficiency optimization of vessel propulsion systems