Fast MPC Research Articles

Data-Driven FMPC Based Dynamic Coordination Control Strategy for Power-Split Hybrid Electric Bus

Since no engine clutch exists in the power-split system of the hybrid electric bus, the torque variations of the power sources (i.e., the engine, motor, and generator) are easy to cause system shock during mode switching. To yield a better control effect, the model predictive control (MPC) based dynamic coordination control strategy (DCCS) is considered as an effective solution to guarantee the drivability and reliability of the system. However, the existing MPC-based DCCS still have the challenge of model accuracy and computational complexity. Therefore, to solve the problem, a data-driven Fast-MPC(FMPC) based DCCS is proposed for a power-split hybrid electric bus in this paper. Firstly, to ensure the accuracy of the engine dynamic model, a piecewise data fitting method is proposed by analyzing the historical data of the engine. Then, considering the high dimension of the control model (based on the dynamics model of the power-split system), a fast solving method for the quadratic optimization problem of MPC is proposed with respect to the proper assumption and simplification. Finally, to verify the effectiveness of the proposed control strategy, offline simulation and hardware-in-the-loop (HIL) simulation experiments are carried out. Simulation results show that good driving comfort and real-time performance have been achieved. This research is expected to promote the application of MPC in the DCCS and further improve the dynamic performance of the power-split system.

Model Predictive Paradigm with Low Computational Burden Based on Dandelion Optimizer for Autonomous Vehicle Considering Vision System Uncertainty

The uncertainty due to road fluctuations and vision system dynamics represents a big challenge to adjusting the steering angle of autonomous vehicles (AVs). Furthermore, AVs require fast action to follow the target lane to overcome lateral deviation with minor errors. In this regard, this paper introduces a fast model predictive controller formulated based on the discrete-time Laguerre function (DTLF) to overcome the high computational burden of the traditional MPC. To improve the hybrid DTLF-MPC performance, a modern and effective dandelion optimizer (DO) strategy is used in this work, which resulted in obtaining the optimal DTLF-MPC parameters and achieving satisfactory results. Furthermore, the proposed hybrid DTLF-MPC is designed based on different algorithms in the literature to evaluate the performance of the DO. Several scenarios are discussed in this paper to confirm the effectiveness and efficiency of the proposed control strategy system against the vision system uncertainty and road fluctuations. The results emphasize that the proposed DTLF-MPC based on the DO can achieve the best damping performance for the lateral deviations with less overshoot; around 0.4533, and a settling time of around 0.01979 s compared with other algorithms.

Fast nonlinear model predictive controller using parallel PSO based on divide and conquer approach

The high computationally expensive nature of nonlinear optimisation algorithms leads to limitations of its use in a real-time era. So, this is the main challenge against researchers to develop a fast algorithm that is used in real-time computations. This paper proposes a fast nonlinear model predictive control algorithm that utilises a parallel particle swarm optimisation with synchronous and asynchronous methods inclusion, that handles nonlinear optimisation problems with constraints. The additional divide and conquer approach of the proposed algorithm improves the speed of computation and disturbance rejection capability which proves its efficacy in real-time applications. A highly nonlinear fast dynamic real-time inverted pendulum system with hybrid embedded hardware platform (ARM + FPGA) is used to validate the performance of this algorithm under constraints. The solution presented in the paper is computationally feasible for smaller sampling times i.e. in miliseconds and it gives promising results with synchronous and asynchonous parallel PSO compared to the state-of-art PSO algorithm.

Nonlinear curve fitting-based fast robust MPC algorithm for nonlinear system

In the existing efficient robust model predictive control (ERMPC) algorithms (see e.g. [14,31,32]), through offline optimization and online lookup table calculation, a fixed state feedback control law or a linear interpolated control law is applied to a system when the system state lies between two adjacent polyhedrons, which undoubtedly will result in conservativeness of the controller. Faced with this issue, an improved ERMPC algorithm is proposed in this paper, which considers the nonlinearity between the state feedback control laws with respect to polyhedrons and the norm distance from system state to origin, and can provide continuously variable state feedback control law varying with the state. First, a set of polyhedral parameters and their corresponding state feedback control law sequences are obtained offline by solving a set of LMIs optimization problems. Next, for each state feedback control law sequence, a nonlinear fitting function is established offline between the state feedback control law and its serial number. Then a simplified lookup table is constructed offline to save memory space and shorten online computation time of the controller. According to the simplified lookup table and information of the norm distance from system state to origin, we online establish the coordinate of current state in the nonlinear fitting curve for getting current feedback control law, which changes continuously with the state. The proposed ERMPC algorithm is successfully applied to an actual fast-responding linear one stage inverted pendulum (LOSIP) system to verify its effectiveness.

A fast tube model predictive control scheme based on sliding mode control for underwater vehicle-manipulator system

This paper presents a novel robust fast tube model predictive control (FTMPC) scheme for controlling the multi-input multi-output (MIMO) underwater vehicle-manipulator system (UVMS) in the case of system unmodeled uncertainties and external disturbances. The structure of the FTMPC is designed by a nominal fast MPC and an ancillary tube sliding mode control (SMC) law. The nominal fast MPC uses the approximated prediction control law for achieving the fast online convex optimization. The ancillary tube law uses the explicit SMC for strong robustness and makes the state error between the actual system and the nominal system converge to zero. Finally, the effectiveness of controlling UVMS is verified by the proposed SMC-based FTMPC scheme through the tracking simulations.

Observer-based fast nonlinear MPC for multi-DOF maglev positioning system: Theory and experiment

This paper presents an observer-based fast nonlinear model predictive control (NMPC) scheme for translation control of magnetically levitated (maglev) positioning system subject to input saturation. The motivation lies in the improvement of transient characteristics and control performance for positioning systems. The nonlinear dynamical translation model of the maglev positioning system is derived that does not affect the rotation dynamics with special current conditions. The disturbance estimation, obtained by nonlinear disturbance observer, is introduced in the state receding prediction to compensate the errors caused by disturbances and uncertainties. To reduce the computational burden, the stability of the proposed NMPC is established without using any stability-related terminal costs or constraints, and only the short prediction horizon is required for real-time feasibility. The online optimization algorithm underlying the NMPC scheme takes the process constraints into account, and solves the optimal control problem using a parallel structure at each iteration. Comparative experiments are carried out on the positioner to validate the proposed controller has the outperformance in transient/steady-state trajectory tracking, frequency characteristics and robustness against disturbances. The proposed scheme also provides a guidance for the application of NMPC in industrial mechatronic system with fast dynamics.

Fast Real-Time Model Predictive Control for a Ball-on-Plate Process

This work is concerned with an original ball-on-plate laboratory process. First, a simplified process model based on state–space process description is derived. Next, a fast state–space MPC algorithm is discussed. Its main advantage is computational simplicity: the manipulated variables are found on-line using explicit formulas with parameters calculated off-line; no real-time optimization is necessary. Software and hardware implementation details of the considered MPC algorithm using the STM32 microcontroller are presented. Tuning of the fast MPC algorithm is discussed. To show the efficacy of the MPC algorithm, it is compared with the classical PID and LQR controllers.

Active vibration suppression for large space structure assembly: A distributed adaptive model predictive control approach

Subject to the limited envelope size and carrying capacity of a rocket, it could be one of the most promising solutions to construct a large space structure through multilaunching and on-orbit assembly. Taking the antenna of the solar power satellite as the research objective, a novel vibration suppression strategy is developed in this article to guarantee high structural stability of the large space structure during on-orbit assembly. The concept of distributed control unit, together with the varying location relationship matrices, reflects the structural characteristics of the large space structure during on-orbit assembly. The explicit expression form of the control unit’s dynamic model is first derived based on the Newmark-β method. Then, the distributed adaptive model predictive controller is proposed to suppress the vibration of the large space structure aroused by weak impact among assembling modules. Through recalculating the control matrices efficiently at each assembly, the proposed controller achieves adaptive updating along with the varying large space structure. The feasibility of the proposed distributed adaptive model predictive controller is investigated in the numerical simulations, and the centralized fast model predictive controller is adopted for better comparison. The results demonstrate that the distributed adaptive model predictive controller can effectively suppress vibration of the large space structure during on-orbit assembly, with good adaptability, robustness, and computation efficiency.

Fast Model-based Predictive Control (FMPC) for grid connected Modular Multilevel Converters (MMC)

Model-based predictive control, or MPC, is a popular technique widely used in three-phase two-level power converters (VSC), in applications such as motor and generator control. One of the main drawbacks of implementing MPC is the high computation time requirements while evaluating the effects of the six available vectors on the cost function. The computing time becomes unacceptable when the number of vectors is very high, as in modular multilevel converters (MMC), making it impossible to run the MPC algorithm in microcontrollers (MCUs) within reasonable cycle times. This paper proposes a fast method capable of finding the reference voltage vector among a large number of available multilevel voltage vectors, in a single step, which greatly reduces the computation time and makes it possible to use MPC in regular MCUs. Unlike other MPCs, after calculating the reference vector, the proposed method discards the duration times obtained by the MPC and the reference vector is modulated using an SVM.MPC has been little developed for MMC and is normally intended to improve the internal operation of the converter. In contrast, this paper presents a fast MPC, designed to control the active and reactive powers exchanged by a grid-connected MMC, providing a fast dynamic response, low current THD and constant switching frequency. In addition, the implementation is compatible with other known MMC vector control algorithms and can even be used with other multilevel converters.

Efficient Solution of Equality Constrained Quadratic Programming Arising in Model Predictive Control

Fast Model Predictive Control (Fast MPC) is a set of techniques which aim at reducing the complexity of solving receding horizon control optimization problems. One method consists in exploiting the structure induced by the system dynamics. This drastically reduces the complexity of the problem from cubic to linear dependence on the horizon length. Such approach is possible for the multi-stage MPC formulation which is characterized by having an almost separable structure, i.e. coupling occurs only between consecutive stages. This paper proposes a novel technique that efficiently solves general linear-quadratic optimal control problems and hence does not require a multi-stage formulation. The method also provides other advantages including: higher solution accuracy, warm starting, and approximate solutions by early termination. This is achieved by embedding the Riccati recursion in a Projected Conjugate Gradient (PCG) method.

An EKF-Based Fast Tube MPC Scheme for Moving Target Tracking of a Redundant Underwater Vehicle-Manipulator System

This paper presents a control scheme for addressing the moving target grabbing problem by a kinematically constrained redundant underwater vehicle-manipulator system (UVMS) in the presence of unmodeled uncertainties, sensory detecting noises, and time-varying external disturbances. Our proposed control scheme is designed by a robust fast tube model predictive controller (FTMPC) with an extended Kalman filter (EKF) target observer. The proposed robust FTMPC consists of an online fast nominal MPC and an online ancillary nonlinear controller to overcome the uncertainties and disturbances of the UVMS. The problem of the UVMS kinematic redundancy and mechanical/physical constraints is translated into a part of online optimization of FTMPC. The feasibility and stability of the FTMPC are proved. The proposed EKF observer is used to estimate the moving target trajectory and overcome the sensory measurement (system) noises, which can eliminate the assumption that most prior existing research works need to know the tracking reference trajectory precisely. Finally, the effectiveness of the proposed control scheme is verified through a series of UWSim simulations by the 6-degree-of-freedom (DoF) vehicle and 5-DoF manipulator GIRONA500 UVMS.

A synthesis approach of fast robust MPC with RBF-ARX model to nonlinear system with uncertain steady status information

The mechanical model of a plant in real industry is usually difficult to obtain. This paper integrates the data-driven RBF-ARX modeling method and a fast Robust Model Predictive Control (RMPC) approach to achieving output-tracking control of a nonlinear system with unknown steady status information. Considering the large online computational burden of online RMPC, this paper proposes a RBF-ARX model-based efficient robust predictive control (RBF-ARX-ERPC) approach. First, based on the RBF-ARX model, a polytopic uncertain linear parameter varying (LPV) state-space model is built to represent the dynamic behavior of the system; next, two convex polytopic sets are constructed to wrap the globally nonlinear behavior of the system. Then, an optimization problem including several linear matrix inequalities (LMIs) is formulated, which is solved offline to synthesize a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids in the state space, of which all the optimization results are stored in a look-up table. For the real-time control online, it only involves simple state-vector computation and bisection search. Two simulation examples, i.e. the modeling and control of a widely used continuously stirred tank reactor (CSTR) and a linear one-stage inverted pendulum (LOSIP) system, and the real-time control experiments on an actual LOSIP plant are provided to demonstrate the effectiveness of the proposed RBF-ARX model-based efficient RPC approach.

Optimal voltage control strategy for grid-feeding power converters in AC microgrids

Predominant power generation by renewable energy sources poses an increasing challenge regarding the maintenance of a stable, reliable, but also affordable electricity supply. Power converters are the key system component to interface distributed generation systems to the electrical power grid and are increasingly required to provide grid supporting measures to an extent comparable to classical centralized power stations. Thus, improving the control performance of power converters in microgrids is becoming more significant. This work proposes an optimal voltage control strategy for a grid-feeding active-front-end power converter, which inherently regulates its bus voltage within a defined tolerance band while simultaneously keeping the provided reactive power at a specified optimal level. The focus is put on the proposed multi-loop control which incorporates a fast model predictive based current controller. Simulations and experiments on a power converter test bench are presented to validate the performance of the proposed voltage regulation scheme. The controller implementation is carried out for a three-level neutral-point-clamped voltage source inverter with an LCL output filter. Based on the results of the experimental validation, a simulation-based case study demonstrates its performance for multiple grid-tied power converters in an AC microgrid.

An Adaptive EKF-FMPC for the Trajectory Tracking of UVMS

This paper addresses the trajectory tracking problem for the constrained dynamical underwater vehicle-manipulator system (UVMS) in the presence of dynamic uncertainties, sensory measurement noises, and time-varying external disturbances. An adaptive robust fast computational optimal control scheme is presented for the large-scale multiple-input–multiple-output (MIMO) constrained dynamical UVMS. The structure of our proposed scheme is based on a fast incremental model predictive controller (MPC) embedded with an extended Kalman filter (EKF). The EKF estimation part is used to compensate the unmodeled uncertainties, sensory noises, and external disturbances. The fast MPC (FMPC) part is a trajectory-tracking controller designed by the terminal constrained MPC with an approximately fast computational cost function, which guarantees the optimal batch control process satisfying the state and input constraints. By resorting to a Lyapunov-based stability analysis, the proposed FMPC is proved to be asymptotically stable with a monotonic decrease in the cost function, and can guarantee the tracking performance of the constrained dynamical UVMS. Finally, the effectiveness of the proposed control scheme is verified through a series of comparative simulations of a six-degree-of-freedom (6DOF) vehicle–6DOF manipulator system.

RBF-ARX model-based fast robust MPC approach to an inverted pendulum

In general, the online computation burden of robust model predictive control (RMPC) is very heavy, and the mechanical model of a plant, which is used in RMPC, is hard to obtain precisely in real industry. These issues may largely restrict the applicability of RMPC in real applications. This paper proposes a RBF-ARX (state-dependent Auto-Regressive model with eXogenous input and Radial Basis Function network type coefficients) model-based efficient robust predictive control (RBF-ARX-ERPC) approach to an inverted pendulum system, which is a complete and systematic method for designing robust MPC controller because it integrates the RBF-ARX modeling method and a fast RMPC approach. First, based on the offline identified RBF-ARX model without offset term, two convex polytopic sets are constructed to wrap the globally nonlinear behavior of the system. Then, the optimization problem of implementing a quasi-min–max MPC algorithm including several linear matrix inequalities (LMIs) is formulated, and it is solved offline to synthesize a sequence of explicit control laws that correspond to a sequence of asymptotically stable invariant ellipsoids, of which all the optimization results are stored in a look-up table. During the online real-time control, the controller only needs to carry out a simple state-vector computation and bisection search. The proposed approach is applied to an actual linear one-stage inverted pendulum (LOSIP), which is a fast-responding and nonlinear plant. The real-time control experiments demonstrate the effectiveness of the proposed RBF-ARX model-based efficient RMPC approach.

Distributed Model Predictive Control and Implementation for Vehicle Active Suspensions

This paper proposes a distributed model predictive control (DMPC) method for a half-vehicle system with active suspensions. First, the half-vehicle system is divided into three subsystems to reduce the system dimension. Considering the distribution characteristics of suspension control systems, a DMPC controller is designed for each suspension subsystem in order to inhibit the vehicle vertical and pitch motion. To evaluate the proposed control system, controllers with low cost micro-control units (MCU) are implemented, where a fast MPC method for real-time optimization based on continuation/general minimum residual (C/GMRES) method is realized and in-vehicle network FlexRay is used to exchange control information among these controllers. Finally, the implementation of DMPC controllers in MCUs is finished and the results show that vehicle comfortability can be improved by the proposed controllers.

Economic MPC-based transient control for a dual-mode power-split HEV

The existing research into hybrid electric vehicle (HEV) control is mainly focussed on the optimisation of the power distribution between a conventional internal combustion engine (ICE) and an alternative power source (usually a battery pack), however, transient control, which is a key technique that affects both fuel economy and the drivability of the HEV, has not been fully addressed. Especially in dual-mode power-split HEVs, due to the different dynamic characteristics of the actuators in the transmission, and its complicated speed-torque relationship, transient control also affects the precision of power distribution and the speed of response of the electric output power. To improve the transient control performance, the design of an economic model predictive control (EMPC)-based transient controller for a dual-mode power-split HEV is developed. By incorporating an experimental identification model of a diesel ICE in a control-oriented transmission model, a better coordination among the actuators involved in HEV transmission can be achieved. Moreover, an ICE efficiency index is also added to the objective function to improve ICE fuel efficiency during this transient process. Then, a fast MPC method is applied to reduce the on-line computation effort required of the proposed control algorithm. By the flexible application of the EMPC and an innovative ICE model which is suited to the control-oriented model in EMPC, the transient control performance was improved. The effectiveness, and the real-time performance, of the control algorithm are validated by way of MATLAB™/Simulink-based simulations, as well as test-bed experiments combined with the use of the RapidECU platform.

Fast Nonlinear MPC for Reference Tracking Subject to Nonlinear Constraints via Quasi-LPV Representations

This paper presents an approach to efficiently implement Nonlinear Model Predictive Control (NMPC) for reference tracking in the presence of nonlinear input and state constraints by making use of quasi-Linear Parameter Varying (quasi-LPV) representations. Using this framework, standard Quadratic Program (QP) solvers can be used for the online optimization problem, making its solution very efficient and viable even for fast plants. This is an extension of a previous result which considered the regulator problem with input constraints. This approach is tested in a simulation study of a 2-DOF robotic manipulator and its efficiency is compared to that of state-of-the-art NMPC approaches.

Experimental investigation of control updating period monitoring in industrial PLC-based fast MPC: Application to the constrained control of a cryogenic refrigerator

In this paper, a complete industrial validation of a recently published scheme for on-line adaptation of the control updating period in model predictive control is proposed. The industrial process that serves in the validation is a cryogenic refrigerator that is used to cool the supra-conductors involved in particle accelerators or experimental nuclear reactors. Two recently predicted features are validated: the first states that it is sometimes better to use less efficient (per iteration) optimizer if the lack of efficiency is over-compensated by an increase in the updating control frequency. The second is that for a given solver, it is worth monitoring the control updating period based on the on-line measured behavior of the cost function.

Fast Model Predictive Control for Multilevel Cascaded H-Bridge STATCOM with Polynomial Computation Time

To solve the issue of exponentially increasing computational burden of finite control set model predictive control (FCS-MPC) for multilevel converters, a fast MPC scheme for multilevel cascaded H-bridge STATCOM is presented. The proposed approach consists of three steps. First, with the partially stratified optimization approach, the multiobjective programming of MPC is divided into two suboptimization problems, i.e., current-control MPC and voltage-balancing MPC. Second, a dynamic programming algorithm is proposed for the optimization of current-control MPC. Third, a mixed algorithm, which combines dynamic programming and greedy algorithm (0-1 programing), is proposed to select the optimal switching combination from all the redundant switching combinations for the voltage balancing MPC achieving a global optimization. Through the analysis of the time complexity, with the proposed scheme, the total computation of FCS-MPC can be reduced to polynomial time from exponential time. The proposed approaches will not deteriorate the control performance. The control performance is validated by simulation results and the effectiveness is further demonstrated by implementing the algorithm on a low-cost DSP (TMS320F28335) in real time.