Efficient Model Predictive Control Research Articles

Open‐circuit fault‐tolerant operation of permanent magnet synchronous generator drives for wind turbine systems using a computationally efficient model predictive current control

Model predictive fault-tolerant current control (MPFTCC) of permanent magnet synchronous generator (PMSG) drives can make a valuable contribution to improving the reliability and availability levels of wind turbines, because back-to-back (BTB) converters are prone to failure. However, MPFTCC suffers from excessive computational burden, because the BTB converter is treated as one system where all feasible voltage vectors (VVs) are used for prediction and evaluation. Accordingly, a computationally efficient MPFTCC algorithm for a PMSG drive is developed and proposed with the ability to handle insulated-gate bipolar transistor open-circuit faults. The candidate VVs of both machine- and grid-side converters are separately predicted and evaluated, which significantly reduces calculation effort. The proposed reconfigurable converter is a five-leg power converter with a common leg that connects the generator first phase to the grid three-phase, ensuring proper postfault reconfiguration of the grid-side inverter. Moreover, a three-switch rectifier is adopted to achieve fault tolerance of the PMSG-side rectifier. Performance of the considered MPFTCC strategies is evaluated by experimental means.

Dynamic Output Feedback MPC of Polytopic Uncertain Systems: Efficient LMI Conditions

We focus on the design of an efficient dynamic output feedback model predictive control (DOFMPC) for linear systems with both polytopic and additive uncertainties. We tackle the problem of bilinear matrix inequality formulation which is often encountered in this type of work. In order to formulate a numerically traceable optimization problem, expressed in terms of linear matrix inequalities (LMIs), we propose a new convex stability condition by the utilization of a relaxation formula. Moreover, other inequality conditions in the optimization problem are tailored so that an efficient LMI optimization problem is formulated. Unlike in previous works, the proposed approach does not require any special structure of system matrices, which results in more flexibility. The effectiveness of the proposed approach is verified through a numerical example.

Advanced Construction of the Dynamic Matrix in Numerically Efficient Fuzzy MPC Algorithms

A method for the advanced construction of the dynamic matrix for Model Predictive Control (MPC) algorithms with linearization is proposed in the paper. It extends numerically efficient fuzzy algorithms utilizing skillful linearization. The algorithms combine the control performance offered by the MPC algorithms with nonlinear optimization (NMPC algorithms) with the numerical efficiency of the MPC algorithms based on linear models in which the optimization problem is a standard, easy-to-solve, quadratic programming problem with linear constraints. In the researched algorithms, the free response obtained using a nonlinear process model and the future trajectory of the control signals is used to construct an advanced dynamic matrix utilizing the easy-to-obtain fuzzy model. This leads to obtaining very good prediction and control quality very close to those offered by NMPC algorithms. The proposed approach is tested in the control system of a nonlinear chemical control plant—a CSTR reactor with the van de Vusse reaction.

Output-Lifted Learning Model Predictive Control

Abstract We propose a computationally efficient Learning Model Predictive Control (LMPC) scheme for constrained optimal control of a class of nonlinear systems where the state and input can be reconstructed using lifted outputs. For the considered class of systems, we show how to use historical trajectory data collected during iterative tasks to construct a convex value function approximation along with a convex safe set in a lifted space of virtual outputs. These constructions are iteratively updated with historical data and used to synthesize predictive control policies. We show that the proposed strategy guarantees recursive constraint satisfaction, asymptotic stability, and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on the kinematic unicycle.

Efficient Model-Predictive Control for Nonlinear Systems in Interval Type-2 T-S Fuzzy Form Under Round-Robin Protocol

This article is concerned with the efficient model-predictive control (EMPC) problem for interval type-2 Takagi–Sugeno (IT2 T-S) fuzzy systems with hard constraints. By applying the round-robin (RR) protocol, all controller nodes are activated in a pregiven order such that the occurrence of network congestion or data collisions can be effectively reduced. The aim of the proposed problem is to design a fuzzy controller in the framework of EMPC so as to obtain a good balance among the computation burden, the initial feasible region, and the control performance. With respect to the RR protocol and IT2 T-S fuzzy nonlinearities, a unified representation is modeled for the underlying system, and then, an augmentation state comprising of the system state, the token-dependent perturbation, and the previous input under the RR protocol is put forward; correspondingly, objective functions are constructed for the controller design. Subsequently, by using the min–max strategy, some token-dependent optimizations are established to facilitate the formation of the EMPC algorithm, where the feedback gain is designed offline, and the perturbation is calculated by solving an online optimization dependent of the token. Moreover, with the help of the matrix partition technique, the feasibility of the proposed EMPC algorithm and the stability of the underlying IT2 T-S fuzzy system are rigidly guaranteed. Finally, two numerical examples are utilized to illustrate the validity of the proposed EMPC strategy.

An efficient model predictive control based on Lyapunov function for doubly fed induction generator fed by a T-type inverter

This paper proposed an efficient model predictive control strategy for a three-level T-type inverter connected to a doubly fed induction generator. A dynamic model is utilized to track the power reference, preserve the DC-link voltage balancing and reduce the inverter switching frequency and common-mode voltage. Unlike the traditional finite control set model predictive control, the stability of the closed-loop system and computational burden reduction are concurrently accomplished as the main contribution to the proposed strategy. At each sampling period, the proposed algorithm only considers the candidate control inputs which satisfy the stability condition taken from a suitable control Lyapunov function for evaluating the optimization problem. Due to model uncertainties and discrete set control input voltages, an attractivity set is employed to determine the stability and converge of the system. Therefore, the lower computation time of the optimization problem is the potential benefit compared with the conventional method. Simulation investigation with different operating conditions of a 2 MW wind turbine is carried out by MATLAB/Simulink. The achieved results confirm the stability guarantees while reducing the computational burden and obtaining the same control performances in comparison with the conventional method.

Model predictive control for path following and roll stabilization of marine vessels based on neurodynamic optimization

The conventional objective of rudder roll stabilization is to control the ship course and roll motion simultaneously. Nevertheless, the ship course control is not competent for advanced requirement nowadays on controlling the position, which motivates the present study. This paper proposes an efficient model predictive control (MPC) for path following and roll stabilization of marine vessels by rudder in waves. It is a typical underactuated problem with multi-objectives; in addition, the control input is constrained in both amplitude and rate. MPC is one of the most favorable solutions for this problem, given its capability of solving optimization problem with constraints; however, there are two major challenges existed in the implementation of MPC, i.e., the computational intensity and closed-loop stability. In this paper, a neurodynamic system based on the projection neural network (PNN), which is well known for the parallel computational capability, is established to optimize the objective function formulated by MPC method, thereby improving the computational efficiency. The closed-loop stability is guaranteed by including a quadratic terminal cost, derived from the solution of a Lyapunov equation. Various simulations are conducted to illustrate the advantages of control design proposed herein, in which the model uncertainty and wave disturbances are taken into account.

A Computationally Efficient Robust Tube-Based MPC for Tracking of Linear Systems

This paper addresses a computationally efficient robust tube-based model predictive control (RTBMPC) strategy of linear systems in the presence of bounded disturbance. In the RTBMPC strategy, a nominal system is introduced by ignoring the disturbances of uncertain system, and then the uncertain system will be controlled in a robust manner through its nominal system as well as an additional feedback term which rejects a bounded additive disturbance. In this paper, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function and simplification of driving the stability theory. On the other hand, RTBMPC strategy solves optimization problem for nominal system which ignores the disturbances. Since in the absence of disturbances, the state measured at the following sample will be the same as the one predicted by model, a variable prediction horizon is suggested to reduce the computational burden. In addition, new constraints are introduced to prove the recursive feasibility, local and asymptotic stability. The constrained sampled double integrator is presented to illustrate the effectiveness of the proposed RTBMPC.

Computationally Efficient Stochastic Model Predictive Controller for Battery Thermal Management of Electric Vehicle

The performance and safety of batteries of electric vehicles deteriorate when the battery temperature is too low or too high. The thermal management system regulating the battery temperature consumes considerable electric energy, particularly, for cooling the battery. To maximize the vehicle driving range, the means of controlling the battery temperature should minimize the energy consumption. In this paper, stochastic model predictive control is applied to the battery-cooling controller. Effective model predictive control requires a good but simple system model with proper estimation of near-future disturbances. The components of the battery cooling system are modeled to represent the energy-consumption and heat exchange mechanism with some assumptions for simplicity. The future information is estimated using historical driving data in a stochastic sense. For real-time implementation, an unequally spaced probability distribution is introduced when designing a stochastic model of future heat generation. The proposed control method shows significantly lower energy consumption while maintaining an acceptable temperature regulation performance compared to other temperature controllers, such as a thermostat-type controller and a model predictive controller with simply assumed future information. The proposed predictive controller shows robust performance compared to typical controllers by utilizing the stochastic estimation of future information.

Explicit nonlinear predictive control algorithms for Laguerre filter and sparse least square support vector machine-based Wiener model

In this paper, three computationally proficient model predictive control (MPC) algorithms for least square support vector machine (LSSVM)-based Wiener model are described. A Wiener model with Laguerre filter as dynamic linear part and LSSVM approximator as nonlinear static part is considered. Even though having excellent approximation abilities, LSSVM suffers from lack of sparseness. A pruning algorithm for LSSVM model is proposed and its comparison is made with classical pruning algorithm. The proposed pruning algorithm is able to remove 99% of support vectors with no remarkable drop in modelling accuracy. Using pruned Wiener model, three computationally efficient MPC algorithms are described. In the first algorithm, linearization of Wiener model is performed at every sampling interval and therefore control vector is determined by carrying out a quadratic optimization task. In the second algorithm, control signal is determined by an explicit control law and parameters of this control law are computed by performing lower-upper (LU) factorization of a matrix and solving linear equations without any online optimization. In the third algorithm, the parameters of explicit control law are calculated directly by another LSSVM approximator, which is trained offline. The advantages and effectiveness of proposed methods are demonstrated on the benchmark pH neutralization reactor. The control performance and computational efficiency of proposed algorithms are compared with computationally complex nonlinear MPC, which repeats a nonlinear optimization task at every sampling interval. The impact of pruning on model accuracy, computational efficiency and control accuracy is also discussed.

Enhanced and Computationally Efficient Model Predictive Flux and Power Control of PMSG Drives for Wind Turbine Applications

Direct model predictive control (DMPC) of permanent magnet synchronous generators with full-scale back-to-back (BTB) converters plays an important role in improving the power quality injected to the grid and to comply with grid codes. However, DMPC suffers from the excessive computational burden since all the feasible voltage vectors (VVs) of the BTB converter are used for the prediction and evaluation. Moreover, the weighting factor in the cost function may affect the control performance and tuning it is a complex process. Accordingly, benefiting from the simplicity of the direct control techniques, new direct model predictive flux and power control are proposed in this article, in combination with the direct torque and power control (DTC and DPC), respectively. By defining new DTC and DPC switching tables, only three out of the eight predictions are required to select the best VV for each converter of the BTB topology, which significantly reduces the algorithm computations. To avoid the weighting factor, the electromagnetic torque is simply converted into an equivalent stator flux and only the latter one is considered in the cost function. Experimental results prove that the execution time can be reduced by 26.9%, while the best control performance can be achieved.

Efficient Model-Predictive Control for Networked Interval Type-2 T–S Fuzzy System With Stochastic Communication Protocol

In this article, the efficient model-predictive control (EMPC) problem of a class of nonlinear systems in the framework of interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy is investigated. In order to improve the reliability of the data transmission while reducing the network communication burden, a so-called stochastic communication protocol (SCP) governed by a Markov chain is adopted to orchestrate the data transmission order from the controller to the actuator. The purpose of the addressed problem is to design a set of desired EMPC controllers so as to guarantee the mean-square system stability and obtain a good balance among the computation burden, initial feasible region, and the control performance. A novel control model is established for the SCP and IT2 T-S fuzzy nonlinearities in a unified representation by using a fuzzy periodic switching related to the transmission token and the membership function. Then, the system state, the SCP-based control perturbation, and the previous input under the SCP are fully taken into consideration for constructing the objective function. By virtue of the “min-max” strategy, a few optimizations are formulated, and the corresponding EMPC algorithm is provided, where the feedback gain is designed offline, while the control perturbation is obtained online. Furthermore, by means of the matrix partition technique, sufficient conditions are presented to rigidly guarantee the feasibility of the proposed EMPC algorithm and the mean-square stability of the underlying IT2 T-S fuzzy system. Finally, two illustrative examples are utilized to demonstrate the validity of the proposed EMPC strategy.

An efficient ship autopilot design using observer-based model predictive control

An efficient model predictive control design for ship autopilot, which is a representative marine application, is proposed based on projection neural network in this article. Ship motion control at sea exhibits the characteristics of large inertia, strong nonlinearity, and large delay; furthermore, it is frequently influenced by the external disturbances, leading to a complex uncertain problem. In addition, the amplitude of control input—the rudder is constrained. Given the mechanism of on-line computing and the advantages of handling constraints, the model predictive control is one of the most favorable solutions for this problem. Nevertheless, the major challenge of the implementation of traditional model predictive control in application is the computation intensity. In this article, the capability of parallel computation of projection neural network is employed to optimize the objective function formulated by traditional model predictive control method, aiming to improve the computational efficiency. The overall information of ship motion is normally difficult to be obtained; therefore, a state observer should be also included. Extensive studies are conducted to illustrate the effectiveness of the proposed control design.

Numerically Efficient Fuzzy MPC Algorithm with Advanced Generation of Prediction—Application to a Chemical Reactor

In Model Predictive Control (MPC) algorithms, control signals are generated after solving optimization problems. If the model used for prediction is linear then the optimization problem is a standard, easy to solve, quadratic programming problem with linear constraints. However, such an algorithm may offer insufficient performance if applied to a nonlinear control plant. On the other hand, if a model used for prediction is nonlinear, then non–convex optimization problem must be solved at each algorithm iteration. Then the numerical problems may occur during solving it and the time needed to calculate the control signals cannot be determined. Therefore approaches based on linearized models are preferred in practical applications. A fuzzy algorithm with an advanced generation of the prediction is proposed in the article. The prediction is obtained in such a way that the algorithm is formulated as a quadratic optimization problem but offers performance very close to that of the MPC algorithm with nonlinear optimization. The efficiency of the proposed approach is demonstrated in the control system of a nonlinear chemical control plant—a CSTR (Continuous Stirred–Tank Reactor) with van de Vusse reaction.

An efficient cooperative-distributed model predictive controller with stability and feasibility guarantees for constrained linear systems

This paper proposes a quadratic programming based cooperative-distributed model predictive control strategy, with stability and feasibility guarantees. Its feasibility is achieved by considering slacked terminal constraints of the optimization problem without the assessment of an invariant terminal set. The stability proof uses Lyapunov arguments and is carried out by properly setting the move suppression matrix elements for each agent. A case study involving a process system composed of two CSTR in series with a flash vessel illustrates the effectiveness of the proposed method, especially in a scenario that limits the information exchanged as well as imposes a short time interval for communication among the agents.

Improved Direct Model Predictive Control for Grid-Connected Power Converters

This paper proposes a computationally efficient and robust direct model predictive control (DMPC) technique with enhanced steady-state performance for power converters tied to the electric utility. The discrete space vector modulation (DSVM) method is considered in the design of the suggested DMPC, where virtual voltage vectors (VVs) besides the real ones are utilized for improving the steady-state response of the proposed controller. Furthermore, for averting the high computational burden and making the proposed control technique simple, a deadbeat (DB) function is employed for calculating the reference VV based on the required reference current. Subsequently, a discrete-time integral term is combined with this DB function to enhance the robustness of the suggested DMPC technique against variations of the model parameters. Finally, the best virtual or real VV is chosen by a certain quality function, which will be applied to the power converter in the next sample. The suggested technique is verified by simulation results and its performance is compared with the classical DMPC and voltage-oriented control (VOC).

Efficient model predictive control for real‐time energy optimization of battery‐supercapacitors in electric vehicles

Efficient model predictive control for <scp>real‐time</scp> energy optimization of <scp>battery‐supercapacitors</scp> in electric vehicles

Computationally efficient model predictive control of three‐level open‐end winding permanent‐magnet synchronous motor drive

The model predictive current control (MPCC) is popular and widely used method for permanent-magnet synchronous motor (PMSM) and the tuning of weighting factor in classical cost function (CF) of MPCC of PMSM is not required. A three-level inversion-fed open-end winding PMSM (OEW-PMSM) would produce lesser torque and stator flux ripples; however, computation time required for the prediction of control variables is large. This study proposes a control method to three-level inversion-fed OEW-PMSM for reduction of computational time without affecting the performance when compared with conventional MPCC. The proposed method uses a maximum four voltage vectors (VVs) instead of 19 VVs in three-level conventional MPCC. The reduced VVs decrease the number of predictions and computational time for predictions. CF in terms of voltage is used, thereby eliminating the need to predict the currents and faster execution of algorithm is achieved. A higher sampling rate is possible to achieve using the proposed method; thereby, reducing the steady-state ripples in developed torque and stator flux, and improving the percentage total harmonic distortion of stator current. The effectiveness of the presented control method is practically verified after comparing its computational time, steady-state response and dynamic response with that of three-level conventional MPCC.

Sparsity-Exploiting Anytime Algorithms for Model Predictive Control: A Relaxed Barrier Approach

We present and analyze a novel class of stabilizing and numerically efficient model predictive control (MPC) algorithms for discrete-time linear systems subject to polytopic input and state constraints. The proposed approach combines the previously presented concept of relaxed barrier function-based MPC with suitable warm-starting and sparsity-exploiting factorization techniques and allows to rigorously prove important stability and constraint satisfaction properties of the resulting closed-loop system independently of the number of performed Newton iterations. The effectiveness of the proposed approach is demonstrated by means of a numerical benchmark example.

Data-driven approximation of the Koopman generator: Model reduction, system identification, and control

We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions, and modes of the generator and for system identification. In addition to learning the governing equations of deterministic systems, which then reduces to SINDy (sparse identification of nonlinear dynamics), it is possible to identify the drift and diffusion terms of stochastic differential equations from data. Moreover, we apply gEDMD to derive coarse-grained models of high-dimensional systems, and also to determine efficient model predictive control strategies. We highlight relationships with other methods and demonstrate the efficacy of the proposed methods using several guiding examples and prototypical molecular dynamics problems.