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Approximate explicit robust model predictive control of a CSTR with fast reactions

CHEMICAL PAPERS 2019年第3期73卷 611-618页

作者： Bakarac, Peter Kvasnica, Michal Slovak Univ Technol Bratislava Inst Informat Engn Automat & Math Fac Chem & Food Technol Radlinskeho 9 Bratislava 81237 Slovakia

This paper presents a novel approach to the construction of explicit representation of robust model predictive feedback laws for constrained linear systems with parametric uncertainties. The approach is based on employing approximate dynamic programming where a large optimal control problem is split into a sequence of problems of smaller size. To be able to solve each such problem explicitly, we employ a bounded approximation of optimal value functions. Such a procedure is demonstrated to be superior, both in terms of construction time as well as in the complexity of the resulting controllers, to traditional approaches based on the one-shot approach. The proposed method is demonstrated on a simulation case study involving a continuous stirred tank reactor (CSTR) where a fast multi-component chemical reaction takes place.

关键词： explicit model predictive control Robust model predictive control Parametric uncertainties Continuous stirred tank reactor

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Robust explicit Nonlinear model predictive control with Integral Sliding Mode

Robust Explicit Nonlinear Model Predictive Control with Inte...

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American control Conference

作者： Chakrabarty, Ankush Vu Dinh Buzzard, Gregery T. Zak, Stanislaw H. Rundell, Ann E. Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA

ISBN: (纸本)9781479932740

A robust control strategy for stabilizing nonlinear systems in the presence of additive bounded disturbances is proposed. The proposed control architecture is a novel combination of explicit nonlinear model predictive control (EMPC) and integral sliding mode control (ISMC). Feasibility analysis of a finite-horizon optimal control problem involved in deriving the EMPC control action is performed over a polytope of interest in the state space. A sparse sampling-based boundary detection algorithm is employed to compute an approximating polynomial bounding the feasible region. A sparse-grid based interpolation scheme with Chebyshev-Gauss-Lobatto nodes and Legendre-basis polynomials are used to design the stabilizing EMPC surface. The proposed method is appealing because of the simplicity of the controller construction in conjunction with its applicability to higher-dimensional problems, which stems from the scale-ability property of sparse-grids. Robustness to the designed EMPC is provided by the ISMC. A simulated example is provided to illustrate the efficacy and performance of the proposed control strategy for the stabilization of an uncertain nonlinear dynamical system.

关键词： explicit model predictive control Integral sliding mode control sparse grid interpolation feasibility analysis

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explicit model predictive controller Design for Thickness and Tension control in a Cold Rolling Mill

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IFAC-PapersOnLine 2016年第20期49卷 126-131页

作者： Ogasahara, Tomoyoshi Hovd, Morten Asano, Kazuya Instrument and Control Engineering Research Dept. Steel Research Lab. JFE Steel Corp. FukuyamaHiroshima721-8510 Japan Department of Engineering Cybernetics Norwegian University of Science and Technology TrondheimN-7491 Norway Steel Research Lab. JFE Steel Corp. KawasakiKanagawa210-0855 Japan

This paper addresses modeling of a cold rolling mill and controller design based on explicit model predictive control(explicit MPC). The control objectives are to track the exit thickness to the reference with high accuracy with minimized strip tension deviation. In the simulation, good control is obtained when the disturbance entering the system is small enough. However, the thickness shows the offset from the reference in case of acceleration, because the approximation error of the linearized model increases and it is different from the model in the design of the controller. In order to compensate for the control offset, an additional integral logic using the estimation error of exit thickness is proposed. The validity of this approach was verified by simulation and offset free control was achieved. © 2016

关键词： controllers Cold rolling Cold rolling mills Iron and steel industry MIMO systems model predictive control predictive control systems Process control Steelmaking Approximation errors control objectives controller designs explicit model predictive control Multi input/multi output systems Optimal controls predictive control Process model

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explicit machine learning-based model predictive control of nonlinear processes via multi-parametric programming

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COMPUTERS & CHEMICAL ENGINEERING 2024年 186卷

作者： Wang, Wenlong Wang, Yujia Tian, Yuhe Wu, Zhe Natl Univ Singapore Dept Chem & Biomol Engn Singapore 117585 Singapore West Virginia Univ Dept Chem & Biomed Engn Morgantown WV 26506 USA

Machine learning-based model predictive control (ML-MPC) has been developed to control nonlinear processes with unknown first-principles models. While ML models can capture nonlinear dynamics of complex systems, the complexity of ML models leads to increased computation time for real-time implementation of ML-MPC. To address this issue, in this work, we propose an explicit ML-MPC framework for nonlinear processes using multi-parametric programming. Specifically, a self-adaptive approximation algorithm is first developed to obtain a piecewise linear affine function that approximates the behaviors of ML models. Then, multi- parametric quadratic programming (mpQP) problems are formulated to generate the solution map for states in discretized state-space. Furthermore, to accelerate the implementation of explicit ML-MPC, a neighbor- first search algorithm is developed. Finally, an example of a chemical reactor is used to demonstrate the effectiveness of the explicit ML-MPC.

关键词： Machine learning explicit model predictive control Multi-parametric programming Nonlinear processes Chemical process control

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control of a Laboratory 3-DOF Helicopter: explicit model predictive Approach

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INTERNATIONAL JOURNAL OF control AUTOMATION AND SYSTEMS 2016年第2期14卷 389-399页

作者： Zhang, Ju Cheng, Xinyan Zhu, Jiaqi Zhejiang Univ Technol Zhijiang Coll 958 Kehua Rd Keqiao Dist Shaoxing Peoples R China

A helicopter flight control system is a typical multi-input, multi-output system with strong channel coupling and nonlinear characteristics. This paper presents an explicit model predictive control (EMPC) for attitude regulation and tracking of a 3-Degree-of-Freedom (3-DOF) helicopter. A state-space representation of the system is established according to the characteristics of each degree-of-freedom motion. Multi-Parametric Quadratic Programming (MPQP) and online computation processes for explicit model predictive control and controller design for a 3-DOF helicopter are discussed. The controller design for set-point regulation and tracking time-varying reference signals of a 3-DOF helicopter are presented respectively. Numerical study of explicit model predictive control for attitude regulation and tracking of a 3-DOF helicopter are conducted. A hardware-in-the-loop experimental study of explicit model predictive control of a 3-DOF helicopter is made. To analyze the performances of an EMPC controlled helicopter system, an Active Mass Disturbance System and manual interference are considered in comparison with PID scheme. Numerical simulation and HIL experimental studies show that explicit model predictive control is valid and has satisfactory performance for a 3-DOF helicopter.

关键词： explicit model predictive control hardware in the loop regulation tracking 3-DOF helicopter

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explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

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AUTOMATICA 2011年第8期47卷 1638-1645页

作者： Kouramasa, K. I. Faisca, N. P. Panos, C. Pistikopoulos, E. N. Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England AspenTech Reading RG2 6DT Berks England

This work presents a new algorithm for solving the explicit/multi-parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： explicit model predictive control model predictive control Multi-parametric control Multi-parametric programming Dynamic programming

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explicit model predictive Based Fault Tolerant control for Turboshaft Engine System

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IEEE ACCESS 2022年 10卷 34637-34653页

作者： Gu, Nannan Wang, Xi Yang, Shubo Beihang Univ Sch Energy & Power Engn Beijing 100191 Peoples R China Collaborat Innovat Ctr Adv Aeroengine Beijing 100191 Peoples R China

In order to tackle the faults of turboshaft engine-rotor systems and the real time implementation difficulty of traditional model predictive control methods, an explicit model predictive (EMPC) fault-tolerant control algorithm is designed based on an active fault-tolerant control scheme that implicitly detects the faults and adjusts the control law online. The proposed real time control algorithm can achieve good control command tracking performance and, at the same time, guarantee limit protection of turboshaft engine-rotor system. Firstly, to start with the algorithm, a dynamic system model library and a fault monitoring mechanism are established, in which the dynamic system model library contains sets of piecewise affine models (PWA) of normal engine mode and modes with faults. Secondly, the EMPC fault-tolerant controller is derived and designed for each sub-model in the modes of dynamic model library. Through the transformation and derivation of the traditional model predictive controller of turboshaft engine-rotor system, the explicit solution of its fault-tolerant controller is obtained. With the explicit solution which is in the form of state feedback control for each partition, controller gains can be designed off-line. Finally, the online engine control process is completed by searching the corresponding controller gain based on engine state, which improves the real-time performance of the control system. The effectiveness of the method for engine systems with modeled or un-modeled compressor faults and the robustness of the algorithm are verified by simulations.

关键词： Engines Turbines Rotors Real-time systems Aerodynamics control systems Fault tolerant systems explicit model predictive control fault tolerant control turboshaft engine-rotor system limit protection

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explicit efficient constrained model predictive control

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INTERNATIONAL JOURNAL OF AUTOMATION AND control 2016年第4期10卷 329-355页

作者： Lamburn, Darren Gibbens, Peter Dumble, Steven Univ Sydney Sch Aerosp Mech & Mechatron Engn Sydney NSW 2006 Australia

A more efficient model predictive control algorithm is algebraic model predictive control. The efficiency is improved by forming the prediction horizon with a non-uniform distribution of points. The most efficient case reduces the problem down to a single prediction point, defining the horizon length as well as removing any redundant control calculations. This paper shows that for this single prediction point case, the constrained control can be easily evaluated explicitly, thus making the control calculation deterministic and more efficient. We also show that because an explicit control can be determined for the system, the closed-loop constrained stability bounds can be evaluated a priori. Using the key constraint of the peak location of the response also allows the system to meet the constraints while still being explicit and deterministic. The proposed explicit algorithm is applied to two numerical simulation examples with the performance, computational efficiency and stability analysed.

关键词： constraints continuous linear systems efficient predictive control explicit model predictive control

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Active Disturbance Rejection explicit model predictive Direct Speed control for Permanent Magnet Synchronous Motors 25

Active Disturbance Rejection Explicit Model Predictive Direc...

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25th International Conference on Electrical Machines and Systems (ICEMS)

作者： Lin, Shiyu Zhao, Mengyuan Cao, Yanfei Lin, Zhichen Shi, Tingna Xia, Changliang Zhejiang Univ Coll Elect Engn Hangzhou Peoples R China

ISBN: (纸本)9781665493024

In the explicit model predictive direct speed (EMPDS) control of the permanent magnet synchronous motor (PMSM), unknown disturbances caused by parameter variations and model mismatches can result in significant speed errors. To solve this problem, this paper proposes an active disturbance explicit model predictive direct speed (ADR-EMPDS) control method. First, a new PMSM linear model is designed, in which the nonlinear terms and the unknown disturbances are unified as lumped disturbances. Then, a new robust EMPDS optimal control law is obtained by designing three components: the linear robust prediction model, the cost function, and the linear system constraints. Subsequently, an extended state observer (ESO) is designed to observe the lumped disturbances in real time, and the observed lumped disturbances are fed into the robust EMPDS optimal control law. In addition, the stabilities of the designed ESO and ADR-EMPDS control system are demonstrated by analyzing whether the characteristic roots of the discrete-time system locate inside the unit circle. The proposed method improves the system's robustness to parameter variations and model mismatches and achieves direct speed tracking for reference commands without steady-state errors. Finally, the experimental results verify the effectiveness and superiority of the proposed method.

关键词： permanent magnet synchronous motor direct speed control disturbance suppression explicit model predictive control

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Weighting Factors Tuning Method in explicit model predictive Direct Speed control of Permanent Magnet Synchronous Motor 24

Weighting Factors Tuning Method in Explicit Model Predictive...

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24th International Conference on Electrical Machines and Systems (ICEMS)

作者： Zhao, Mengyuan Cao, Yanfei Yan, Yan Zhang, Zhen Shi, Tingna Xia, Changliang Zhejiang Univ Coll Elect Engn Hangzhou Peoples R China Zhejiang Univ Adv Elect Equipment Innovat Ctr Hangzhou Peoples R China

ISBN: (纸本)9788986510218

To solve the problem that it's difficult to tune the weighting factors of the cost function in the explicit model predictive direct speed control strategy for permanent magnet synchronous motors (PMSMs), this paper proposes a unified method for tuning multiple weighting factors. First, the effective constraint matrices of the control system under typical working conditions are derived, and the optimal control laws and closed-loop transfer functions in the corresponding critical regions are calculated. Then trajectories of the closed-loop poles are drawn and the ideal segments are defined. Finally, combining the physical meaning of weighting factors and the characteristics of PMSMs, the weighting factors selection formulas that can configure the closed-loop poles on the ideal segments are proposed for the first time. This method greatly reduces the tuning time and optimizes the control performance. Its superiority is verified through simulations and experiments.

关键词： permanent magnet synchronous motor explicit model predictive control direct speed control weighting factor

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