Nonlinear Model Predictive Control for Processes with Complex Dynamics: A Parameterisation Approach Using Laguerre Functions

Abstract Classical model predictive control (MPC) algorithms need very long horizons when the controlled process has complex dynamics. In particular, the control horizon, which determines the number of decision variables optimised on-line at each sampling instant, is crucial since it significantly affects computational complexity. This work discusses a nonlinear MPC algorithm with on-line trajectory linearisation, which makes it possible to formulate a quadratic optimisation problem, as well as parameterisation using Laguerre functions, which reduces the number of decision variables. Simulation results of classical (not parameterised) MPC algorithms and some strategies with parameterisation are thoroughly compared. It is shown that for a benchmark system the MPC algorithm with on-line linearisation and parameterisation gives very good quality of control, comparable with that possible in classical MPC with long horizons and nonlinear optimisation.

[1]  Bilal Khan,et al.  Alternative parameterisation within predictive control: a systematic selection , 2013, Int. J. Control.

[2]  Addy Wahyudie,et al.  Robust predictive control for heaving wave energy converters , 2018, Control Engineering Practice.

[3]  K. Lim,et al.  Generalized Predictive Control of , 2022 .

[4]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[5]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[6]  Liuping Wang.  Discrete model predictive controller design using Laguerre functions , 2004 .

[7]  Jian-zhong Zhou,et al.  A distributed model predictive control based load frequency control scheme for multi-area interconnected power system using discrete-time Laguerre functions. , 2017, ISA transactions.

[8]  Mansour Souissi,et al.  Control Strategies for the Grid Side Converter in a Wind Generation System Based on a Fuzzy Approach , 2018, Int. J. Appl. Math. Comput. Sci..

[9]  Ricardo J. G. B. Campello,et al.  An introduction to models based on Laguerre, Kautz and other related orthonormal functions - Part II: non-linear models , 2012, Int. J. Model. Identif. Control..

[10]  Piotr Tatjewski,et al.  Advanced Control of Industrial Processes: Structures and Algorithms , 2006 .

[11]  Ricardo J. G. B. Campello,et al.  An introduction to models based on Laguerre, Kautz and other related orthonormal functions - part I: linear and uncertain models , 2011, Int. J. Model. Identif. Control..

[12]  Józef Korbicz,et al.  Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities , 2019, Int. J. Appl. Math. Comput. Sci..

[13]  Okko H. Bosgra,et al.  Model predictive control with generalized input parametrization , 1999, 1999 European Control Conference (ECC).

[14]  Yongkun Li,et al.  Almost Periodic Synchronization of Fuzzy Cellular Neural Networks with Time–Varying Delays via State–Feedback and Impulsive Control , 2019, Int. J. Appl. Math. Comput. Sci..

[15]  Grzegorz Mzyk,et al.  Combined Parametric-Nonparametric Identification of Block-Oriented Systems , 2013 .

[16]  Roman Smierzchalski,et al.  Adaptive Backstepping Tracking Control for an over–Actuated DP Marine Vessel with Inertia Uncertainties , 2018, Int. J. Appl. Math. Comput. Sci..

[17]  Hyochoong Bang,et al.  Linear time-varying model predictive control of magnetically actuated satellites in elliptic orbits , 2018 .

[18]  Boris Rohaľ-Ilkiv,et al.  Embedded explicit model predictive vibration control , 2016 .

[19]  Vicenç Puig,et al.  Multi-layer health-aware economic predictive control of a pasteurization pilot plant , 2018, Int. J. Appl. Math. Comput. Sci..

[20]  Maciej Ławryńczuk,et al.  Fast Analytical Model Predictive Controllers and Their Implementation for STM32 ARM Microcontroller , 2019, IEEE Transactions on Industrial Informatics.

[21]  Wlodzimierz Greblicki.  Nonparametric Input Density-Free Estimation of the Nonlinearity in Wiener Systems , 2010, IEEE Transactions on Information Theory.

[22]  Abdel Latif Elshafei,et al.  Continuous-time tube-based explicit model predictive control for collective pitching of wind turbines , 2017 .

[23]  Liuping Wang.  Continuous time model predictive control design using orthonormal functions , 2001 .

[24]  Donal O'Donovan,et al.  Predictive Functional Control: Principles and Industrial Applications , 2009 .

[25]  Florian Holzapfel,et al.  Adaptive Fault–Tolerant Position Control of a Hexacopter Subject to an Unknown Motor Failure , 2018, Int. J. Appl. Math. Comput. Sci..

[26]  Leonardo Trujillo,et al.  Systematic selection of tuning parameters for efficient predictive controllers using a multiobjective evolutionary algorithm , 2015, Appl. Soft Comput..

[27]  Henk Nijmeijer,et al.  Experimentally validated model predictive controller for a hexacopter , 2017 .

[28]  Marcin Witczak,et al.  Robust Multiple Sensor Fault–Tolerant Control For Dynamic Non–Linear Systems: Application To The Aerodynamical Twin–Rotor System , 2018, Int. J. Appl. Math. Comput. Sci..

[29]  B. Wahlberg.  System identification using Laguerre models , 1991 .

[30]  Maciej Lawrynczuk.  Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach , 2014 .

[31]  Ola Alhaj Hasan,et al.  Development of a Model Based Predictive Control System for Heating Buildings , 2017 .

[32]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..

[33]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..