Tube-based model predictive control for linear parameter-varying systems with bounded rate of parameter variation

Abbas, Hossam S.; Männel, Georg; Hoffmann, Christian; Rostalski, Philipp

doi:10.1016/j.automatica.2019.04.046

Cited by 38 publications

(31 citation statements)

References 13 publications

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“…• Very recently, papers (Abbas et al, 2019;Hanema et al, 2020) deploy TMPC s for LPV systems with bounded rates of parameter variations. The first paper considers the maximal and minimal evolution sequence for the scheduling variables for the next N p steps, considering the rates of variations, and thus computes the tube that encompasses all these possible trajectories.…”

Section: Tube-based Methodsmentioning

confidence: 99%

Model predictive control design for linear parameter varying systems: A survey

Morato

Normey‐Rico

Sename

2020

Annual Reviews in Control

140

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Motivated by the fact that many nonlinear plants can be represented through Linear Parameter Varying (LPV) embedding, and being this framework very popular for control design, this paper investigates the available Model Predictive Control (MPC) policies that can be applied for such systems. This paper reviews the available works considering LPV MPC design, ranging from the sub-optimal, simplified, yet Quadratic Programming (QP) algorithms, the tube-based tools, the set-constrained procedures, the Nonlinear Programming procedures and the robust ones; the main features of the recent research body on this topic are examined. A simulation example is given comparing some of the important techniques. Finally, some suggestions are given for future investigation threads, seeking further applicability of these methods.

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Section: Tube-based Methodsmentioning

confidence: 99%

Model predictive control design for linear parameter varying systems: A survey

Morato

Normey‐Rico

Sename

2020

Annual Reviews in Control

140

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“…There exist algorithms in the literature for computing these ingredients; however, due to the involved computational complexity, the application of most of these algorithms can be carried out for very simple 2nd-to 4th-order systems in simulation with one or two scheduling parameters in the LPV case [30], [31]. In contrast, with the system considered in this work, which is of 8th order and 18 scheduling parameters with affine dependence, computing the terminal cost and the terminal constraint set is intractable with available tools in the literature, e.g., [32], [33].…”

Section: B the Lpv Modelingmentioning

confidence: 99%

“…where C d is given in (31), which is a constant matrix, however, A d , B d are dependent on x s and u s as well, see ( 29) and (30). Therefore, computing x s and u s for a given reference value is a matter of solving a nonlinear set of algebraic equations, which can be solved using any of the Newton methods for solving nonlinear equations [37].…”

Section: B Model Predictive Controlmentioning

confidence: 99%

Model Predictive Control Based on Linear Parameter-Varying Models of Active Magnetic Bearing Systems

et al. 2021

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Active magnetic bearing (AMB) system has been recently employed widely as an ideal equipment for high-speed rotating machines. The inherent challenges to control the system include instability, nonlinearity and constricted range of operation. Therefore, advanced control technology is essential to optimize AMB system performance. This paper presents an application of model predictive control (MPC) based on linear parameter-varying (LPV) models to control an AMB system subject to input and state constraints. For this purpose, an LPV model representation is derived from the nonlinear dynamic model of the AMB system. In order to provide stability guarantees and since the obtained LPV model has a large number of scheduling parameters, the parameter set mapping (PSM) technique is used to reduce their number. Based on the reduced model, a terminal cost and an ellipsoidal terminal set are determined offline and included into the MPC optimization problem which are the essential ingredients for guaranteeing the closed-loop asymptotic stability. Moreover, for recursive feasibility of the MPC optimization problem, a slack variable is included into its cost function. The goal of the proposed feedback control system is twofold. First is to demonstrate high performance by achieving stable levitation of the rotor shaft as well as high capability of reference tracking without violating input and state constraints, which increases the overall safety of the system under disturbances effects. Second is to provide a computationally tractable LPVMPC algorithm, which is a substantial requirement in practice for operating the AMB system with high performance over its full range. Therefore, we propose an LPVMPC scheme with frozen scheduling parameter over the prediction horizon of the MPC. Furthermore, we demonstrate in simulation that such frozen LPVMPC can achieve comparable performance to a more sophisticated LPVMPC scheme developed recently and a standard NL MPC (NMPC) approach. Moreover, to verify the performance of the proposed frozen LPVMPC, a comparison with a classical controller, which is commonly applied to the system in practice, is provided.INDEX TERMS Model predictive control, linear parameter-varying models, magnetic bearing systems, parameter set mapping, asymptotic stability.

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“…The theory of tube‐based MPC is well‐developed for linear systems [8–13] and some extensions to non‐linear systems exist [14–18]. In [14], the tube‐based MPC is proposed for a certain class of non‐linear discrete‐time systems in which simple robust control invariant tubes, corresponding to the parameterised feedback control policy, are constructed.…”

Section: Introductionmentioning

confidence: 99%