Dual-mode global stabilization of high-order saturated integrator chains: LMI-based MPC combined with a nested saturated
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ORIGINAL PAPER
Dual-mode global stabilization of high-order saturated integrator chains: LMI-based MPC combined with a nested saturated feedback Saeed Adelipour · Behzad Ahi · Mohammad Haeri
Received: 9 March 2020 / Accepted: 11 September 2020 © Springer Nature B.V. 2020
Abstract This paper considers the problem of highperformance global stabilization of an integrator chain via a bounded control at the presence of input disturbance. While nested saturated feedback (NSF) is known as the most inspiring existing solution in the literature, we shall highlight the inherent shortcomings of this approach which cause a poor performance in terms of convergence rate. Then, a novel dual-mode control scheme combining an improved NSF law with a linear matrix inequality (LMI)-based model predictive controller (MPC) is developed to overcome the weaknesses of pure NSF. By offline calculations, a set of nested robust invariant attraction regions and their attributed feedback gains are computed respecting the known bound for disturbance. In online implementation, an improved NSF law is adopted (as the first mode) to bring states within the largest invariant set. The proposed LMI-based state feedback law is applied thereafter (as the second mode) to bring state vector toward the origin with a fast convergence rate. In both modes, the well-known extended state observer (ESO) is employed to effectively suppress the external disturbance. The superiority of the proposed globally stabilizing scheme in terms of faster convergence and improved disturbance rejection ability is demonstrated comparing performances of foremost existing solutions in case of a triple integrator chain. S. Adelipour · B. Ahi · M. Haeri (B) Advanced Control Systems Lab, Sharif University of Technology, Tehran, Iran e-mail: [email protected]
Keywords Integrators chain · Bounded control · Nested saturated feedback · Model predictive control · Linear matrix inequality · Extended state observer
1 Introduction In real applications, input saturation is an inevitable challenge that typically causes the main nonlinearity of system dynamics. In this regard, the problem of global and semi-global stabilization of linear systems subjected to bounded control has been extensively studied in the literature. Specifically, particular attention is devoted to the family of pure integrator chains respecting their functionality in modeling of various control systems [1,2]. Besides this, in some twofold control structures, the system is first converted to an integrator chain with the aid of a feedforward law, and then a feedback strategy is designed to attain global stability for the achieved integrator chain [3–6]. For instance, the well-known active disturbance rejection control (ADRC) approach benefits from the same structure [7]. It is well known that a control which is achieved by saturating output of a linear feedback strategy, would not guarantee the global stability of an integrator chain with order n ≥ 3. Hence, it is inevitable to utilize nonlinear feedback schemes. The fir
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