Predictive Control of Linear Systems with Switched Actuators Subject to Dwell-Time Constraints
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Predictive Control of Linear Systems with Switched Actuators Subject to Dwell-Time Constraints Matheus Henrique Marcolino1
· Roberto Kawakami Harrop Galvão2 · Karl Heinz Kienitz2
Received: 28 February 2020 / Revised: 5 October 2020 / Accepted: 5 November 2020 © Brazilian Society for Automatics–SBA 2020
Abstract This paper is concerned with the control of linear systems with switched actuators subject to lower bounds on dwell times. The problem addressed herein consists of driving the system state to a desired periodic trajectory through suitable perturbations in the switching times. For this purpose, a linearization procedure is derived to describe the relationship between the switchingtime perturbations and the resulting state trajectory. This procedure allows the constrained predictive control problem to be cast in the form of a convex quadratic program, which is a key contribution of the present work. Simulation examples with single-input and two-input models are presented for illustration. In all cases, the system state is driven to the desired trajectory with satisfaction of the dwell-time constraints on the switched input signal. Keywords Switched systems · Dwell-time constraints · Predictive control · Periodic trajectories
1 Introduction Switched control problems involving transitions between two or more subsystems, commutation among different controllers, or discontinuous control actions have been the object of extensive research (Egerstedt et al. 2003; Wu et al. 2013; Liu et al. 2014). In the context of optimal control, difficulties may arise if the problem is subjected to constraints on the minimum dwell time at every switching level. For instance, these constraints must be addressed in the operation of distributed generation systems due to a minimum period of time required to turn on or shut down individual generators (Ferrari-Trecate et al. 2004; Larsen et al. 2013, 2014; Parisio et al. 2014). The operation of power electronic systems may also be subject to time constraints between
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Matheus Henrique Marcolino [email protected] Roberto Kawakami Harrop Galvão [email protected] Karl Heinz Kienitz [email protected]
1
Technological Science Institute, Universidade Federal de Itajubá, Rua Irmã Ivone Drummond, 200, Distrito Industrial II, Itabira, Minas Gerais 35903-087, Brazil
2
Electronics Engineering Division, Instituto Tecnológico de Aeronáutica, Praça Marechal Eduardo Gomes, 50,Vila das Acácias, São José dos Campos, São Paulo 12228-900, Brazil
successive switchings, owing to physical limitations of the semiconductor components (Loxton et al. 2009) as well as the loss of energy caused by high-frequency switching (Arntzen and Maksimovic 1998). In the attitude regulation of rockets or satellites in the upper atmosphere, the use of on/off thrusters may involve dwell-time constraints due to the time required to initialize or extinguish the flow/burn of propellant (Antropov et al. 1999; Rom and Gany 1992). Optimal control methods which take into account dwelltime constraints typically compris
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