Global Stability and Simultaneous Compensation of State and Output Delays for Nonlinear Systems via Output-Feedback Slid
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Global Stability and Simultaneous Compensation of State and Output Delays for Nonlinear Systems via Output-Feedback Sliding Mode Control Tiago Roux Oliveira1 · José Paulo V. S. Cunha1 · Andrei Battistel1
Received: 9 November 2015 / Revised: 5 May 2016 / Accepted: 10 July 2016 © Brazilian Society for Automatics–SBA 2016
Abstract This paper proposes a sliding mode control scheme for a class of nonlinear systems with multiple time delays, in the state variables and in the output signal. The unmeasured state of the system is estimated by an asymptotic observer for the zero dynamics and by cascaded highgain observers for a chain of integrators with a nonlinear input disturbance which compose the complete state. Global asymptotic stability of the closed-loop system is obtained using only output feedback. The use of observers prevents undesirable chattering phenomena. Simulation results show effective performance in different scenarios, including application to missile guidance in the presence of seeker delays. Keywords Variable-structure control · Sliding mode control · Output feedback · Time delay · Nonlinear systems · Global stability · Norm observer · Cascade high-gain observers
1 Introduction The study of systems with time-delayed signals is of continuous interest of a wide variety of fields, such as biology, ecoA preliminary version of the manuscript was presented at 19th IFAC World Congress, see reference (Oliveira and Cunha 2014).
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Andrei Battistel [email protected] Tiago Roux Oliveira [email protected] José Paulo V. S. Cunha [email protected]
1
Department of Electronics and Telecommunication Engineering, State University of Rio de Janeiro, Rio de Janeiro, Brazil
nomics, mechanics, physics and engineering, which include communication and information technologies, networked controlled systems, teleoperation, robotics and pipelines, to name a few (Richard 2003). The presence of delays in control systems often leads to instability and poor performance (Si-Ammour et al. 2009; Gomes da Silva Jr. et al. 2009). Sliding mode control (SMC) is an attractive methodology for nonlinear systems, being robust to parameter uncertainties and disturbances (Utkin et al. 1999). On the other hand, actuator and sensor delays are among the most common dynamic phenomena that arise in control engineering practice (Krstic 2009). In SMC, time delays deteriorate the control performance, since they cause chattering and may even destabilize the system. Despite this, sliding mode controllers for systems with state delays were proposed by Li and DeCarlo (2003), Orlov et al. (2003) and Gouaisbaut et al. (2004) assuming full-state feedback. The use of state observers is an alternative for output-feedback stabilization of systems with state delay, as developed in Niu et al. (2004); Yan et al. (2010, 2014b). However, such observers may not be applied to a wide class of systems. Adaptive stabilizers based on compensators (e.g., Bobtsov et al. 2014) have wellknown noise sensitivity. Observers can be applied in SMC to avoid chattering cau
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