Van der Pol Oscillator

Casaleiro, João; Oliveira, Luís B.; Filanovsky, I.M.

doi:10.1007/978-3-030-00740-9_3

Cited by 1 publication

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“…The Van der Pol oscillator is composed of a non-conservative system with nonlinear damping to follow a second-order dynamic [33]. For the VDP system with input delay, replacing ( ) u t with ( ) u t h − throughout the system gives, , for reduced delay feedback.…”

Section: Van De Pol (Vdp) Oscillator Dynamics With Input Delaymentioning

confidence: 99%

Non-Predictive Model-Free Control of Nonlinear Systems with Unknown Input Time Delay

Zhu

Zhang

2023

Entropy

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This study presents a general framework for the control of unknown dynamic systems with unknown input delay. A concise output feedback control system is structured with tuning stabilization/dynamic response by an output feedback low gain, removing steady state error against step reference with a feedforward gain. A series of stability analyses are presented for the designed control systems, (1) a gain/phase margin theorem is proposed for stability analysis by regulating the feedback gain, and (2) a stability theorem based on rational function approximation of the time delay is presented for dealing with the transcendental polynomial characteristic equations, which is equivalent to the analysis from the algebraic polynomial characteristic equation. Both approaches give coherent results for stability analysis by regulating the feedback gain. The approaches are applicable to nonlinear systems, which are linearizable in the neighborhood of the operating points. The low complexity of the controllers does not require hard analytical derivation/numerical calculations to produce an acceptable control performance for the considered systems. Several representative simulation case studies provide demonstrations of computational experiments against those analytically derived and guidance for potential applications.

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Section: Van De Pol (Vdp) Oscillator Dynamics With Input Delaymentioning

confidence: 99%