Switching between periodic orbits in impact oscillator by time-delayed feedback methods

Costa, Dimitri Danulussi Alves; Vaziri, Vahid; Pavlovskaia, Ekaterina; Savi, Marcelo A.; Wiercigroch, Marian

doi:10.1016/j.physd.2022.133587

Cited by 10 publications

(5 citation statements)

References 48 publications

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“…2, (d). Note this frequency range is chosen following the experimentally obtained diagram in [28]. As shown in Fig.…”

Section: Mathematical Modelling and System Dynamicsmentioning

confidence: 99%

“…Note in the impact oscillator Y (t) = [x(t), ẋ(t)] ′ . Following the work presented in [28], we can calculate the control signal as follows:…”

Section: First Case Study: Switching To Non-impacting Attractormentioning

confidence: 99%

“…So as long as the system is in p1, the control signal remains zero (even when τ = 2T ). To resolve this issue, a two-staged TDF is applied to the system [28]. During the first stage, the controller takes the system out of the basing of attraction of p1 with a non-integer delay (τ = 0.5T in this case).…”

Section: Second Case Study: Switching To High Amplitude Attractormentioning

confidence: 99%

“…Active control methods should be applied to achieve the exchange between coexisting attractors, utilising actuators [27,28]. However, actuators such as electrical motors, hydraulic and pneumatic valves do not typically have instantaneous responses in real-world engineering systems.…”

Section: Introductionmentioning

confidence: 99%

“…The impact oscillator can exhibit many different attractors, which is a suitable platform for such an analysis. The mass-excited impact oscillator developed in the Centre for Applied Dynamics Research (CADR) [35,36] is then selected so the experimentally validated model [28] can be employed for this analysis.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Constrained Control of Coexisting Attractors in Impact Oscillator with Delay

Lalehparvar

Vaziri

Aphale

2023

J. Vib. Eng. Technol.

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The coexistence of attractors is a characteristic of a range of nonlinear systems that results in systems exhibiting different dynamics for varying initial conditions with invariant system parameters. This characteristic often provides an effective means to jump between different behaviours by employing control methods. However, control signals are influenced by delay and constraint, which affect controllers' performance. In this paper, we investigate the effects of actuator and memory delay, start time and actuator constraints on the performance of the timedelayed feedback (TDF) control scheme enabling the switching between coexisting attractors of the impact oscillator. Looking at two potential applications, we focused on two case studies with two desired stable orbits: Case 1: Non-impacting attractor and Case 2: High amplitude attractor. In both case studies, the effects of the actuator and memory delay in the control signal are investigated. Then, within a meaningful range of delay, their effects on the controller performance are predicted and compared. One notable observation is that by increasing the delay, settling time follows similar patterns in two case studies, experiencing a decrease followed by an increase and then failure of the controller to jump between the targeted coexisting attractors. Furthermore, the effects of the start time and the actuator constraints (force limit) on the controllers' performances in these case studies are also investigated.

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“…2, (d). Note this frequency range is chosen following the experimentally obtained diagram in [28]. As shown in Fig.…”

Section: Mathematical Modelling and System Dynamicsmentioning

confidence: 99%

“…Note in the impact oscillator Y (t) = [x(t), ẋ(t)] ′ . Following the work presented in [28], we can calculate the control signal as follows:…”

Section: First Case Study: Switching To Non-impacting Attractormentioning

confidence: 99%

Section: Second Case Study: Switching To High Amplitude Attractormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%