Spectral, Convolution and Numerical Techniques in Circuit Theory

Badrieh, Fuad

doi:10.1007/978-3-319-71437-0

Cited by 6 publications

(6 citation statements)

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“…are recently proposed methods seeking to mitigate the deleterious effects of step inputs which theoretically exhibit infinite bandwidth. [28,29] While predictable response can also be tuned to desired performance specification (as with classical structural filtering), these methods also suffer from limited robustness to variation in system natural frequencies and are mentioned here contextually, but not included in analytic treatment. Most recently whiplash compensation has been proposed in the literature, [23] and direct comparison is made in this manuscript.…”

Section: Trade-off Study On Application Of Classical Methodsmentioning

confidence: 99%

“…The Fourier transform of a unit step function f(t) as displayed in equation (28). Notice the impulse occurrence is summed with an extra term with variable 𝜔 resulting in the response containing all the frequencies.…”

Section: Frequency Responses Of Step and Periodic Functions [24]mentioning

confidence: 99%

“…Trajectory optimalization utilizing the methods of Pontryagin [28] is a competing option stemming from the just published [29] including nonlinear constrained optimization, real-time optimal control, and instantiations of such with and without singular switching and nonlinear decoupling of transport theorem terms. The intention in this manuscript is to establish a new benchmark for comparison of these just published methods in a proposed sequel.…”

Section: Rigid Body Optimal Input Trajectory Shapingmentioning

confidence: 99%

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Flattening the Curve of Flexible Space Robotics

Sands¹

2022

Preprint

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Infrastructure monitoring, inspection, repair, and replacement in space is crucial for continued usage and safety, yet it is expensive, time-consuming, and technical very challenging. New robotics technologies and artificial intelligence algorithms are potentially novel approaches that may alleviate such demanding operations using existing or novel sensing technologies. Space structures must necessarily be very light weight due to high costs of placing robots in space. Several methods are proposed and compared to control highly flexible space robotics, where a key challenge is the presence of flexible resonant modes at frequencies so low as to reside inside typical feedback controller bandwidths. Such conditions imply the very action of sending control signals to the ultra-light weight robotics will cause structural resonance. Implementations of incrementally increasing order are offered, achieving over ninety percent performance improvement in trajectory tracking errors, while improvement using unshaped methods merely achieve twenty-four percent improvement in direct comparison (where the only modification is the proposed control methodology). Based on superior performance, single-sinusoidal trajectory shaping is recommended with a corollary benefit of preparing future research into applying deterministic artificial intelligence whose current instantiation relies on single-sinusoidal, autonomous trajectory generation.

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Section: Trade-off Study On Application Of Classical Methodsmentioning

confidence: 99%

Section: Frequency Responses Of Step and Periodic Functions [24]mentioning

confidence: 99%

Section: Rigid Body Optimal Input Trajectory Shapingmentioning

confidence: 99%

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Flattening the Curve of Flexible Space Robotics

Sands¹

2022

Preprint

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“…In doing so, the Laplace transforms of the periodic input and output signals should be calculated first. Using the relationship X s 9 the Laplace transforms of the input signal v i t ð Þ and the output signal v 0 t ð Þ are obtained as follows:…”

Section: Comparison With Laplace Modified Z-transform Methodsmentioning

confidence: 99%

“…Finally, the final value theorem for the modified z‐transform is employed to determine the steady‐state solution of the output. Laplace transforms of periodic signals can be determined easily 9 ; however, calculation of the modified z‐transform involves contour integration in the complex plane which may make the utilization of this method appear tedious. The method becomes easier to implement for a number of signals whose modified z‐transforms have been calculated and tabulated 8 .…”

Section: Introductionmentioning

confidence: 99%

Analytical non‐Fourier solution of linear time‐invariant circuits with periodic inputs

Safaai‐Jazi

2022

Circuit Theory & Apps

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A systematic approach for solving linear time-invariant electric circuits with periodic input signals is presented. The method involves the following steps:(1) The governing differential equation for the desired output is solved for each time segment of the input signal in one period, leaving the constant coefficients of the homogeneous parts of the solution as unknowns. For an nth-order circuit with a source consisting of q segments in one period, there are n Â q such unknown coefficients. (2) Using the solution obtained in step 1, the voltage of each capacitor and the current of each inductor are determined.(3) Transition conditions for the voltages and currents found in step 2 at the transition points of successive segments and also periodicity conditions for the beginning and end points of the period are applied. (4) Implementation of step 3 results in a system of n Â q equations in terms of the n Â q unknown coefficients described in step 1. Solving this system of equations, the circuit response in one period becomes readily available.

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