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Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
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Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

91
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
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State Space to Transfer Function01:21

State Space to Transfer Function

206
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
206
Transfer Function to State Space01:23

Transfer Function to State Space

259
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
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Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

251
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
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Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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High-factor interpolation method based on space-time modulation and a Kalman filter for optical encoders.

Yaowen Ban, Guobo Zhao, Zhenghui Zhang

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    This study introduces a novel interpolation method for optical encoders using space-time modulation and a Kalman filter. This technique enhances displacement measurement accuracy and real-time performance, proving effective in simulations and experiments.

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    Area of Science:

    • Instrumentation and Measurement
    • Signal Processing
    • Control Systems Engineering

    Background:

    • Optical encoders are crucial for precise displacement measurement.
    • Existing methods face limitations in interpolation factor and real-time performance.
    • High-factor interpolation is essential for advanced motion control applications.

    Purpose of the Study:

    • To propose a novel high-factor interpolation method for optical encoders.
    • To improve the accuracy and real-time performance of displacement measurements.
    • To develop a method implementable on Field-Programmable Gate Arrays (FPGAs).

    Main Methods:

    • Space-time modulation to convert encoder output into a displacement space-time signal.
    • High-frequency pulse signal interpolation based on phase detection.
    • Kalman filter application for velocity estimation and time lag error compensation.

    Main Results:

    • Achieved high-factor interpolation independent of moving speed.
    • Improved real-time displacement output by compensating for time lag errors.
    • Demonstrated method effectiveness through simulations and experimental validation.

    Conclusions:

    • The proposed space-time modulation and Kalman filter method offers a simple and effective solution for high-factor optical encoder interpolation.
    • The technique enhances measurement accuracy and real-time performance.
    • Feasibility for FPGA implementation makes it suitable for practical applications.