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State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Linear time-invariant Systems01:23

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Time and frequency -Domain Interpretation of Phase-lead Control01:24

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Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
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Time and frequency -Domain Interpretation of Phase-lag Control01:21

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Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Time and frequency -Domain Interpretation of PI Control01:27

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Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
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Related Experiment Video

Updated: Jan 17, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantum state preparation of time-bin encoding based on SOI integrated chips.

Hanming Yang, Chunxue Zhang, Pengwei Cui

    Applied Optics
    |September 22, 2025
    PubMed
    Summary

    This study presents a novel quantum key distribution (QKD) chip on a silicon-on-insulator platform. The chip efficiently encodes quantum states for secure communication, paving the way for practical QKD implementation.

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    Area of Science:

    • Quantum Information Science
    • Integrated Photonics
    • Quantum Cryptography

    Background:

    • Quantum key distribution (QKD) offers unconditional security for public-key encryption using quantum mechanics.
    • Existing QKD technologies face challenges in high-speed encoding and stability.
    • The silicon-on-insulator (SOI) platform is a promising candidate for integrated photonic devices.

    Purpose of the Study:

    • To design and fabricate a high-performance QKD chip.
    • To implement a time-bin encoding scheme with decoy states for enhanced security.
    • To develop a heterogeneous integration approach for improved stability and performance.

    Main Methods:

    • Integration of a thermo-optic phase modulator and a carrier-depletion modulator on an SOI platform.
    • Utilizing a time-bin encoding scheme with four BB84 quantum states.
    • Employing a heterogeneous SOI and silicon nitride (Si3N4) structure for waveguides and delay lines.

    Main Results:

    • Achieved encoding and decoding of four BB84 quantum states at a 100 MHz repetition rate.
    • Demonstrated high interference fringe visibility (93.66% for |+⟩, 92.36% for |-⟩).
    • Obtained high extinction ratios for time states (19.33 dB for |0⟩, 18.72 dB for |1⟩).

    Conclusions:

    • The fabricated QKD chip exhibits efficient quantum state preparation capabilities.
    • The heterogeneous SOI/Si3N4 structure addresses temperature-induced stability issues.
    • This work significantly supports the practical realization of QKD technology.