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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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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Extended State Functional Observer-Based Event-Driven Disturbance Rejection Control for Discrete-Time Systems.

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    This study introduces event-driven control for discrete-time systems facing unknown disturbances. The proposed methods significantly reduce event-triggering frequency while ensuring complete disturbance compensation.

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    Area of Science:

    • Control Systems Engineering
    • Systems Theory
    • Signal Processing

    Background:

    • Discrete-time systems are susceptible to unknown mismatched disturbances.
    • Traditional time-driven control can be resource-intensive.
    • State and disturbance estimation are crucial for effective control.

    Purpose of the Study:

    • To develop an event-driven output feedback control approach for discrete-time systems with unknown mismatched disturbances.
    • To reduce network resource usage through event-triggered control.
    • To ensure stability and effective disturbance rejection.

    Main Methods:

    • A reduced-order extended state functional observer was designed to estimate unavailable states and disturbances.
    • A Zero-Order Hold (ZOH)-based event-driven output feedback disturbance rejection controller was designed.
    • A predictive event-driven output feedback disturbance rejection control approach was proposed to further save network resources.

    Main Results:

    • The proposed event-driven control methods achieve complete disturbance compensation in the system's output channels.
    • Event-triggering frequency is significantly reduced compared to time-driven control schemes.
    • Stability and disturbance rejection capabilities were demonstrated through numerical simulations.

    Conclusions:

    • Event-driven output feedback control offers an effective strategy for discrete-time systems with unknown disturbances.
    • The proposed observer-based and predictive control approaches enhance resource efficiency.
    • The methods provide a robust solution for disturbance rejection and system stability.