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Feedback control systems

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...

Linear time-invariant Systems

Linear time-invariant Systems

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.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...

Time-Domain Interpretation of PD Control

Time-Domain Interpretation of PD Control

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.
Consider the example of control of motor torque. Initially, a positive...

Time and frequency -Domain Interpretation of PI Control

Time and frequency -Domain Interpretation of PI Control

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.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires...

BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

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.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....

State Space Representation

State Space Representation

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.
Consider an RLC circuit, a...

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Related Experiment Video

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Interactive and Visualized Online Experimentation System for Engineering Education and Research

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Published on: November 24, 2021

Network-Based Robust H₂/H∞ Control for Linear Systems With Two-Channel Random Packet Dropouts and Time Delays.

Li Qiu, Yang Shi, Fengqi Yao

IEEE Transactions on Cybernetics

|September 16, 2014

Summary

This study presents a robust control strategy for networked systems facing packet loss and delays. The method ensures system stability and performance despite uncertainties and disturbances.

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Area of Science:

Control Systems Engineering
Networked Systems
Stochastic Systems

Background:

Networked control systems (NCS) are susceptible to packet dropouts and time delays, impacting stability and performance.
Uncertain parameters and external disturbances further challenge the robust control design for NCS.
Existing methods often struggle to simultaneously address multi-channel packet loss and time delays in discrete-time NCS.

Purpose of the Study:

To develop a robust output feedback H₂/H∞ control strategy for discrete-time NCS.
To address simultaneous sensor-to-controller and controller-to-actuator packet dropouts and time delays.
To ensure robust stability and performance in the presence of system uncertainties and external disturbances.

Main Methods:

A Markov jump system framework is employed to model the stochastic nature of packet dropouts and time delays.
A Lyapunov function is utilized to analyze the robust stability of the closed-loop system.
Sufficient conditions for controller existence are derived using linear matrix inequalities (LMIs).

Main Results:

The proposed method guarantees robust stochastic stability for the NCS.
Prescribed H₂ and H∞ performance levels are achieved despite uncertainties and disturbances.
The derived conditions in LMIs facilitate the practical design of the robust controller.

Conclusions:

The developed robust output feedback H₂/H∞ control strategy effectively handles packet dropouts and time delays in NCS.
The Markov jump system approach combined with LMI conditions provides a systematic way to design controllers for uncertain NCS.
The angular positioning system example validates the effectiveness and applicability of the proposed control design.