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Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

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.

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...

PD Controller: Design

PD Controller: Design

In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...

PI Controller: Design

PI Controller: Design

Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...

Open and closed-loop control systems

Open and closed-loop control systems

Control systems are foundational elements in automation and engineering. They are broadly categorized into open-loop and closed-loop systems. These classifications hinge on the presence or absence of feedback mechanisms, significantly influencing the system's performance, complexity, and application.
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal and...

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...

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Related Experiment Videos

Neural network controller using autotuning method for nonlinear functions.

T Yamada¹, T Yabuta

¹NTT Telecommun. Field Syst., RandD Center, Ibaraki.

IEEE Transactions on Neural Networks

|January 1, 1992

Summary

A new autotuning method optimizes sigmoid functions in neural networks using the steepest descent method. Simulated results demonstrate the effectiveness of this approach for learning-type direct controllers.

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Area of Science:

Artificial Intelligence
Machine Learning
Neural Networks

Background:

Sigmoid functions are crucial in neural networks for introducing non-linearity.
Optimizing sigmoid function parameters is essential for effective network training.
Existing methods for parameter tuning can be complex and computationally intensive.

Purpose of the Study:

To propose an automated method for tuning the optimal sigmoid function in neural networks.
To leverage the steepest descent method for efficient parameter optimization.
To validate the proposed autotuning method through simulations.

Main Methods:

Developed an autotuning algorithm based on the steepest descent optimization technique.
Applied the method to adjust sigmoid function parameters within a neural network architecture.
Utilized a learning-type direct controller for simulation and performance evaluation.

Main Results:

The proposed autotuning method successfully identified optimal sigmoid function parameters.
Simulations confirmed the practicality and effectiveness of the autotuning approach.
The method demonstrated robust performance in the context of learning-type direct control.

Conclusions:

The steepest descent-based autotuning method offers an efficient way to optimize sigmoid functions in neural networks.
This approach enhances the performance and adaptability of neural network controllers.
The findings support the integration of automated tuning for improved neural network design.