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PD Controller: Design

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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.
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A Novel Path-Following-Method-Based Polynomial Fuzzy Control Design.

Ying-Jen Chen, Kazuo Tanaka, Motoyasu Tanaka

IEEE Transactions on Cybernetics

|December 25, 2019

Summary

This study introduces a new fuzzy control design using a path-following method for polynomial systems. It offers a nonconvex stabilization criterion that avoids conservativeness and expands applicability for fuzzy control systems.

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Area of Science:

Control Systems Engineering
Fuzzy Logic Systems
Nonlinear Control Theory

Background:

Polynomial fuzzy control systems present stabilization challenges.
Existing convex stabilization criteria can be conservative and restrictive.

Purpose of the Study:

To propose a novel nonconvex stabilization criterion for polynomial fuzzy control.
To develop a path-following method for solving bilinear sum-of-squares (SOS) constraints.
To enhance the region of attraction (ROA) analysis for fuzzy control systems.

Main Methods:

Design of a polynomial fuzzy control using a path-following method.
Formulation of a nonconvex stabilization criterion using bilinear SOS constraints.
Application of SOS-based copositive relaxation for stabilization analysis.

Main Results:

The proposed nonconvex criterion avoids conservativeness associated with convex transformations.
The method removes restrictions on Lyapunov function candidates.
Demonstrated effectiveness through design examples, complementing existing convex criteria.

Conclusions:

The novel nonconvex stabilization criterion offers a less conservative approach.
The path-following method effectively solves the bilinear SOS problem.
This approach expands the applicability and ROA analysis of polynomial fuzzy control systems.