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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 101650, 8 pages
Research Article

A Hyperbolic Tangent Adaptive PID + LQR Control Applied to a Step-Down Converter Using Poles Placement Design Implemented in FPGA

Federal University of Technology-Paraná, Avenida Monteiro Lobato km 4, s/n, 84016-210 Ponta Grossa, PR, Brazil

Received 28 June 2013; Revised 24 September 2013; Accepted 4 October 2013

Academic Editor: Zhiqiang Ma

Copyright © 2013 Marcelo Dias Pedroso et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work presents an adaptive control that integrates two linear control strategies applied to a step-down converter: Proportional Integral Derivative (PID) and Linear Quadratic Regulator (LQR) controls. Considering the converter open loop transfer function and using the poles placement technique, the designs of the two controllers are set so that the operating point of the closed loop system presents the same natural frequency. With poles placement design, the overshoot problems of the LQR controller are avoided. To achieve the best performance of each controller, a hyperbolic tangent weight function is applied. The limits of the hyperbolic tangent function are defined based on the system error range. Simulation results using the Altera DSP Builder software in a MATLAB/SIMULINK environment of the proposed control schemes are presented.