Sigmoid based PID controller implementation for rotor control

Abstract

This paper presents a sigmoid based variable coefficient PID (SBVC-PID) controller design for Twin Rotor MIMO System (TRMS). The proposed SBVC-PID controller dynamically changes controller coefficients according to a modified sigmoid function of the error signal. The modified sigmoid function is used to limit variability of PID controller coefficients in a predefined range. In the proposed method, each parameters of PID, namely p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> , k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> and k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> , alter between predefined upper and lower bounds. A modified sigmoid function adjusted by a transition coefficient is used to alter each of the PID parameters between these bound limits. The variable coefficients of SBVC-PID maintain a hypercube in k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> and k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> parameter space satisfying robust stability of the system. Well-known Kharitonov polynomials are used to ensure that the SBVC-PID coefficient alteration takes place in the robust stability intervals. Due to dynamically change of PID coefficients depending on magnitude of error signal, the control performance can be improved compared to conventional PID control. Performance of SBVC-PID controller is demonstrated via theoretical examples and TRMS rotor control simulations.