Decentralized PID Controllers Synthesis for Linear Interconnected Systems using Shifted Legendre Polynomials

A new method for synthesising decentralized proportional integral derivative (PID) controllers for interconnected linear systems is proposed by the mean of orthogonal functions. The use of these interesting tools makes it possible the transformation of differential state equations into some algebraic equations thus by expanding the system inputs and states over an orthogonal function and exploiting the operational matrices of these bases. The main objective of the proposed technique is to simplify the determination of the controller gain parameters so that the performance of each single controlled system among the global system can be matched to a chosen linear reference model.