MIMO PID Controllers Synthesis using Orthogonal Functions

This paper presents a new method for the synthesis of a PID controller structure for multi-input multi-output (MIMO) linear dynamic systems in closed loop.The parameters setting of the MIMO PID controller (composed by many simple standard PID controllers) uses interesting properties of a complete set of orthogonal functions in general and shifted Legendre polynomials in particular and specifically the operational matrix of integration. The considered technique allows the conversion of differential state equations in a set of algebraic ones depending on PID structure parameters by expanding the system inputs and outputs variables into orthogonal functions. The parameters setting of the MIMO PID controller is leaded by reference to a model system in open loop having all desired performances.