Optimal Static State-Feedback Controller Design for MIMO LTI Systems Based on Constraints Block Roots and Interior-Point Algorithm: Application to Gas Compressor System

摘要

The paper presents, An optimal Static State Feedback controller (SSF) approach, addressed to class of Multi-Input/Multi-Output (MIMO) Linear Invariant-Time (LTI) systems. The block roots of the matrix polynomial are the main key in the design of the proposed SSF controller, an optimal set of diagonally block roots have been chosen with constraints conditions, where the SSF matrix gain controller K is formulated as a nonlinear convex optimization problem, and it is solved using the Interior-Point Algorithm (IPA), the optimal block roots are assigned based on the canonical controller block transformations and the right block Vandermonde matrix respectively. To show the performances of the proposed SSF controller, a centrifugal gas compressor system is introduced as case study. Based on this application, a comparative study is carried out, with two well known controllers: SSF based Pole Placement (PP) and SSF based Linear Quadratic Regulator (LQR), aims to demonstrate the feasibility of our proposed design methodology.