Control of Generalized Decoupled MIMO Systems Based on Linear Programming Method

Abstract

In this work, a control method is suggested to generalize decoupled multi-input multi-output (MIMO) plant to get satisfactory results. The phenomena of decoupling converts a p × q MIMO plant to p number of equivalent single-input single-output (SISO) loops which enables one to control q number of outputs independently even due to the effect of coupling present in control inputs and outputs. The effect of these cross-couplings causes the disturbances. The decoupler aim is to eradicate the effect of these disturbances on outputs. In order to achieve it, this work proposed a novel generalized decoupling technique on the basis of linear programming. Infinity ( ∞ ) − norm method is considered to minimize the effect of decoupler gain of the cross-couplings of the MIMO system, over all frequencies, that minimizes undesired mutual couplings of the resulting decoupled plant also nullifying coupling effect completely at steady state as well. The proposed method of decoupling is compared with the relative gain array (RGA) and further modified RGA (MRGA) technique of decoupling which is also elaborated in this paper. To achieve the desired response from the decoupled plant proportional integral derivative (PID) control method is suggested using the Kharitonov theorem. The ensued technique is employed on different types of MIMO systems including square, non-square and time-delayed.