Relative Gain Array Calculator

Description| How it works

The Relative Gain Array (RGA) is a powerful tool that helps in determining the optimal pairing of Controlled Variables (CVs) and Manipulated Variables in a multivariable control scheme. The RGA is easy to compute for a system consisting of 2 MVs and 2 CVs, but gets harder for bigger systems. This tool allows the user to compute the RGA for any system upto 20 MVs and 20 CVs.

RGA elements that are closest to 1 should have the corresponding manipulated and controlled variables paired for the most effective control.

A good explanation of RGA is given in this controls wiki page.


.xlsx file (20 KB)

How to Use

Key in the size of the system (number of CVs or number of MVs - note that the RGA is only applicable to a square system, that is one with an equal number of MVs and CVs). As soon as that is keyed in, yellow cells get highlighted indicating the entry points for the open loop gains of the system. Once the gains are all keyed in, the RGA values show up from row 29 onwards.

TThe following figure shows the inputs and results for a 4 x 4 system.


Also See:

Simulation of a Model Predictive Controller (MPC)

Simulation of a PID Controller

PI Control of First Order Process

PI Control of Integrating Process