Bristol array

The RGA or the Bristol array takes into account the relative gains for all combinations of input-output pairs in a multi-loop SISO system so that... 

The most popular and widely used technique for determining the best controller pairing is the relative gain array (RGA) method (Bristol, On a New Measure of Process Interaction, IEEE Trans. Auto. Control, AC-11, 133, 1966). The RGA method provides two important items of information ... 

Interaction among control loops in a multivariable system has been the subject of much research over the last 20 years. Various types of decouplers were explored to separate the loops. Rosenbrock presented the inverse Nyquist array (INA) to quantify the amount of interaction. Bristol, Shinskey, and McAvoy developed the relative gain array (RGA) as an index of loop interaction... 

The degrees of interaction between different sets of control loops controlling a MIMO plant can usually be determined by the use of the relative gain array technique due to BRISTOL 36. This approach can be illustrated by considering the process shown in Fig. 7.74 which has two inputs and two outputs. The procedure is as follows ... 

A related idea in process control which has received much interest recently is the analysis of interactions among states, outputs, and controls. The analytical technique used in many commercial applications is the relative gain array (Bristol,... 

The idea of the relative-gain array and its use for selecting the control loops can be found in the original paper by Bristol ... 

Bristol s relative-gain array initiated an extensive and vigorous research effort in interaction and decoupling of control loops. There is a large number of papers with applications of Bristol s array, as well as several theoretical treatments. Today it has been shown that if dynamic interaction is important Bristol s method may lead to the wrong couplings. The following paper demonstrates this point ... 

VI.14 Consider the processes with input-output relationships given in Problem VI.12. Using Bristol s relative-gain array, select the loops with the minimum steady-state interaction. 

Using Bristol s relative-gain array, select the control loops with minimum steady-state interaction. 

All of the linear C R measures use the approximations, F s and which describe the effects of the control variables and disturbances, respectively, on the process outputs. A commonly used controllability measure is the relative-gain array (RGA Bristol, 1966), which relies only on F s. The disturbance condition number (DCN Skogestad and Morari, 1987) and the disturbance cost (DC Lewin, 1996) are resiliency measures that require a disturbance model, in addition to P s. These C R measures are especially useful in... 

J.-M. Delosme and L Ipsen. Efficient systolic arrays for the solution of Toeplitz systems. In W. Moore, A. McCabe, and R. Urquhart, editors. Systolic arrays, pages 37-46. Adam Hilger, Bristol, 1987. 

The issue of this kind of control configuration has been investigated using frequency dependent formulations of measures such as the condition number, the Relative Gain Array by Bristol (1966) and the Relative Disturbance Gain by Stanley et al (1985). This paper will focus on discussing the dynamic control structure on the heat pump section and how each dynamic control structure affects on the stability of the integrated distillation column. 

A very well known indicator of interaction is Bristol s relative gain array (RGA) [8], typically denoted as a matrix A and calculated as ... 

A standard measure of the couplings in a plant which is frequently used in the process industry is the relative gain array (RGA) introduced by Bristol [5]. The relative gain array of the process is defined as... 

The relative-gain matrix, or relative-gain array (RGA), was originally su ested by Bristol as a means of determining the steady-state interaction between process variables. Shinskey and McAvoy have been assiduous in exploring the 2 p]ications to distillation columns. One of the most ludd and concise treatments we have seen is that of Ray. The implication is that by proper pairing of variables one may arrive, in some instances, at a control loop structure that promises less interaction than other feasible structures. 

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