Relative Gain Analysis

For simphcity, consider first a 2 x 2 system. Plant testing, with all controllers on manual, has determined process gains as follows 

While we have, from steptesting, the numerator (the process gain with all other controllers on manual) we cannot use steptesting to determine the denominator (the process gain with 

No matter what units are used for process gains, provided they are consistent, the relative 

This is clearly the ideal situation since it tells us that PVi can be controlled by MVi and PV2 by MV2 with no interaction between the controllers. 

For All to be 1 orO, at least one element of the process gain matrix must be zero. If only one process gain is zero the controllers will display a one-way interaction. T vo diagonal elements must be zero for there to be no interaction in either direction. 

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We can apply relative gain analysis to determine the level of interaction. If Fi is the flow and F2 the other then, if the cross-sectional area of the drum is A, then the rate of change of level is given by... 

If dual composition control is required then relative gain analysis, as described in Chapter 8, will help assess the level of interaction. While not an entirely accurate tool, because it only considers steady state interactions, it in indicative of the severity of the problem. Since we need to perform steptests to tune the composition controllers the additional effort involved is minor. 

Woolverton, P. E., How to Use Relative Gain Analysis in Systems with Integrating Variables, InTech, 27 (9), 63 (1980). 

The NI [4] is a useful tool to analyse the stability of the control loop pairings determined using the relative gain analysis. If a manipulated variable is to be used to control an output variable, then the loop must not become unstable in dynamic situations. The NI can be used to prove that a 2 x 2 matrix is stable however, when n > 2 (if there are more than two input-output variables being paired) the NI can only be used to prove that the control loop is definitely not stable. Then, for the steady-state matrix G described in Equation 9.7, where each element in 6 is rational and open-loop stable [3], the system will definitely be imstable if the NI is negative, i.e. if... 

A SISO eontroller was designed (for mean erystal size), even though relative gain array analysis showed possible interaetions between all of the three eontrol... 

Thorium. Multiple-collector measurement protocols by TIMS for thorium isotopic analysis typically involve the simultaneous measurement of Th and °Th (for silicate rocks), or Th and °Th, then Th and Th (for low- Th samples), using an axial ion counter and off-axis Faraday collector (Table 1). Various methods are used to correct for the relative gain between the low-level and Faraday detectors and 2a-uncertainties of l-5%o are typically obtained (Palacz et al. 1992 Cohen et al. 1992 McDermott et al. 1993 Rubin 2001). Charge-collection TIMS protocols enable Th, °Th and Th to be monitored simultaneously on a multiple-Faraday array and can achieve measurement uncertainties at the sub-permil level (Esat et al. 1995 Stirling et al. 1995). 

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,... 

Evaluate the feasibility of inpuf output combinations by single value decomposition (SVD) analysis. Estimate feasible pairing by relative gain array (RGA) and Niederllnski index. 

Shows how to use quantitative analysis with steady-state and dynamic relative gain arrays (RGA and DRGA) to select control loop pairings reliably and to use the IMC model-based approach to provide preliminary tuning of single-loop PI controllers. 

A process known as the carbonitric process" has been used commercially but has not gained much success, mainly because of the relatively low analysis and the absence of water soluble P2O5 in the end product. Nevertheless, CO2 is primarily the cheapest precipitant for calcium. The process consists of four st s ... 

Next, we consider a systematic approach for determining the best pairing of controlled and manipulated variables, the relative gain array method. An alternative approach based on singular value analysis is described later in this chapter. 

Chen, D. and D. E. Seborg, Relative Gain Array Analysis for Uncertain Process Models, AIChEJ., 48,302 (2002). 

Wu and Yu (1996) performed an extensive steady-state analysis of these control structures using a 2 X 2 RGA analysis (see Chapter 18). For each structure, one controlled variable is selected from z and one manipulated variable from F, HR p. The relative gains are... 

A relatively new methodology caEed aroma dEution analysis (ada), which combines aroma dEution and gas chromatography-olfactometry to gain a better understanding of the relative importance of aroma compounds, was recently done for coffee. In a roasted Colombian coffee brew, 41 impact compounds were found with flavor dEution threshold factors (FD) greater than 25, and 26 compounds had FD factors of 100 or above. WhEe the technique permits assessment of the impact of individual compounds, it does not evaluate synergistic effects among compounds (13). 

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