A general method to calculate input-output gains and the relative gain array for integrating processes

Plant-wide control design for fuel processor system with PEMFC

“…c j ¼ 1 indicates that a sensor in the location j is needed and c j ¼ 0 the opposite situation, with j ¼ 1, ., 14. The best solution called C 1 in Table 3 suggests that the controlled variables should be y 1 : ESR exit temperature y 3 : Burner exit temperature y 8 : CO-PrOx exit temperature y 9 : CO-PrOx molar ratio O 2 /CO Molar ratio O 2 /CO u 9 LTS exit flow(*) y 10 Burner exit molar flow u 10 CO-PrOx exit flow(*) y 11 CO-PrOx CO exit concentration u 11 Bio-ethanol flow(*) y 12 Net power y 13 Oxygen excess y 14 Stack voltage y 15 ESR pressure(*) y 16 HTS pressure(*) y 17 LTS pressure(*) y 18 CO-PrOx pressure(*) y 19 H 2 production rate(*) i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 7 ( 2 0 1 2 ) 1 4 8 0 1 e1 4 8 1 1 y 10 : Burner exit molar flow y 13 : Oxygen excess in the FC A first attempt to propose a decentralized plant-wide control policy is the well-known RGA approach. The RGA (and its variants) allows to define the inputeoutput pairing by using steady-state information, the results are shown in Table 4, where the highlighted values represent a suitable inputeoutput pairing with the following control loops: 1, y 9 À u 1 ; 2, y 1 À u 2 ; 3, y 3 À u 3 ; 4, y 10 À u 4 ; 5, y 8 À u 5 and 6, y 13 À u 6 .…”

“…The starting point of the proposed strategy is to define these loops. The works of [11] and [12] can be mentioned as examples on how to define them.…”

“…The conditions stated in (11) and (12) allow to compute both A G and B G matrices from a particular model parametrizationG sG . The constraint in (11) allows to check the stability condition in steady state for the current control structure, in the context of IMC [13]. Where l i ðG sG À1 sG Þ is the i eigenvalue of the matrix G sG À1 sG and Re½$ the real part function.…”

Small-signal stability enhancement of communicationless parallel connected inverters

“…The interaction can be objectively measured through the relative gain [12], which has the advantage of being independent of the scaling and units employed for the input and output variables. It has successfully been used to suggest input-output pairings in a wide range of multivariable systems [13]- [17]. The relative gain λ ij between the output i and the input j is defined as the ratio of the (steady-state) gain with all other loops open to the (steady-state) gain with all other loops closed.…”

“…For integrating or non self-regulating processes, as it is the present case, the steady-state gain is undefined and the procedure described in [13] is to be followed when calculating the relative gains. If (6)-(9) are substituted in (12), the terms R 2 +X 2 will cancel out, implying that the relative gain is independent of |Z|.…”