Defining the cost function

Given a specification of control logic in terms of FSMs, we estimate the total control cost COSTarta of the control implementation as  

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To define the cost function that will drive the control optimization, we briefly outine the mapping from a constraint graph model of hardware behavior to a control implementation. The details are presented in Chapters 6 and 8 we summarize in this section the major results as background for defining the control optimization criterion. 

Define a cost function assuming that the cost increases with Pi and Gf and that the enrichment of stream 3 gives profits according to... 

The objective function used in the zero effluent synthesis formulation is the minimisation of cost. The cost function is defined in constraint (8.62). The cost in... 

The match is obtained for the value As that maximizes (or minimizes) C. The cost function chosen to maximize is the cross-correlation, G, defined as ... 

One s first reaction is to reject the adequacy of casting the problem as a linear one, but, as Grossmann and Santibanez show, the use of discrete (zero/one) decisions allow one to include to a very good approximation many of the nonlinearities. For example, a zero/one variable can be associated with the existence or non-existence of a unit. In the cost function that discrete variable can cause one to add in a fixed charge for the unit only if it exists. Also one can define a continuous "flow11 variable for the unit which can be forced to zero if the unit does not exist by the linear constraint ... 

For closest-packed oxides, a Pannetier-type cost function [58] is more robust and faster to evaluate than the lattice energy as defined earlier. Here, the bond valence model [59] is used to calculate the charge on the ions and the discrepancy with the expected value is used to measure the quality of the structure. With an additional term, the discrepancy in the expected and calculated coordination numbers, the cost function becomes... 

A value of the cost function suitable to be the historical benchmark and a design case that performs acceptably is selected. Two performance measures for on-line monitoring are defined after a benchmark is obtained. lhist k) is extended for computation at each sampling time to determine controller performance, ydes(k) is extended for computation at each sampling time to assist in diagnosis of types of causes for poor performance. CPM is implemented by using the LQG benchmark or a benchmark obtained from case studies and )hist k). When the controller performance is declared poor, ydes(k) is used to make diagnostic decisions. 

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