Reliability index, model performance

If a reliable process model is available and can provide solutions in real time, the model can be used to provide the corrected setpoint trajectories for u without decouphng or empirical tuning of controller gains. If a process performance index is defined, then the controller action can be computed directly by inverting the process model. For instance, if it is assumed that the current process states [x(f),y(f)] are known and that it is desired to reach the optimum reference trajectory after tf time units, then Equations 8.18b and 8.35 can be written as... 

The reliability index, J3, may be calculated as an alternative for obtaining the design point from FORM and SORM. To evaluate the model performance, two measures are considered the estimated variance in the dependent variable and reliability index for the remediation design. 

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