General Optimisation

Later, in Chapter 4.4, General Optimisation, we discuss non-linear least-squares methods where the sum of squares is minimised directly. What is meant with that statement is, that ssq is calculated for different sets of parameters p and the changes of ssq as a function of the changes in p are used to direct the parameter vector towards the minimum. 

Before discussing how the general optimisation problem mentioned in the previous section is decomposed into a series of independent dynamic optimisation problem and before presenting the mathematical formulation for such problem the following discussions are worthwhile. 

In Greaves et al. (2001), a hybrid model for an actual pilot plant batch distillation column is developed. However, taking advantage of some of the inherent properties of batch distillation processes a simpler version (new algorithm) of the general optimisation framework is developed to find optimal reflux ratio policies which minimises the batch time for a given separation task. 

Figure 12.4 illustrates a general optimisation framework (developed by Mujtaba and Hussain, 1998) to obtain optimal operation policies for dynamic processes with process-model mismatches. 

Figure 12.4. General Optimisation Framework For Dynamic Processes with Process-model Mismatch...

Mujtaba and Hussain (1998) implemented the general optimisation framework based on the hybrid scheme for a binary batch distillation process. It was shown that the optimal control policy using a detailed process model was very close to that obtained using the hybrid model. 

Greaves et al. (2001) and Greaves (2003) presented two simple algorithms which is computationally less expensive to obtain the minimum batch time for a given separation task. These algorithms are the results of the application of some of the unique properties of batch distillation process to the general optimisation framework discussed earlier. The algorithm-1 is based on experiment and is presented in section 3.4 of Chapter 3. 

Every technique offers a balance between resolution, speed, capacity and recovery and should be selected to meet the objectives for each purification step. In general, optimisation of any one of these four parameters can only be achieved at the expense of the others and a purification step will be a compromise. The importance of each parameter will vary depending on whether a purification step is used for capture, intermediate purification or polishing. This will steer the optimisation of the critical parameters, as well as the selection of the most suitable media for the step. 

In general, optimisation of the Ai and A2 delays for the COLOC experiment can be problematic. In addition to the one-bond modulation effects already described, the transfer efficiency is also influenced by homonuclear proton couplings evolving during A[. The fixed Ai period also limits ti(max) (ti(max)/2... 

When industrial-grade oxygen is combusted with either gaseous, liquid or solid fuels in a furnace, it generally optimises thermal efficiency and fuel burnout. Thanks to the higher partial pressure of O2 and the exclusion of nitrogen ballast, reactivity in furnaces improves and flue gas volume decreases (see Fig. 2.41). 

In general, optimisation of electrode materials for analytical tasks is desirable and worthwhile, while noting that sensitivity in terms of peak current (but not peak potential) in linear sweep voltammetry is essentially controlled by the rate of diffusion to the electrode and hence, provided a signal is seen at some potential, relatively insensitive to the electrode material. 

Generally, optimised reactions give higher yields with fewer impurities, resulting in simpler and easier work-up processes... 

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