ACSL-OPTIMIZE

Integral error criteria are ideally suited to simulation applications since only one additional program statement is required for the simulation. The optimal control parameters Kp, %i and td can be then found at minimal ITAE. For this, it is useful to be able to apply the available optimisation tools implemented in such programs as MATLAB, ACSL-OPTIMIZE or MADONNA. 

If basic assumptions concerning the error structure are incorrect (e.g., non-Gaussian distribution) or cannot be specified, more robust estimation techniques may be necessary, e.g., Maria and Heinzle (1998). In addition to the above considerations, it is often important to introduce constraints on the estimated parameters (e.g., the parameters can only be positive). Such constraints are included in the simulation and parameter estimation package ACSL-OPTIMIZE and in the MATLAB Optimisation Toolbox. Because of numerical inaccuracy, scaling of parameters and data may be necessary if the numerical values are of greatly differing order. Plots of the residuals, difference between model and measurement value, are very useful in identifying systematic or model errors. 

Non-linear parameter estimation is far from a trivial task, even though it is greatly simplified by the availability of user-friendly program packages such as (a) ACSL-OPTIMIZE, (b) MADONNA, (c) a set of BASIC programs (supplied with the book of Nash and Walker-Smith, 1987) or (d) by mathematical software (MATLAB). MADONNA has only limited possibilities for parameter estimation, but MADONNA programs can easily be translated into other more powerful languages. 

Model parameters are usually determined from experimental data. In doing this, sensitivity analysis is valuable in identifying the best experimental conditions for the estimation of a particular model parameter. Sensitivity analysis is easy effected with MADONNA, and sensitivity analysis is also provided in other more advanced software packages, such as ACSL-OPTIMIZE. 

ACSL- OPTIMIZE PC Powerful mathematics, building blocks especially for control purposes, includes powerful and user-friendly optimisation and parameter estimation. 

In non-linear systems one can usually not predict a priori whether the optimum found is global or whether the optimum obtained represents only a local condition. A good judgement on the behaviour of the model can be seen in contour and three-dimensional plots, which are easily obtained using other alternative software packages, such as ACSL-Optimize or Matlab. 

Here the objective is to demonstrate the power of other modern simulation packages in the estimation of model parameters. Here the parameters are estimated using the ACSL-Optimize software. 

Optimisation with ACSL-Optimize employs the log-likelihood function as the objective function. The statistical procedures are highly sophisticated, and an example output of the statistical information is given below for the simulation example ESTERFIT of Case B. 

A small selection of available software is given in Table 5.1. Madonna is very user-friendly and is used in this book. This recent version has a facility for parameter estimation and optimisation. ModelMaker is also a more recent powerful and easy to use program, which also allows optimisation and parameter estimation. ACSL-Optimize has quite a long history of application in the control field, and also for chemical reaction engineering. 

Berkeley Madonna, University of California at Berkeley, http //www.berkeleymadonna.com/ ModelMaker, Cherwell Scientific Publishing Ltd., The Magdalen Centre, Oxford Science Park, Oxford 0X4 4GA, http //www.cherwell.com/. UK Matlab, The MathWorks, Inc., 24 Prime Park Way, Natick, MA 01760, http //www.mathworks.com. USA ACSL-Optimize, Aegis Research Corporation, 6703 Odyssey Drive, Suite 200, Huntsville, Alabama 35806, http //www.aegisrc.com/. USA SPEEDUP, Aspen Technology, Inc. Ten Canal Park, Cambridge, Mass. 02141. http //www.aspentec.com. USA. 

Numerous Dynamic Simulation Examples, Hands on Experience with ISIM at the PC s. Advance programming with a Workstation, Optimization with ACSL and SimuSolvc... 

---