Model reduction of high‐order multistage systems by the method of orthogonal collocation

A straightforward model reduction procedure is developed for high-order multistage systems. It is proposed to generate a partial differential equation from the original system and then to use the orthogonal collocation procedure to establish a low-order reduced model. This low-order model can then be used for time-optimal control with the assurance that the optimal control, as determined for the reduced system, can be applied to the original system. The procedure is illustrated with a 20-plate gas absorber which is eventually reduced to 5 state equations. On a etabli une methode directe de reduction de modeles dans le cas de systemes multietages d'ordre eleve. Pour obtenir un modele reduit et d'ordre plus petit, on propose de produire une equation differentielle partielle a partir du systeme original, puis d'employer le procede de collocation orthogonale. On peut ensuite utiliser le modele d'ordre faible pour un contrǒle optimal dans le temps, en etant sǔr que le contrǒle optimal determine pour le systeme reduit peut appliquer au systeme original. On illustre la methode au moyen d'un absorbeur de gaz a 20 plateaux, reduit a un modele a cinq equations.