Optimal control of an object in pulp and paper industry by a combined criterion

Abstract

A new method is proposed for the synthesis of an optimal control system by a combined criterion “energy-tim”. It is illustrated on a concrete object in paper industry - paper machine producing wrapping paper. As an example of control, one of the channels for regulation of the steam pressure coming in the machine, is chosen. The model is a consecutive combination of an aperiodic and an integrating unit with a pure time delay. The optimal criterion is a minimum steam expenditure per a fixed time of the transition process. The synthesis applies the phase plane method. The original quality of the method applied for the synthesis of optimal control is that another modified switch-off line is used, invariant to input effects. The new switch-off line depends only on the time given to the transition process and the parameters of the object. An equation is deduced for the modified switch-off line in the case in discussion. Its construction is represented by a graphic method which may be used for all second order systems. A method can be applied for compensation of time delay where the parameters of auto-variations are minimal in the system. The control lines for switch-off and -on are approximated by some sequences by the method of the equivalent signum functions. This formulation facilitates considerably the technical realization of the system. A digital modelling is made to the transition process in the steam regulating channel with a synthesized control equipment. It is shown, that the synthesized quasi-optimal control equipment forms effects close to the optimal in form and duration, for the whole range of variation of input effects. The comparison made between the optimal and the quasi-optimal systems shows that the steam expenditure does not differ for the two systems. The time of completion of the process remains constant at that.