Analysis and Control Design of a Class of Time-Varying Systems.

摘要

A method for analyzing time-varying flow processes by classical techniques is developed, and its properties are studied theoretically. If the time-varying nature of the process is caused by variable flow, the model equations can be transformed into a form with constant coefficients by replacing time with a new variable, which is an integral of the flow rate. With respect to the new time scale classical methods for analysis and control design can be applied, and the results can then be used in time domain. The PID control algorithm is formulated with respect to the new variable, after which it is transformed into time domain. The result is a time-varying PID-controller, which can be regarded as an adaptive controller, because it eliminates disturbances caused by variable flow by changing its parameters continuously based on flow measurements from the process. The text serves both as an introduction to the method and also as a link to the previously known results, in which the flow process has been modelled by the residence time distribution. A similar change of variables changes the distribution into a form which is valid even when the flow rate is varying. Many results obtained earlier by means of the residence time distribution theory are confirmed by using the approach described in the text.