On Finite-Dimensional Transformations of Anisochronic Controllers Designed by Algebraic Means: A User Interface

This chapter intended to propound the reader a methodology for algebraic controller design for systems with internal delays, followed by a comparison of several easy-handling techniques for rational (i.e. finite-dimensional) approximation of anisochronic (i.e. infinite-dimensional) controllers – or their transfer functions, more precisely. Matlab with Simulink was a very useful assistant here. The authors programmed a simple user interface which enables the user to enter a nominal transfer function and select approximation methods to be used and their orders. As a result, the program returns the accuracies in both text and graphical forms. Simulation experiments with the program were made. Control of a simple stable TDS, control of unstable TDS of a skater on the swaying bow and control of a laboratory circuits heating plant were benchmark examples. The results were very interesting and startling because the habitual Padé approximation proved to be very good and, moreover, the higher order approximation did not automatically mean the better result for systems with internal delays.P(ED2.1.00/03.0089

Aplikace pro graficko-textové srovnání racionálních aproximací přenosových funkcí systémů s vnitřním zpožděním

P(ED2.1.00/03.0089), Z(MSM7088352102

Does the higher order mean the better internal delay rational approximation?

The aim of this contribution is to test by simulations whether the higher order rational approximation for exponential elements in linear time-invariant time-delay systems (LTI-TDS) automatically means the better (i.e. more accurate) finite dimensional approximating model. The presented approximations are utilized to the Laplace transfer function model in the form of fractions of socalled quasipolynomials and the methods are chosen so that they are easy to handle with. Namely, Padé approximation, shift operator approximations-Laguerre and Kautz shift-and Fourier analysis based method are introduced and benchmarked. The work is motivated i.a. by the fact that direct controller design for LTI-TDS based on such models is mostly rather intricate and there are no theoretical results for internal delays. Moreover, the authors intend to use the results for rationalization of so-called anisochronic controllers when their discretization. The quality of approximation is measured by the well known H2 and H∞ norms instead of exact analytic calculations since it is sufficient for practical engineering problems. Some simulation examples for anisochronic controllers by means of a developed program testing interface in Matlab-Simulink environment are presented as well

Cascade control of a tubular chemical reactor

The paper presents the cascade control design of a tubular chemical reactor with an exothermic consecutive reaction. The control is performed in primary and secondary control-loops where the primary controlled output of the reactor is the concentration of the main reaction product and the secondary output is the mean temperature of the reactant. A common control input is the coolant flow rate. The controller in the primary control-loop is a P-controller with the gain calculated using simulated or measured steady-state characteristics of the reactor. The controller in the secondary control-loop is an adaptive controller. The proposed method is verified by control simulations