Ein neues Verfahren zum Entwurf zeitvarianter Ausgangsregler für eine spezielle Klasse linearer zeitvarianter Systeme

Algebraic modelling of linear systems by means of Walsh functions

“…In this section we turn back to the algebraic description of linear time-variant systems according to (19) and in what follows the design of a multivariable time-variant PI controller for such a system is presented [12]. To that purpose first the controller is described in state space notation _ x C ðtÞ ¼ 0 Á x C ðtÞ þ I Á ðwðtÞ À yðtÞÞ uðtÞ ¼ K I ðtÞx C ðtÞ þ K P ðtÞðwðtÞ À yðtÞÞ According to (19) we then get the algebraic controller model Algebraic modelling of linear systems 601…”

“…With a = ln (2) and N = 64 (according to (12) with this choice of a the last or 64th interval in the t-domain starts at t = 6 s) the resulting time-variant controller matrices K P ðtÞand K I ðtÞcan be seen from figures 6(a) and 6(b). Obviously, all elements of both controller matrices become constant for t??…”

“…This is especially true if one is interested in the design of approved control schemes like PI or PID control. For this purpose in [12] a collocation approach based on the results of [1] is presented. In a rather analogous manner in what follows a new approach for the design of linear time-variant systems is developed which is based on the use of the complete orthonormal set of Walsh functions and the corresponding Walsh transform.…”