Error analysis of digital controller using \(\delta\) operators (Q2726012)

The present paper is devoted to the error analysis of digital control systems using the delta operator. The well-known theory on delta operators given by \textit{R. H. Middleton} and \textit{G. C. Goodwin} [IEEE Trans. Autom. Control 31, 1015-1021 (1986; Zbl 0608.93053)] is applied.NEWLINENEWLINENEWLINEThe authors consider a single-input and single-output second-order system of the form NEWLINE\[NEWLINE\delta x(k)= a_1 x(k-1)+ a_2 x(k-2)+ bu(k),NEWLINE\]NEWLINE with the \(\delta\)-form solution NEWLINE\[NEWLINEx(k)= x(k-1)+ T[a_1 x(k-1)+ a_2x(k- 2)+ bu(k)].NEWLINE\]NEWLINE A comparison of the floating error caused by Z-transformation and that by the corresponding \(\delta\)-operator shows that the \(\delta\)-operator is better. A numerical simulation for a second-order integral system and a pole-assignment controller tracking an ideal output in the discrete field are also discussed in detail.NEWLINENEWLINENEWLINEThe simulation results show that the \(\delta\)-operator has better performance for round-off noise caused by finite word length, higher accuracy and stability than the z-operator.