The paper presents a computational technique through operational matrices using a set of mutually disjoint delta functions (DF) for the analysis of linear discrete control systems. Following a brief review of the well known block pulse functions (BPF), a new set of delta functions is viewed in the same light. This set is used to develop operational transfer functions in the delta function domain (DOTF) and employed for discrete system analysis which results in the same accuracy as the conventional z-transform method. The presented technique uses simple matrix manipulations and is able to do away with laborious and involved algebraic steps, including inverse transformation, associated with the z-transform analysis without losing accuracy. Also, the accuracy of sample values of the output does not depend upon m (or the sampling interval h). A few linear discrete SISO control systems, open loop as well as closed loop, having different typical plant transfer functions, are analysed as illustrative examples.
References
-
-
1)
-
P.A.M. Dirac
.
The physical interpretation of the quantumdynamics.
Proc. Roy. Soc. A
,
621 -
641
-
2)
-
W.L. Chen ,
S.G. Wu
.
Analysis of sampled-data system by block-pulsefunctions.
Int. J. Syst. Sci.
,
6 ,
747 -
752
-
3)
-
K.G. Beauchamp
.
(1984)
Application of Walsh and related functions.
-
4)
-
G. Temple
.
The theory of generalized functions.
Proc. Roy. Soc. A
,
175 -
190
-
5)
-
A. Deb ,
G. Sarkar ,
S.K. Sen
.
A new set of pulse-widthmodulated generalized block pulse functions (PWM-GBPF) andtheir application to cross-/auto-correlation of time varying functions.
Int. J. Syst. Sci.
,
1 ,
65 -
89
-
6)
-
A. Deb ,
G. Sarkar ,
S.K. Sen ,
M. Bhattacharjee
.
On improvement of the integral operational matrix in blockpulse function analysis.
J. Franklin Inst.
,
4 ,
469 -
478
-
7)
-
G.P. Rao ,
K.R. Palanisamy
.
Improved algorithms for parameteridentification in lumped continuous systems via Walshfunctions.
IEE Proc. D
,
1 ,
9 -
16
-
8)
-
J.H. Jiang ,
W. Schaufelberger
.
(1992)
Block pulse functions and theirapplications in control systems.
-
9)
-
A. Deb ,
G. Sarkar ,
S.K. Sen
.
A set of linearly pulse-widthmodulated block pulse functions and their application tolinear SISO feedback control system identification.
IEE Proc. D
,
1 ,
44 -
50
-
10)
-
C.F. Chen ,
Y.T. Tsay ,
T.T. Wu
.
Walsh operational matricesfor fractional calculus and their application to distributedsystems.
J. Franklin Inst.
,
3 ,
267 -
284
-
11)
-
A. Deb ,
G. Sarkar ,
M. Bhattacharjee ,
S.K. Sen
.
All-integrator approach to linear SISO control systemanalysis using block pulse functions (BPF).
J. Franklin Inst.
-
12)
-
A. Deb ,
G. Sarkar ,
S.K. Sen
.
Block pulse functions,the most fundamental of all piecewise constant basisfunctions.
Int. J. Syst. Sci.
,
2 ,
351 -
363
-
13)
-
G.P. Rao
.
(1983)
Piecewise constant orthogonal functions and theirapplication to systems and control.
http://iet.metastore.ingenta.com/content/journals/10.1049/ip-cta_19960629
Related content
content/journals/10.1049/ip-cta_19960629
pub_keyword,iet_inspecKeyword,pub_concept
6
6