The implementation issues of digital controllers with finite word length (FWL) considerations are addressed. Both the shift and delta operator parameterisations of a general controller structure are considered. A unified formulation is adopted to derive a computationally tractable stability related measure that describes FWL closed-loop stability characteristics of different controller realisations. Within a given operator parameterisation, the optimal FWL controller realisation, which maximises the proposed stability related measure, is the solution of a nonlinear optimisation problem. The relationship between the z-operator and δ-operator controller parameterisations is analysed, and it is shown that the δ parameterisation has a better FWL closed-loop stability margin than the z-domain approach under a mild condition. A design example is included to verify the theoretical analysis and to illustrate the proposed optimisation procedure.
References
-
-
1)
-
C.M. FONSECA ,
P.J. FLEMING
.
Multiobjective optimisation and multiple constraint handling with evolutionary algorithms - Part I: A unified formulation.
IEEE Trans. Syst. Man Cybern. A, Syst. Humans
,
26 -
37
-
2)
-
K.F. MAN ,
K.S. TANG ,
S. KWONG
.
(1998)
, Genetic algorithms: Concepts and design.
-
3)
-
S. CHEN ,
J. WU ,
R.H. ISTEPANIAN ,
J. CHU
.
Optimising stability bounds of finite-precision PID controller structures.
IEEE Trans. Autom. Control
,
11 ,
2149 -
2153
-
4)
-
G. LI ,
M. GEVERS
.
Comparative study of finite wordlength effects in shift and delta operator parameterisations.
IEEE Trans. Autom. Control
,
5 ,
803 -
807
-
5)
-
FIALHO, I.J., GEORGIOU, T.T.: `Optimal finite worldlength digital controller realisation', Proceedings of American control conference, 1999, San Diego, USA, p. 4326–4327.
-
6)
-
J. O'Reilly
.
(1983)
, Observers for linear systems.
-
7)
-
S. BOYD ,
L. EL GHAOUI ,
E. FERON ,
V. BALAKRISHNAN
.
(1994)
, Linear matrix inequalities in system and control theory.
-
8)
-
R.M. GOODALL ,
B.J. DONOGHUE
.
Very high sample rate digital filters using the δ operator.
IEE Proc., Circuits Devices Syst.
,
199 -
206
-
9)
-
L.C.W. DIXON
.
(1972)
, Nonlinear optimisation.
-
10)
-
D.E. GOLDBERG
.
(1989)
, Genetic algorithms in search, optimisation and machine learning.
-
11)
-
R.H. MIDDLETON ,
G.C. GOODWIN
.
(1990)
, Digital control and estimation: A unified approach.
-
12)
-
S. CHEN ,
J. WU ,
R.H. ISTEPANIAN ,
J. CHU ,
J.F. WHIDBORNE
.
Optimising stability bounds of finite-precision controller structures for sampled-data systems in the delta operator domain.
IEE Proc., Control Theory Appl.
,
6 ,
517 -
526
-
13)
-
L. INGBER
.
Adaptive simulated annealing (ASA): lessons learned.
J. Control Cybern.
,
1 ,
33 -
54
-
14)
-
G. Li
.
On the structure of digital controllers with finite word length consideration.
IEEE Trans. Autom. Control
,
689 -
693
-
15)
-
G.S.G. BEVERIDGE ,
R.S. SCHECHTER
.
(1970)
, Optimisation: Theory and practice.
-
16)
-
C.P. NEUMAN
.
Properties of the delta operator model of dynamic physical systems.
IEEE Trans. Syst. Man Cybern.
,
296 -
301
-
17)
-
J. WU ,
S. CHEN ,
G. LI ,
J. CHU
.
Optimal finite-precision state-estimate feedback controller realisation of discrete-time systems.
IEEE Trans. Autom. Control
,
1550 -
1557
-
18)
-
M. GEVERS ,
G. LI
.
(1993)
, Parameterisations in control, estimation and filtering problems: Accuracy aspects.
-
19)
-
G. LI ,
M. GEVERS
.
Optimal finite precision implementation of a state-estimate feedback controller.
IEEE Trans. Circuits Syst.
,
1487 -
1498
-
20)
-
R.H. ISTEPANIAN ,
G. LI ,
J. WU ,
J. CHU
.
Analysis of sensitivity measures of finite-precision digital controller structures with closed-loop stability bounds.
IEE Proc., Control Theory Appl.
,
5 ,
472 -
478
-
21)
-
R.J. Schwarz ,
B. Friedland
.
(1965)
, Linear systems.
-
22)
-
S. CHEN ,
B.L. LUK
.
Adaptive simulated annealing for optimisation in signal processing applications.
Signal Process.
,
11 ,
117 -
128
-
23)
-
I.J. FIALHO ,
T.T. GEORGIOU
.
On stability and performance of sampled data systems subject to word length constraint.
IEEE Trans. Autom. Control
,
12 ,
2476 -
2481
-
24)
-
C.P. NEUMAN
.
Transformations between delta and forward shift operator transfer function models.
IEEE Trans. Syst. Man Cybern.
,
295 -
296
-
25)
-
R.E. SKELTON ,
T. IWASAKI ,
K.M. GRIGORIADID
.
(1998)
, A unified algebraic approach to linear control design.
-
26)
-
L. Ingber
.
Simulated annealing: practice versus theory.
Math. Comput.Model.
,
11 ,
29 -
57
-
27)
-
ISTEPANIAN, R.H.: `Implementational issues for discrete PID algorithms using shift and delta operator parameterisations', Proceedings of 4th IFAC workshop on Algorithms and architectures for real-time control, 1997, Vilamoura, Portugal, p. 117–122.
-
28)
-
Y. SUNG ,
M. KUNG
.
Lower finite word length effect on state space digital filter by δ operator realisation.
Int. J. Electron.
,
1135 -
1141
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