A tractable closed-loop stability-related measure for controller structures, realised using the δ operator and digitally implemented with `finite word length' (FWL), is derived. The optimal realisations of the general finite-precision controller are defined as those that maximise this measure and are shown to be the solutions of a constrained nonlinear optimisation problem. For the special case of digital PID controllers, the constrained problem can be decoupled into two simpler unconstrained optimisation problems. A global optimisation strategy based on the adaptive simulated annealing (ASA) is adopted to provide an efficient method for solving this complex optimal realisation problem. Two numerical examples are presented to illustrate the design procedure, and the simulation results confirm that the optimal FWL realizations of the δ-operator based controller have better closed-loop stability margins than those of the usual shift-operator based controller, especially under fast sampling conditions.
References
-
-
1)
-
L. INGBER
.
Adaptive simulated annealing (ASA): lessons learned.
J. Control and Cybern.
,
1 ,
33 -
54
-
2)
-
P. DORATO ,
C. ABDULLAH ,
V. CERONE
.
(1995)
, Linear-Quadratic Control: An Introduction.
-
3)
-
C.P. NEUMAN
.
Transformations between delta and forward shift operator transfer function models.
IEEE Trans. Syst. Man and Cybern.
,
295 -
296
-
4)
-
ISTEPANIAN, R.H.: `Implementational issues for discrete PID algorithms using shift and delta operators parameterizations', Proceedings 4th IFAC workshop on Algorithms and architectures for Real-Time Control, 1997, Vilamoura, Portugal, p. 117–122.
-
5)
-
M. GEVERS ,
G. LI
.
(1993)
, Parameterizations in Control, estimation and filtering problems: Accuracy aspects.
-
6)
-
G. Li
.
On the structure of digital controllers with finite word length consideration.
IEEE Trans. Autom. Control
,
689 -
693
-
7)
-
Y. SUNG ,
M. KUNG
.
Lower finite word-length effect on state space digital filter by δ operator realization.
Int. J. Electron
,
6 ,
1135 -
1141
-
8)
-
I.J. FIALHO ,
T.T. GEORGIO
.
On stability and performance of sampled data systems subject to word length constraint.
IEEE Trans. Autom. Control
,
2476 -
2481
-
9)
-
J. WU ,
R.H. ISTEPANIAN ,
S. CHEN
.
Stability issues of finite precision controller structures for sampled data systems.
Int. J. Control
,
15 ,
1331 -
1342
-
10)
-
ISTEPANIAN, R.H., WU, J., CHU, J., WHIDBORN, J.F.: `Maximizing lower bound stability measure of finite precision PID controller realizations by nonlinear programming', Proceedings 1998 American control conference, 1998, Philadelphia, p. 2596–2600.
-
11)
-
ISTEPANIAN, R.H., PRATT, I., GOODALL, R., JONES, S.: `Effect of fixed point parameterization on the performance of active suspension control systems', Proceedings 13th IFAC world congress, 1996, San Francisco, p. 291–295.
-
12)
-
R.H. MIDDLETON ,
G.C. GOODWIN
.
(1990)
, Digital control and estimation: a unified approach.
-
13)
-
A.G. MADIEVSKI ,
B.D.O. ANDERSON ,
M. GEVERS
.
Optimum realizations of sampled-data controllers for FWL sensitivity minimization.
Automatica
,
367 -
379
-
14)
-
S. CHEN ,
B.L. LUK
.
Adaptive simulated annealing for optimisation in signal processing applications.
Signal Process.
,
117 -
128
-
15)
-
L.C.W. DIXON
.
(1972)
, Nonlinear Optimisation.
-
16)
-
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
-
17)
-
J. KOWALIK ,
M.R. OSBORNE
.
(1968)
, Methods for unconstrained optimisation problems.
-
18)
-
ISTEPANIAN, R.H., WU, J., WHIDBORNE, J.F., YAN, J., SALCUDEA, S.E.: `Finite-word-length stability issues of teleoperation motion-scaling control system', Proceedings UKACC control'98, 1998, Swansea, UK, p. 1676–1681.
-
19)
-
S. CHEN ,
J. WU ,
R.H. ISTEPANIAN ,
J. CHU
.
Optimizing stability bounds of finite-precision PID controller structures.
IEEE Trans. Autom. Control
,
1 ,
2149 -
2153
-
20)
-
CHEN, S., ISTEPANIAN, R.H., WU, J.: `Optimizing stability bounds of finite-precision PID controllers using adaptive simulated annealing', Proceedings 1999 American Control Conference, 1999, San Diego, p. 4316–4320.
-
21)
-
P. Moroney ,
A.S. Willsky ,
P.K. Houpt
.
The digital implementation of control compensators: the coefficient wordlength issue.
IEEE Trans. Autom. Control
,
8 ,
621 -
630
-
22)
-
G.S.G. BEVERIDGE ,
R.S. SCHECHTER
.
(1970)
, Optimisation: theory and practice.
-
23)
-
C.P. NEUMAN
.
Properties of the delta operator model of dynamic physical systems.
IEEE Trans. Syst. Man and Cybern.
,
296 -
301
-
24)
-
S. CHEN ,
B.L. LUK ,
Y. LI
.
Application of adaptive simulated annealing to blind channel identification with HOC fitting.
Electron. Lett.
,
3 ,
234 -
235
-
25)
-
R.M. GOODALL ,
B.J. DONOGHUE
.
Very high sample rate digital filters using the δ operator.
IEE Proc. G, Circuits Devices Syst.
,
199 -
206
-
26)
-
J.F. WHIDBORNE ,
G. MURAD ,
D.W. GU ,
I. POSTLETHWAITE
.
Robust control of an unknown plant – the IFAC93 benchmark.
Int. J. Control
,
589 -
640
-
27)
-
G. LI ,
M. GEVERS
.
Comparative study of finite word length effects in shift and delta operator parameterizations.
IEEE Trans. Autom. Control
,
5 ,
803 -
807
-
28)
-
L. Ingber
.
Simulated annealing: practice versus theory.
Math. Comput.Model.
,
11 ,
29 -
57
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