A new indirect adaptive algorithm is derived for pole placement control of linear continuous-time systems with unknown parameters. The control structure proposed relies on a periodic controller, which suitably modulates the sampled output and discrete reference signals by a multirate periodically time-varying function. Such a control strategy allows us to assign the poles of the sampled closed-loop system to desired prespecified values, and does not make assumptions on the plant other than controllability, observability, and known order. The proposed indirect adaptive control scheme estimates the unknown plant parameters (and consequently the controller parameters) on-line, from sequential data of the inputs and the outputs of the plant, which are recursively updated within the time limit imposed by a fundamental sampling period T0. On the basis of the proposed algorithm, the adaptive pole placement problem is reduced to a controller determination based on the well-known Ackermann’s formula. Known indirect adaptive pole placement schemes usually resort to the computation of dynamic controllers through the solution of a polynomial Diophantine equation, thus introducing high order exogenous dynamics in the control loop. Moreover, in many cases, the solution of the Diophantine equation for a desired set of closed-loop eigenvalues might yield an unstable controller, and the overall adaptive pole placement scheme is then unstable with unstable compensators because their outputs are unbounded. The proposed control strategy avoids these problems, since here gain controllers are needed to be designed. Moreover, persistency of excitation and, therefore, parameter convergence, of the continuous-time plant is provided without making any assumption either on the existence of specific convex sets in which the estimated parameters belong or on the coprimeness of the polynomials describing the ARMA model, or finally on the richness of the reference signals, as compared to known adaptive pole placement schemes.

1.
Chammas
A. B.
, and
Leondes
C. T.
,
1978
, “
On the Design of Linear Time Invariant Systems by Periodic Output Feedback, Parts I and II
,”
Int. J. Control
, Vol.
27
, pp.
885
903
.
2.
Greshak
J. P.
, and
Vergese
G. C.
,
1982
, “
Periodically Varying Compensation of Time-Invariant Systems
,”
Syst. Control Lett.
, Vol.
2
, pp.
88
93
.
3.
Khargonekar
P. P.
,
Poolla
K.
, and
Tannenbaum
A.
,
1985
, “
Robust Control of Linear Time-Invariant Plants Using Periodic Compensation
,”
IEEE Trans. Autom. Control
, Vol.
AC-30
, pp.
1088
1096
.
4.
Araki
M.
, and
Hagiwara
T.
,
1986
, “
Pole Assignment by Multirate Sampled Data Output Feedback
,”
Int. J. Control
, Vol.
44
, pp.
1661
1673
.
5.
Mita
T.
,
Pang
B. C.
, and
Liu
K. Z.
,
1987
, “
Design of Optimal Strongly Stable Digital Control Systems and Application to Output Feedback Control of Mechanical Systems
,”
Int. J. Control
, Vol.
45
, pp.
2071
2082
.
6.
Hagiwara
T.
, and
Araki
M.
,
1988
, “
Design of a Stable State Feedback Controller Based on the Multirate Sampling of the Plant Output
,”
IEEE Trans. Autom. Control
, Vol.
AC-33
, pp.
812
819
.
7.
Kabamba
P. T.
,
1987
, “
Control of Linear Systems Using Generalized Sampled-Data Hold Functions
,”
IEEE Trans. Autom. Control
, Vol.
AC-32
, pp.
772
783
.
8.
Arvanitis
K. G.
,
1995
, “
Adaptive Decoupling of Linear Systems Using Multirate Generalized Sampled-Data Hold Functions
,”
IMA J. Math. Control Inf.
, Vol.
12
, pp.
157
177
.
9.
Paraskevopoulos
P. N.
, and
Arvanitis
K. G.
,
1994
, “
Exact Model Matching of Linear Systems Using Generalized Sampled-Data Hold Functions
,”
Automatica
, Vol.
30
, pp.
503
506
.
10.
Arvanitis
K. G.
, and
Paraskevopoulos
P. N.
,
1995
, “
Discrete Model Reference Adaptive Control of Linear Multivariable Continuous-Time Systems Via Multirate Sampled-Data Controllers
,”
J. Optim. Theory Appl.
, Vol.
84
, pp.
471
493
.
11.
Arvanitis
K. G.
,
1996
, “
An Indirect Model Reference Adaptive Controller Based on the Multirate Sampling of the Plant Output
,”
Int. J. Adaptive Contr. Sign. Process.
, Vol.
10
, pp.
673
705
.
12.
Arvanitis, K. G., and Paraskevopoulos, P. N., 1994, “Exact Model Matching of Linear Systems Using Multirate Digital Controllers,” Proc. 2nd E.C.C., Groningen, The Netherlands, Vol. 3, pp. 1648–1652.
13.
Elliott
H.
,
1982
, “
Direct Adaptive Pole Placement With Application to Nonminimum Phase Systems
,”
IEEE Trans. Autom. Control
, Vol.
AC-27
, pp.
720
722
.
14.
Elliott
H.
,
Wolovich
W. A.
, and
Das
M.
,
1984
, “
Arbitrary Adaptive Pole Placement for Linear Multivariable Systems
,”
IEEE Trans. Autom. Control
, Vol.
AC-29
, pp.
221
229
.
15.
Anderson
B. D. O.
, and
Johnstone
R. M.
,
1985
, “
Global Adaptive Pole Positioning
,”
IEEE Trans. Autom. Control
, Vol.
AC-30
, pp.
11
22
.
16.
Elliott
H.
,
Cristi
R.
, and
Das
M.
,
1985
, “
Global Stability Adaptive Pole Placement Algorithms
,”
IEEE Trans. Autom. Control
, Vol.
Ac–30
, pp.
348
356
.
17.
Lozano-Leal
R.
, and
Goodwin
G. C.
,
1985
, “
A Globally Convergent Adaptive Pole Placement Algorithm Without a Persistency of Excitation Requirement
,”
IEEE Trans. Autom. Control
, Vol.
AC-30
, pp.
795
798
.
18.
Giri
F.
,
M’Saad
M.
,
Dugard
L.
, and
Dion
J. M.
,
1988
, “
Robust Pole Placement Indirect Adaptive Controller
,”
Int. J. Adaptive Contr. Sign. Proc.
, Vol.
2
, pp.
33
47
.
19.
Mo
L.
, and
Bayoumi
M. M.
,
1989
, “
A Novel Approach to the Explicit Pole Assignment Self-Tuning Controller Design
,”
IEEE Trans. Autom. Control
, Vol.
AC-34
, pp.
359
363
.
20.
Youla
D. C.
,
Bongiorno
J. J.
, and
Lu
C. N.
,
1992
, “
Single-Loop Feedback Stabilization of Linear Multivariable Dynamical Systems
,”
Automatica
, Vol.
10
, pp.
159
173
, 1974.
21.
Kinnaert
M.
, and
Blondel
V.
, “
Discrete-Time Pole Placement With Stable Controller
,”
Automatica
, Vol.
28
, pp.
935
943
.
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