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In this study, an attempt has been made to design an output feedback controller for local stabilisation of uncertain linear time-invariant plant with bounded control inputs. The design is accomplished via parametric H∞ loop-shaping control by describing the uncertainty as perturbations to normalised coprime factors of the shaped plant. The shaped plant is designed based on the closed-loop design specifications by appropriately choosing the weighting transfer function matrices. For the existence of stabilising controller, a set of sufficient conditions has been derived in linear matrix inequality framework and subsequently, a region of attraction is estimated such that the control inputs never exceed the pre-specified bounds. To illustrate the effectiveness of the proposed method, a numerical example has been elucidated.
References
-
-
1)
-
T. Hu ,
Z. Lin
.
(2001)
Control systems with actuator saturation: analysis and design.
-
2)
-
M. Osinuga ,
S. Patra ,
A. Lanzon
.
Smooth weight optimization in H∞ loop shaping control.
Syst. Control Lett.
,
663 -
670
-
3)
-
S. Patra ,
S. Sen ,
G. Ray
.
Robust control of uncertain LTI plant with input saturation constraint: H∞ loop shaping approach.
Int. J. Syst. Sci.
,
11 ,
1337 -
1351
-
4)
-
D. McFarlane ,
K. Glover
.
(1990)
Robust controller design using normalized coprime factor plant descriptions.
-
5)
-
D. Dai ,
T. Hu ,
A.R. Teel ,
L. Zaccarian
.
Output feedback design for saturated linear plants using deadzone loops.
Automatica
,
12 ,
2917 -
2924
-
6)
-
A.R. Teel
.
Linear systems with input nonlinearities: global stabilization by scheduling a family of H∞ controllers.
Int. J. Robust Nonlinear Control
,
5 ,
399 -
411
-
7)
-
F. Wu ,
Z. Lin ,
Q. Zheng
.
Output fedback stabilization of linear systems with actuator saturation.
IEEE Trans. Autom. Control
,
1 ,
122 -
128
-
8)
-
T. Nguyen ,
F. Jabbari
.
Output feedback controllers for disturbance attenuation with actuator amplitude and rate saturation.
Automatica
,
1339 -
1346
-
9)
-
K. Glover ,
D. Mcfarlane
.
Robust stabilization of normalized coprime factor plant descriptions with H∞ bounded uncertainty.
IEEE Trans. Autom. Control
,
8 ,
821 -
830
-
10)
-
K. Zhou ,
J.C. Doyle ,
K. Glover
.
(1996)
Robust and optimal control.
-
11)
-
G. Gu ,
J. Chen ,
E.B. Lee
.
Parametric H∞ loop shaping and weighted mixed sensitivity minimization.
IEEE Trans. Autom. Control
,
4 ,
846 -
852
-
12)
-
S.P. Boyd
.
(1994)
Linear matrix inequalities in system and control theory.
-
13)
-
J. Wang ,
N. Sundararajan
.
A nonlinear flight controller design for aircraft.
Control Eng. Pract.
,
6 ,
813 -
825
-
14)
-
B. Zhou ,
G. Duan ,
Z. Li
.
On improving transient performance in global control of multiple integrators system by bounded feedback.
Syst. Control Lett.
,
867 -
875
-
15)
-
J.K. Kim
.
New design method on memoryless H∞ control for singular systems with delayed state and control using LMI.
J. Franklin Institute
,
3 ,
321 -
327
-
16)
-
K. Takaba
.
Local stability analysis of a saturating feedback systen based on LPV descriptor representation.
Int. J. Control
,
5 ,
478 -
487
-
17)
-
N. Wada ,
M. Saeki
.
An LMI based scheduling algorithm for constrained stabilization problems.
Syst. Control Lett.
,
255 -
261
-
18)
-
Hindi, H., Boyd, S.: `Analysis of linear systems with saturation using convex optimization', Proc. 40th Conf. on Decision and Control, 1998, p. 903–908.
-
19)
-
D. Henrion ,
S. Tarbouriech ,
G. Garcia
.
Output feedback robust stabilization of uncertain linear systems with saturating controls: an LMI approach.
IEEE Trans. Autom. Control
,
11 ,
2230 -
2237
-
20)
-
J. Wang ,
Y. Miao
.
Invariant ellipsoids for single-input system with actuator saturation by employing output feedback.
J. Franklin Inst.
,
301 -
308
-
21)
-
G. Valmorbida ,
S. Tarbouriech ,
G. Garcia
.
State feedback design for input-saturating quadratic systems.
Automatica
,
7 ,
1196 -
1202
-
22)
-
V. Kapila ,
K. Grigoriadis
.
(2002)
Actuator saturation control.
-
23)
-
S. Patra ,
S. Sen ,
G. Ray
.
A linear matrix inequality approach to parametric H∞ loop shaping control.
J. Franklin Inst.
,
1832 -
1846
-
24)
-
D. McFarlane ,
K. Glover
.
A loop-shaping design procedure using H∞ synthesis.
IEEE Trans. Autom. Control.
,
759 -
769
-
25)
-
S. Patra ,
S. Sen ,
G. Ray
.
Design of H∞ loop shaping controller for LTI system with input saturation: polytopic gain scheduled approach.
J. Dyn. Syst. Meas. Control
,
1 ,
1 -
6
-
26)
-
S.A.K. Al-Assadi ,
R.V. Patel ,
M.Z. Uddin ,
M.S. Verma ,
J. Breitinger
.
Robust decentralized control of HVAC systems using H∞-performance measures.
J. Franklin Inst.
,
543 -
567
-
27)
-
Edwards, C., Postlethwaith, I.: `Anti-windup and bumpless transfer schemes', UKACC Int. Conf. on Control, 1996, p. 394–399.
-
28)
-
Pittet, C., Tarbouriech, S., Burgat, C.: `Stability regions for linear systems with saturating controls via circle and popov criteria', Proc. 36th Conf. on Decision and Control, 1997, p. 4518–4523.
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