The problem of controller design in linear systems is well understood. Often, however, when linear controllers are implemented on a physical system, the anticipated performance is not met. In some cases, this can be attributed to nonlinearities in the instrumentation, i.e., sensors and actuators. Intuition suggests that to compensate for this instrumentation, one can boost, i.e., increase, the controller gain. This paper formally pursues this strategy and develops the theory of boosting. It provides conditions under which the controller gain can be modified to offset the effects of instrumentation, thus recovering the performance of the intended linear design. Experimental verification of the technique developed is reported using a magnetic levitation device.

References

References
1.
Liberzon
,
D.
, and
Brockett
,
R. W.
, 2000, “
Nonlinear Feedback Systems Perturbed by Noise: Steady-State Probability Distributions and Optimal Control
,”
IEEE Trans. Autom. Control
,
45
, pp.
1116
1130
.
2.
Boonton
,
R. C.
, 1954, “
Nonlinear Control Systems With Random Inputs
,”
IRE Trans. Circuit Theory
,
CT-1
, pp.
9
18
.
3.
Kazakov
,
I. E.
, 1954, “
Approximate Method for the Statistical Analysis of Nonlinear Systems
,” Technical Report VVIA 394, Trudy.
4.
Gelb
,
A.
, and
Velde
,
W. E. V.
, 1968,
Multiple Input Describing Function and Nonlinear Design,
McGraw-Hill
,
New York
.
5.
Roberts
,
J.
, and
Spanos
,
P.
, 1990,
Random Vibration and Statistical Linearization
,
Wiley
,
New York, NY, USA
.
6.
Eun
,
Y.
,
Gökçek
,
C.
,
Kabamba
,
P. T.
, and
Meerkov
,
S. M.
, 2001, “
Selecting the Level of Actuator Saturation for Small Performance Degradation of Linear Designs
,”
Proceedings of the 40th IEEE Conference on Decision and Control
, pp.
1769
1774
.
7.
Gökçek
,
C.
,
Kabamba
,
P. T.
, and
Meerkov
,
S. M.
, 2000, “
Disturbance Rejection in Control Systems With Saturating Actuators
,”
Nonlinear Analysis
,
40
, pp.
213
226
.
8.
Skrzypczyk
,
J.
, 1995, “
Accuracy Analysis of Statistical Linearization Methods Applied to Nonlinear Dynamical Systems
,”
Rep. Math. Phys.
,
36
, pp.
1
20
.
9.
Wonham
,
W. M.
, and
Cashman
,
W. F.
, 1969, “
A Computational Approach to Optimal Control of Stochastic Saturating Systems
,”
Int. J. Control
,
10
, pp.
77
98
.
10.
Ching
,
S.
Meerkov
,
S. M.
, and
Kabamba
,
P. T.
, 2009, “
Root Locus for Random Reference Tracking in Systems With Saturating Actuators
,”
IEEE Trans. Autom. Control
,
54
, pp.
79
91
.
11.
Gökçek
,
C.
,
Kabamba
,
P. T.
, and
Meerkov
,
S. M.
, 2001, “
An LQR/LQG Theory for Systems With Saturating Actuators
,”
IEEE Trans. Autom. Control
,
46
(
10
), pp.
1529
1542
.
12.
Hu
,
T.
, and
Lin
,
Z.
2001,
Control Systems With Actuator Saturation: Analysis and Design
,
Birkhauser
,
Boston, MA, USA
.
13.
Kapila
,
V.
2001,
Actuator Saturation Control
,
Marcel Dekker
,
New York, NY, USA
.
14.
Astrom
,
K. J.
, and
Rundqwist
,
L.
, 1982, “
Integrator Windup and How to Avoid It
,”
American Control Conference
, p.
26
.
15.
Kapoor
,
N.
,
Teel
,
A. R.
, and
Daoutidis
,
P.
, 1998, “
An Anti-Windup Design for Linear Systems With Input Saturation
,”
Automatica
,
34
, pp.
559
574
.
16.
Kothare
,
M. V.
,
Campo
,
P. J.
,
Morari
,
M.
, and
Nett
,
C. N.
, 1994, “
A Unified Framework for the Study of Anti-Windup Designs
,
Automatica
,
30
, pp.
1869
1883
.
17.
Kanamori
,
M.
, and
Tomizuka
,
M.
, 2007, “
Dynamic Anti-Integrator-Windup Controller Design for Linear Systems With Actuator Saturation
,”
J. Dyn. Syst., Meas., Control
,
129
(
1
), pp.
1
12
.
18.
Niu
,
W.
, and
Tomizuka
,
M.
, 2000, “
An Anti-Windup Design for Linear System with Asymptotic Tracking Subjected to Actuator Saturation
,”
J. Dyn. Syst., Meas., Control
,
122
(
2
), pp.
369
374
.
19.
Grigoriadis
,
K. M.
, and
Skelton
,
R. E.
, 1997, “
Minimum-Energy Covariance Controllers
,”
Automatica
,
33–34
, pp.
569
578
.
20.
Eun
,
Y.
,
Kabamba
,
P. T.
, and
Meerkov
,
S. M.
, 2005, “
Analysis of Random Reference Tracking in Systems With Saturating Actuators
,”
IEEE Trans. Autom. Control
,
50
(
11
), pp.
1861
1866
.
You do not currently have access to this content.