This paper presents a robust noniterative algorithm for the design of controllers of a given structure satisfying frequency-dependent sensitivity specifications. The method is well suited for automatic loop shaping, particularly in the context of Quantitative Feedback Theory (QFT), and offers several advantages, including (i) it can be applied to unstructured uncertain plants, be they stable, unstable or nonminimum phase, (ii) it can be used to design a satisfactory controller of a given structure for plants which are typically difficult to control, such as highly underdamped plants, and (iii) it is suited for design problems incorporating hard restrictions such as bounds on the high-frequency gain or damping of a notch filter. It is assumed that the designer has some idea of the controller structure appropriate for the loop shaping problem.

1.
Gera
,
A.
, and
Horowitz
,
I.
, 1980, “
Optimization of the Loop Transfer Function
,”
Int. J. Control
0020-7179
31
, pp.
389
398
.
2.
Ballance
,
D. J.
, and
Gawthrop
,
P. J.
, 1991, “
Control System Design Via a Quantitative Feedback Approach
,”
Proceedings of the IEE Conference Control-91, Heriot-Watt University, Edinburgh UK
, Vol.
1
, pp.
476
480
.
3.
Chait
,
Y.
,
Chen
,
Q.
, and
Hollot
,
C. V.
, 1999, “
Automatic Loop-Shaping of QFT Controllers Via Linear Programing
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
121
, pp.
351
357
.
4.
Thompson
,
D. F.
, and
Nwokah
,
O. D. I.
, 1994, “
Analytic Loop Shaping Methods in Quantitative Feedback Theory
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434
116
, pp.
169
177
.
5.
Thompson
,
D. F.
, 1998, “
Gain-Bandwidth Optimal Design for the New Formulation Quantitative Feedback Theory
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434
120
, pp.
401
404
.
6.
Garcia-Sanz
,
M.
, and
Guillen
,
J. C.
, 2000, “
Automatic Loop Shaping of QFT Controllers Via Genetic Algorithm
,”
Proceedings of the 3rd IFAC Symposium on Robust Control Design (RO-COND 2000), Kidlington, UK
,
Elsevier Science
, New York, Vol.
2
, pp.
603
608
.
7.
Zolotas
,
A. C.
, and
Halikias
,
G. D.
, 1999, “
Optimal Design of PID Controllers Using the QFT Method
,”
IEE Proc.: Control Theory Appl.
1350-2379
146
(
6
), pp.
585
589
.
8.
Besson
,
V.
, and
Shenton
,
A. T.
, 2000, “
Interactive Parameter Space Design for Robust Performance of MISO Control Systems
,”
IEEE Trans. Autom. Control
0018-9286,
45
(
10
), pp.
1917
1924
.
9.
Fransson
,
C. M.
,
Lennartson
,
B.
,
Wik
,
T.
,
Holmstrom
,
K.
,
Saunders
,
M.
, and
Gutman
,
P. O.
, 2002, “
Global Controller Optimization Using Horowitz Bounds
.”
IFAC World Congress
,
Barcelona
, Spain,
21
26
July 2002.
10.
Yaniv
,
O.
, 1999,
Quantitative Feedback Design of Linear and Nonlinear Control Systems
,
Kluwer Academic
, Dordrecht.
11.
Yaniv
,
O.
, and
Nagurka
,
M.
, 2003, “
Robust PI Controller Design Satisfying Sensitivity and Uncertainty Specifications
,”
IEEE Trans. Autom. Control
0018-9286
48
(
11
), pp.
2069
2072
.
12.
Yaniv
,
O.
, and
Nagurka
,
M.
, 2004, “
Design of PID Controllers Satisfying Gain Margin and Sensitivity Constraints on a Set of Plants
,”
Automatica
0005-1098
40
(
1
) pp.
111
116
.
13.
Panagopoulos
,
H.
,
Astrom
,
K. J.
, and
Hagglund
,
T.
, 1998, “
Design of PI Controllers Based on Non-convex Optimization
,”
Automatica
0005-1098
34
(
5
), pp.
585
601
.
14.
Horowitz
,
I. M.
, and
Sidi
,
M.
, 1972, “
Synthesis of Feedback Systems with Large Plant Ignorance for Prescribed Time Domain Tolerances
,”
Int. J. Control
0020-7179
16
(
2
), pp.
287
3098
.
15.
Astrom
,
K. J.
, and
Hagglund
,
T.
, 2001, “
The Future of PID Control
,”
Control Eng. Pract.
0967-0661,
9
, pp.
1163
1175
.
16.
Ho
,
W. K.
,
Lee
,
T. H.
,
Han
,
H. P.
, and
Hong
,
Y.
, 2001, “
Self Tuning IMC-PID Control with Interval Gain and Phase Margin Assignment
,”
IEEE Trans. Control Syst. Technol.
1063-6536
9
(
3
), pp.
535
541
.
This content is only available via PDF.
You do not currently have access to this content.