The purpose of this paper is to provide a set of synthesis and design tools for a wide class of H2 preview control systems. A generic preview design problem, which features both previewable and nonpreviewable disturbances, is embedded in a standard generalized regulator framework. Preview regulation is accomplished by a two-degrees-of-freedom output-feedback controller. A number of theoretical issues are studied, including the efficient solution of the standard H2 full-information Riccati equation and the efficient evaluation of the full-information preview gain matrices. The full-information problem is then extended to include the efficient implementation of the output-feedback controller. The synthesis of feedforward controllers with preview is analyzed as a special case—this problem is of interest to designers who wish to introduce preview as a separate part of a system design. The way in which preview reduces the H2-norm of the closed-loop system is analyzed in detail. Closed-loop norm reduction formulas provide a systematic way of establishing how much preview is required to solve a particular problem, and determine when extending the preview horizon will not produce worthwhile benefits. The paper concludes with a summary of the main features of preview control, as well as some controller design insights. New application examples are introduced by reference.

1.
Sheridan
,
T. B.
, 1966, “
Three Models of Preview Control
,”
IEEE Trans on Human Factors in Electronics
,
HFE-7
(
2
), pp.
91
102
.
2.
Bender
,
E. K.
, 1968, “
Optimal Linear Preview Control With Application to Vehicle Suspension
,”
ASME J. Basic Eng., Ser. D
,
90
(
2
), pp.
213
221
.
3.
Tomizuka
,
M.
, 1973, “
The Optimal Finite Preview Problem and Its Application to Man-Machine Systems
,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
4.
Tomizuka
,
M.
, 1975, “
Optimal Continuous Finite Preview Problem
,”
IEEE Trans. Autom. Control
0018-9286,
20
(
3
), pp.
362
365
.
5.
Lindquist
,
A.
, 1968, “
On Optimal Stochastic Control With Smoothed Information
,”
Inf. Sci. (N.Y.)
0020-0255,
1
(
1
), pp.
55
85
.
6.
Tomizuka
,
M.
, and
Whitney
,
D. E.
, 1975, “
Optimal Discrete Finite Preview Problems (Why and How Is Future Information Important?)
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
97
(
4
), pp.
319
325
.
7.
Tomizuka
,
M.
, and
Rosenthal
,
D. E.
, 1979, “
On the Optimal Digital State Vector Feedback Controller With Integral and Preview Actions
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
101
(
2
), pp.
172
178
.
8.
Tomizuka
,
M.
, and
Fung
,
D.
, 1980, “
Design of Digital Feedfoward/Preview Controllers for Processes With Predetermined Feedback Controllers
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
102
(
4
), pp.
218
225
.
9.
Zattoni
,
E.
, 2006, “
H2-Optimal Decoupling With Preview: A Dynamic Feedforward Solution Based on Factorization Techniques
,”
Proceedings of the 2006 American Control Conference
, IEEE, pp.
316
320
.
10.
Marro
,
G.
, and
Zattoni
,
E.
, 2005, “
H2-Optimal Rejection With Preview in the Continuous-Time Domain
,”
Automatica
0005-1098,
41
(
5
), pp.
815
821
.
11.
Tomizuka
,
M.
, 1976, “
Optimal Preview Control With Application to Vehicle Suspension—Revisited
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
98
(
3
), pp.
362
365
.
12.
Hac
,
A.
, 1992, “
Optimal Linear Preview Control of Active Vehicle Suspension
,”
Veh. Syst. Dyn.
0042-3114,
21
(
1
), pp.
167
195
.
13.
Marzbanrad
,
J.
,
Ahmadi
,
G.
,
Zohoor
,
H.
, and
Hojjat
,
Y.
, 2004, “
Stochastic Optimal Preview Control of a Vehicle Suspension
,”
J. Sound Vib.
0022-460X,
275
(
3–5
), pp.
973
990
.
14.
Roh
,
H. S.
, and
Park
,
Y.
, 1999, “
Stochastic Optimal Preview Control of an Active Vehicle Suspension
,”
J. Sound Vib.
0022-460X,
220
(
2
), pp.
313
330
.
15.
Sharp
,
R. S.
, 2005, “
Driver Steering Control and a New Perspective on Car Handling Qualities
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
219
(
10
), pp.
1041
1051
.
16.
Green
,
M.
, and
Limebeer
,
D. J. N.
, 1995,
Linear Robust Control
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
17.
Zhou
,
K.
,
Doyle
,
J.
, and
Glover
,
K.
, 1996,
Robust and Optimal Control
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
18.
Doyle
,
J. C.
,
Francis
,
B. A.
, and
Tannenbaum
,
A. R.
, 1990,
Feedback Control Theory
,
Macmillan
,
New York
.
19.
Middleton
,
R. H.
,
Chen
,
J.
, and
Freudenberg
,
J. S.
, 2004, “
Tracking Sensitivity and Achievable H∞ Performance in Preview Control
,”
Automatica
0005-1098,
40
(
8
), pp.
1297
1306
.
20.
Houpis
,
C. H.
, and
Lamont
,
G. B.
, 1991,
Digital Control Systems
,
2nd ed.
,
McGraw-Hill
,
New York
.
21.
Hazell
,
A. J.
, 2008, “
Discrete-Time Optimal Preview Control
,” Ph.D. thesis, Imperial College, London, http://deposit.depot.edina.ac.uk/145/http://deposit.depot.edina.ac.uk/145/
22.
Moelja
,
A. A.
, and
Meinsma
,
G.
, 2006, “
H2 Control of Preview Systems
,”
Automatica
0005-1098,
42
(
6
), pp.
945
952
.
23.
Hazell
,
A. J.
, and
Limebeer
,
D. J. N.
, 2008, “
An Efficient Algorithm for Discrete-Time H∞ Preview Control
,”
Automatica
0005-1098,
44
(
9
), pp.
2441
2448
.
24.
Anderson
,
B. D. O.
, and
Moore
,
J. B.
, 1979,
Optimal Filtering
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
25.
Katayama
,
T.
, and
Hirono
,
T.
, 1987, “
Design of an Optimal Servomechanism With Preview Action and Its Dual Problem
,”
Int. J. Control
0020-7179,
45
, pp.
407
420
.
26.
Paulino
,
N.
,
Cunha
,
R.
, and
Silvestre
,
C.
, 2006, “
Affine Parameter-Dependent Preview Control for Rotorcraft Terrain Following Flight
,”
J. Guid. Control Dyn.
0731-5090,
29
(
6
), pp.
1350
1359
.
27.
Cole
,
D. J.
,
Pick
,
A. J.
, and
Odhams
,
A. M. C.
, 2006, “
Predictive and Linear Quadratic Methods for Potential Application to Modelling Driver Steering Control
,”
Veh. Syst. Dyn.
0042-3114,
44
(
3
), pp.
259
284
.
You do not currently have access to this content.