© The Institution of Engineering and Technology
A relatively simple approach to nonlinear predictive generalised minimum variance (NPGMV) control is introduced for nonlinear discretetime multivariable systems. The system is represented by a combination of a stable nonlinear subsystem where no structure is assumed and a linear subsystem that may be unstable and modelled in polynomial matrix form. The multistep predictive control cost index to be minimised involves both weighted error and control signal costing terms. The NPGMV control law involves an assumption on the choice of costfunction weights to ensure the existence of a stable nonlinear closedloop operator. A valuable feature of the control law is that in the asymptotic case, where the plant is linear, the controller reduces to a polynomial matrix version of the well known generalised predictive control (GPC) controller. In the limiting case when the plant is nonlinear and the costfunction is single step the controller becomes equal to the polynomial matrix version of the socalled nonlinear generalised minimum variance controller. The controller can be implemented in a form related to a nonlinear version of the Smith predictor but unlike this compensator a stabilising control law can be obtained for openloop unstable processes.
References


1)

Cutler, C.R., Ramaker, B.L.: `Dynamic matrix control – a computer control algorithm', A.I.C.H.E, 86th National Meeting, April 1979.

2)

D.W. Clarke ,
C. Mohtadi ,
P.S. Tuffs
.
Generalized predictive control – Part 1, The basic algorithm, Part 2, Extensions and interpretations.
Automatica
,
2 ,
137 
148

3)

D.W. Clarke ,
C. Montadi
.
Properties of generalised predictive control.
Automatica
,
6 ,
859 
875

4)

J. Richalet ,
A. Rault ,
J.L. Testud ,
J. Papon
.
Model predictive heuristic control applications to industrial processes.
Automatica
,
413 
428

5)

J. Richalet
.
Industrial applications of model based predictive control.
Automatica
,
8 ,
1251 
1274

6)

R. Bitmead ,
M. Gevers ,
V. Wertz
.
(1990)
Adaptive optimal control: the thinking man's GPC.

7)

Grimble, M.J.: `GMV control of nonlinear multivariable systems', UKACC Conf. Control 2004, University of Bath, 6–9 September 2004.

8)

M.J. Grimble
.
Nonlinear generalised minimum variance feedback, feedforward and tracking control.
Automatica
,
957 
969

9)

Grimble, M.J., Majecki, P.: `Nonlinear generalised minimum variance control under actuator saturation', IFAC World Congress, 8 July 2005, Prague.

10)

M. Cannon ,
B. Kouvaritakis
.
(2001)
Openloop and closedloop optimality in interpolation MPC, Nonlinear predictive control: theory and practice.

11)

M. Cannon ,
B. Kouvaritakis
.
Efficient constrained model predictive control with asymptotic optimality.
Siam J. Control Optim.
,
1 ,
60 
82

12)

M. Cannon ,
B. Kouvaritakis ,
Y.I. Lee ,
A.C. Brooms
.
Efficient nonlinear predictive control.
Int. J. Control
,
4 ,
361 
372

13)

M. Cannon ,
V. Deshmukh ,
B. Kouvaritakis
.
Nonlinear model predictive control with polytopic invariant sets.
Automatica
,
8 ,
1487 
1494

14)

M.V. Kothare ,
V. Balakrishnan ,
M. Morari
.
Robust constrained model predictive control using linear matrix inequalities.
Automatica
,
10 ,
1361 
1379

15)

H. Michalska ,
D.Q. Mayne
.
Robust receding horizon control of constrained nonlinear systems.
IEEE Trans. Autom. Control
,
1623 
1633

16)

J.S. Shamma ,
M. Athans
.
Analysis of gain scheduled control for nonlinear plants.
IEEE Trans. Autom. Control
,
898 
907

17)

B. Kouvaritakis ,
M. Cannon ,
J.A. Rossiter
.
Nonlinear model based predictive control.
Int. J. Control
,
10 ,
919 
928

18)

Y.I. Lee ,
B. Kouvaritakis ,
M. Cannon
.
Constrained receding horizon predictive control for nonlinear systems.
Automatica
,
12 ,
2093 
2102

19)

D.Q. Mayne ,
J.B. Rawlings ,
C.V. Rao ,
P.O.M. Scokaert
.
Constrained model predictive control: stability and optimality.
Automatica
,
6 ,
789 
814

20)

P.O.M. Scokaert ,
D.Q. Mayne ,
J.B. Rawlings
.
Suboptimal model predictive control (feasibility implies stability).
IEEE Trans. Autom. Control
,
3 ,
648 
654

21)

A.C. Brooms ,
B. Kouvaritakis
.
Successive constrained optimisation and interpolation in nonlinear model based predictive control.
Int. J. Control
,
4 ,
312 
316

22)

Allgower, F., Findeisen, R.: `Nonlinear predictive control of a distillation column', Int. Symp. Nonlinear Model Predictive Control, 1998, Ascona, Switzerland.

23)

E.F. Camacho
.
Constrained generalized predictive control.
IEEE Trans. Autom. Control
,
327 
332

24)

M.J. Grimble
.
(2006)
Robust industrial control.

25)

M.J. Grimble
.
(2001)
Industrial control systems design.

26)

M.J. Grimble ,
M.A. Johnson
.
(1988)
Optimal control and stochastic estimation.

27)

W.H. Kwon ,
A.E. Pearson
.
A modified quadratic cost problem and feedback stabilization of a linear system.
IEEE Trans. Autom. Control
,
5 ,
838 
842

28)

T. Perez
.
(2005)
Ship motion control.
http://iet.metastore.ingenta.com/content/journals/10.1049/ietcta.2009.0043
Related content
content/journals/10.1049/ietcta.2009.0043
pub_keyword,iet_inspecKeyword,pub_concept
6
6