Variable displacement axial piston units are the core components of many hydrostatic and hydraulic hybrid drive trains. Therein, the fast and accurate control of the swash plate angle, utilizing the full possible dynamics of the displacement system, is essential for a good performance of the overall drive train. This paper describes the development, implementation, and the experimental validation of a control strategy for the swash plate angle based on nonlinear model predictive control (NMPC). A tailored mathematical model, which serves as the basis for the NMPC, is described in the first part of the paper. Two versions of NMPC, an indirect and a direct method, are compared with respect to their numerical complexity and their capability of handling input and state constraints. An observer strategy, which is designed to obtain the nonmeasurable states and varying parameters of the system, completes the overall control strategy. To reduce the negative influence of stick–slip friction, the concept of dithering is applied in the experimental implementation. The differences of the NMPC methods are analyzed by simulation studies and experiments. Finally, the experimental results, using an industrial electronic control unit (ECU), prove the practical feasibility and the improved control accuracy and robustness in comparison to classical (nonlinear) control strategies.

References

References
1.
Manring
,
N. D.
,
2005
,
Hydraulic Control Systems
,
Wiley
,
Hoboken, NJ
.
2.
Cundiff
,
J. S.
,
2002
,
Fluid Power Circuits and Controls: Fundamentals and Applications
,
CRC Press
,
Boca Raton, FL
.
3.
Deppen
,
T. O.
,
Alleyne
,
A. G.
,
Stelson
,
K. A.
, and
Meyer
,
J. J.
,
2012
, “
Optimal Energy Use in a Light Weight Hydraulic Hybrid Passenger Vehicle
,”
ASME J. Dyn. Syst. Meas. Control
,
134
(
4
), p.
041009
.
4.
Grabbel
,
J.
, and
Ivantysynova
,
M.
,
2005
, “
An Investigation of Swash Plate Control Concepts for Displacement Controlled Actuators
,”
Int. J. Fluid Power
,
6
(
2
), pp.
19
36
.
5.
Akers
,
S.
, and
Lin
,
S. J.
,
1988
, “
Optimal Control Theory Applied to a Pump With Single-Stage Electrohydraulic Servovalve
,”
ASME J. Dyn. Syst. Meas. Control
,
110
(
2
), pp.
120
125
.
6.
Kemmetmüller
,
W.
,
Fuchshumer
,
F.
, and
Kugi
,
A.
,
2010
, “
Nonlinear Pressure Control of Self-Supplied Variable Displacement Axial Piston Pumps
,”
Control Eng. Pract.
,
18
(
1
), pp.
84
93
.
7.
Wei
,
J.
,
Guo
,
K.
,
Fang
,
J.
, and
Tian
,
Q.
,
2015
, “
Nonlinear Supply Pressure Control for a Variable Displacement Axial Piston Pump
,”
Proc. Inst. Mech. Eng., Part I
,
229
(
7
), pp.
614
624
.
8.
Rawlings
,
J. B.
, and
Mayne
,
D. Q.
,
2009
,
Model Predictive Control: Theory and Design
,
Nob Hill Publishing
,
Madison, WI
.
9.
Zeman
,
P.
,
Kemmetmüller
,
W.
, and
Kugi
,
A.
,
2015
, “
Mathematical Modeling and Analysis of a Hydrostatic Drive Train
,”
IFAC-PapersOnLine
,
48
(
1
), pp.
508
513
.
10.
Rao
,
A. V.
,
2009
, “
A Survey of Numerical Methods for Optimal Control
,”
Adv. Astronaut. Sci.
,
135
(
1
), pp.
497
528
.
11.
Bryson
,
A. E.
, and
Ho
,
Y.-C.
,
1969
,
Applied Optimal Control: Optimization, Estimation, and Control
,
Ginn & Company
,
Waltham, MA
.
12.
Nocedal
,
J.
, and
Wright
,
S. J.
,
2006
,
Numerical Optimization
,
Springer
,
New York
.
13.
Graichen
,
K.
, and
Kugi
,
A.
,
2010
, “
Stability and Incremental Improvement of Suboptimal MPC Without Terminal Constraints
,”
IEEE Trans. Autom. Control
,
55
(
11
), pp.
2576
2580
.
14.
Graichen
,
K.
, and
Käpernick
,
B.
,
2012
, “
A Real-Time Gradient Method for Nonlinear Model Predictive Control
,”
Frontiers of Model Predictive Control
,
T.
Zheng
, ed.,
InTech
,
Rijeka, Croatia
, pp.
9
28
.
15.
Graichen
,
K.
, and
Petit
,
N.
,
2009
, “
Incorporating a Class of Constraints Into the Dynamics of Optimal Control Problems
,”
Optim. Control Appl. Methods
,
30
(
6
), pp.
537
561
.
16.
Diehl
,
M.
,
Ferreau
,
H. J.
, and
Haverbeke
,
N.
,
2009
, “
Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation
,”
Nonlinear Model Predictive Control
(Lecture Notes in Control and Information Sciences),
L.
Magni
,
D. M.
Raimondo
, and
F.
Allgöwer
, eds., Vol.
384
,
Springer
,
Berlin
, pp.
391
417
.
17.
Diehl
,
M.
,
2001
, “
Real-Time Optimization for Large Scale Nonlinear Processes
,”
Ph.D. thesis
,
Universität Heidelberg
,
Heidelberg, Germany
.
18.
Houska
,
B.
,
Ferreau
,
H. J.
, and
Diehl
,
M.
,
2011
, “
An Auto-Generated Real-Time Iteration Algorithm for Nonlinear MPC in the Microsecond Range
,”
Automatica
,
47
(
10
), pp.
2279
2285
.
19.
Bock
,
H. G.
,
1983
, “
Recent Advances in Parameter Identification Techniques for O.D.E.
,”
Numerical Treatment of Inverse Problems in Differential and Integral Equations
(Progress in Scientific Computing),
P.
Deuflhard
and
E.
Hairer
, eds., Vol.
2
,
Birkhäuser
,
MA
, pp.
95
121
.
20.
Mattingley
,
J.
, and
Boyd
,
S.
,
2012
, “
CVXGEN: A Code Generator for Embedded Convex Optimization
,”
Optim, Eng.
,
13
(
1
), pp.
1
27
.
21.
Armstrong-Hélouvry
,
B.
,
Dupont
,
P.
, and
De Wit
,
C. C.
,
1994
, “
A Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction
,”
Automatica
,
30
(
7
), pp.
1083
1138
.
22.
Kugi
,
A.
,
Schlacher
,
K.
,
Aitzetmüller
,
H.
, and
Hirmann
,
G.
,
2000
, “
Modeling and Simulation of a Hydrostatic Transmission With Variable-Displacement Pump
,”
Math. Comput. Simul.
,
53
(
4–6
), pp.
409
414
.
23.
Simon
,
D.
,
2006
,
Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches
,
Wiley
,
Hoboken, NJ
.
24.
Ferreau
,
H. J.
,
Kozma
,
A.
, and
Diehl
,
M.
,
2012
, “
A Parallel Active-Set Strategy to Solve Sparse Parametric Quadratic Programs Arising in MPC
,”
IFAC Proc.
,
45
(
17
), pp.
74
79
.
25.
Iannelli
,
L.
,
Johansson
,
K. H.
,
Jönsson
,
U. T.
, and
Vasca
,
F.
,
2006
, “
Averaging of Nonsmooth Systems Using Dither
,”
Automatica
,
42
(
4
), pp.
669
676
.
26.
Lucente
,
G.
,
Montanari
,
M.
, and
Rossi
,
C.
,
2007
, “
Modelling of an Automated Manual Transmission System
,”
Mechatronics
,
17
(
2–3
), pp.
73
91
.
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