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80 Chapter Two

Note that there are no significant differences between the local
amplifications at two engine speed levels. The solid line represents a
piecewise linear approximation. For the sake of clarity, amplification
has already been rescaled by multiplying with the minimal engine
speed (1300 rpm).

Dynamic Model
Because a change in travel speed requires acceleration and decelera-
tion of the combine harvester subject to friction, it is clear that the
system will only respond to relatively low frequencies due to inertial
forces. Based on Sec. 2.6.4, in which the static model structure was
shown, a dynamic state–space model structure can be proposed.
Relying on physical knowledge, three states can be defined:

1. Actual pump setting to the hydrostatic valve
2. Actual engine speed of the diesel engine
3. Actual machine speed
The last state—machine speed—was shown to depend nonlinearly
on the two other states through the earlier-derived static model.
Before we can determine the dynamic model, relationships in the
system that may contain dynamic effects need to be identified.
Assuming that there are no dynamic effects within the nonlinear rela-
tion (of the static model), three relationships remain in which dynamic
effects can be present:
1. Between the pump setting set point and the actual pump
setting
2. Between the engine speed set point and the actual engine
speed
3. Between the static model and the actual machine speed
The general system structure, shown in Fig. 2.27, is called a Wiener–
Hammerstein structure (Nesic 1999; Nelles 2001), because it is a linear
dynamic system followed by a nonlinearity and a linear dynamic system.
Experiments have shown that the engine speed and the pump
setting to the hydrostatic valve respond sufficiently fast so that those
dynamics can be neglected. This means that only the relationship
between the nonlinear transformation (of the pump setting and the
engine speed) and the actual machine speed contains dynamics.
Multisine excitations (Pintelon and Schoukens 2001) show that the
dynamics form a low-pass filter, as could be expected.
The prediction performance of the model is essential for model-
based predictive control (MPC). In addition, because the system is
nonlinear, the system response depends on the type of input. Because
the most typical input for the controller will be a stepwise increase of