Page 105 - Biosystems Engineering

86 Chapter Two

A logical way to define the trade-off between both control inputs
is to base it on the squared ratio of their ranges. The maximal pump-
setting change (ΔPS , ΔPS ) is limited to ±5 per time step, whereas
min max
the engine speed change (ΔES , ΔES ) is limited to ±100 per time
min max
step. Assume that the weight of the change of pump setting is 1, the
weight of the change of engine speed then becomes 0 0025 ( /= 5 100) .
2
.
The weight of the control error is tuned experimentally. The best
results (trade-off between performance and comfort) are obtained
with a control error weight equal to 1. If the control error weight is 1,
a 1 km/h error leads to the same cost as a 1 percent change of the
pump setting. Note that this trade-off is influenced by the control
rate. For this application, the control rate is 20 Hz.
This formulation of the objective means that the system will
always try to lower the engine speed to the minimum. Because high
speeds can only be maintained if the engine speed is greater than the
minimal engine speed, a trade-off will occur between the control error
and the minimization of the engine speed. In other words, the engine
speed will not return to its minimal value, but there will remain a
control error in the steady state.
This issue can be solved by including an extra integrator state I in
the system (enlarge the system to six states). This extra state will inte-
grate the difference between the set point and the actual speed. In order
not to interfere with fast acceleration dynamics, integrator I will be
very slow. The objective function is then extended with a penalty term
on this integrator state. As long as there is a control error present, the
integrator term will increase, allowing for a larger engine speed.
Integrator I always needs to remain larger than zero and has to
integrate the sum of the control error and the difference between the
pump setting and the maximal pump setting. This way, I will increase
if there is a control error and decrease if the pump setting is not at the
maximal value. The combination of these two terms de facto disables
the integrator during transients as long as the pump setting is increas-
ing. The result of this approach is illustrated in the following section.

2.6.6 Experimental Setup
For the experiments, a New Holland CR combine harvester was used.
This machine was equipped with a LabView PXI system (National
Instruments). In order to test the controller, step changes were applied
to the reference input of the controller. The experiments were per-
formed on a private parking lot (asphalt road).

2.6.7 Results
The aforementioned controller is tested on the road for accelerations
up until 12 km/h. The controller is tested with and without the
engine-speed minimization term. The effect of adding this engine-speed
minimization term is shown in Fig. 2.28. Because the engine-speed