Page 107 - Biosystems Engineering

88 Chapter Two

8

6
Speed (km h –1 ) 4

2

0
0 5 10 15 20
Time (s)

FIGURE 2.29 Response to a step change in the desired speed for an MPC
controller with engine-speed minimization. The pump setting is limited to
50 percent to provoke a steady-state error at low speeds. The solid line
represents the reference speed at 7 km/h, the dotted line represents the
standard controller, and the dashed line represents the same controller with
an extra integrator to avoid a steady-state error.

will cause problems at high speeds because the pump setting cannot
become sufficiently large to compensate for the decreasing engine
speed. Due to limitations at the test site, upper limit on the pump set-
ting was lowered to 50 percent to be able to show this effect at lower
speeds. The maximal speed at minimum engine speed was approx-
imately 5.5 km/h. In Fig. 2.29, a step response to 7 km/h of the con-
troller is shown with and without the integrator term. Adding the extra
integrator state thus removes the steady-state error while keeping the
engine speed as low as possible.

References
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Springer.
Coen, T., Anthonis, J., and De Baerdemaeker, J. 2008a. Cruise control on a combine
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Coen, T., Saeys, W., Missotten, B., and De Baerdemaeker, J. 2008b. Cruise con-
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