Page 43 - Mechatronics with Experiments

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INTRODUCTION 29
and its Laplace transform (readers who are not familiar with Laplace transforms can skip
related material in the rest of this section without loss of continuity),
1 lug
T (s) = ⋅ T (s) (1.6)
eng eng
( ⋅ s + 1)
eng
where eng represents the time constant of the combustion to torque generation process,
lug
T is the torque prediction based on lug-curve, and T is the torque produced including
eng eng
the filtering delay.
Special Case: Simple Engine Model Simpler versions of this model can be
used to represent engine steady-state dynamics as follows,
T eng = f (u fuel ) − f (w eng ) (1.7)
1
2
where T is the torque generated by the engine, u is the injected fuel rate, w is engine
eng fuel eng
speed, f (⋅, ⋅) represents the nonlinear mapping function between the two independent
0
variables (fuel rate and engine speed) and the generated torque. The function f (⋅) represent
1
the fuel rate to torque generation through the combustion process, f (⋅) represents the load
2
torque due to friction in the engine as a function of engine speed (Figure 1.23).
1.1.4 Engine Control Algorithms: Engine Speed
Regulation using Fuel Map and a Proportional
Control Algorithm

A very simple engine control algorithm may decide on the fuel rate based on the accelerator
pedal position and engine speed sensors as follows (Figure 1.23),
u = g (w ) ⋅ K ⋅ (w − w ) (1.8)
fuel 1 eng p cmd eng
where g (⋅) is fuel rate look-up table as a function of engine speed and K is a gain
1
p
multiplying the speed error.
An actual engine control algorithm is more complicated, uses more sensory data and
embedded engine data in the form of look-up tables, estimators, and various logic functions
such as cruise control mode and cold start mode. In addition, the control algorithm decides
not only on the fuel rate (u fuel ) but also on the injection timing relative to the crank shaft
position. Other controlled variables include the exhaust gas recirculation (EGR) and idle
air control valves. However, simple engine control algorithms like this are useful in various
stages of control system development in vehicle applications.

Example: Electronic Governor for Engine Control The word “electronic
governor” is an industry standard name used to define the digital closed-loop controller
(or the embedded control module or electronic control module (ECM)) which is used
to control (“regulate”, “govern”) the engine speed (Figure 1.24). It is simply the digital
implementation of the mechanical governor, except that in addition to controlling speed,
the digital controller can take many other factors into consideration when deciding on “how
much” and “when” and “how” (injection pulse pattern) to inject fuel to control the engine
speed.
Let us consider the steady-state torque-speed relationship for an engine, that is the
lug curve (Fig. 1.19). Under a properly designed electronic governor, we can have the
engine operate at any point under the lug curve. At low idle speed, which is the minimum
speed allowed, the torque-speed curve is generally maintained to be a straight vertical
line. If the throttle pedal sensor output is zero, which means the throttle pedal is not
pressed at all, the desired engine speed is interpreted as the low idle speed, and the engine