F/A feedback oscillations

[John S Gwynne]

--------

     A friend happen to find a section in a controls book (Feedback
Control of Dynamic Systems, 3rd ed. by Franklin, Powell, and
Emami-Naeini) that touched upon automotive engine control. It's only
eight pages and written for someone not familiar with engines, but
what I read seemed reasonable and consistent with other thing I've
seen. It's not informative enough that I would recommend getting the book.

     The author assumes a fairly simplistic model for the control
system which I'll try to show below.


                                      ----> C2 --->|
                                      |            |
desired F/A --> + --(error)--> C1 --->|            + ---> C4--->exhaust F/A
                                      |            |         |
                ^ (-)                 ----> C3 --->|         |
                |                                            |
                |                                            |
                 ----- [sensor] <-------- C5 <---------------

where C1 = Control law
      C2 = Inlet manifold (fast fuel) = 1/(t_1 s + 1)
      C3 = Inlet manifold (slow fuel) = 1/(t_2 s + 1)
      C4 = time delay (engine rotation...) = e^(-s T)
      C5 = Sensor lag (exhaust gases mixing in the manifold)
         = 1/(t s + 1)
      sensor = sensor characteristic; Vout as a function of F/A

I imaging this is as simple of a model that one could use to show the
desired results and and is of little other value to us. A proportional
plus integral (PI) controller (control law = K_p + K_1/s) was
rationalized and bode and root locus plots are shown for for the
special case of t_1 = 0.02 sec., t_2 = 1 sec., T = 0.2 sec.,
t=0.1sec., and a linearized sensor model around the stoichiometric
point.  The analysis continues with a look at feed back gain and and
system stability. What is then shown that is of interest is the
problems induced by the highly nonlinear sensor response. The bottom
line was that because of saturation, the effective sensor gain is much
less (when away from stoichiometric) and the system settling time was
much longer then desired; on the order of 13 seconds. By increasing
the gain the system becomes unstable and the F/A ratio begins to
oscillate with increasing "swings" until the saturation reduces the
effective sensor gain and the system reaches a limit cycle
corresponding to the point where the root locus crosses the imaginary
axis. With this approach, the settling time is more like 2 sec. but
the output F/A ratio will oscillate with a "swing" dependent on the
gain parameters.

So what's the bottom line? Well, it would seem that *in part* (1) the
oscillation in the feedback is due to the desire to greatly improve
the settling time of the system. (2) By controlling the PI gain factors
the amplitude of the oscillations are controlled (clearly a function of
sensor characteristics and engine speed/load).

So, Dale, if we were to add a differentiation term to help the
oscillation, would this seem consistent with what you have found in
other controllers? (also excluding the terms to induce more/faster
oscillations)





                                       John S Gwynne
                                          Gwynne.1 at osu.edu
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