Fix inconsistencies in ranges of steering angles for car steering running example [modeling, linsys, statefbk, outputfbk, xferfcns, loopsyn, limits, running]

[Richard Murray]

On 5 Mar 2018, Karl says:

• There is a problem with the simulation [of car in Examples 8.4 and 12.2]. We say that thelargest steering angle is slightly less than 0.1 rad ($6^\circ$), according to the figure it is more like 0.5 rad ($30^\circ$). Also compare with Exercises 8.4 which also has steering angles up to 0.5 radians which I find excessive. Lower values are used in Exercise 7.4. I suggest that we change the parameter a=0.5 to a smaller value, say a=0.1, the maximum steering angle will be reduced from 0.5 rad to about 0.02 rad. Let us discuss this it may enter in a few more places.

Karl checked with a few people and we got some different responses:

• Johan Andreasson says 4 degrees, and he also says that peak slip for modern tires correspond to 6 degrees. This means that for vehicle steering we should change simulations so that the steering angles are never larger than 4-6 degrees i.e 0.07 to 0.1 rad.
• Bjorn says wheel angles of 10 degrees and Karl says 0.6 to 2.5 degrees. I will ask a third person at Volvo and hear what he says before we start editing steering.

[Richard Murray]

Karl and I looked through the running example. Steering angle range from 0.005 radians (for "gentle" lane change) to 0.5 rad (in output feedback and loop shaping).

Karl and I agree that, roughly,

• High speed driving (30 m/s): Currently using a max of 0.005 rad, which is a bit gentle. Could probably go up to 0.05 radians (3 deg)
• Modest speed driving (10 m/s): Use Johan Andreasson estimates of 0.05-0.1 rad.
• Slow driving (1-2 ms/s): Can probably go up to 0.1 rad (6 deg)

Richard to work through simulations and come up with a consistent set of numbers throughout.

[Richard Murray]

Working on this via a Jupyter notebook that pulls together all of the pieces into a single file. PDF version attached with notes.

[Richard Murray]

Fixed in commits 55b6463 and ad36fea.