Page 121 - Handbook of Biomechatronics

Model-Based Control of Biomechatronic Systems 117

driver-vehicle model, an observer-based disturbance rejection EPS control-
ler described in Mehrabi et al. (2015b) was used to deliver the desired assist
torque to the steering system; in the simplified model, an ideal controller
delivers the desired assist torque to the steering system.

3.3.1 Steering Feel Optimization Procedure
In this section, a systematic approach to tune the EPS characteristic curves to
provide a good steering feel is introduced. However, the word “good” is
very subjective and is a function of many variables, including the driver’s
physical ability. To achieve a good steering feel, the average energy trans-
ferred from road to driver (road feel) should be as strong as possible, while
the physical workload of the driver should be minimized (Zaremba and
Davis, 1995). The transferred torque to the steering wheel can be separated
into two portions: (1) the torque due to road-tire friction and the suspension
mechanism and (2) the torque due to external disturbances. Since the exter-
nal disturbance is random and dependent on road conditions, this portion is
neglected here.
To tune the EPS characteristic curves for a particular population, the
muscle parameters of the control-oriented integrated driver-vehicle model
are adjusted to represent that population. Then, an optimization is per-
formed to find the optimum EPS assist gain (K a ) for that specific population,
as follows:

0 1
t f
1 Z
2
K a ¼ arg min @ q 1 F rf + q 2 G aðÞ + q 3 i dt A (31)
t f
0
subjected to
2
j Y desired Y actual j < E (32)
where F rf and G(a) are, respectively, the inverse of road feel and a driver’s
physical measure during the steering task, and i is the EPS electric motor
current. q 1 , q 2 , and q 3 are the weighting factors, which have been chosen
to normalize each term in the cost. The q 1 and q 2 weighting factors are used
to adjust the steering stiffness while q 3 is used to reduce the EPS electric
motor size. Y actual and Y desired are the actual and desired trajectory of the
vehicle in the simulations; the desired trajectory is defined to satisfy the
ISO double lane change (DLC) maneuver constraints as shown in Fig. 9.
The steering assist (K a ) is tuned for an ISO double lane-change maneuver