Page 112 - Handbook of Biomechatronics

108 Naser Mehrabi and John McPhee

Controller Controller State variables
State variables
MHE
Reference Reference
trajectory Control trajectory
NMPC Plant NMPC
input
System System
output output
Control
input Plant
(A) (B)
Fig. 5 Schematic representation of a NMPC in conjunction (A) with moving horizon esti-
mator (MHE) and (B) without moving horizon estimator.
The optimal dynamics over the prediction horizon can be calculated
using any optimal control method. Several software packages can automat-
ically formulate and execute an NMPC controller (e.g., YANE (Grune and
Pannek, 2011), MUSCOD-II (Schafer et al., 2007), ACADO (Diehl et al.,
2002), MPsee (Tajeddin and Azad, 2017), SCDE (Walker et al., 2016)).
In the presence of incomplete measurements and for a constrained
nonlinear system, an optimization method can be used to estimate the state
variables. If all the measurements from the initial to the current time are used
to estimate the state at the current time, the observer is called a full-
information estimator. However, this technique is not suitable for real-time
implementation, since the computational burden grows exponentially with
time. By only considering the information in a window moving behind the
current time, and approximating older information by a simple function, the
computation time can be significantly reduced. This so-called “moving
horizon estimator” (MHE) has been shown to work for real-time vehicle
dynamics applications and rehabilitation robots with current computational
resources (Fig. 5). The required online solution of the optimization problem
can be computationally demanding, but can provide significant benefits in
estimator accuracy and rate of convergence (Soechting et al., 1995). The
optimal estimations at each given horizon (window) can be computed using
indirect or direct optimal control methods (Crowninshield and
Brand, 1981).

3 CASE STUDY: DESIGN OF POPULATION-BASED
ELECTRIC POWER STEERING SYSTEMS

In this section, we examine a case study in which a systematic model-
based method to design individualized electric power steering (EPS) systems
for different driver populations is introduced. An EPS system is a
biomechatronic driver-assist device because it is a mechatronic system that
interacts with a human driver, and supports the driver to have a better