Page 293 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

296 Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics

In this chapter, we will present an alternative modeling and control
method for a semi-active suspension system with MR dampers. First, sev-
eral widely used MR damper models are reviewed, and a hyperbolic MR
damper model depending on the hysteresis variable and damper force is
adopted. Inspired by our recent work [18,19], we propose an adaptive
parameter estimation method to online identify the unknown model pa-
rameters. Furthermore, an adaptive control is introduced for semi-active
vehicle suspension systems with unknown hyperbolic MR damper model.
This control can regulate the vehicle vertical displacement by manipulating
the applied current. In order to achieve simultaneous online modeling and
control, a new leakage term as [19]isintroducedinthe adaptive law,such
that the estimated parameters converge to their true values. The suspension
performance requirements are also studied. Simulation results are given to
illustrate the efficacy of the proposed method.

19.2 MODELING OF MAGNETO-RHEOLOGICAL (MR) DAMPER
19.2.1 MR Damper Dynamics
Magneto-rheological fluid consists of ferromagnetic particles, base liquid,
and stabilizer. Under zero magnetic field conditions, MR fluid can present a
low viscosity Newtonian fluid state. However, with the increased magnetic
field intensity, the fluid transforms into the Bingham liquid with high vis-
cosity and low liquidity [2,3]. This conversion is continuous and reversible,
which can occur in the millisecond time, and thus MR fluid can be taken
as a kind of controllable fluids [13]. This salient feature makes it possible
to use MR fluid as the working medium for constructing MR damper as
a semi-active control device. This kind of MR dampers have advantages
of simple structure, fast response, low power consumption, continuously
adjustable and high damping force. In the vehicle suspension systems, the
work process of MR damper is shown in Fig. 19.1. The vehicle’s ECU can
calculate a current (control signal) applied to the MR damper based on the
interference information. When the input current increases, the magnetic
field intensity of the electromagnetic coil inside the damper increases, and
thus the shear yield force also increases. Then the generated damping force
can be used to mitigate the vehicle vibrations.
It is noted that MR dampers may have non-smooth dynamics, e.g.,
hysteresis, thus accurate modeling of MR damper is essential in the control
design. For this purpose, several different dynamic models have been pro-
posed, e.g., Bingham model [11], Bouc-Wen model [12], modified Bouc-