Page 253 - Adaptive Identification and Control of Uncertain Systems with Nonsmooth Dynamics

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

Based on the solution (16.9), we can see that the model is composed of
a line with the slope c, together with a bounded disturbance term h[(v(t))].
This also allows to facilitate adaptive control designs. In fact, most of non-
linear control systems with Backlash-like hysteresis do not need inverse
model.
More hysteresis models will be introduced in the following chapters
when it is necessary.

16.3 EXAMPLESWITHHYSTERESIS
16.3.1 Magneto-Rheological (MR) Dampers for Suspension

As widely used as a semi-active control device, magneto-rheological (MR)
fluids have been well recognized as specific smart materials. Their rheolog-
ical properties can be changed in millisecond time period by tuning the
electric field or magnetic field. It is noted that the suspension system with
MR dampers can be taken as semi-active suspension device [13], because
the damper force can be changed by using variable damping or energy dis-
sipation components. 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 Bing-
ham liquid with high viscosity and low liquidity. Thus, MR dampers may
have non-smooth dynamics, e.g., hysteresis, which lead to difficulties in the
modeling and the associated control synthesis.

16.3.2 Piezoelectric Motor

A piezoelectric actuator [14] is an electrically controllable positioning el-
ement with high precision, which has been recently used in many micro-
scale systems. These kinds of actuators are designed based on the piezo-
electric effect. However, a major limitation of piezoelectric actuator is the
rate-independent hysteresis [15] exhibited between the input voltage and
the output displacement, which severely deteriorates the positioning accu-
racy if such hysteresis dynamics are not compensated appropriately. In fact,
the existence of hysteresis in the control system could lead to undesirable
oscillations, and even trigger system instability.