r - The Hong Kong Polytechnic University

Figure 2 is a photograph of the interior layout of the PFD. The photograph shows that a piezoelectric actuator
embedded in the PFD provides a controllable normal force (or called clamping force) between the friction pads
and friction bar, so the friction force provided by the PFD can be regulated by a control law. When the
SAF-TMD is excited during an earthquake, the friction force produced by the relative motion between the
friction pad of the PFD and the friction bar will provide energy dissipation capability for the SAF-TMD, and as
a result the response of primary structure and the TMD stroke can be attenuated.
Control of PFD
Figure 2 is a control block diagram of the PFD. The figure shows that a voltage amplifier and a controller are
usually needed to control the PFD. The controller can be a simple digital controller consisting of a
micro-computer (or a PC) and an analog/digital (A/D) converter card. The micro-computer calculates the control
command based on the sensor measurement of the current system response whereas the A/D card converts the
computed digital command to an analog signal, which is usually a DC voltage below 10V. However, the
piezoelectric actuator may require a driving DC voltage up to 1000V or higher; therefore, the control voltage
provided by the controller is not sufficient to drive the piezoelectric actuator directly. Therefore, a voltage
amplifier is needed to obtain a control voltage sufficient for controlling the piezoelectric actuator. The
experiment in this study used an amplifier with a gain of 100V/V to amplify a 10V control signal to a driving
voltage of 1000V. On the other hand, the electric current required for the piezoelectric actuator is usually at a
range of several mA, so the control energy demand for the PFD is minimal.
As mentioned above, the friction force of the PFD is controlled by regulating the normal force produced by a
piezoelectric actuator. The normal force, which is applied to the friction interface of the PFD, can be expressed
by the following equation
N( t)
= N0 + C V ( t)
(1)
z
where N(t) is total normal force, N 0 is pre-compression force (which produced by adjusting the pre-compression
screw shown in Figure 2), V(t) is driving voltage for the piezoelectric actuator, and C z , which is the key
parameter, is the piezoelectric coefficient of the piezoelectric actuator. Equation (1) shows that the force increase
is proportional to the piezoelectric coefficient C z . In terms of physical properties, C z is the trusting force of the
actuator generated by a unit driving voltage; therefore, C z provides a measure of the efficiency of the
piezoelectric actuator. A larger C z implies that a higher thrusting force can be generated by the actuator with a
given voltage. Since the piezoelectric actuator induced by the input voltage is elongated by only several tens μm
(10 -6 meters), the value of C z is highly dependent on the confinement boundary condition of the actuator. In this
study, a test was conducted to identify the actual value of the coefficient C z for the SAF-TMD.
According to the Coulomb friction law, the maximum friction force u d,max (t), i.e., slip force, of the PFD should
correlate with normal force N(t). By using Eq. (1), this slip force can be written as
u
t)
= μ N ( t)
= μ ( N C V ( ))
(2)
d , max ( d
d 0 + z t
where μ d denotes the friction coefficient of the PFD. Note that u d,max (t) in Eq. (2) represents the absolute value of
the maximum friction. Equations (1) and (2) show that, by controlling the driving voltage V(t), the normal force
N(t) as well as the slip force u d,max (t) of the PFD can be altered in a desired manner.
Non-sticking friction control
As noted above, an SAF-TMD generally requires an on-line control algorithm to determine the driving voltage
V(t) of the piezoelectric actuator. This section explains the control law and its important role in the performance
of the SAF-TMD system, and this section will explain the control law employed in this study. This control law
is developed based on the non-sticking friction (NSF) controller (He et al. 2003; Ng and Xu 2007). In order to
suit the control of the SAF-TMD system, whose control command is the driving voltage V(t), the NSF control
method is expressed as
V ( t)
= Vmax tanh( β v&
( t) )
(3)
s
where β is a control parameter set by the control designer. A larger value of β leads to the voltage ratio
increasing more rapidly from 0.0 to 1.0 as the sliding velocity v& s
(t)
increases. By employing the smooth
function tanh(x), Eq. (3) is able to prevent the abrupt change of the normal force N(t), as seen in Eq. (1). A larger
β leads to a function value increasing rapidly to 1.0. Therefore, clamping force V(t) increases rapidly as β
increases. Equation (3) was used as the control law in the shaking table test to compute the on-line command of
V(t). This control law is very easily implemented since it only requires measurement of sliding velocity v&
s
(t)
for the SAF-TMD. Finally, substituting V(t) from Eq. (3) in (1) gives the following normal force function:
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