Instrumentation & Measurement Magazine 25-2 - 40

where * represents convolution. The error signal is the superposition
of the original response and secondary response of the
structure, and reads:
e      
n d n sn y n
 
Where the weight of controller is updated by:
      
wn wn s n x n e n
  
1
2
ˆ
(6)
(N/m2), and S is the strain. εT
mittivity) under constant stress, sE
is the dielectric constant (peris
the compliance when the
electric field is constant (inverse of the Young's modulus), and
d33
(7)
in which n is the time index and μ is the coefficient of
convergence.
The active control methods based on the DVF and FxLMS
have been widely applied in AVC in China. A large amount
of modification and practical implementation have been conducted
by Chinese researchers. Actually, the implementation
of AVC demands controllers with higher performance compared
to other fields of automation since it requires smaller
cycle times. The global brands of controller include dSPACE
and NI (USA), M+P (Germany) and Speedgoat (Switzerland),
among others. Nowadays, Chinese brands have gradually
occupied a place in the domestic market, such as ECON,
ZHONGPU, and MODELINGTECH. For example, ECON
in Hangzhou city launches the VT80XX series of multi-channel
vibration controllers, combining the PXI bus and gigabit
ethernet technology and integrating with multiple data-acquisition
boards and signal output boards, which can be applied
to vibration control of MISO and MIMO. The IM16XX series
of hardware equipment of ZHONGPU also adopts PXI bus
technology. Along with LabGenius software system, synchronized
vibration test control of MIMO with high precision can
be conducted. MODELINGTECH, Shanghai, developed independently
the MT 6020 real-time control simulator with FPGA
as its processing core, which can conduct the hardware in-theloop
control simulation with 1 μs level step-size. The outside
view of those controllers can be found in Fig. 3.
Actuator Techniques
Actuators are the executive component of AVC system,
whose performance directly affects the vibration control. The
actuators used in AVC include piezoelectric actuators, electromagnetic
actuators, hydraulic actuators, pneumatic actuators,
electrorheological fluids, magnetorheological fluids, electro-strictive
material, magneto-strictive material, and shape
memory alloys, for example, in which the piezoelectric actuators
and electromagnetic actuators are the most widely used.
The working principle of the piezoelectric actuators is to
produce a certain displacement and force under the action of
external driving electric field by using the inverse piezoelectric
effect. The constitutive equations of the transducer made
by one-dimensional piezoelectric material can be expressed as:
D E dT
S d E sT
  33
  E

33
T




(8)
where D is the electric displacement (charge per unit area, expressed
in C/m2
), E is the electric field (V/m), T is the stress
40
where C = n2
is the piezoelectric constant, expressed in m/V or C/N.
In this case, one assumes that all the electrical and mechanical
quantities are uniformly distributed in a linear transducer
formed by a stack of n disks with thickness t and cross section
A. According to (8), the relationship between the electric
charges Q and the elongation δ can be expressed as:
  
  
  
QVC nd
 nd K F
33
33
1/
a
A/l is the capacitance of the transducer with no
external load (F = 0), l = nt is the total thickness of all the disks,
V is the voltage applied between the electrodes of the transducer,
and Ka
(V = 0).
Piezoelectric actuators have been widely applied in the
control of vibration, ultra-precision machine tool spindles,
nano-positioning, optical microscopes, etc. The typical international
commercial products of piezoelectric stack actuators
include PI (Germany), APC (USA) and Thorlabs (USA), while
the Chinse representative commercial products are COREMORROW
and SINOCERA. According to different applications,
the piezoelectric stack actuators have working voltage from 0
to 1000 V, output thrust from 650 to 78000 N, and maximum
output displacement from 5 to 300 μm.
An electromagnetic actuator is a device that converts
electric energy into mechanical energy, with wide working
frequency band, fast response, large output force and strong
controllability. There are two main forms of electromagnetic
actuators. One is the traditional top-rod actuator and the other
is the inertial-type actuator. The latter one is more suitable
for AVC since it can be installed on the controlled structure
without external reaction force. The output force of inertial
electromagnetic actuator is:
F cxkxF mx
   

s
EM

(10)
where m, c, k are vibrator mass, equivalent damping and
equivalent stiffness of actuator, respectively, FEM
is the electromagnetic
force, and Fs is the output force of actuator. It can be
seen that the inertial actuator only reserves inertial force of an
oscillator. Let s = jω, and conducting Laplace transform to (10),
the output displacement of the actuator is:
xs 

k m jc


F EM
2
where j is imaginary unit, and xs
(11)
is the output displacement of
the actuator. The working principle and physical appearance
of inertial-type electromagnetic actuator can be found in Fig. 4.
The international well-known electromagnetic actuator
manufacturers are American-based MOOG CAS and MOTRAN.
The SA series of inertial actuator produced by MOOG
CAS have total weight within 3 kg, working frequency band of
20 to 1000 Hz, and output force range of 4.5 to 155 N. The IFX
IEEE Instrumentation & Measurement Magazine
April 2022
is the stiffness with short-circuited electrodes
(9)
Instrumentation & Measurement Magazine 25-2

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 25-2
