Vibration Suppression of Adaptive Truss Structure
Using Fuzzy Neural Network
Shaoze Yan1, Kai Zheng1, and Yangmin Li2
1
Department of Precision Instruments and Mechanology, Tsinghua University,
Beijing 100084, P.R. China
yansz@mail.tsinghua.edu.cn
2
Department of Electromechanical Engineering, University of Macau,
Macao SAR, P.R. China
ymli@umac.mo
Abstract. An adaptive truss structure with self-learning active vibration control
system is developed. A fuzzy-neural network (FNN) controller with adaptive
membership functions is presented. The experimental setup of a two-bay truss
structure with active members is constructed, and the FNN controller is applied
to vibration suppression of the truss. The controller first senses the output of the
accelerometer as an error to activate the adaptation of the weights of the controller, and then a control command signal is calculated based on the FNN inference mechanism to drive the active members. This paper describes active vibration control experiments of the truss structure using fuzzy neural network.
1 Introduction
Among the modern structures of huge spacecrafts, the truss is one of the most commonly used structures. In order to reduce the cost of launching and to increase the
payload, the structural weight must be as light as possible. On the other hand, they
must possess excellent dynamic behaviors to ensure the safety and stability of the
structures, and be able to keep the instruments and equipment fixed on them in good
condition. However, these two requirements are often contradictory. It may be possible to create adaptive space structures capable of adapting to or correcting for changing operating conditions, since the subject areas of smart/intelligent materials and
intelligent control have experienced tremendous growth in terms of research and development in the last two decades. The fuzzy adaptive back-propagation algorithm
which combined fuzzy theory with artificial neural network techniques was applied to
the identification of restoring forces in non-linear vibration systems [1]. An artificial
neural network was used for the active vibration control of a flexible aluminum cantilever beam employing a piezoactuator [2]. The length adjustable active members were
employed to suppress vibration of adaptive truss structures with a direct output feedback control [3]. Adaptive neural control for space structure vibration suppression
was also developed [4].
This article describes vibration suppression of adaptive truss structures using fuzzy
neural network (FNN) control scheme. The proposed scheme is based on the structure
of the self-tuning regulator and employs neural network and genetic algorithm (GA)
techniques. The scheme is described in Section 2. An adaptive truss structure with
self-learning active vibration control system using the FNN and experimental results
are presented in Section 3. The final section is the conclusions.
J. Wang, X. Liao, and Z. Yi (Eds.): ISNN 2005, LNCS 3498, pp. 155–160, 2005.
© Springer-Verlag Berlin Heidelberg 2005
156
Shaoze Yan, Kai Zheng, and Yangmin Li
2 Fuzzy Neural Network
A five-layered fuzzy neural network (FNN) is presented to construct self-learning
active vibration control system of adaptive truss structure with PZT active members.
The structure diagram of the FNN with two inputs and one output is shown in Fig.1.
The coherent binding of the neural network and fuzzy logic represents an advanced
intelligent system architecture.
wij
w
NB
…
PB
…
…
…
xx2
…
NB
…
…
…
ZE
…
xx1
wwjk k
y
Precision Output
Layer
ZE
Input Layer
…
Rule Layer
PB
Fuzzy Output
Layer
Fuzzy Layer
Fig. 1. The structure diagram of the FNN
2.1 Layered Operation of FNN
Let xki be the ith input of the kth layer. netkj and ykj denote the input and the output of
the jth node in the kth layer respectively, so we can obtain ykj = x(k+1)j. In the following, we will explain the physical meaning and the node functions of each layer. Layer
1 is the input layer whose nodes are the input ones,
y1 j = net1 j , net1 j = x1i ,
j =i,
(1)
where x1i is the ith input of the first layer, i=1,2. Layer 2 is the linguistic term layer
which uses Gaussian function as membership function, so these term nodes map input
xi onto their membership degree yj by using the jth term node of xi , i.e.,
y 2 j = exp(−( xi − mij ) 2 / σ ij2 ) ,
(2)
where mij and σ ij denote mean (center) and variance (width) with respect to the j th
fuzzy set of the i th input. Layer 3 is the rule layer that implements the related link for
preconditions (term node) and consequence (output node). The jth output of layer 3 is
p
y3 j = net3 j = ∏ x3i .
(3)
i =1
Layer 4 is the fuzzy output layer whose output is membership degree. Layer 5 is the
output layer, which performs the centroid defuzzification to get numerical output, i.e.,
Vibration Suppression of Adaptive Truss Structure Using Fuzzy Neural Network
y5 j = net5 j / ∑ (σ ij x5i ),
net5 j = ∑ w5ij xi = ∑ (mijσ ij ) x5i ,
157
(4)
where y51 is the final output of the neutral net, and w5ij denotes the weight value of
the 5th layer, w5ij = mijσ ij .
2.2 Definition and Adjustment of Fuzzy Rules
The adjusted parameters in the FNN can be divided into two categories based on IF
(premise) part and THEN (consequence) part in the fuzzy rules. A gradient descent
based BP algorithm is employed to adjust the FNN’s parameters [5]. In the premise
part, the parameters are mean and width of Gaussian function. For initializing these
terms, we use normal fuzzy sets.
The problem in designing fuzzy control systems is how to determine the free parameters of the fuzzy controller, i.e. rules and membership functions. Membership
functions are used for the fuzzy input and output variables. We use the membership
functions with seven linguistic variables (NB, NM, NS, ZE, PS, PM, PB), which
represent negative big, negative medium, negative small, zero, positive small, positive
medium, and positive big, respectively. They can be scaled into the range of -6 and +6
with equal span. For the vibration suppression of the truss structure, the Gaussian
function is employed as initial membership function, shown in Fig. 2. Forty-nine
fuzzy rules based on the displacement or acceleration and the difference in subsequent
time are shown in Table 1. We can describe the fuzzy rules in Table 1 as follows,
If ( A is Ai , B is B j ) then ( U is U ij ),
i, j = 1,2,...,7 ,
(5)
where A and B are inputs of the controller, and U is output of the controller;
Ai and B j are the antecedent linguistic values for the ith and jth rule respectively, and
U ij is the consequent linguistic values.
The training set consists of input vectors and corresponding desired output vectors.
The output of the neuron is a function of the total weighted input. The membership
functions are tuned by the delta rule [6]. The error function for the FNN controller is
defined as
E = ( y d − y51 ) 2 / 2 ,
(6)
where y d and y51 are the desired and actual outputs of the FNN.
Table 1. The fuzzy rules of the FNN
Uij
Bj
NB
NM
NS
ZE
PS
PM
PB
PB
PB
PM
PM
PM
PS
ZE
PB
PB
PM
PM
PS
ZE
ZE
PB
PB
PM
PS
ZE
ZE
ZE
PM
PM
PS
ZE
NS
NM
NM
PM
PM
ZE
NS
NM
NM
NM
ZE
ZE
NS
NS
NM
NB
NB
ZE
ZE
NS
NS
NM
NB
NB
Ai
NB
NM
NS
ZE
PS
PM
PB
158
Shaoze Yan, Kai Zheng, and Yangmin Li
NB NM NS ZE PS PM PB
1.0
NB NM NS
1.0
ZE
PS
PM
PB
NB NM
1.0
0.5
0.5
0.0
-6
-4
-2
0
2
A
4
6
NS
ZE
PS
PM
PB
0
2
4
6
0.5
0.0
-6
(a) Input A
-4
-2
0
B
2
4
(b) Input B
6
0.0
-6
-4
-2
U
(c) Output U
Fig. 2. Fuzzy input and output membership functions
The error signals are propagated backward from the 5th layer to the 1st layer in order to align themselves with the error signals. The controller weights are updated
according to
w(t + 1) = w(t ) − η∂E / ∂w ,
(7)
where η is the learning rate which is generally between 0.01 and 1, and
∂E
∂E ∂net ∂y
.
(8)
=
⋅
⋅
∂w ∂net ∂y ∂E
The training continues until the error is within acceptable limits. Since the system
dynamics are usually unknown, the sensitivity is unknown. However, this can be
estimated using the neural identifier. After the identifier is sufficiently trained, the
dynamic behavior of the identifier is close to that of the structure [5]. In order to avoid
BP network converging to local optimum, a hybrid training algorithm combined genetic algorithm (GA) with BP algorithm is established. The mean and width of Gaussian function can be adjusted and optimized by GA. We can obtain structure coarse
optimization of fuzzy neural network by using the coding method, the fitness function, and the genetic operations (crossover, mutation, and selection), and fine tuning
of weights wij can be performed by BP [6].
B
2
5
6
C
A
1
3
4
8
D
7
Fig. 3. Two-bay truss structure with active members
Fig. 4. Experimental setup
3 Active Vibration Control Experiments
Figures 3 and 4 show a two-bay truss structure and the photograph of the experimental setup with active members. The active members 3 and 5 shown in Fig.5 are posed
as a diagonal brace of each bay truss for vibration control. The other truss bars are
made of aluminum alloy tubs. The FNN controller is applied to the truss vibration
suppression. The FNN controller first senses the output of the accelerometer as an
Vibration Suppression of Adaptive Truss Structure Using Fuzzy Neural Network
159
error to activate the adaptation of the weights of the controllers. Then a control command signal is calculate based on the FNN inference mechanism to drive the active
members. The initial populations size of GA is chosen as 20. Probability of the mutation operation is 0.02, and the crossover rate 0.5. The BP algorithm with learning rate
α = 0.02 and β = 0.02 is used to train the FNN for obtaining weight value of the
nodes. The sampling frequency is selected as 1kHz.
Fixed
Ball
End
PZT Stack
Displacement Sensor
Targat
Sensor
Load
Member
Sensor
Preload
Spring
Output Stem
Nut
Fig. 5. PZT active member architecture
8
Vibration amplitude, V
Vibration amplitude, V
An impulse force excitation is given at the node C of the truss, and we only use the
active member 3 to control vibration of the truss. Figure 6 shows acceleration responses at the node A of the truss in the time domain. As expected, the amplitude of
vibrations decreases significantly by using the closed-loop control with the FNN. The
stable times of vibration amplitudes for open-loop (uncontrolled) and closed-loop
control are about 0.15s and 0.06s respectively under an impulse excitation. It can be
seen that the controller provides excellent damping. We have also swiped the excitation frequency to examine the adaptation capability of this control system. The controller of the adaptive truss structure offered the similar performance for different
frequency disturbance.
4
电
0
-4
-8
0.0
0.1
0.2
Time, s
(a) Open-loop
0.3
8
4
0
-4
-8
0.0
0.1
0.2
0.3
Time, s
(b) Closed-loop
Fig. 6. Responses of the truss under a pulse excitation
4 Conclusions
In this paper the adaptive truss structure with active vibration control system is developed. A fuzzy neural network architecture to design and implement a self-learning
control system for active vibration suppression applications is described. Active control is achieved by processing sensor voltage through a compensator and amplifying
the voltage signal to the PZT active members. We have experimentally demonstrated
the application of a FNN controller to active vibration control of the truss structure
160
Shaoze Yan, Kai Zheng, and Yangmin Li
with the active members. Experimental results show that the FNN controller is efficient for vibration control of the truss structure.
Acknowledgement
This work is supported by the National Science Foundation of China under grant
59905016 and 50275080.
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