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Introduction to Motion Control
Application of an Auto-Tuning Neuronto Sliding Mode Control
Wei-Der Chang, Rey-Chue Hwang, and Jer-Guang Hsieh
IEEE TRANSACTIONS ON SYSTEMS, MAN, AND
CYBERNETICS—PART C: APPLICATIONS AND REVIEWS,
VOL. 32, NO. 4, NOVEMBER 2002
Professor: Ming-Shyan Wang
Student: Yi-De Lin
Outline
Abstract
Introduction
ILLUSTRATIVE EXAMPLES
CONCLUSION
REFERENCES
Abstract
This paper presents a control strategy that incorporates an
auto-tuning neuron into the sliding mode control (SMC) in
order to eliminate the high control activity and chattering
due to the SMC. The main difference between the autotuning neuron and the general one is that a modified
hyperbolic tangent function with adjustable parameters is
employed. In this proposed control structure, an autotuning neuron is then used as the neural controller without
any connection weights.. The control law will be switched
from the sliding control to the neural control, when the
state trajectory of system enters in some boundary layer. In
this way, the chattering phenomenon will not occur. The
results of numerical simulations are provided to show the
control performance of our proposed method.
Introduction
A useful and powerful control scheme to deal with the existence of the model uncertainty, or
imprecision, is the sliding mode control (SMC) [1]. As we know, the model uncertainty or
imprecision may arise from insufficient information about the system or from the purposeful
simplification of mathematical model representation of plant, e.g., order reduction. The control
law of SMC, however, is an intense switching action similar to that of bang-bang control, when
the state trajectory of system reaches around the sliding surface. This leads to the appearance of
chattering across the sliding surface and may excite the high-frequency unmodeled dynamics of
the system, undesirable in most real applications. A simple method for solving the discontinuous
control law and chattering action is to introduce a boundary layer. This method, however, does
not ensure the convergence of the state trajectory of system to the sliding surface, and probably
results in the existence of the steady-state error. In addition, analysis of a system dynamics
within the boundary layer is very complicated [2]. For solving the drawbacks, a number of
studies have been published. In [2], a control strategy was proposed based upon an on-line
estimator constructed by a recurrent neural network to eliminate the chattering. In [3], the
controller consists of the traditional SMC and Gaussian neural network. At the beginning, the
SMC is used to force the state trajectory of system toward the sliding surface. Then the control
law is switched
from the SMC to Gaussian neural network control if the state trajectory of system reaches the
boundary layer.
Introduction
Fig. 1. Basic structure of an auto-tuning neuron.
Introduction
Fig. 2. Modified activation functions for different a
and b.
Introduction
Fig. 3. Control structure using an auto-tuning neuron
with the SMC.
Introduction
Fig. 4. Boundary layer and intermediate region.
ILLUSTRATIVE EXAMPLES
To illustrate the use of the proposed method, the following
two examples
are provided. Note, that the sampling time is set to be 0.02 in
these simulations.
Example 1: Consider a first-order unstable nonlinear system
described
as [7]
In (18), the nonlinear function
ILLUSTRATIVE EXAMPLES
The parameters used in the neural control are given by = 0:0001
and (0) = ['(0); a(0); b(0)]T = [􀀀0:5; 2; 0]T .
Our control objective is also to regulate the system output x1
from the initial state (x1(0); x2(0)) = (1:5; 0) to the desired
output xd = 0. The results are shown in Figs. 7 and 8 by using
only the traditional SMC and the proposed method, respectively.
Again, we can find out that better control performance can be
achieved by using our proposed method.
CONCLUSION
In this paper, we have proposed a control strategy that consists of a general
SMC and a neural control constructed by an auto-tuning neuron. In order to
eliminate the high control activity and chattering due to the SMC, the control
law here is smoothly switched from the sliding
control to the neural control, when the state trajectory of system enters in some
boundary layer. Thus, the chattering phenomenon around the sliding surface
will never occur. For the adaptive neural control, we have presented a stable
tuning mechanism based on the Lyapunov stability
theory to guarantee the convergence of the system output. From the results of
two numerical simulations, we conclude that the proposed method can perform
successful control. It is interesting to consider the switching between SMC and
PID control, whether the PID control is
produced by some classical rules, e.g., Ziegler-Nichols tuning, or by rules
based on auto-tuning neurons. The latter is still under our investigation. No fair
comments can be made at this point.
REFERENCES
[1] J. J. E. Slotine and W. P. Li, Applied Nonlinear Control. Englewood
Cliffs, NJ: Prentice-Hall, 1991.
[2] Y. Fang, T.W. S. Chow, and X. D. Li, “Use of a recurrent neural network
in discrete sliding-mode control,” in Proc. Inst. Electr. Eng., Control
Theory Appl., vol. 146, Jan. 1999, pp. 84–90.
[3] R. M. Sanner and J. J. E. Slotine, “Gaussian networks for direct adaptive
control,” IEEE Trans. Neural Networks, vol. 3, pp. 837–863, Nov. 1992.
[4] F. P. Da andW. Z. Song, “Sliding mode adaptive control based on fuzzy
neural networks,” Control and Decision, vol. 13, no. 4, pp. 301–305,
1998. in Chinese.
[5] C. T. Chen andW. D. Chang, “A feedforward neural network with function
shape autotuning,” Neural Netw., vol. 9, no. 4, pp. 627–641, 1996.
[6] W. D. Chang, R. C. Hwang, and J. G. Hsieh, “Adaptive control of multivariable
dynamic systems using independent self-tuning neurons,” in
Proc. 10th Int. Conf. Tools with Artificial Intelligence, Taipei, Taiwan,
R.O.C, 1998, pp. 68–73.
[7] L. X. Wang, A Course in Fuzzy Systems and Control. Englewood
Cliffs, NJ: Prentice-Hall, 1997.
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