Cerebellar Model Articulation Controller Simple Adaptive
Automation and Electrical Engineering Institute
Qingdao University of Science & Technology
Qingdao, Shandong Province, China
Abstract - Combined Cerebellar Model Articulation
Controller neural network with Simple Adaptive Control, a kind
of new control method, Cerebellar Model Articulation Controller
Simple Adaptive Control is proposed, structures and learning
algorithms of this control method are derived in this paper. In
the design, fast learning of Cerebellar Model Articulation
Controller neural network and simple structure of Simple
Adaptive Control are combined. The simulation results show that
the proposed method has fine accuracy, dynamic performance
and robustness, and it is feasible and effective to be used to
control high-order linear systems and nonlinear systems.
Index Terms - Cerebellar Model Articulation Controller;
neural network; learning algorithm; Simple Adaptive Control;
Most self-tuning and adaptive control algorithms usually
use reference models, controllers, or identifiers of the same
order as the controlled plant. Since the dimension of the plants
in the real word may be very large or unknown,
implementation of adaptive control may be difficult, or
sometimes impossible. Simple Adaptive Control (SAC)
techniques that have been developed for over 20 years that
can use low-order model reference and controllers, no
observers or identifiers are used in the adaptation process.
But the traditional SAC is limited to the linear controlled
plants, adopting PI control algorithms, its function and scope
is limited. In fact, the form of the SAC algorithms are various,
the controlled plants may be linear ones, or nonlinear ones.
This paper adopts cerebella model neural network and
learning algorithms to single input and single output system,
proposes the Cerebellar Model Articulation Controller
II. CEREBELLAR MODEL ARTICULATION CONTROLLER
The CMAC is a kind of neural network proposed by
Albus in 1970’s . CMAC has the characteristic of the local
association and learning ability by Lookup Table. It has the
advantages of fast learning, so it is suitable for real-time
Learning in the network of the CMAC uses the ? learning
rate. Its formula is
? is learning rate, C is the constant of generalization, F0 is
teacher's signal, F(si) is for the actual output of the network,
F(si)=wx0? x0 is the output vector, chooses C unit
components from unit components of x0, equals 1, and the
others are zero.
If ? =1, then the modification of the weight
F0 means the expectation output, F(si) means the actual
output, and the required accuracy can be satisfied by
regulating weight. Rewrite the formula (2) to be each weight
The characteristics of the CMAC are as follows:
(1) Learning structure based on the local area.
(2) Adopting simple ? learning rule.
(3) Because the CMAC is local network, the weight
adjusted each time is C, the learning speed is quick, and the
local smallest value does not exist.
(4) The CMAC generalization ability is related to
generalization constant C, as C enlarges, the generalization
(5) The main parameters
performance are generalization constant C, overlap extent
between close network input and input quantification, which
influence approximation accuracy, generalization ability and
(6) When the input dimensions increase, the storage also
III. SAMPLE ADAPTIVE CONTROL
SAC is a new direct adaptive control algorithm proposed
by K.Sobel and H.Kaufman, SAC has the characteristics of
simple control structure and less regulated parameters. The
system performance relates to the reference model selected. It
is irrespective to the controlled plant in control system design
and applicable to the single variable, multi-variable and
nonlinear system. The SAC has the extensive development
foreground in the industry process control.
The structure of SAC is showed in figure 1.
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1-4244-0828-8/07/$20.00 © 2007 IEEE.
Proceedings of the 2007 IEEE
International Conference on Mechatronics and Automation
August 5 - 8, 2007, Harbin, China