Chatter mode is used advantageously if the ideal model dynamics is described by a switching function, the chatter mode is reached quickly and then sustained, the chatter frequency is reduced, and any zero in the plant transfer function is cancelled

Yasui, S.

English

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NASA TECH BRIEF 
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C
April1970	 Brief 70-10274 
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be directed to the Technology Utilization Division, NASA, Code UT, Washington, D.C. 20546. 
The Use of the Chatter Mode in Self-Adaptive Systems 
Disturbances 
Self-Adaptive System 
Most conventional control systems, although adap-
tive to some extent, need not or cannot cope with a 
wide range of environmental conditions. They usually 
deal with a limited range of internal parameter varia-
tions, limited kinds of external disturbances and com-
mand reference inputs, which are anticipated in the 
design stage. A self-adaptive control system (defined 
as one which can maintain satisfactory performance 
over a wide range of changing conditions) has the 
capability of organizing itself to accomplish its objec-
tives through the internal processes of measurement, 
evaluation and adjustment.
As a result of an analytical study of chatter motion 
(limit cycle oscillations when a linear switching func-
tion is non-optimum) in a control system with a simple 
relay as the controller, a new self-adaptive control 
principle, the block diagram shown in the figure, has 
been proposed which uses chatter motion advanta-
geously. In the on-off control system under the chatter 
mode, the average motion of the plant is completely 
determined by the equation of the switching function. 
This relationship can then be applied in a self-adaptive 
control system in which the switching function de-
scribes the model dynamics, and the chatter mode is 
(continued overleuo) 
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reached. A switching level adjustment can then reduce 
the chatter frequency and the control force magnitude, 
in addition to sustaining the chatter mode. The funda-
mental goal is to achieve the chatter mode as quickly 
as possible for any initial condition, and once it starts, 
to maintain it regardless of any change in operating 
conditions. An automatic adjustment device for the 
switching level or controllable gain has been proposed 
to meet this requirement. The scheme for the adjust-
ment requires only two pieces of information: the 
instantaneous switching function and its time deriva-
tive. Furthermore, it can remove any excess amount of 
gain and reduce the chatter frequency as well. 
The conclusions and recommendations of this study 
indicate advantageous use can be made of the chatter 
mode for self-adaptive control systems if the following 
basic requirements are met: the ideal model dynamics 
must be described by a switching function; the chatter 
mode must be reached quickly and then be sustained; 
the chatter frequency must be reduced; and, finally, 
any zero in the plant transfer function must be can-
celled. Several examples are presented to demonstrate 
the analog computer simulation; the results indicate 
the gain adjustment mechanism performs satisfactorily. 
In addition, known self-adaptive control systems are 
outlined with emphasis on those using a relay as a key
element, and consideration is given for the application 
to a class of distributed parameter control systems. 
As a byproduct of this study, a numerical method 
without integrations is proposed for the solution of 
ordinary differential equations. 
Note: 
The following documentation may be obtained 
from:
Clearinghouse for Federal Scientific 
and Technical Information 
Springfield, Virginia 22151 
Single document price $3.00 
(or microfiche $0.65) 
Reference: 
NASA-CR-88700 (N67-37384), The Use 
of the Chatter Mode in Self-Adaptive 
Systems 
Patent status: 
No patent action is contemplated by NASA. 
Source: Syozo Yasui of 
Massachusetts Institute of Technology 
under contract to 
NASA Headquarters 
(HQN- 10159) 
Brief 70-10274	 Category 06


The use of the chatter mode in self-adaptive systems

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