化学式的意义英文翻译(2006.5.30)

2021年1月18日发(作者：曼谷皇宫)
新疆大学毕业论文（设计）

外文翻译


Inverted Pendulum System synopsis
What is an Inverted Pendulum? Remember when you were a child and you trie
dto balance a broom-stick or baseball bat on your index finger or the palm of your han
d? You had to constantly adjust the position of your hand to keep the object upright.
An Inverted Pendulum does basically the same thing. However, it is limited in that it
only moves in one dimension, while your hand could move up, down, sideways, etc.
Check out the video provided to see exactly how the Inverted Pendulum works.
An inverted pendulum is a physical device consisting in a cylindrical bar (usuall
y of aluminium) free to oscillate around a fixed pivot. The pivot is mounted on a carri
age, which in its turn can move on a horizontal direction. The carriage is driven by a
motor, which can exert on it a variable force. The bar would naturally tend to fall do
wn from the top vertical position, which is a position of unsteady equilibrium.
The goal of the experiment is to stabilize the pendulum (bar) on the top vertical po
sition. This is possible by exerting on the carriage through the motor a force which t
ends to contrast the 'free' pendulum dynamics. The correct force has to be calculated
measuring the instant values of the horizontal position and the pendulum angle (obtai
ned e.g. through two potentiometers).
The system pendulum+cart+motor can be modeled as a linear system if all the pa
rameters are known (masses, lengths, etc.), in order to find a controller to stabilize it.
If not all the parameters are known, one can however try to 'reconstruct' the system p
arameters using measured data on the dynamics of the pendulum.
What is it used for?
Just like the broom- stick, an Inverted Pendulum is an inherently unstable system. F
orce must be properly applied to keep the system intact. To achieve this, proper contr
ol theory is required. The Inverted Pendulum is essential in the evaluating and compa
ring of various control theories.
The inverted pendulum is a traditional example ( neither difficult nor trivial) of a c
ontrolled system. Thus it is used in simulations and experiments to show the performa
nce of different controllers ( e.g. PID controllers, state space controllers, fuzzy contro
llers....).
The Real-Time Inverted Pendulum is used as a benchmark, to test the validity and the
performance of the software underlying the state-space controller alogorithm, i.e. the
used operating system. Actually the algorithm is implement form the numerical point
of view as a set of mutually co-operating tasks, which are periodically activated by t
he kernel, and which perform different calculations. The way how these tasks are acti
vated (e.g. the activation order) is calleding scheduling of the tasks. It is obvious that
a correct scheduling of each task is crucial for a good performance of the controller, a
nd hence for an effective pendulum stabilization. Thus the inverted pendulum is very
useful in determing whether a particular scheduling choice is better than another one,
新疆大学毕业论文（设计）
in which cases, to which extent, and so on.
Modeling an inverted pendulum
Generally the inverted pendulum system is modeled as a linear system, and hence t
he modeling is valid only for small oscillations of the pendulum.
Prescribed trajectory tracking with certain accuracy is a main task of robotic contro
l. The control is often based on a mathematical model of the system. This model is ne
ver an exact representation of reality, since modeling errors are inevitable. Moreover,
one can use a simplified model on purpose. In this paper, the structured and unstruct
ured uncertainties are of primary interest, i.e., the modeling error due to the paramete
rs variation and unmodeled modes, especially the friction and sensor dynamics, negle
cted time delays, etc.
The erroneous model and the demand for high performance require the controller t
o be robust. The sliding mode controllers(SMC) based on variable structure control c
an be used if the inaccuracies in the model structure are bounded with known bounds.
However, an SMC has some disadvantages, related to chattering of the control input
signal. Often this phenomenon is undesirable, since it causes excessive control action
leading to increase wear of the actuators and to excitation of unmodeled dynamics.
The attempts to attenuate this undesirable effect result in the deterioration of the robu
stness characteristics. This is a well- known problem and widely treated in the literatur
e. In order to obtain smoothing in the bang-bang typed discontinuities of the sliding
mode controller different schemes have been suggested.
Another important issue limiting the practical applicability of SMC is the over cons
ervative control law due to the upper bounds of the uncertainties. In practice most oft
en the worst case implemented in control law does not take place and the resulting lar
ge control inputs become unnecessary and uneconomical In this paper we suggest
an approach to the design of decentralized motion controllers for mechatronics syste
ms besides the sliding mode motion controller structure and disturbance torque estim
ation. The accuracy of the estimation is the critical parameter for robustness in this sc
heme, as opposed to the upper bounds of the perturbations themselves. Consequently,
the driving terms of the error dynamics are reduced from the uncertainties (as in the c
onventional SMC) to the accuracy in their estimates. The result is a much better track
ing accuracy without being over conservative in control. Experimental robustness
properties of fuzzy controllers remain theoretically difficult to prove and their synthe
sis is still an open problem . The non- linear structure of the final controller is derived
from all controllers at the different stages of fuzzy control, particularly from common
defuzzification methods (such as Centre of Area) . In general , fuzzy controllers have
a region-wise structure given the partition of its input space by the fuzzification stag
e . Local controls designed in these regions are then combined into sets to make up th
e final global control . A partition of the state space can be found for which the contr
oller has region-wise constant parameters . Moreover, each fuzzy controller tuning pa
rameter (i.e. the shapes and the values of input or output variables membership functi
ons) influences the values of parameters in several regions at the same time . In the p
articular case of a switching line separating the phase plane into one region where the
control is positive whereas in the other it is negative , the fuzzy controller may be se
新疆大学毕业论文（设计）
en as a variable structure controller . This kind of a fuzzy controller can be assimilate
d to a variable structure controller with boundary layer such as in , for which stability
theorems exist , but with a non-linear switching surface .
With the use of trapezoidal input membership functions and appropriate compositi
on and inference methods, it will be shown that it is possible to obtain rule membersh
ip functions which are region-wise affine functions of the controller input variable. W
e propose a linear defuzzification algorithm that keeps this region- wise affine structur
e and yields a piece-wise affine controller . A particular and systematic parameter tun
ing method will be given which allows to turn this controller into a variable structure-
like controller. We will compare this region-wise affine controller with a Fuzzy and
Variable Structure Controller through the application to an inverted pendulum control
So far, in the application note series, we have provided several examples showing
how to create fuzzy controllers with FIDE. However, these examples do not provide
topics on implementation of the designed system. In this application note, we use an
example of an inverted pendulum to provide details on all aspects of fuzzy logic base
d system design.
We will begin with system design; analyzing control behavior of a two-stage inver
ted pendulum. We will then show how to design a fuzzy controller for the system. W
e will describe a control curve and how it differs from that of conventional controller
s when using a fuzzy controller. Finally, we will discuss how to use this curve to defi
ne labels and membership functions for variables, as well as how to create rules for th
e controller.
In the formulation of any control problem there will typically be discrepancies bet
ween the actual plant and the mathematical model developed for controller
is mismatch may be due to un-modelled dynamics, variation in system parameters or
the approximation of complex plant behaviour by a straightforward engin
eer must ensure that the resulting controller has the ability to produce the required per
formance levels in practice despite such plant/model mismatches. This has led to an i
ntense interest in the development of so-called robust control methods which seek to
solve this problem. One particular approach to robust control controller design is the
so-called sliding mode control methodology.
Sliding mode control is a particular type of Variable Structure Control System (VSCS
). A VSCS is characterised by a suite of feedback control laws and a decision rule. Th
e decision rule, termed the switching function, has as its input some measure of the c
urrent system behaviour and produces as an output the particular feedback controller
which should be used at that instant in time. A variable structure system,which may b
e regarded as a combination of subsystems where each subsystem has a fixed control
structure and is valid for specified regions of system behaviour, results. One of the ad
vantages of introducing this additional complexity into the system is the ability to co
mbine useful properties of each of the composite structures of the system. Furthermor
e, the system may be designed to possess new properties not present in any of the co
mposite structures alone. Utilisation of these natural ideas began in the Soviet Union
in the late 1950's.
In sliding mode control, the VSCS is designed to drive and then constrain the system s