Bzyyfgz毕业设计论文外文参考资料及译文封面.docx
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Bzyyfgz毕业设计论文外文参考资料及译文封面.docx
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Bzyyfgz毕业设计论文外文参考资料及译文封面
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1我们‖打〈败〉了敌人。
②我们‖〔把敌人〕打〈败〉了。
毕业设计(论文)外文参考资料及译文
译文题目:
InvertedPendulum
学生姓名:
徐飞马学号:
0704111030
专业:
07自动化
所在学院:
机电学院
指导教师:
陈丽换
职称:
讲师
2011年2月24日
\
Theinvertedpendulum
Keywords:
inverted pendulum,modeling,PID controllers,
LQRcontrollers
What is an Inverted Pendulum?
Remember when you were a child and you tried to balance a broom-stick or baseball bat on your index finger or the palm of your hand?
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 (usually of aluminum) free to oscillate around a fixed pivot. The pivot is mounted on a carriage, 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 down 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 position. This is possible by exerting on the carriage through the motor a force which tends 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 (obtained e.g. through two potentiometers).
The system pendulum+cart+motor can be modeled as a linear system if all the parameters 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 parameters using measured data on the dynamics of the pendulum.
The inverted pendulum is a traditional example (neither difficult nor trivial) of a controlled system. Thus it is used in simulations and experiments to show the performance of different controllers (e.g. PID controllers, state space controllers, fuzzy controllers....).
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 algorithm, 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 the kernel, and which perform different calculations. The way how these tasks are activated (e.g. the activation order) is called scheduling of the tasks. It is obvious that a correct scheduling of each task is crucial for a good performance of the controller, and hence for an effective pendulum stabilization. Thus the inverted pendulum is very useful in determining whether a particular scheduling choice is better than another one, 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 the modeling is valid only for small oscillations of the pendulum.
With the use of trapezoidal input membership functions and appropriate composition and inference methods, it will be shown that it is possible to obtain rule membership functions which are region-wise affine functions of the controller input variable. We propose a linear defuzzification algorithm that keeps this region-wise affine structure and yields a piece-wise affine controller. A particular and systematic parameter tuning method will be given which allows turning 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.
We will begin with system design; analyzing control behavior of a two-stage inverted pendulum. We will then show how to design a fuzzy controller for the system. We will describe a control curve and how it differs from that of conventional controllers when using a fuzzy controller. Finally, we will discuss how to use this curve to define labels and membership functions for variables, as well as how to create rules for the controller.
In the formulation of any control problem there will typically be discrepancies between the actual plant and the mathematical model developed for controller design.This mismatch may be due to unmodelled dynamics, variation in system parameters or the approximation of complex plant behavior by a straightforward model.The engineer must ensure that the resulting controller has the ability to produce the required performance levels in practice despite such plant/model mismatches. This has led to an intense 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.
The Inverted Pendulum is one of the most important classical problems of Control Engineering.Broom Balancing (Inverted Pendulum on a cart) is a well known example of nonlinear, unstable control problem. This problem becomes further complicated when a flexible broom, in place of a rigid broom, is employed. Degree of complexity and difficulty in its control increases with its flexibility. This problem has been a research interest of control engineers.
Control of Inverted Pendulum is a Control Engineering project based on the FLIGHT SIMULATION OF ROCKET OR MISSILE DURING THE INITIAL STAGES OF FLIGHT. The AIM OF THIS STUDY is to stabilize the Inverted Pendulum such that the position of the carriage on the track is controlled quickly and accurately so that the pendulum is always erected in its inverted position during such movements.
This practical exercise is a presentation of the analysis and practical implementation of the results of the solutions presented in the papers, “Robust Controller for Nonlinear & Unstable System:
Inverted Pendulum” and “Flexible Broom Balancing” , in which this complex problem was analyzed and a simple yet effective solution was presented.
Prescribed trajectory tracking with certain accuracy is a main task of robotic control. The control is often based on a mathematical model of the system. This model is never 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 unstructured uncertainties are of primary interest, i.e., the modeling error due to the parameters variation and unmodeled modes, especially the friction and sensor dynamics, neglected time delays,
The erroneous model and the demand for high performance require the controller to be robust. The sliding mode controllers(SMC) based on variable structure control can 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 robustness characteristics. This is a well-known problem and widely treated in the literature. 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 conservative control law due to the upper bounds of the uncertainties. In practice most often the worst case implemented in control law does not take place and the resulting large control inputs become unnecessary and uneconomical.
In this paper we suggest an approach to the design of decentralized motion controllers for electromechanical systems besides the sliding mode motion controller structure and disturbance torque estimation. The accuracy of the estimation is the critical parameter for robustness in this scheme, 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 conventional SMC) to the accuracy in their estimates. The result is a much better tracking accuracy without being over conservative in control.
Experimental robustness properties of fuzzy controllers remain theoretically difficult to prove and their synthesis 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 stage. Local controls designed in these regions are then combined into sets to make up the final global control. A partition of the state space can be found for which the controller has region-wise constant parameters. Moreover, each fuzzy controller tuning parameter (i.e. the shapes and the values of input or output variables membership functions) influences the values of parameters in several regions at the same time. In the particular 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 seen as a variable structure controller. This kind of a fuzzy controller can be assimilated to a variable structure controller with boundary layer such as in, for which stability theorems exist, but with a non-linear switching surface.
We will begin with system design; analyzing control behavior of a two-stage inverted pendulum. We will then show how to design a
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