倒立摆外文翻译
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电093 0912002035 高小燕The inverted pendulumKey words: inverted pendulum, modeling, PID controllers,Fuzzy controllers, state space controllersWhat 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 t he same thing. However, it is limited in that it only moves in one dimension, while your hand coul d move up, down, sideways, etc. Check out the video provided to see exactly how the Inverted Pe ndulum 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 mo ve on a horizontal direction. The carriage is driven by a motor, which can exert on it a variable for ce. 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' pe ndulum dynamics. The correct force has to be calculated measuring the instant values of the horiz ontal 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 k nown (masses, lengths, etc.), in order to find a controller to stabilize it. If not all the parameters ar e known, one can however try to 'reconstruct' the system parameters using measured data on the d ynamics of the pendulum.What is it used for?Just like the broom-stick, an Inverted Pendulum is an inherently unstable sys tem. Force must be properly applied to keep the system intact. To achieve this, proper control theo ry is required. The Inverted Pendulum is essential in the evaluating and comparing of various cont rol theories.The inverted pendulum is a traditional example (neither difficult nor trivial) of a controlled syst em. Thus it is used in simulations and experiments to show the performance of different controller s (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 performa nce 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-oper ating tasks, which are periodically activated by the kernel, and which perform different calculation s. 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 contro ller, and hence for an effective pendulum stabilization. Thus the inverted pendulum is very useful i n 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.Prescribed trajectory tracking with certain accuracy is a main task of robotic control. The contr ol is often based on a mathematical model of the system. This model is never an exact representati on of reality, since modeling errors are inevitable. Moreover, one can use a simplified model on pu rpose. In this paper, the structured and unstructured uncertainties are of primary interest, i.e., the m odeling error due to the parameters variation and unmodeled modes, especially the friction and sen sor dynamics, neglected time delays, etc.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 inaccura cies in the model structure are bounded with known bounds. However, an SMC has some disadvan tages, 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 un modeled dynamics.The attempts to attenuate this undesirable effect result in the deterioration of the robustness char acteristics. This is a well-known problem and widely treated in the literature. In order to obtain s moothing 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 con trol law due to the upper bounds of the uncertainties. In practice most often the worst case implem ented 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 electr omechanical 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, a s 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 accurac y 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 a nd their synthesis is still an open problem. The non-linear structure of the final controller is derive d from all controllers at the different stages of fuzzy control, particularly from common defuzzific ation 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 re gions 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 particula r 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 controll er. This kind of a fuzzy controller can be assimilated to a variable structure controller with bounda ry 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 composition and infere nce methods, it will be shown that it is possible to obtain rule membership functions which are reg ion-wise affine functions of the controller input variable. We propose a linear defuzzification algor ithm that keeps this region-wise affine structure and yields a piece-wise affine controller. A particu lar 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 Fuzz y 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 o f the designed system. In this application note, we use an example of an inverted pendulum to pro vide details on all aspects of fuzzy logic based system design.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 cur ve 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 act ual 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 b ehavior 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 mismatche s. 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-cal led sliding mode control methodology.Sliding mode control is a particular type of Variable Structure Control System (VSCS). A VSC S is characterized by a suite of feedback control laws and a decision rule. The decision rule, terme d the switching function, has as its input some measure of the current system behavior and produc es as an output the particular feedback controller which should be used at that instant in time. A va riable structure system,which may be regarded as a combination of subsystems where each subsys tem has a fixed control structure and is valid for specified regions of system behavior, results. On e of the advantages of introducing this additional complexity into the system is the ability to comb ine useful properties of each of the composite structures of the system. Furthermore, the system m ay be designed to possess new properties not present in any of the composite structures alone. Util ization 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 state to li e within a neighborhood of the switching function. There are two main advantages to this approac h. Firstly, the dynamic behavior of the system may be tailored by the particular choice of switchin g function. Secondly, the closed-loop response becomes totally insensitive to a particular class of u ncertainty. The latter invariance property clearly makes the methodology an appropriate candidate for robust control. In addition, the ability to specify performance directly makes sliding mode cont rol attractive from the design perspective.The sliding mode design approach consists of two components. The first involves the design of a switching function so that the sliding motion satisfies design specifications. The second is conce rned with the selection of a control law which will make the switching function attractive to the system state. Note that this control law is not necessarily discontinuous.We will provide the reader with a thorough grounding in the sliding mode control area and as su ch is appropriate for the graduate with a basic knowledge of classical control theory and some kno wledge of state-space methods. From this basis, more advanced theoretical results are developed. Resulting design procedures are emphasized using Matlab files. Fully worked design examples are an additional tutorial feature. Industrial case studies, which present the results of sliding mode co ntroller implementations, are used to illustrate the successful practical application of the theory. The “INVERTED PENDULUM, ANAL YSIS, DESIGN AND IMPLEMENTATION” is a collec tion of MATLAB functions and scripts, and SIMULINK models, useful for analyzing Inverted Pe ndulum System and designing Control System for it. This report & MA TLAB-files collection are developed as a part of practical assignment on Control System Analysis, Design & Development p ractical problem. The assigned problem of INVERTED PENDULUM is a part of Lab Work of Co ntrol System.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 c ontrol problem. This problem becomes further complicated when a flexible broom, in place of a ri gid broom, is employed. Degree of complexity and difficulty in its control increases with its flexib ility. This problem has been a research interest of control engineers.Control of Inverted Pendulum is a Control Engineering project based on the FLIGHT SIMUL ATION OF ROCKET OR MISSILE DURING THE INITIAL STAGES OF FLIGHT. The AIM O F THIS STUDY is to stabilize the Inverted Pendulum such that the position of the carriage on the t rack is controlled quickly and accurately so that the pendulum is always erected in its inverted pos ition during such movements.This practical exercise is a presentation of the analysis and practical implementation of the resul ts of the solutions presented in the papers, “Robust Controller for Nonlinear & Unstable System: I nverted Pendulum” and “Flexible Broom Balancing” , in which this complex problem was analy zed and a simple yet effective solution was presented.倒立摆系统关键词:倒立摆,建模,PID控制器,模糊控制器,状态空间控制器什么是倒立摆?记得你在儿童时期用你的食指或者掌心试图去平衡一扫帚柄或者棒球棍吗?你需要不停地动你手的位置来让对象垂直。