| Professor L.A. Zadeh, an American expert in automation control, established fuzzy set theory in1965.This theory has been extensively used in many fields, such as metallurgy, chemical industry, domesticappliance, finance, medicine and so on. But the accurate choice of membership function of fuzzy sets is noteasy. Interval-valued fuzzy sets have its advantages in expressing uncertain information. Interval values caninclude more information, which may effectively reduce error rates and cause that the final decision isrational, scientific and correct. So, the study of the interval-valued fuzzy set theory and its application ininterval-valued fuzzy control is significant. This paper researches the application of interval-valued fuzzyset theory and interval-valued fuzzy logic in inverted pendulum system and develops a new method ofinterval-valued fuzzy control for the inverted pendulum system.The interval-valued fuzzy control of the inverted pendulum system is researched in this paper. Firstly,the interval-valued fuzzy logical reasoning and the basic principle of the interval-valued fuzzy control arepresented, and then the curves of membership function with interval structure are designed. Meantime, thefuzzy controllers and fuzzy control systems of the single and double inverted pendulum systems are builtby using inference rules and inference mechanism based on interval-valued implication. Finally, theinterval-valued fuzzy controls of the single and double inverted pendulum systems are successfullyachieved and the stability, servo and anti-interference of the systems are investigated.In the paper, the main contents are studied as follows:First, based on fuzzy set theory and fuzzy logical reasoning, we design the point-valued fuzzycontrollers and fuzzy control systems by respectively choosing the triangle, trapezoid, Gaussian and Gaussian combination membership function as the one of the input and output variables. The simulationand real-time control experiments are carried out and the point-valued fuzzy controls of the single anddouble inverted pendulum systems are successfully achieved.Second, based on the interval-valued fuzzy set theory, we design the curves of membership functionwith interval structure and establish the trapezoid-triangle and Gaussian-Gaussian combination discrete andsynthetic fuzzy controllers and their fuzzy control systems by using the interval-valued R implicationoperator presented by Prof. Xue zhan-ao and respectively choosing the trapezoid-triangle andGaussian-Gaussian combination membership function as the one of the input and output variables. Thesimulation and real-time control experiments are carried out and the interval-valued fuzzy controls of thesingle and double inverted pendulum systems are successfully achieved.Third, we establish six fuzzy inference systems and nine fuzzy control systems and analyze theexperimental results by comparison. The stability, servo and anti-interference of the built fuzzy controlsystems of the inverted pendulum systems are investigated.The experimental results demonstrate that the application of the interval-valued fuzzy control in thesystems as multi-variable, strong-coupling, natural-instability and nonlinear as the inverted pendulumsystem is successful. Point-valued fuzzy control will produce the problems of stability and servo due to theimproper selection of membership function or the improper setting in the parameters. The problems may besolved when using the interval-valued fuzzy control. Because the structure of interval-valued membershipfunction curves is banded and the one of point-valued membership function curves is linear, theinterval-valued fuzzy control system has the obvious advantage over the point-valued one in the aspect ofanti-interference. |
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