This paper focuses on the control problem of the quadruple inverted pendulum by variable universe adaptive fuzzy control.First,the mathematical model on the quadruple inverted pendulum is described and its controllability is versified.Then,an efficient controller on the quadruple inverted pendulum is designed by using variable universe adaptive fuzzy control theory.Finally the simulation of the quadruple inverted pendulum is shown in detail.Besides,the experimental results on the hardware systems,i.e.real object systems,on a single inverted pendulum,a double inverted pendulum and a triple inverted pendulum are briefly introduced.
A kind of modelling method for fuzzy control systems is first proposed here, which is called modelling method based on fuzzy inference (MMFI). It should be regarded as the third modelling method that is different from two well-known modelling methods, that is, the first modelling method, mechanism modelling method (MMM), and the second modelling method, system identification modelling method (SIMM). This method can, based on the interpolation mechanism on fuzzy logic system, transfer a group of fuzzy inference rules describing a practice system into a kind of nonlinear differential equation with variable coefficients, called HX equations, so that the mathematical model of the system can be obtained. This means that we solve the difficult problem of how to get a model represented as differential equations on a complicated or fuzzy control system.
A kind of stable adaptive fuzzy control of nonlinear system is implemented using variable universe method. First of all, the basic structure of variable universe adaptive fuzzy controllers is briefly introduced. Then the contraction-expansion factor that is a key tool of variable universe method is defined by means of integral regulation idea, and a kind of adaptive fuzzy controllers is designed by using such a contraction-expansion factor. The simulation on first order nonlinear system is done. Secondly, it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of Lyapunov theory. The simulation on the second order nonlinear system shows that its simulation effect is also quite good. Finally a useful tool, called symbolic factor, is proposed, which may be of universal significance. It can greatly reduce the settling time and enhance the robustness of the system.
By establishing some suitable partitions of input and output spaces, a novel fuzzy neural network (FNN) which is called selection type FNN is developed. Such a system is a multilayer feedforward neural network, which can be a universal approximator with maximum norm. Based on a family of fuzzy inference rules that are of real senses, a simple and useful inference type FNN is constructed. As a result, the fusion of selection type FNN and inference type FNN results in a novel filter-FNN filter. It is simple in structure. And also it is convenient to design the learning algorithm for structural parameters. Further, FNN filter can efficiently suppress impulse noise superimposed on image and preserve fine image structure, simultaneously. Some examples are simulated to confirm the advantages of FNN filter over other filters, such as median filter and adaptive weighted fuzzy mean (AWFM) filter and so on, in suppression of noises and preservation of image structure.
