Abstract
Establishing an accurate inverse model is a key problem in the design of adaptive inverse controllers. Most real objects have nonlinear characteristics, so mathematical expression of an inverse model cannot be obtained in most situation. A Takagi–Sugeno(T-S)fuzzy model can approximate real objects with high precision, and is often applied in the modeling of nonlinear systems. Since the consequent parameters of T-S fuzzy models are linear expressions, this paper firstly uses a fuzzy c-regression model (FCRM) clustering algorithm to establish inverse fuzzy model. As the least mean square (LMS) algorithm is only used to adjust consequent parameters of the T-S fuzzy model in the process of parameter adjustment, the premise parameters are fixed and unchanged in the process of adjustment. In this paper, the back propagation (BP) algorithm is applied to adjust the premise and consequent parameters of the T-S fuzzy model, simultaneously online. The simulation results show that the error between the system output controlled by proposed adaptive inverse controller and the desired output is smaller, also the system stability can be maintained when the system output has disturbances.
Highlights
The inverse problem has been a research hotspot in recent years; the basic idea of the inverse problem is to use the results and some general principles to determine the parameters that represent the characteristics of the problem
The inverse problem was usually implemented by artificial intelligence algorithms, which had the function of learning and reasoning, such as the simulated annealing algorithm, tabu search algorithm, fuzzy clustering algorithm, improved
The adaptive inverse controller based on the least mean square (LMS) algorithm only adjusts consequent parameters of T-S fuzzy model, and premise parameters are fixed
Summary
The inverse problem has been a research hotspot in recent years; the basic idea of the inverse problem is to use the results and some general principles (or models) to determine the parameters (or model parameters) that represent the characteristics of the problem. As there is a lack of exact mathematical model of the controlled object, data driving modeling methods were used for modeling of the controlled object, such as artificial neural network systems, fuzzy systems, and so on These methods included the mathematical optimization process, which determined model parameters by system operation input and output data, called training data. Compared with article [5,6], where the FCRM clustering algorithm is applied to determine model parameters and tabu search and simulated annealing methods were adopted. The adaptive inverse controller based on the least mean square (LMS) algorithm only adjusts consequent parameters of T-S fuzzy model, and premise parameters are fixed. The simulation results show that the proposed adaptive inverse controller has smaller errors and when system output has disturbances, the controller has stronger robustness
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