Modelling of an electro-hydraulic actutor using extended adaptive distance gap statistic approach

Abstract

The existence of high degree of non-linearity in Electro-Hydraulic Actuator (EHA) system has imposed a challenging task in developing its model so that effective control algorithm can be proposed. In general, there are two modelling approaches available for EHA system, which are the dynamic equation modelling method and the system identification modelling method. Both approaches have disadvantages, where the dynamic equation modelling is hard to apply and some parameters are difficult to obtain, while the system identification method is less accurate when the system’s nature is complicated with wide variety of parameters, nonlinearity and uncertainties. This thesis presents a new modelling procedure of an EHA system by using fuzzy approach. Two sets of input variables are obtained, where the first set of variables are selected based on mathematical modelling of the EHA system. The reduction of input dimension is done by the Principal Component Analysis (PCA) method for the second set of input variables. A new gap statistic with a new within-cluster dispersion calculation is proposed by introducing an adaptive distance norm in distance calculation. The new gap statistic applies Gustafson Kessel (GK) clustering algorithm to obtain the optimal number of cluster of each input. GK clustering algorithm also provides the location and characteristic of every cluster detected. The information of input variables, number of clusters, cluster’s locations and characteristics, and fuzzy rules are used to generate initial Fuzzy Inference System (FIS) with Takagi-Sugeno type. The initial FIS is trained using Adaptive Network Fuzzy Inference System (ANFIS) hybrid training algorithm with an identification data set. The ANFIS EHA model and ANFIS PCA model obtained using proposed modelling procedure, have shown the ability to accurately estimate EHA system’s performance at 99.58% and 99.11% best fitting accuracy compared to conventional linear Autoregressive with External Input (ARX) model at 94.97%. The models validation result on different data sets also suggests high accuracy in ANFIS EHA and ANFIS PCA model compared to ARX model.