DCT basis function learning control

In this paper, a basis function learning control is developed in away parallel to time domain learning control. Basis function approach aims to reduce the dimension and computation of learning gain matrices while maintaining minimal loss of tracking precision. Here, we transplant two learning gain matrices, the transpose and the partial isometry, from time domain learning control into basis function learning control. These two learning gain matrices have no ill-conditioned problems in matrix computation and ensure a monotonic decay of tracking error. The basis vector of discrete cosine transform (DCT) is chosen as basis function for its high energy compression ratio and energy preservation feature. Experiments on two joints of a SCARA type robot verify the effectiveness of the proposed approaches. A few DCT coefficients may meet learning control specification and tracking precision can be improved by increasing the number of the DCT coefficients.