A variable-order adaptive controller for a manipulator with a sliding flexible link

A digital adaptive controller is presented for a manipulator with two links, the second of which is a flexible beam that slides out of the first link (i.e., there is a prismatic joint). The simulation model of the manipulator is nonlinear with time-varying coefficients, but the adaptive controller is based on a linear autoregressive moving-average (ARMA) model of the input/output characteristics of the plant. Both the parameters and the order of this ARMA model vary adaptively. Because the control law is based explicitly on the ARMA model, the adaptive control algorithm is indirect. The most important feature of the adaptive controller is that its order can vary adaptively. This capability results from using a lattice filter for adaptive parameter estimation. The superiority of the variable-order adaptive controller to a fixed-order adaptive controller is demonstrated by numerical simulations in which the manipulator is represented by the nonlinear equations of motion for a finite-element model of the manipulator