Estimation of dynamical-varying parameters by the internal model principle

A novel design method of recursive algorithms for identification of linear deterministic SISO stable discrete systems with dynamical-varying parameters is presented. An algorithm for parameter identification of such systems, based on the known internal model principle and on the recursive least squares parameter estimation, is proposed. The system parameters are assumed to satisfy a linear difference equation with constant coefficients. A persistent excitation condition of the measurement vector automatically guarantees exponential stability and therefore there is no need to use any resetting procedures. This condition is similar in form to the observability gramian property of a linear time-varying system. Simulation and practical application of the algorithm on an experimental robot system show good tracking even when the parameters vary drastically and in an abrupt manner.<>