Nonlinearity estimation and compensation by linear observers: theory and applications

Systems are often influenced by troublesome nonlinear effects such as Coulomb friction, hysteresis or backlash. In this contribution an indirect measuring technique of the actual values of these nonlinearities is presented. Based on a fictitious model of the time behavior of the nonlinearities a linear state observer of an extended dynamical system is designed resulting in estimates of the nonlinear effects. In case of control design the disturbance rejection control method is applied to counteract the nonlinearities by the estimated signals. Some sufficient criteria for the asymtotic stability of the estimation error are given. Additionally some applications are shown in the fields of highly accurate position control of robots and of fault detection of cracks in turbo rotors.