Linearization of rate-dependent nonlinearity with a compensator in feedback configuration

• A new linearization algorithm is proposed for rate-dependent nonlinearities.
• The proposed strategy is so general that the nonlinearity is allowed to be uncertain.
• The linearization technique can be applied to control systems to cover nonlinearities.
• The linear control strategy is sufficient to achieve good control performance.

A rate-dependent nonlinearity presents different dynamics in response to variations of the input signal frequency. Both the Jacobian linearization and feedback linearization strategies cannot give proper performance for systems with these nonlinearities. In this paper, a new linearization algorithm is proposed for rate-dependent nonlinearities where a Fourier series based function approximator in feedback configuration is designed to cover the effect of the nonlinearity such that a desired linearity between the input and output signals can be realized. The proposed strategy is so general that the nonlinearity is allowed to be uncertain. The linearization error is verified by the Lyapunov-like method to be uniformly ultimately bounded. Linearization of a rate-dependent hysteresis with experimental justifications is presented to show the efficacy of the proposed design. Application of the proposed method in a control system is also given with experimental results.