Backlash compensation with filtered prediction in discrete time nonlinear systems by dynamic inversion using neural networks

A discrete time adaptive neural network compensator for compensating backlash of a mechanical system, comprising:

• a filter in a feedforward path;
• a neural network in the feedforward path, the neural network configured to compensate the backlash by estimating an inverse of the backlash and applying the inverse to an input of the mechanical system;
• and
• means for tuning the neural network in discrete time without a certainty equivalence assumption.

A method for compensating backlash in a mechanical system, comprising:

• estimating an inverse of the backlash using a discrete-time neural network in a feedforward path;
• weighting a tracking error r(k), a backlash estimation error {tilde over (τ)}(k), and a weight estimation error {tilde over (W)}(k) of the neural network in the same Lyapunov function;
• and
• applying the inverse to an input of the mechanical system to compensate the backlash.

A discrete-time method of adaptively compensating backlash in a mechanical system, comprising:

• estimating an inverse of the backlash using a neural network in a feedforward path;
• adjusting weights of the neural network using an algorithm to achieve closed loop stability without a certainty equivalence assumption;
• and
• applying the inverse to an input of the mechanical system to compensate the backlash.