Nussbaum-Based Fixed-Time Tracking Control for Uncertain Nonlinear Systems Driven by Piezoelectric Actuators

The piezoelectric actuator will exhibit the problem of unknown control direction under high-speed operating conditions. Hence, the realization of high-speed control for nonlinear systems driven by piezoelectric actuators requires the fixed-time stability to enhance the convergence rate and the Nussbaum technique to handle the problem of unknown control directions. However, these two techniques are incompatible because the required conditional inequalities for each are different. To resolve this incompatibility, we have incorporated the projection operator into the design of the adaptive updating law. On the basis of ensuring that the adaptive estimation parameter is bounded, we have established the conditional inequality for Nussbaum technique. Then, some nonlinear damping terms are incorporated into the stability analysis to counteract a term containing Nussbaum function, thereby reducing the difficulty of the fixed-time stability analysis. Furthermore, the predefined tracking accuracy and fixed-time stability are theoretically proven through the stability analysis. Finally, the efficiency of the proposed control method is validated through semi-physical experiments on a cylindrical piezoelectric actuator.