Tracking control of nonlinear systems actuated by saturated oscillatory force generator

Abstract

This research has been devoted to the construction of a permanent-stable algorithm for tracking control of a nonlinear 1-degree of freedom (DOF) mechanical system affected by a second-order vibratory constrained actuator. The dynamics of the actuator is involved in governing equation of the mechanical system, and using the two-step Adams-Bashforth and Adams-Moulton methods, the resultant continuous-time model is formulated in the discrete-time domain. The discrete-time model of the whole system is then employed in a discrete-time power reaching law-based controller architecture. Using the reaching law strategy and considering the saturation boundaries of the actuation system, various available bounds of position and velocity control signals can be determined with respect to the reaching law coefficients. Then, special optimization algorithms are employed to determine the optimal value of position and velocity power reaching law coefficients as well as the optimally modified trajectory references. The position and velocity control commands resulting from the concept of optimal trajectory reference, along with the optimal reaching law coefficient, ensure the permanent-stable tracking control of both position and velocity modes regarding the actuation constraint. In the next step, another concept, namely the optimal combined position-velocity controller, is taken into account, which is a Gaussian-weighted average of the position and velocity control commands to form the main control command of the proposed controller. Consequently, the designed controller will be a permanent-stable control approach that never violates the actuation constraint. Finally, numerical simulations are conducted to evaluate the performance of the proposed method for two types of desired inputs, including piecewise-step and harmonic trajectories. The results suggest the proposed controller efficiency in satisfying pre-determined characteristics.