ROBUST-OPTIMAL STABILIZATION OF NONLINEAR DYNAMIC SYSTEMS

Abstract

Context. Increasing quality requirements for a transient control (stabilization) of various types (mechanical, electrodynamic) of dynamic
systems require usage of engineering methods of optimal design, which allow solving practical problems of multidimensional nonlinear object
control under the influence of disturbances taking into account physical feasibility of control actions.
Objective. Improvement of the robust-optimal stabilization of nonlinear dynamic systems.
Method. Design of the proposed robust-optimal systems with variable structure is based on the preliminary formation of optimal trajectories
for direct optimality conditions, determination of switching moments, synthesis of control functions which provide movement along preliminary
trajectories and robust correction based on incomplete information of the physical system. The mechanism for optimal trajectories formation
contains calculation of the required amount of sections for zero values of the corresponding derivatives of control coordinates, and applicable for
the general case of multidimensional nonlinear nonstationary dynamic systems. Control switching moments in the feedback loop of the controlled
object are calculated based on the solution of algebraic system of equation and, for dynamic systems of the sixth order, include usage of
leading, sub-leading and driven control coordinates. The stabilization process of the dynamic system on the corresponding predefined segments
of the trajectories is provided by control actions which are calculated on the basis of the balance regimes for the forces and moments (and their
required derivatives) that are applied to the control object. The robustness of the dynamic system to the incomplete certainty of the control object
and to the influence of uncontrolled external and parametric perturbations is achieved by usage of corrective control based on the mismatch of the
current and optimal stabilization trajectory. The robust control tries to meet the requirement for control errors’ and its derivatives minimization.
Results. Examples of the circuit implementation of robust-optimal systems with variable structure and simulation results for the tasks of
maximum speed during a marine vessel maneuvering and minimal energy costs during quadcopter flight control are given.
Conclusions. Shown results demonstrate correctness of the general design principles for various types of objects and control efficiency
under influence of disturbances.