Abstract Summary
The contribution presents recent progress in development of predictive control methods for optimal mitigation of impact excitations. The attention is focused on a control of semi-active system subjected to an impact of a rigid object moving with initial velocity. Objective of the solved control problem is dissipation of the entire impact energy with minimal value of generated force and minimal corresponding value of impacting object’s deceleration. Challenges in problem solution result from unknown parameters of the impact as well as occurrence of unknown process disturbances and uncertainties. The proposed novel solution method effectively utilizes the paradigm of model predictive control combined with techniques of system parameters identification. As a result, adaptive system operation ensuring efficient impact mitigation is provided. As an illustrative example, we discuss control of the semi-active fluid-based damper equipped with fast-operating piezoelectric valve. The system is subjected to an impact of a rigid object of unknown mass moving with initial unknown velocity and unknown external force. The considered disturbances include unknown friction forces and leakages of the fluid through the valve. The corresponding control problem is formulated as state-dependent kinematic path-tracking aimed at minimization of the difference between actual and currently optimal value of object’s deceleration. The main unknown of this problem is time-dependent voltage signal which controls operation of the valve and resulting fluid flow. The proposed solution approach is based on repetitive solution of the control problems defined at subsequent time intervals of arbitrary lengths. Solution of each control problem is preceded by identification of the actual values of friction force and fluid leakage which are required for prediction of object deceleration as well as computation of the currently optimal deceleration value using the condition of kinematic optimality of the process. The proposed solution methods utilize specific parametrisations of the control function with a special focus on those providing analytical solution of equations governing system dynamics. The entirely novel aspects covered by the contribution include: i) application of the realistic model of piezoelectric valve and investigation of the influence of its operating time on impact mitigation process, ii) comparison of the effectiveness of semi-active and active control systems with and without leakage identification, iii) investigation of the influence of control cost on the applied control strategy.
