A STOCHASTIC OPTIMAL SEMI-ACTIVE CONTROL STRATEGY FOR ER/MR DAMPERS

• Published in: Journal of sound and vibration Vol. 259; no. 1; pp. 45 - 62
• Main Authors: YING, Z.G., ZHU, W.Q., SOONG, T.T.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 2003; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Machine components; Mechanical engineering. Machine design; Physics; Solid mechanics; Springs and dampers; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Averaging method; Itô equation; LQG control; Passive system; Modeling; Magnetorheological fluid; Stochastic integral; Stochastic programming; Non linear oscillator; Active system; Optimal control; Electrorheological fluid; Hamiltonian system; Vibration control; Dynamic programming; Hydraulic damper; Random vibration
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.2002.5136

A stochastic optimal semi-active control strategy for randomly excited systems using electrorheological/magnetorheological (ER/MR) dampers is proposed. A system excited by random loading and controlled by using ER/MR dampers is modelled as a controlled, stochastically excited and dissipated Hamiltonian system with n degrees of freedom. The control forces produced by ER/MR dampers are split into a passive part and an active part. The passive control force is further split into a conservative part and a dissipative part, which are combined with the conservative force and dissipative force of the uncontrolled system, respectively, to form a new Hamiltonian and an overall passive dissipative force. The stochastic averaging method for quasi-Hamiltonian systems is applied to the modified system to obtain partially completed averaged Itô stochastic differential equations. Then, the stochastic dynamical programming principle is applied to the partially averaged Itô equations to establish a dynamical programming equation. The optimal control law is obtained from minimizing the dynamical programming equation subject to the constraints of ER/MR damping forces, and the fully completed averaged Itô equations are obtained from the partially completed averaged Itô equations by replacing the control forces with the optimal control forces and by averaging the terms involving the control forces. Finally, the response of semi-actively controlled system is obtained from solving the final dynamical programming equation and the Fokker–Planck–Kolmogorov equation associated with the fully completed averaged Itô equations of the system. Two examples are given to illustrate the application and effectiveness of the proposed stochastic optimal semi-active control strategy.