Nonlinear optimal-based vibration control for systems with MR tuned vibration absorbers

Abstract

In this paper, the author proposes several approaches to nonlinear optimal-based control implementation. The vibrating system (structure) equipped with two tuned vibration absorbers (TVAs) is analysed against a system with one TVA. For control purposes, MR dampers are used instead of TVAs' passive viscous dampers. The main contribution of this research is the development and numerical verification of three nonlinear optimal-based vibration control concepts (the implementation of one-step optimal control, quasi-optimal control, and the optimal-based modified ground-hook law) that produce MR damper required current (not required force) as their output (thus force tracking algorithm that results in control inaccuracy is entirely omitted here), and that may be directly applicable for online and real-time control; moreover, all of the MR damper force constraints (no active forces; lower and upper limits; nonlinear, hysteresis-type dynamics) are embedded in the control technique, thus the solution is optimal for the assumed actuator respecting its limitations. The proposed approaches are investigated against the standard ground-hook law and passive TVA(s) with optimally tuned (i.e. having a frequency response maxima of equal and lowest values) parameters. The performance of all the solutions for the one- and two-TVA systems is compared, confirming the validity and efficiency of the three proposed concepts: almost 50% reduction of the Dynamic Amplification Factor is possible with regard to the respective optimally tuned passive 1 TVA and 2 TVA configurations. No offline calculation, excitations/disturbances assumption, or frequency determination is necessary.

Real-time implementation of nonlinear optimal-based vibration control for a wind turbine model

“…2.0 are more than adequate for the assumed 7.69% TVA mass ratio, proving the effectiveness and validity of the control approach. 30 Neither MR damper force tracking nor oscillation frequency determination is necessary online; thus, control quality is not compromised by MR damper force constraints, while real-time control during transient, polyperiodic or random vibration phases is unimpeded; also neither offline calculation nor disturbances assumption is necessary, all essential for continual real-time control.…”

“…Recently, a numerical implementation of one-step nonlinear optimal control for systems with MR TVAs was realised with MATLAB/Simulink dedicated level-2 s-function and bvp4c algorithm; 30 it was also shown that iteration procedures implicating large computational loads may be omitted, utilising very short time range basis optimal problem tasks with a high-frequency resetting function and zero initial conditions for all co-state integrators. In such a case, it was demonstrated that the influence of the transversality condition (10) error was negligible for the regarded MR TVA(s) control application.…”

“…A modified two-level displacement ground-hook law ( Mod.GND ) – the simple implementation of the optimal control for the case when primary system/structure displacement amplitude minimisation is the sole objective 5,6,30 – was additionally tested during the present experimental study. This control law switches the control current between 0 and imax with regard to x1 and Fmr signs.…”

“…Recently, an entirely different concept was proposed 30 – all of the MR damper force constraints are assumed to be an intrinsic part of a control method. This requires the utilisation of nonlinear control techniques, which include maximum principle-based methods, 4,13,31 control Lyapunov function-based methods 8 including backstepping, 10,32 (feedback) linearization methods / linear optimal control theory based on the Riccati equation solution, 10,33 etc.…”

“…The concept which real-time implementation is presented in the paper was originally developed for the vibration attenuation of systems/structures equipped with MR TVAs, 30 from among which, a wind turbine tower-nacelle system is investigated currently in particular, using its scaled model. 34–37 Wind turbines undergo external loads that vary in time, including wind load variations, wind shear, Karman vortices, the blade passing effect, differences in inflow conditions for each of the blades, sea waves and/or ice load, etc., as well as rotating elements’ unbalance, all of them contributing to the structural vibration and fatigue wear of towers and blades.…”