Resonant-Dynamics LTV Feedforward for Flexible Motion Systems

Abstract

Distributed parameter flexible systems face increasingly tighter specifications and performance requirements, which are typically handled by improving and developing novel feedforward control design methods. In the control synthesis of these systems, taking into account flexible dynamics play an increasingly important role. This work proposes an LTV feedforward control scheme which is based on the feasible and stable inversion of a minimum-phase fourth-order LTV approximation of the plant. This approximation takes into account resonant dynamics and (as a result) provides improved phase tracking. The results are validated through measurement results obtained through a rotational two-mass-spring-damper system.

Linear-time-varying feedforward control for position-dependent flexible structures

“…From the state-space model, it can be observed that all the matrices are time-dependent, hence resulting in the LTV feedforward controller. Note that the time-varying compliance function C(t), and its derivativesĊ,C are included in the parameter values, see (11)- (13). Furthermore, the second time-derivative of y d is often known a priori, and as such available for calculation of the feedforward control signal u f f (t).…”

“…The feedforward controller should avoid any division by zero, i.e., 1 + ω 2 s mC(t) = 0, see (11), (12) and (13). The resonance frequency ω s ensures the feasibility of the feedforward controller under the following conditions:…”

“…Similar to [11], it mostly accounts for the compliant part of the positiondependent structure, since it only considers a low frequency approximation of the plant. In a more recent extension [13], LTV feedforward control addresses one resonance of the flexible structure as well as the low frequency contribution of the NRB modes as a whole. It has been shown that the performance of this system is much improved.…”

“…The method is validated for a rotational two-mass-spring-damper system. Following the previous works, specially [12], [13], the main contribution of this work is to design a feedforward controller for an LTV system in which the stable plant inversion is based on an LTV fourth-order model. The model considers the quasi-static deformation of the plant besides the dominant resonant dynamics of the system.…”

“…The feedforward controller improves the accuracy in tracking the desired output. Furthermore, the model is validated for the damped Euler-Bernoulli beam, which is different from [13]. The outline of this work is as follows, in section II the mathematical representation of the time-varying flexible motion system is introduced.…”