Robust output feedback control of non-collocated low-damped oscillating load

For systems with order of dynamics higher than two and oscillating loads with low damping, a non-collocation of the sensing and control can deteriorate robustness of the feedback and, in worst case, even bring it to instability. Furthermore, for a contactless sensing of the oscillating mechanical load, like in the system under investigation, the control structure is often restricted to the single proportional feedback only. This paper proposes a novel robust feedback control scheme for a low-damped fourth-order system using solely the measured load displacement. For reference tracking, the loop shaping design relies on a band reject filter, while the plant uncertainties are used as robustness measure for determining the feedback gain. Since prime uncertainties are due to the stiffness of elastic link, correspondingly connecting spring, and due to the gain of actuator transducer, the loop sensitivity function with additive plant variation is used for robustness measure. In order to deal with unknown disturbances, which are inherently exciting the load oscillations independently of the loop shaping performance, an output delay-based compensator is proposed as a second control-degree-of-freedom. That one requires an estimate of the load oscillation frequency only and does not affect the shaped open-loop behavior, correspondingly sensitivity function. An extensive numerical setup of the modeled system, a two-mass oscillator with contactless sensing of the load under gravity and low damping of the connecting spring, is used for the control evaluation and assessment of its robustness.