Dan Pilbauer

Delayed Resonator With Distributed Delay in Acceleration Feedback—Design and Experimental Verification

The main results of this paper are design, analysis, and experimental verification of a delayed resonator with a distributed-time-delay acceleration feedback. Analogously to the classical delayed resonator, the novel resonator is applied to suppress vibrations of a mechanical system. The theoretical part of this paper includes control parameter design and analysis of their ranges. Next, dynamical properties of the resonator are analyzed including the derivation of a complete stability picture for the combined resonator with the single-degree-of-freedom mechanical system. For the stability analysis, spectral methods are applied including the method of cluster treatment of characteristic roots. Utilizing the distributed delay instead of the lumped delay on the acceleration feedback, both the resonator and the overall system dynamics are converted from neutral to more convenient retarded character. Another positive aspect of the distributed delay is that it acts like a moving average filter on the acceleration measurements. Furthermore, we perform a computational analysis of spectral properties using a numerical root-finding QPmR algorithm. All these stability findings are also verified experimentally on a laboratory setup designed and implemented for this purpose.

Distributed delay input shaper design by optimizing smooth kernel functions

Abstract The aim of this paper is the development of a general class of input shapers with distributed time delay which leads to retarded spectral properties. The design of the shaper is formulated as a multi-objective optimization problem, where response time and robustness, expressed in terms of residual vibrations, are the main objectives. As a part of the optimization formulation, common requirements for input shapers such as non-decreasing step response and unity steady state gain are considered in the design. Moreover, additional optional requirements, such as smoothness of a step response, jerk and even jounce limits can be added to optimization procedure. The resulting problem can be solved using convex optimization techniques. Several illustrative examples are presented in comparison with classical input shaping techniques. Finally, implementation aspects are discussed. The paper is accompanied by an implementation in MATLAB, including a user-friendly interface for the interactive shaper design.

Control design and experimental validation for flexible multi-body systems pre-compensated by inverse shapers

Abstract A complex methodology for control of flexible multi-body systems is proposed with the objective to achieve a favorable distribution of system motion so that the oscillatory mode of the flexible part is not excited. As the key element, the recently proposed concept of a feedback loop with an inverse distributed delay shaper is adopted. Unlike in existing works, the mutual coupling between the primary (controlled) structure and secondary (flexible) structure of oscillatory nature is explicitly taken into account in the controller design. First, an easy to apply method to isolate the flexible mode to be targeted in the shaper design is proposed. Secondly, the interconnection of the system, shaper and the controller is formulated as a set of delay differential algebraic equations. Then the spectral optimization control design technique is applied to achieve fast dynamics of the infinite dimensional system. The viability of the overall methodology is validated by both simulations and experiments in an extensive case study example.