Abstract
This paper proposes a method for active vibration control to a two-link flexible robot arm in the presence of time delay, by means of robust pole placement. The issue is of practical and theoretical interest as time delay in vibration control can cause instability if not properly taken into account in the controller design. The controller design is performed through the receptance method to exactly assign a pair of pole and to achieve a given stability margin for ensuring robustness to uncertainty. The desired stability margin is achieved by solving an optimization problem based on the Nyquist stability criterion. The method is applied on a laboratory testbed that mimic a typical flexible robotic system employed for pick-and-place applications. The linearization assumption about an equilibrium configuration leads to the identification of the local receptances, holding for infinitesimal displacements about it, and hence applying the proposed control design technique. Nonlinear terms, due to the finite displacements, uncertainty, disturbances, and the coarse encoder quantization, are effectively handled by embedding the robustness requirement into the design. The experimental results, and the consistence with the numerical expectations, demonstrate the method effectiveness and ease of application.
Highlights
The presence of time delay in controlled systems degrades the closed-loop performance if it is not taken into account in the controller design, and in the worst case, might lead to instability
A technique attracting an ever-growing interest for active vibration control of vibrating linear systems with time delay is pole placement, borrowed by the traditional approaches for systems without time delay [14,15]
This paper provides the experimental application of the method proposed by Araujo, Dantas, and Dorea for pole placement in flexible linear systems with time delay
Summary
The presence of time delay in controlled systems degrades the closed-loop performance if it is not taken into account in the controller design, and in the worst case, might lead to instability. Matrix Inequalities (LMI) and ensures the placement of the dominant poles of interest while imposing stability of the remaining unassigned poles, either those due to the mechanical resonances and those induced by the time delay This method uses both the measured receptances to assign the dominant poles, and the system matrices, that are required by the LMIs. Inspired by the controller parametrization proposed in the paper of Belotti and Richiedei, a method that only exploits the measured receptances has been proposed by Araujo, Dantas, and Dorea in [22]. The arm flexibility is due to the passive joint torsional spring, that is an approach commonly used to represent flexibility of robots through a lumped model (see, e.g., the milestone paper in [23]) Time delays in this kind of system usually arise due to the instrumentation employed for real-time control. The proposed method is implemented by means of local linearization of the nonlinear dynamic model of the flexible robot and nonlinearities, as well as other uncertainty sources, are handled by imposing adequate robustness in the controller design
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