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.
In this work we propose a method to design state-derivative feedback controllers for linear systems represented by second-order differential matrix equations with time-delay in the control signal. Based on the representation in the frequency domain known as the receptance model, an optimization problem is formulated for the computation of controller gains that limit the peak of a sensitivity function, thereby ensuring robust closed-loop stability, in spite of the delay. Genetic Algorithm is used to solve the optimization problem and numerical experiments illustrate the effectiveness of the proposed method, including comparison with state feedback controllers. Resumo: Neste trabalho é proposto um método para o projeto de controladores por realimentação derivativa de estado de sistemas lineares representados por equações diferenciais matriciais de segunda ordem com atraso no sinal de controle. A partir da representação no domínio da frequência conhecida como modelo por receptância, é formulado um problema de otimização para o cálculo de ganhos do controlador que limitem o pico em frequência de uma função de sensibilidade, garantindo assim estabilidade robusta em malha fechada, mesmo diante do atraso. Algoritmo Genético é usado na resolução do problema de otimização e experimentos numéricos ilustram a eficácia do método proposto, incluindo comparação com controladores por realimentação de estado.
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