State-Derivative Control for Second-Order Dynamic Systems with Time-Delay
Second-order systems, frequency response, state-derivative feedback, singular systems, regularization.
The work proposes a method for designing controllers by state-derivative feedback of linear systems represented by second order matrix differential equations with time-delay in the control signal. From the frequency domain representation known as the receptance model, an optimization problem is formulated for the calculation of controller gains that limit the frequency peak of the sensitivity function, thus ensuring robust stability in closed loop, even in the face of 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. At the end, the difficulty of implementing such a control proposal with derivative feedback is demonstrated for the case of second-order systems with delay that have a singular mass matrix, proposing a schedule for further studies to enable the regularization of these systems and the collection of future new ones results.