Control Design for Second-Order Systems with Time-Delay via Frequency Response Methods
Second Order Systems, Frequency Response, Receptance Matrix, Genetic Algorithm.
Solving control problems for delayed second order systems is one of the engineering challenges. Phenomena such as mechanical vibrations, resonance and others can be described mathematically by this type of system. This work has as main objective to propose a solution to a problem of design of a state feedback controller for second order systems with time-delay using frequency response approach. Differently from many approaches available in the literature, ou rapproach does not require either the use of approximations for the delay, or a posteriori analysis of the solution. By mathematically defining the control problem as an optimization problem, a search for controller gains is carried out using a genetic algorithm, with the goal of ensuring that the Nyquist curve of the system remains at a safe distance from the instability region . The computed control gains then result in a robust closed-loop system, in the sense that it remains stable in spite of small changes un the system parameters.
The simulation results obtained at the end of the work proved satisfactory within the desired specifications.