Design of optimal controller for structures using differential evolution algorithm

One of the most important goals of optimal control of structures is the achieving the desired reduction in responses using minimal control forces. In many research efforts that have been studied over the past few decades in the field of active control, several control algorithms have been proposed that most of them calculates the required control forces by optimizing a second-order performance index. There are simplifying assumptions in formulation of these classic algorithms and constraints in mathematical optimization techniques that have been used in optimizing the performance index, for example, because of unknown nature of earthquakes, the LQR classic controller don’t consider the external forces such as earthquake excitation in calculation of control signal. This may make difficult to finding the optimal solution in optimization process and obtained relatively optimal solutions for optimization problem. Metaheuristic optimization methods, such as differential evolution are modern algorithms and because of their special capabilities in finding global optima are powerful tools that can be used in solving of complex problems. But despite the many advantages, these methods has not been used extensively for solving civil engineering problems especially in field of active control of structures. In this paper we considered the active control of structures as an optimization problem and proposed a controller that used the differential evolution metaheuristic algorithm for finding gain matrix elements of active control problem. The gain matrix elements were globally searched by differential evolution algorithm to minimizing the LQR performance index. Because of the proposed method is repetitive and does not need to solve the Ricatti differential equation; it is possible to consider the effect of external excitation in finding the gain matrix and calculation of control signal. The controller was applied on sample 2DOF and 10DOF structures and responses of these structures under the excitation of several historical earthquake records were obtained by MATLAB programming. In addition to the performance index, the maximum control force and maximum control displacement, 9 benchmark indexes that measured in controlled structures are calculated in this study. These indexes represented the reduction of controlled maximum and average responses of structure in comparison with uncontrolled responses. In order to evaluate the effectiveness of the proposed controller, these 9 performance index for 2DOF and 10DOF examples against 7 historical earthquakes for proposed and LQR controller was calculated and compared. The simulation results indicate that the proposed method is effective in keeping the controlled responses of structures in desired range and reducing the vibrations of structures with lower need to control energy in comparison with LQR algorithm. Because of great capabilities of DE algorithm in searching large spaces and the iterative nature of controller unlike the LQR method, this controller consider the effects of external forces in control process. Numerical simulation showed that the performance of the presented control algorithm is better than the LQR controller approach in finding of optimal displacements and control forces. Therefore, metaheuristic algorithms such as differential evolution can be used in active control of structures to achieving more efficient results in comparison with classic controllers.