Keywords: differential evolution, particle swarm optimization, genetic algorithms, active control of structures, fuzzy control, smart structures.

Smart structures include elements of active, passive or hybrid control. For complicated structures, mainly the ones including nonlinearities, or nonlinear control laws, the theoretical results from the area of control are not very helpful. Global optimization techniques can help in this case. In this paper, fuzzy control is considered, which is a suitable tool for the systematic development of active control strategies, and the differential evolution (DE) algorithm is proposed and used for the calculation of the continuous and discrete free parameters in the fuzzy control system. Numerical applications for smart piezoelastic beams are presented. The results obtained are compared with the ones obtained with the fuzzy controller optimized using particle swarm optimization (PSO) and with the fuzzy controller optimized by a genetic algorithm (GA).

More precisely, a smart structure with bonded sensors and actuators as well as an associated control system, which enables the structure to respond to external excitations in such a way that it suppresses undesired effects, is considered. In order to reduce the displacement field of the cantilever beam system, a non-linear fuzzy controller was constructed. The system receives as inputs the displacement and the velocity, while giving as output the increment of the control force. Some parameters of the fuzzy control system were optimized using differential evolution. More precisely, the parameters (the break points) of the triangular and trapezoidal membership functions, the weights of the rules, and the logical operator are considered as variables.

The beam has been discretized with four finite elements resulting in a model with eight degrees of freedom. A dynamic loading is used as disturbance that simulates a strong wind and is a periodic sinusoidal loading pressure that influences the displacement of the fourth (free end) finite elements. The purpose of the fuzzy controller is to reduce the oscillation.

The fuzzy controllers optimized using DE, PSO and GA give superior control results compared to the classical fuzzy controller (without any optimization procedure). Also, the fuzzy controller optimized using DE gives better control results than the fuzzy controller optimized using PSO and the fuzzy controller optimized using a GA, because the displacements, the rotations, the displacement velocities and the rotation velocities obtained from the fuzzy controller optimized using DE have smaller values compared with the ones of the fuzzy controller optimized using PSO and of the fuzzy controller optimized using GAs.

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