Keywords: particle swarm optimization, active control of structures, fuzzy control, smart structures.

Smart structures include elements of active, passive or hybrid control. In the case of linear structures with linear control laws, many classical methods for the design of the control system exist. For more complicated structures or nonlinear control laws, mainly the ones including nonlinearities, the theoretical results from the area of control are not very helpful. Global optimization techniques can help in this case. The method of particle swarm optimization is a method of global optimization which has been used in a variety of structural optimization problems. We propose and test the usage of particle swarm optimization for the calculation of the free parameters in active control systems. We consider especially the fuzzy control, which is a suitable tool for the systematic development of active control strategies. In particular, fuzzy control can be fine tuned if no experience exists or if one designs more complicated control schemes (e.g. non-collocated control rules).

We propose the use of particle swarm optimization (PSO) for the optimal design of the controller. PSO uses the physical movements of the individuals in the swarm and has a flexible and well-balanced mechanism to enhance and adapt to provide the global and local exploration abilities. Most applications of PSO have concentrated on the optimization in continuous space while recently, some work has been done on discrete optimization problem. The wide use of PSO, mainly during recent years, is due to the number of advantages that this method has compared to other optimization methods. Some of the key advantages are that this optimization method does not need the calculation of derivatives, that the knowledge of good solutions is retained by all particles and that particles in the swarm share information between them. PSO is less sensitive to the nature of the objective function, can be used for stochastic objective functions and can easily escape from local minima. Concerning its implementation, PSO can easily be programmed, has few parameters to regulate and the assessment of the optimum is independent of the initial solution.

The parameters of the fuzzy control system that are optimized by PSO are the parameters (the break points) of the triangular and trapezodial membership functions, the weights of the rules, and the logical operator. In each particle, the first values correspond to the parameters of the membership functions and can take continuous values, the next values correspond to the weights of the rules and can take continuous values in the range [0,1] while the last values correspond to the AND/OR - type logical operator and can take discrete values equal to 1 for AND and 2 for OR. It should be noted that in previously published PSO implementations one can find only continuous or discrete values. In our case, there is a combination of both continuous and discrete variables in each particle and in order to solve the problem we used a combination of the equations used for finding the new position of the particle for continuous and discrete problems.

Numerical applications on vibration suppression of smart piezoelastic beams are presented in order to demonstrate the proposed technique. The results obtained revealed the high performance of the proposed method. More precisely, the fuzzy controller optimized by PSO gave almost zero displacements and rotations while the displacement and rotation velocities of the fuzzy controller optimized by PSO are significantly smaller than the ones obtained by the classic fuzzy controller.

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