Design of a command shaper for vibration control of flexible systems: A genetic algorithm optimisation approach

This paper presents investigations into the design of a command-shaping technique for vibration control of flexible structure systems using genetic algorithms (GAs). Designing a command shaper requires a priori knowledge about the damping ratio and natural frequency of the system, which may not be available for complex flexible systems. Moreover, the amount of vibration reduction and response rise-time are usually in conflict with one another in most flexible systems due to their construction and modes of operation. Conventional methods can hardly provide a solution satisfying several objectives as demanded by a practical application due to the competing nature of these objectives. Assuming that the system parameters are unknown, GAs are used to determine the optimum amplitudes and corresponding time-locations of impulses that are convolved with the reference input to form the shaped command. A new objective function based on weighted sum approach is proposed that provides good solution within single-objective GA formulation and trades-off between these two objectives. In order to maintain and enhance diversity in the population and hence to improve search capability of the conventional GA, a new algorithm is also proposed in this work. Initially this algorithm works as a traditional GA then some individuals are replaced periodically based on shared fitness values in order to maintain diversity in the population set. A scaled and simplified version of practical helicopter is used as the experimental flexible set-up. The effectiveness of the control strategy is assessed in terms of controller performance on the test rig in vibration suppression, mainly, at dominant modes.