Stable Tuning of Extended State Observers using PSO and Penalty Functions

This work studies the gain tuning of an Extended State Observer (ESO) by means of Particle Swarm Optimization (PSO). The performance index used in the PSO includes penalty functions, which allow ensuring a stable ESO characteristic polynomial by penalizing PSO solutions associated to gains producing observer poles with positive real parts. Thus, observer poles with negative real parts do not significantly increase the performance index whereas poles with positive real parts produce a large grow of the index. This feature precludes using explicit bounds on the observer gains to build a constraint set, which must be used during the PSO execution. A disadvantage of this latter approach is the possibility that the constraint set may no contain the optimal solution. The proposed approach is compared to a PSO tuning based on a constraint set, and numerical simulations show that the PSO based on penalty functions provides smaller observation errors.