Fractional‐order controllers for irrational systems

Abstract

In this contribution, fractional-order controllers of the type PD and PI are applied to a class of irrational transfer function models that appear in large-scale systems, such as networks of mechanical/electrical elements and distributed parameter systems. More precisely, by considering the fractional-order controller k p + k s in the Laplace domain with −1 ≤ ≤ 1, a stability analysis in the parameter-space (k p , k ,) is presented. Furthermore, as a way to measure the controller robustness, the controller's fragility analysis using the parameter-space (k p , k ,) is derived. Finally, several applications that demonstrate the utility of our results are included.

Information Geometric Theory in the Prediction of Abrupt Changes in System Dynamics

“…We expect that some of the results presented in this work would be useful in different engineering applications [34,35] since linear approximations are often useful [36] for control engineering applications. For instance, one can develop an information-geometric cost function for control design to achieve a guided self-organisation [37,38], instead of using entropy as a cost function [39].…”

Model Reduction and Control Design of a Multi-agent Line Formation of Mobile Robots

“…The results of our algorithm are discussed together with some simulations. Future work includes exploring several novel and well known linear control design techniques (for instance, see [9,10]), the generalisation of the model to a multidimen- sional framework and the improvement of the optimisation method for the controller's design.…”

“…For instance, to find a linear representation of the interactions between agents that also includes the control actions. If every agent is controlled by simple low-order controllers, we may use well known linear system control design techniques (see [8,9]) or new low-order control approaches (see [10,11,12]). On the other hand, there are other approaches that could be explored, for example the use of information metrics for guided self-organisation in the MAS formation [13] or the use of a fokker-planck control approach [14,15].…”

Fastest with No-Overshoot Velocity Control Design of a Two-Differential Robotic Formation

“…Based on the concept of sigma-stability and the theory of D-partitions [4,5,12,13], we can design PI controllers that allows us to obtain the maximum achievable exponential decay in the closed-loop system response.…”