Generalized homogenization of linear controllers: Theory and experiment

Abstract

A procedure for an "upgrade" of a linear PID controller to a non-linear homogeneous one is developed and verified by real experiments with quadrotor. The controller design is based on a generalized homogeneity (dilation symmetry) of the system. Its parameters are obtained from the gains of linear controller. The issues of digital implementation of the proposed controller are discussed. Finally, the stability and robustness properties of the homogeneous PID controller are validated on the quadrotor QDrone platform of Quanser T M .

Generalized homogenization of linear observers: Theory and experiment

“…Since the movement of is coupled with other direction movements in practice, when , and z converge faster with a higher precision, the precision of has been improved as well which coincides with the result in Table 1. Please notice that, compared with the result of Reference 5, Table 1 demonstrates an additional improvement by using the homogeneous observer with homogeneous controller.…”

“…For QDrone platform, Quanser realized four independent PID controllers for the regulation of , and , respectively. Recently, we presented an efficient homogeneous PID controller, 5 by upgrading the Quanser's PID controller, which shows a substantial improvement of the control performance. However, two important problems need to be solved before applying those mentioned control methods Unavailable information : OptiTrack and IMU cannot provide the velocity information , which is necessary for the control method mentioned above.…”

“…In this part, two experimental results will be presented. The first one is using Quanser's filters and homogeneous controller proposed in Reference 5. The second one is based on the homogeneous observer (37) and the same homogeneous controller.…”

“…Recently, the homogeneous controller has been implemented to guarantee the finite‐time convergence by upgrading a linear controller, which means the gains of homogeneous controller were calculated via the gains of this linear controller 5 . As a dual result, this article aims at extending the same idea to upgrade the linear observer to a homogeneous (nonlinear) one.…”

“…In order to further improve the estimation precision, the homogeneity as a certain relaxation of linearity could provide additional tools for it. In our previous paper, 5 the methodology of “upgrading” linear controllers to homogeneous (nonlinear) ones has already been developed, and it has been validated via Quanser's quadrotor platform (see the video https://youtu.be/wnSi6jj1TwE) where the set point tracking precision has been improved about and the homogeneous controller has shown its better robustness than linear controller. However the observer used in Reference 5 is still linear one, and we did not prove the global convergence since the separate principle is not valid.…”