Optimal Tuning of High-Order Super-Twisting Differentiators

The performances of Super-Twisting Differentiators (STD) may worsen depending on the noise affecting their input signal. Indeed, STDs tend to amplify such noise, thus deteriorating the performances of feedback control systems. This work proposes an optimal tuning method for STDs, which minimizes possible negative effects caused by noise. A Nelder-Mead optimization algorithm is used to this purpose. A comparative analysis is proposed between the performances that can be achieved with STDs of different orders, so as to look for the best solution in terms of noise reduction. The approach has been tested in simulation and with an actual mechatronic system. The paper will show that, despite STDs are not based on the model of the controlled system, the derivatives they provide have almost the same characteristics of the ones returned by Kalman Filters, which are conversely model based estimators.

I. Introduction

In many control applications signals derivatives are required for the closure of feedback loops. When such derivatives can not be directly acquired through sensors, they are estimated by means of differentiators. In industrial ap-plications, the most widely used differentiators are based on backward difference approaches. The resulting signals are typically noisy, thus they are subsequently low-pass filtered. More advanced numerical differentiators are the ones proposed in [1] or [2]. The main advantages of such differentiators are represented by their low computational burden and easy implementation. Conversely, their main drawback is given by the undesired phase-lag affecting the estimates, which may worsen the performances of feedback control systems.