Real-Time Algebraic Derivative Estimations Using a Novel Low-Cost Architecture Based on Reconfigurable Logic

Abstract

Time derivative estimation of signals plays a very important role in several fields, such as signal processing and control engineering, just to name a few of them. For that purpose, a non-asymptotic algebraic procedure for the approximate estimation of the system states is used in this work. The method is based on results from differential algebra and furnishes some general formulae for the time derivatives of a measurable signal in which two algebraic derivative estimators run simultaneously, but in an overlapping fashion. The algebraic derivative algorithm presented in this paper is computed online and in real-time, offering high robustness properties with regard to corrupting noises, versatility and ease of implementation. Besides, in this work, we introduce a novel architecture to accelerate this algebraic derivative estimator using reconfigurable logic. The core of the algorithm is implemented in an FPGA, improving the speed of the system and achieving real-time performance. Finally, this work proposes a low-cost platform for the integration of hardware in the loop in MATLAB.

Linear active disturbance rejection control of the hovercraft vessel model

“…In this case, several algorithms based on the GPI philosophy have been carried out in electronic applications such as the control of Buck converters (Zurita-Bustamante et al, 2011) or the control of single-phase multilevel cascade inverters (Juárez-Abad et al, 2014). Taking into consideration the slow dynamics of the hovercraft vessel model in comparison with the electronic applications described above, the synthesization of the robust controller designed on a field programmable gate array (FPGA) (Juárez-Abad et al, 2014;Morales et al, 2014aMorales et al, , 2013Zurita-Bustamante et al, 2011) or low-cost architectures based on reconfigurable logic (Morales et al, 2014b) does not present any problem regarding computation time requirements.…”

Online signal filtering based on the algebraic method and its experimental validation

“…1 shows the settings of each of the two time lines when T ¼ T r . It is necessary to denote the first, second and third time derivative estimations of the signal y(t) as _ y e ðtÞ, € y e ðtÞ and y € y e ðtÞ ¼ € y dirty ðtÞ for 0 r t rϵ € y 2e ðtÞ for ð0 r t mod T r oT r =2Þ AND ðt 4ϵÞ € y 1e ðtÞ for ðT r =2 r t mod T r oT r Þ AND ðt 4 ϵÞ: The overlapping derivative estimator technique can be performed in a low cost architecture based on reconfigurable logic [28], in which the core of the algorithm can be implemented in a Field Programmable Gate Array (FPGA), improving the speed of the system and achieving real-time performance.…”

Novel algebraic meal disturbance estimation based adaptive robust control design for blood glucose regulation in type 1 diabetes patients

“…It should be noted that the estimator in [43] is used for parameters which are independent of time, whereas this paper is estimating meal disturbance being a continuous function of time. In order to implement the disturbance estimator given in (50), the first derivative of the state is obtained using algebraic derivative estimator proposed in [46]. The derivative estimator proposed in [46] is robust to measurable noise.…”

“…In order to implement the disturbance estimator given in (50), the first derivative of the state is obtained using algebraic derivative estimator proposed in [46]. The derivative estimator proposed in [46] is robust to measurable noise. The following assumptions are also needed.…”