The classical relay feedback method for tuning proportional-integral-derivative (PID) controllers cannot be applied to plants whose Nyquist diagrams do not cross the negative real axis; these are customarily tuned based on the reaction curve experiment. In this brief, we propose a tuning method based on a modified relay feedback experiment. In this experiment, a transfer function of constant phase in an arbitrarily large range of frequencies is inserted in the loop. The proposed methodology thus unifies the Ziegler-Nichols-like tuning methods, by allowing PID tuning based on relay feedback for a class of plants without ultimate frequency.

Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear time-invariant transfer functions and are possibly excited by known external excitation signals and/or unknown noise signals. So far all results on the identifiability of the whole network have assumed that all node signals are measured. Under this assumption, it has been shown that such networks are identifiable only if some prior knowledge is available about the structure of the network, in particular the structure of the excitation. In this paper we present the first results for the situation where not all node signals are measurable, under the assumptions that the topology of the network is known, that each node is excited by a known signal and that the nodes are noise-free. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. An important outcome of our research is that, under those assumptions, a network can often be identified using only a small subset of node measurements.

Remote biomass estimation can benefit agricultural practices in several ways, especially larger areas since it does not require local measurements. The advances of the last few decades in machine learning techniques have created new possibilities for estimating aboveground biomass. A pipeline was established from image acquisition to modelling shoot biomass of two wheat cultivars used in Southern Brazil (TBIO Toruk and BRS Parrudo). A UAV was used to acquire multispectral images with high spatial resolution to calculate vegetation indices (VIs). These VIs along with machine learning approaches are used to model the measured biomass of crops in different growth phases. To correlate the wheat images with measured shoot dry biomass, the following regression models were investigated: random forest, support vector regression, and artificial neural networks. An experiment was designed and conducted at the Agriculture Experimental Station of the Federal University of Rio Grande do Sul (EEA/UFRGS) to assess wheat growth. Variability in crop growth was created for all test areas by varying nitrogen availability. To determine shoot biomass, plants were sampled at three different crop growth stages: V6 (stage of six fully developed leaves), three nodes, and flowering. Our results indicate the importance of the radiometric calibration used. Also, the features extracted from images, such as the VIs combined with machine learning models can be used in precision agriculture for predicting the spatial variability of shoot biomass. The best model for Brazilian wheat cultivars was an artificial neural network with $R^2$ of 0.90, RMSE of 0.83t/ha, and nRMSE of 8.95%. We also found a strong correlation between ground NDVI with image-based NDVI, with an $R^2$ of 0.84.