Control of the Toycopter Using a Flat Approximation

International audienceThis paper considers a helicopter-like setup called the Toycopter. Its particularities reside first in the fact that the toycopter motion is constrained to remain on a sphere and second in the use of a variable rotational speed of the propellers to vary the propeller thrust. A complete model using Lagrangian mechanics is derived. The Toycopter is shown to be nondifferentially flat. Nevertheless, by neglecting specific cross-couplings, a differentially flat approximation can be generated and used for controller design, provided the controller gains do not exceed certain bounds that are given explicitly. The achieved performance is better than with standard linear controllers, especially during large displacements that induce strong nonlinear gyroscopical forces. The results are illustrated both in simulation and experimentally on the setup

On the Design of Integral Observers for Unbiased Output Estimation in the Presence of Uncertainty

Integral observers are useful tools for estimating the plant states in the presence of non-vanishing disturbances resulting from plant-model mismatch and exogenous disturbances. It is well known that these observers can eliminate bias in all states, given that as many independent measurements are available as there are independent sources of disturbance. In the most general case, the dimensionality of the disturbance vector affecting the plant states corresponds to the order of the system and thus all states need to be measured. This condition, which is termed integral observability in the literature, represents a fairly restrictive situation. This study focuses on the more realistic case, where only the output variables are measured. Accordingly, the objective reduces to the unbiased estimation of the output variables. It is shown that both stability and asymptotically unbiased output estimation can be achieved if the system is observable, regardless of the dimensionality of the disturbance vector. Furthermore, a condition is provided under which, using output measurements, the errors in all states can be pushed to zero. It is also proposed to use off-line output measurements to tune the observer using a calibration-like approach. Integral observers and integral Kalman filters are evaluated via the simulation of a fourth-order linear system perturbed by unknown non-vanishing disturbances

Inheritance and relationships of flowering time and seed size in kabuli chickpea

Flowering time and seed size are the important traits for adaptation in chickpea. Early phenology (time of flowering, podding and maturity) enhance chickpea adaptation to short season environments. Along with a trait of consumer preference, seed size has also been considered as an important factor for subsequent plant growth parameters including germination, seedling vigour and seedling mass. Small seeded kabuli genotype ICC 16644 was crossed with four genotypes (JGK 2, KAK 2, KRIPA and ICC 17109) to study inheritance of flowering time and seed size. The relationships of phenology with seed size, grain yield and its component traits were studied. The study included parents, F1, F2 and F3 of four crosses. The segregation data of F2 indicated flowering time in chickpea was governed by two genes with duplicate recessive epistasis and lateness was dominant to earliness. Two genes were controlling 100-seed weight where small seed size was dominant over large seed size. Early phenology had significant negative or no association (ICC 16644 × ICC 17109) with 100-seed weight. Yield per plant had significant positive association with number of seeds per plant, number of pods per plant, biological yield per plant, 100-seed weight, harvest index and plant height and hence could be considered as factors for seed yield improvement. Phenology had no correlation with yield per se (seed yield per plant) in any of the crosses studied. Thus, present study shows that in certain genetic background it might be possible to breed early flowering genotypes with large seed size in chickpea and selection of early flowering genotypes may not essentially have a yield penalty