Modified Implicit Discretization of the Super-Twisting Controller

In this paper a novel discrete-time realization of the super-twisting controller is proposed. The closed-loop system is proven to be globally asymptotically stable in the absence of a disturbance by means of Lyapunov theory. Furthermore, the steady-state error in the disturbed case is computed analytically and shown to be independent of the parameters. The steady-state error only depends on the sampling time and the unknown disturbance. The proposed discrete-time controller is compared to previously published discrete-time super-twisting controllers by means of the controller structure. In extensive simulation studies the proposed controller is evaluated comparative to known controllers. The continuous-time super-twisting controller is capable of rejecting any unknown Lipschitz-continuous perturbation. Furthermore, the convergence time decreases, if any of the gains is increased. The simulations demonstrate that the systems closed in the loop with each of the known controllers lose one of these properties, introduce discretization-chattering effects, or do not yield the same accuracy level as with the proposed controller. The proposed controller, in contrast, is beneficial in terms of the above described properties of the continuous-time super-twisting controller

Observer design for a nonlinear heat equation: Application to semiconductor wafer processing

In this paper, the problem of observer design for a class of 1D nonlinear heat equations with pointwise in-domain temperature measurements is addressed. A pointwise measurement injection observer is designed and the robust convergence of its estimation error in presence of bounded distributed perturbations is established by verifying input-to-state stability. The obtained convergence conditions express the underlying interplay between heat conduction and radiation and include specific dependencies on the sensor locations which are the main degrees of freedom in the design approach. The theoretical results are experimentally validated on a semiconductor wafer processing unit

Automatic Levothyroxine Dosing Algorithm for Patients Suffering from Hashimoto’s Thyroiditis

Hypothyroidism is a condition where the patient’s thyroid gland cannot produce sufficient thyroid hormones (mainly triiodothyronine and thyroxine). The primary cause of hypothyroidism is autoimmune-mediated destruction of the thyroid gland, referred to as Hashimoto’s thyroiditis. A patient’s desired thyroid hormone concentration is achieved by oral administration of thyroid hormone, usually levothyroxine. Establishing individual levothyroxine doses to achieve desired thyroid hormone concentrations requires several patient visits. Additionally, clear guidance for the dosing regimen is lacking, and significant inter-individual differences exist. This study aims to design a digital automatic dosing algorithm for patients suffering from Hashimoto’s thyroiditis. The dynamic behaviour of the relevant thyroid function is mathematically modelled. Methods of automatic control are exploited for the design of the proposed robust model-based levothyroxine dosing algorithm. Numerical simulations are performed to evaluate the mathematical model and the dosing algorithm. With the help of the developed controller thyroid hormone concentrations of patients, emulated using Thyrosim, have been regulated under the euthyroid state. The proposed concept demonstrates reliable responses amidst varying patient parameters. Our developed model provides a useful basis for the design of automatic levothyroxine dosing algorithms. The proposed robust feedback loop contributes to the first results for computer-assisted thyroid dosing algorithms