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Robots are one of the most useful tools in today’s world. They are widely used to move objects and perform everyday tasks. Segways are one of these tools that are commonly used nowadays for transportation and even entertainment. In this case study, the dynamical model of a two-wheeled self-balancing mobile device has been proposed. Additionally, a µ robust controller for the device has been designed. All necessary sources are available in the repository: https://github.com/abolfazldelavar/Two_wheeled_self_balancing_mu_approach_CS

The main goal of the present work is proposing a new approach to determine stability margins for a class of nonlinear systems. In particular, we propose a new approach to find the gain and phase margins of Lur’e type nonlinear systems with higher accuracy. To do so, we use multi-section extended circle criterion which is based on Lyapunov stability theorem. To find more precise values of the stability margins, an optimization problem is defined and solved using a nonlinear estimator. Two examples are provided to evaluate the effectiveness of the proposed approach and compare the results to those of the existing methods.

Spreading Covid19 has significantly impacted humans' affairs worldwide, either economically or in a sanitary manner. Besides social distance and hospitalization, making and introducing different vaccines help us ameliorate infection and mortality rates. In this research, we use a nonlinear dynamic model for Covid19, with eight states named susceptible, exposed, infected, quarantined, hospitalized, recovered, deceased, and insusceptible populations. Also, we use social distancing, hospitalization, and vaccination rate as three control inputs. This research aims to stop the Covid-19 from spreading worldwide and minimize exposed, infected and deceased populations using model predictive control. Meanwhile, the measurements data defined in terms of the hospitalized and deceased populations are used to estimate other unmeasurable states by an unscented Kalman filter. In other words, the insusceptible, exposed, infected, quarantined, recovered, and susceptible individuals cannot be identified precisely because of the asymptomatic infection of the Covid-19 in some cases, its incubation period, and the lack of an adequate community screening. Finally, experimental results show that the proposed algorithm is feasible and efficient to decrease infection and mortality rates compared to the uncontrolled scenario.