This study proposes an adaptive barrier functions-based non-singular terminal sliding mode control approach for the trajectory tracking of a quadrotor unmanned aerial vehicle subject to bounded uncertainties and input constraints. First, the state-space equations of the six degrees-of-freedom quadrotor system is introduced in the presence of bounded uncertainty and constrained input. Then, a compensation system is designed with the aim of removing the constrained input and leading to high performance. Afterwards, a linear switching surface is defined using the tracking error and virtual control input to guarantee the convergence of the tracking error in the presence of parametric uncertainties and input saturation. Later, a non-singular terminal sliding surface is proposed for fast convergence of the linear switching surface. To eliminate the need for approximating the upper bounds of uncertainties and ensure the fast convergence of the non-singular terminal sliding surface to a pre-specified neighborhood of the origin, we considered an adaptive barrier function scheme. The fast convergence rate of the proposed approach is verified via the Lyapunov stability theory. The accuracy and performance of the proposed approach is assessed using MATLAB/Simulink simulations and robustness analysis using the random number noise.

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Barrier Function-Based Nonsingular Finite-Time Tracker for Quadrotor UAVs Subject to Uncertainties and Input Constraints

Unmanned aerial vehicles (UAVs) are subject to the wind and other environmental disturbances that can destabilize them. The high performance and robustness of the Linear Quadratic Regulator (LQR) controllers ensure the ability to reduce the deviations in state trajectories with minimum control effort. In this paper, the weighting matrices are adjusted automatically via a novel method implemented through state variables matrix of the quadrotor together with a preference factor. This proposed factor is determined by the designer via penalizing or rewarding a certain state of the quadrotor out of others so that the model insufficiencies against disturbances are compensated. The effectiveness of the proposed method of selecting these matrices is evaluated for the cases of LQR and LQR with a PI controller. They were evaluated with respect to the convergence of state variables to their reference values within a specific time and compliance with their desired performance characteristics. The experimental results revealed that both control strategies could stabilize the quadrotor in the desired position and attitude with better performance and robustness characteristics. The results also showed that the LQR-PI control method is a more reliable and effective approach in achieving higher tracking performances compared to the LQR only. 

Robust LQR and LQR-PI control strategies based on adaptive weighting matrix selection for a UAV position and attitude tracking control

In this paper, we propose a novel Interval Type-2 (IT2) Fuzzy Cognitive Map (FCM)-based flight control system to solve the altitude, attitude and position control problems of quadcopters. The proposed IT2-FCM encompasses all concepts related to drone for a satisfactory path-tracking and stabilizing control performance. The degree of mutual influences of the concepts is designed with opinions of three experts that take account the dynamics of drone and rules governing proportional integral derivative (PID) controllers. To model the inter-uncertainty of the experts’ opinions, IT2 fuzzy logic systems are utilized as they are powerful tools to model high level of uncertainties. Thus, the proposed IT2-FCM has a qualitative representation as it merges the advantages of IT2 fuzzy logic systems and FCMs. We present comparative simulations results in presence of uncertainties where the superiority of the proposed IT2-FCM-based flight control system is shown in comparison with its type-1 fuzzy counterpart.

Interval Type-2 Fuzzy Cognitive Map-Based Flight Control System for Quadcopters

Quadrotor is an inherently nonlinear, coupled and unstable system which require an efficient controller to perform accurate tracking without losing the target trajectory. This paper concerns the development of an optimal backstepping controller (OBS) for the quadrotor attitude. A mathematical modeling for the quadrotor dynamics was derived by taking into account its nonlinear dynamics. Ant colony optimization algorithm (ACO) was used to select the optimal parameters of the BS controller. However, the obsession behind the use of this optimization algorithm is the development of a reliable flight controller ensuring optimal performances. In order to highlight the accuracy of the proposed approach, we carried out numerical experiments using two trajectory scenarios.

Control System of a Quadrotor UAV with an Optimized Backstepping Controller

At present, switched reluctance motors (SRM) become very interesting for many industrial applications in variable speed control. For such systems, the linear quadratic regulator with integral action (LQI) method is commonly used when using plants in state spaces due to its robustness and easy adjustment. All methods from the linear quadratic regulator (LQR) project provide a weighting of the Q and R matrices, which are manually adjusted to achieve the desired performance. The manual fine tuning of LQI controller parameters is a difficult task that requires a high level of domain knowledge. In this work, metaheuristic algorithms are explored to design the LQI controller and a comprehensive comparison is made between these algorithms and Proportional-Integral-Derivative (PID) controller as well as to select the best technique for the LQI controller design and adjustment of the Q and R parameters in SR Motor. Simulation and experimental results on a setup prototype are shown to validate the proposed control schemes. This paper has as main contributions the weighting of the parameters of the LQI in an optimized way and adjustment of the gains of the controller more quickly and the hybrid controller (LQI + GA) becomes more powerful in the sense of a possible extension of the control of a multivariable system.

Optimal LQI and PID Synthesis for Speed Control of Switched Reluctance Motor Using Metaheuristic Techniques

This paper presents an analysis and performance of a LQR control algorithm for quadrotor helicopters. For a successful analysis, first the dynamic model has been developed for the quadcopter and then the controller was designed, tuned, and tested. In tuning the LQR, much attention was given to the feedback gain matrix (K). The controller's performance was verified in terms of delay time, rise time, overshoot, settling time, and tolerance limits. The overall performance of the LQR controller was analysed.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/joe.2018.8126

LQR controller design for quad-rotor helicopters

Based on a 2012 Ghanaian social accounting matrix, it was determined how different leisure levels and labour endowments affect household welfare and sectoral output. The findings of the leisure experiments point to a pattern in which the wellbeing of wealthiest households are negatively impacted. On the other hand, all other households see an increase in their welfare with rural farmer head savannah (hh01) always seeing the highest each time. Clearly there are redistribution impacts of leisure labour choice through income and substitution effects. When leisure is reduced in an effort to increase productivity, these rich households see a decrease in their consumption levels and the relatively poorer households see an increase in their welfare. So the question then is how can policy makers make such rich households contribute more to national development through income distributional effects by enhancement in their efficiency. Similar effects are noted when endowments change. Outputs in sectors increases. Some household save, spend more on health and education whiles others spend more consumption, specially on imported goods. The income gap between affluent and poor households is reduced when leisure is reduced (productivity is increased), but the income gap is increased when endowments are increased. The question is, “How might policymakers encourage measures that will boost economic happiness and satisfaction for both wealthy and disadvantaged households?” Rawalsian versus Benthamite notions of utility should be considered while setting policy options to achieve the aim of the MDGs.

/pdf/welfare-effects-and-importance-of-skills-and-human-capital-wd5xx2gm.pdf

Emmanuel Okyere

Papers

LQR controller design for quad-rotor helicopters

Welfare effects and importance of skills and human capital development policies in a dcge model of ghana