No abstract

This study is concerned with the design of a nonsingular decoupled terminal sliding mode controller for a class of fourth-order under-actuated uncertain nonlinear systems with unknown external disturbance. For the unmeasured disturbance, a disturbance observer with finite-time convergence of estimation error to zero is proposed. The nonsingular decoupled terminal sliding mode controller is designed by utilizing the output of the proposed disturbance observer. Also, an input saturation constraint and control singularity are considered in the controller design. The finite-time stability and convergence of the disturbance observer are proved for the closed-loop system. In addition, the control of an electrostatically actuated Timoshenko nanobeam subjected to Casimir force is simulated to demonstrate the effectiveness and performance of the proposed control scheme.

No abstract

This paper uses the singular value decomposition approach to find the optimal distribution of a set of piezoelectric actuators and sensors in order to suppress the vibrations of a thick plate. The dynamic model of the system is derived using Mindlin plate theory and consequently, the finite difference method is employed to divide the thick plate to a finite number of nodes with appropriate horizontal and vertical distances. To compute the control force of piezoelectric actuators, the singular value decomposition approach for the column control matrix is supposed as the fitness function of an optimization problem. Through a genetic algorithm, the optimized solution is obtained. The results of numerical simulations indicate the optimal location achieved by the proposed method outperforms the previous results in suppressing the vibrations of a thick plate.

No abstract

No abstract

Drill strings are subjected to complex coupled dynamics. Therefore, accurate dynamic modeling, which can represent the physical behavior of real drill strings, is of great importance for system analysis and control. The most widely used dynamic models for such systems are the lumped element models, which neglect the system distributed feature. In this paper, a dynamic model called neutral-type time delay model is modified to investigate the coupled axial–torsional vibrations in drill strings. This model is derived directly from the distributed parameter model by employing the d'Alembert method. Coupling of axial and torsional vibration modes occurs in the bit–rock interface. For the first time, the neutral-type time delay model is combined with a bit–rock interaction model that regards cutting process in addition to frictional contact. Moreover, mistakes made in some of the related previous studies are corrected. The resulting equations of motion are in terms of neutral-type delay differential equations with two constant delays, related to the oscillatory behavior of the system, and a state-dependent delay, induced by the bit–rock interaction. Illustrative simulation results are presented for a representative drill string, which demonstrates intense axial and torsional vibrations that may lead to system failure without a controller.

SUMMARYThis paper proposes a systematic technique to design multiple robust H ∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed-loop performance when a single robust controller cannot achieve satisfactory performance.