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In this study out of plane active vibration control of a laminated composite rectangular plate with intermediate line support coupled with piezoelectric patches on both sides, upper and lower surface of the plate, is presented based on First order shear deformation plate theory (FSDT). Is this study, the piezoelectric patch is used as a sensor. In the relation of piezoelectric, electrical potential in the transverse direction earned by satisfaction of electric boundary conditions (open circuit) and Maxwell's electricity equation. The Rayleigh-Ritz approach is used to obtain natural frequencies and vibration mode shapes of the plate. Forced vibration response is obtained by using by the modal expansion method.In this paper, the Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) and Fuzzy Logic Controller (FLC) are used to control and reduce the amplitude of the transversely deformation of a laminated composite rectangular plate which is excited by external forced. In the numerical results, the effect of various inputs, e.g. positions of the external forced, on the responses of the system are examined and discussed in detail. The proposed analytical method is validated with available data in the literature.

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In this article, the linear quadratic regulator method (LQR) for voltage control of a linear time-varying model of a robot is used to design an on line adaptive optimal stable controller to trace the robot arm path. Normally, off line solving of Riccati differential equations in backward with final conditions for linear time-varying system or converting the Riccati differential equation to algebraic one in linear time-invariant system is inevitable in LQR. However, in this paper, the differential Riccati equations are considered as the adaptation laws along with a voltage control strategy to be solved on line in forward method with initial conditions. Choosing a proper Lyapunov function guarantees the asymptotic stability of the tracking. Furthermore, parametric model uncertainties such as mass parameter variation and external disturbances which affect the dynamics of the model, are also taken into account. Simulation results show the energy used by dc motors of the voltage optimal control strategy is less than that of the torque control strategy and as well as the classical PID one. The superior performance of the voltage optimal control over torque control strategy is also shown in presence of disturbance.

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Comparison of Back stepping method optimized via particle swarm optimization algorithm and LQR method for hovering control of a quadrotor is presented in this paper. Quadrotor is not a stable dynamical system and development of high performance controllers for it is important. First the dynamic model of a quadrotor is introduced and state-space equations are presented in order to simulate the dynamic model. Then two Back stepping and LQR controllers are designed to control Euler angles and height of the quadrotor. In order to optimize back stepping controller, its parameters are determined using particle swarm optimization algorithm to minimize cost function considered for LQR controller. Also commands to the motors are calculated and plotted to show the feasibility of the controller. To obtain better comparison, the cost function is calculated for different weighting matrices of Q and R for two controllers and the results are compared. The results show that Back stepping controller has more ability to minimize the cost function in comparison to LQR and the cost function in Back stepping has less values for several choices of weighting matrices.

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In hovering, the deputy satellite must use fuel regularly to maintain a constant distance from a source point. Since the amount of fuel in satellites is a key element, it has also a great value to optimize its consumption. The system speed and the time of reaching stability are also other important elements that have been studied in this study. For this purpose, three useful controllers are used. These controllers are LQR controller, Pole Placement and sliding mode controller. In the following, these controllers were optimized using particle swarm optimization algorithm in order to compromise the amount of fuel consumption and the time of reaching stability. Comparing the final results shows that the sliding mode controller can be the best option for optimizing hovering system.

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In this paper, a robust linear quadratic regulator (LQR) based Reinforcement learning method is designed for a four degree of freedom inverted pendulum. The considered system contains a four degree of freedom inverted pendulum with a concentrated mass at the tip of it. The bottom of inverted pendulum is moved in x-y plane in x and y directions. For tracking control of two angles of inverted pendulum, two plane forces are applied in x and y directions at the bottom of pendulum. The governing equations of the system are derived using the Lagrange method and then a robust linear quadratic regulator (LQR) based Reinforcement learning controller is designed. The inverted pendulum is learned for a range of different angles, different lengths and different masses. The parametric uncertainties are defined as various lengths and masses of inverted pendulum and the disturbances are defined as impact and continuous forces which are applied on the inverted pendulum. After learning, the controller can learn online the system for any arbitrary angle, length, mass or disturbance which are not learned in the defined range. Numerical results show that the good performance of the reinforcement learning controller for the inverted pendulum in the presence of structural and parametric uncertainties, impact and continuous disturbances and sensor noises.