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In this paper, LQG/LTR controller is designed for attitude control of the geostationary satellite at nominal mode. Usage actuator in this paper is the reaction wheel and control torque is determined by the LQR regulator. Usage sensors in this article are sun and earth sensors and EKF are used for estimation of noisy states. LQR controller signal has good performance, if all system's states are considered in system output feedback. But this method is ideal and does not include model noise and sensors noise. Therefore, LQG and LQG/LTR controllers are designed based on the estimated states, and are compared with LQR controller. Controllers gain coefficients are obtained based on linearization about working point. It caused to robustness and similarity of LQG and LQG/LTR response. The results show that control overshoot of LQR is greater than the others.

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In this paper, a LQG/LTR controller is proposed for attitude control a geostationary satellite at nominal phase. Basically, proposed methodology includes three parts: LQR regulator, EKF, and loop transfer recovery. Controller design is based on the linearized equations of the spacecraft dynamics using reduced quaternion model. Reduced quaternion model solve uncontrollable problem in some subspaces in the linearized state space quaternion model using all four components of quaternion. Spacecraft actuators are reaction wheels and attitude determination sensors are sun and earth sensors. LQR controller is ideal and it doesn’t account for the model uncertainty and sensor noise and it uses the feedback of the full states. To consider the model uncertainty and sensor noise, we have designed EKF which is used by LQG and LQG/LTR controllers. Controller gain coefficients are obtained using a reduced quaternion model, and based on linearization around the equilibrium point and the natural frequency of the closed loop system. To increase the robustness of the design with respect to solar radiation disturbance, singular values of LQG are approximated to Kalman filter, in LTR section. The results demonstrate that LQG/LTR performance is better than LQG’s and LQG/LTR has a good robust stability margin with respect to disturbances.

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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 paper, designing optimal linear controller for non-holonomic wheeled mobile robots based on Linear Quadratic Gaussian (LQG) controller is considered. Parameters of the governing kinematics equation of motion are derived based on system identification techniques by using real experimental data. The autoregressive moving average-exogenous input (ARMAX) models are taken into account. The least square (LS) algorithm is utilized to estimate the parameters of the model. Thereafter, optimal model order and the performance of the model are determined using several statistical analyses. Also, the recursive LS (RLS) with forgetting factor is employed to demonstrate the convergence of the model parameters. Verification of discrete linear model implies the possibility of using the linear controllers. Therefore, the optimal LQG controller for wheeled mobile robots is designed to track the reference trajectory. The Kalman observer is used to estimate un-measurable states of the robot. Furthermore, the optimal linear control together with system identification techniques yields simpler controller than nonlinear controllers. Designed controller and verified model are simulated using the MATLAB-Simulink software. Results show the effectiveness of the controller in tracking the desired reference trajectory.

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In this paper, a modified linear-quadratic-Gaussian (MLQG) optimal control algorithm is proposed for controlling the seismic response of frame structures. Environmental loads (e.g., earthquakes) at the moment of calculation and exertion of control forces to structures, can not be measured. So these loads are not included in the conventional control algorithms, such as linear quadratic regulator and linear-quadratic-Gaussian control. Therefore the command of LQG optimal controller is merely a proportional feedback of estimated state of structure at the moment of exertion. This state approximation is performed by optimal state stimator or Kalman filter. In the proposed control algorithm, using a new variable, including control force andearthquake force, acceleration of gound motion, which is non-measurable duting exertion of control force, is considered in the state space equation of motion and also in both of Kalman Filter estimator and the optimal regulator. According to the proposed control algorithm, two ways are selected. So first command control are sum of the control force and ratios of the estimated state and measurement output of sensors, which are obtained and used in previous time step. The estimated state of system, used in the first command control, is calculated by the conventional and knownKalman Filter. but in second strategy of control, First, the Kalman Filter estimator is modified based on new state space equations, and then the estimated state of structure obtained from it, is used for calculation of command control. Numerical simulation of a seven-storey structure with active control system under several far-fault and near-fault earthquakes are performed to show effectiveness of two proposed controls on mitigation of structural responses and compare to those of a uncontrolled structure and a structure controlled with conventional control. Also sensitivity of some perforemance measures for controllers are investigated against changes of some controlling and perturbation parameters of systems or uncertainties. The alalysis results demonstrate that control performance of the proposed controllers, specially the second one, are better and also stable and robust under variations of uncertainties. So that the greatest reduction in maximum displacement (even up to 80 percent) compared to uncontrolled displacement of structure and meanwhile, very low energy consumption are attained by the second proposed control strategy.but in second strategy of control, First, the Kalman Filter estimator is modified based on new state space equations, and then the estimated state of structure obtained from it, is used for calculation of command control. Numerical simulation of a seven-storey structure with active control system under several far-fault and near-fault earthquakes are performed to show effectiveness of two proposed controls on mitigation of structural responses and compare to those of a uncontrolled structure and a structure controlled with conventional control. Also sensitivity of some perforemance measures for controllers are investigated against changes of some controlling and perturbation parameters of systems or uncertainties. The alalysis results demonstrate that control performance of the proposed controllers, specially the second one, are better and also stable and robust under variations of uncertainties. So that the greatest reduction in maximum displacement (even up to 80 percent) compared to uncontrolled displacement of structure and meanwhile, very low energy consumption are attained by the second proposed control strategy.