Analysis of the Lqr Algorithm in the Field of Testing the Dynamics of Quadcopter Movement

The subject of this article is to present the issues related to the LQR control algorithm used in the linear model describing the dynamics of the flying object in terms of tracking its flight trajectory. The use of the LQR regulator is also a method of calculating the optimal K-feedback reinforcement, with this type of reinforcement used to control the system in the form of a control signal can be determined by tuning the Q and R weight matrix elements in the LQR method. Based on the above, the main research goal of the article is to develop an algorithm for the control system implemented on the quadrotor using the LQR method to obtain the best K-feedback gain in flight state with unstable motion. To this end, a mathematical model describing the essence of linear-quadratic control using the LQR controller is presented in this paper. It should be noted that due to the fact that only four states can be controlled at the same time in a quadrotor, hence the flight trajectories are determined on the basis of four states, while the three-dimensional position, position of the tested object in the coordinate system and rotation along the axis are described as deviation movement. In addition, the work also designed on the basis of the created linear model of a linear quadrotor LQR control approach for this model due to the fact that the performance of the linear model and non-linear model around a specified nominal point is almost identical. The control system based on the LQR algorithm was developed in the Matlab/Simulink environment, and the results obtained in the form of graphs for the quantities characterizing the dynamics of the tested object were used to assess the effectiveness of the LQR method used. In the final part of the work, practical conclusions have been formulated based on the research (analysis, models, simulations) and analysis of the results obtained.

SYNTHESIS OF A TRACKING CONTROL SYSTEM OVER THE FLOTATION PROCESS BASED ON LQR-ALGORITHM

The studies are devoted to the synthesis of the tracking control system of the flotation process based on the LQR-algorithm. The algorithm of finding the parameters of the optimal regulator is given. The results of modelling of the system with the regulator are obtained, and also the comparative analysis of the results of modelling of the system with and without the regulator is shown, which is performed with the help of Matlab software package and the Simulink toolkit.

Advanced two-step integrated optimization of actively controlled nonlinear structure under mainshock–aftershock sequences

In this paper, an attempt is made to examine a new method for designing and applying the active vibration control system to improve building performance under mainshock–aftershock sequences. In this regard, three different structures are considered; 5-, 10-, and 15-story buildings. Seven mainshock–aftershock sequences are selected from the Iranian accelerogram database for analyzing the structures. By implementing an advanced two-step optimization method, buildings equipped with the active vibration control system (linear–quadratic regulator (LQR) algorithm) are designed to withstand all events of mainshock–aftershock sequences. In the first optimization step, a multi-objective optimization with the genetic algorithm is performed and a set of optimal Pareto front results is obtained. In the next step, the life-cycle cost of each optimal design sample of the Pareto front is calculated by considering the cumulative damage and the design sample with the minimum cost is selected as a final optimal property. The results prove that the active vibration control system is capable of reducing structural responses, including acceleration, drift, and residual drift under mainshock–aftershock sequences, and consequently the life-cycle cost of buildings, especially the taller ones. In addition, obtaining the building design variables (story stiffness and yielding force) and active LQR algorithm properties simultaneously leads to a slightly softer final building model than the conventional structure designed by the common building design code. Moreover, it is revealed that, by considering the aftershocks, the building life-cycle cost increases significantly.

Dual PD Control of Flexible Smart Structure Based on LQR Algorithm

The flexible smart structure is broadly applied in various fields. In order to reduce the vibration of smart structures, a dual loop PD control strategy is proposed based on the Lagrangian dynamics mathematical modeling of the flexible system and a revision of the traditional LQR algorithm, the simulation and physical experiments show that the proposed approach is efficient in controlling and damping out the vibration and disturbance in flexible smart structure system.

Study on the Optimization of the Double-Layer Hybrid Vibration Isolation System Based on the LQR Algorithm

The LQR algorithm has been widely used in the hybrid vibration isolation system. However, it cannot make the hybrid vibration isolation system global optimal with the coupling of structure and controller. Hence, the multi-object optimal design of the double-layer hybrid vibration isolation system based on the LQR algorithm was made by the NCGA method. The results showed that the vibration of the mechanical equipment did not get worse with the reduction of the force transmission ratio, and it made an approach to the optimal design of the hybrid vibration isolation system.