The LQR (linear quadratic regulator) control problem subject to singular system constitutes a optimization problem in which one must be find an optimal control that satisfy the singular system and simultaneously to optimize the quadratic objective functional. In this paper we establish a sufficient condition to obtain the optimal control of discounted LQR optimization problem subject to disturbanced singular system where the disturbance is time varying. The considered problem is solved by transforming the discounted LQR control problem subject to disturbanced singular system into the normal LQR control problem. Some available results in literatures of the normal LQR control problem be used to find the sufficient conditions for the existence of the optimal control for discounted LQR control problem subject to disturbanced singular system. The final result of this paper is in the form a method to find the optimal control of discounted LQR optimization problem subject to disturbanced singular system. The result shows that the disturbance is vanish with the passage of time.

The static synchronous compensator (STATCOM) is the multipurpose FACTS device with the multiple input and multiple output system for the enhancement of its dynamic performance in power system. Based on artificial intelligence (AI) optimization technique, a novel controller is proposed for CSC based STATCOM. In this paper, the CSC based STATCOM is controlled by the LQR. But the best constant values for LQR controller's parameters are obtained laboriously through trial and error method, although time consuming. So the goal of this paper is to investigate the ability of AI techniques such as genetic algorithm (GA) and particle swarm optimization (PSO) methods to search the best values of LQR controller's parameters in a very short time with the desired criterion for the test system. Performances of the GA, PSO & ABC based LQR controllers are also compared. Applicability of the proposed scheme is demonstrated through simulation in MATLAB and the simulation results are shown an improvement in the input-output response of CSC-STATCOM.

The aim of this study is to design a control strategy for the angular rate (speed) of a DC motor by varying the terminal voltage. This paper describes various designs for the control of direct current (DC) motors. We derive a transfer function for the system and connect it to a controller as feedback, taking the applied voltage as the system input and the angular velocity as the output. Different strategies combining proportional, integral, and derivative controllers along with phase lag compensators and lead integral compensators are investigated alongside the linear quadratic regulator. For each controller transfer function, the step response, root locus, and Bode plot are analysed to ascertain the behaviour of the system, and the results are compared to identify the optimal strategy. It is found that the linear quadratic controller provides the best overall performance in terms of steady-state error, response time, and system stability. The purpose of the study that took place was to design the most appropriate controller for the steadiness of DC motors. Throughout this study, analytical means like tuning methods, loop control, and stability criteria were adopted. The reason for this was to suffice the preconditions and obligations. Furthermore, for the sake of verifying the legitimacy of the controller results, modelling by MATLAB and Simulink was practiced on every controller.

This paper presents an adaptive particle swarm optimization (APSO) based LQR controller for optimal tuning of state feedback controller gains for a class of under actuated system (Inverted pendulum). Normally, the weights of LQR controller are chosen based on trial and error approach to obtain the optimum controller gains, but it is often cumbersome and tedious to tune the controller gains via trial and error method. To address this problem, an intelligent approach employing adaptive PSO (APSO) for optimum tuning of LQR is proposed. In this approach, an adaptive inertia weight factor (AIWF), which adjusts the inertia weight according to the success rate of the particles, is employed to not only speed up the search process but also to increase the accuracy of the algorithm towards obtaining the optimum controller gain. The performance of the proposed approach is tested on a bench mark inverted pendulum system, and the experimental results of APSO are compared with that of the conventional PSO and GA. Experimental results prove that the proposed algorithm remarkably improves the convergence speed and precision of PSO in obtaining the robust trajectory tracking of inverted pendulum.

The underframe passive inerter-based suspended device, based on the inerter-spring-damper vibration attenuation structure, could improve the dynamic performance of the train body, but its parameters are fixed and cannot meet the dynamic performance requirements under different operating conditions. Therefore, a semi-active inerter-based suspended device based on the linear quadratic regulator (LQR) control strategy is proposed to further enhance the dynamic performance. The rigid-flexible coupling vertical dynamic model of the train body and an underframe semi-active inerter-based suspended device are established. The structural parameters of the semi-active inerter-based suspended device are adjusted using LQR control strategy. Dynamic response of the system is obtained using the virtual excitation method. The dynamic characteristic of the system is evaluated using the Sperling index and compared with those of the passive and semi-active traditional suspended devices as well as the passive inerter-based suspended devices. The vertical vibration acceleration of the train body and Sperling index using the semi-active inerter-based suspended device is the smallest among the four suspended devices, which denotes the advantages of using the inerter and LQR control strategy. The semi-active inerter-based suspended device could decrease the vertical vibration acceleration of the train body and further suppress its elastic vibration in the lower frequency band, more effectively than the other three suspended devices. Overall, the semi-active inerter-based suspended device could significantly reduce elastic vibration of the train body and improve its dynamical performance.