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This paper presents the design of optimal controller for nonlinear Rotary Inverted Pendulum (RIP) dynamic system using Linear Quadratic Regulator (LQR). LQR, an optimal control technique is generally used for control of the linear...
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This paper presents the design of optimal controller for nonlinear Rotary Inverted Pendulum (RIP) dynamic system using Linear Quadratic Regulator (LQR). LQR, an optimal control technique is generally used for control of the linear dynamical systems, have been used in this paper to control the non linear dynamical system. The non linear system states are fed to LQR which is designed using linear state-space model. Inverted pendulum, a highly nonlinear unstable system is used as a benchmark for implementing the control methods. Here the controller objective is to control the system such that the arm reaches at a desired position and the inverted pendulum stabilizes in upright position. The MATLAB-SIMULINK model has been developed for implementation of control schemes. The same controllers have been tested on a test bed of Quanser QUBE-Servo hardware system and the results are compared in various aspects to verify the efficiency of the proposed controller.
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In this paper, the authors propose an optimal controller for the ship motion. Firstly, the model and dynamic equations of the ship motion are presented. Based on the model of the ship motion, the authors build the linear quadratic...
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In this paper, the authors propose an optimal controller for the ship motion. Firstly, the model and dynamic equations of the ship motion are presented. Based on the model of the ship motion, the authors build the linear quadratic regular algorithm-based control system of ship motion to minimize the error between the desired trajectory and the response trajectory. The task of the controller is to control the trajectory of the ship to coincide with the desired trajectory. The ship model and controller are built to investigate the system quality through Matlab-Simulink software. The results show that the quality of the hold control system is very high. The trajectory of a ship always follows the desired trajectory with very small errors.
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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 qu...
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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.
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We study a linear-quadratic optimal control problem in a Hilbert space where the state equation is unsolvable with respect to the derivative and contains an unbounded operator. The performance index is the sum of the integral of a...
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We study a linear-quadratic optimal control problem in a Hilbert space where the state equation is unsolvable with respect to the derivative and contains an unbounded operator. The performance index is the sum of the integral of a quadratic form with respect to the control and the state variable on a finite or infinite time interval and also quadratic forms with respect to the differences between the state variable values at fixed points and given values. The optimal control is presented in the feedback form using the implicit differential operator Riccati equation or the operator equation of the Riccati type under a special symmetry condition for the solution. The minimal value of the minimized functional is calculated. Some illustrative examples are also given.
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Under extreme working conditions such as high-speed driving on roads with a large road surface unevenness coefficient, turning on a road with a low road surface adhesion coefficient, and emergency acceleration and braking, a vehic...
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Under extreme working conditions such as high-speed driving on roads with a large road surface unevenness coefficient, turning on a road with a low road surface adhesion coefficient, and emergency acceleration and braking, a vehicle’s stability deteriorates sharply and reduces ride comfort. There is extensive existing research on vehicle active suspension control, trajectory tracking, and control methods. However, most of these studies focus on conventional operating conditions, while vehicle stability analysis under extreme operating conditions is much less studied. In order to improve the stability of the whole vehicle under extreme operating conditions, this paper investigates the stability of a vehicle under extreme operating conditions based on linear quadratic regulator (LQR) control. First, a seven degrees of freedom (7-DOF) dynamics model of the whole vehicle is established based on the use of electromagnetic active suspension, and then an LQR controller of the electromagnetic active suspension is designed. A joint simulation platform incorporating MATLAB and CarSim was built, and the CarSim model is verified by real vehicle tests. Finally, the stability of the vehicle under four different ultimate operating conditions was analyzed. The simulation results show that the root mean square (RMS) values of body droop acceleration and pitch angle acceleration are improved by 57.48% and 28.81%, respectively, under high-speed driving conditions on Class C roads. Under the double-shift condition with a low adhesion coefficient, the RMS values of body droop acceleration, pitch acceleration, and roll angle acceleration are improved by 58.25%, 55.41%, and 31.39%, respectively. These results indicate that electromagnetic active suspension can significantly improve vehicle stability and reduce driving risk under extreme working conditions when combined with an LQR controller.
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Designing a control structure for the Ball on Beam offer important results and conclusions at the level of experience of design and implementation. However, the comparison between the two algorithms implement on the same process c...
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Designing a control structure for the Ball on Beam offer important results and conclusions at the level of experience of design and implementation. However, the comparison between the two algorithms implement on the same process control, highlight the advantages or disadvantages of their level of functioning. The process Ball on Beam presented, although at first seems just a "toy", but, because it is a process unstable, nonlinear, underactuated, can provide a basis for implementing and testing real-time control of many principles.
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This study focuses on the control of a humanoid robot in a new environment, whose parameters were not accounted for during the design of the robot’s control system. The environments in question are an active and a passive tilting...
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This study focuses on the control of a humanoid robot in a new environment, whose parameters were not accounted for during the design of the robot’s control system. The environments in question are an active and a passive tilting platform. The study shows that the humanoid robot behaves similar to a human subject in the experiments with low viscous friction. In the experiment with high viscous friction, it was demonstrated that the robot is capable of balancing on the platform. Same result was achieved in the case of an active platform. The paper provides a discussion of how the task of standing on a passive platform deviated from the model-based control formulation with constrained linear quadratic regulator and projected inverse dynamics, designed for the case of walking on stationary horizontal plane. The results in the paper suggest that while there are limitations to how well standard control approaches can adapt to the unknown environments, it is still possible to use them directly.
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The optimal guidance law of an autonomous four-rotor helicopter, called the Quadrotor, using linear quadratic regulators (LQR) is presented in this paper. The dynamic equations of the Quadrotor are considered nonlinear so to find ...
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The optimal guidance law of an autonomous four-rotor helicopter, called the Quadrotor, using linear quadratic regulators (LQR) is presented in this paper. The dynamic equations of the Quadrotor are considered nonlinear so to find an LQR controller, it is necessary that these equations be linearized in different operation points. Due to importance of energy consumption in Quadrotors, minimum energy is selected as the optimal criteria.
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Any practical control system is affected by external signals. Some of them are “informative” (e.g. reference signals), and the others (disturbances, measurement noises etc.) are undesired as they can visibly deteriorate the syst...
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Any practical control system is affected by external signals. Some of them are “informative” (e.g. reference signals), and the others (disturbances, measurement noises etc.) are undesired as they can visibly deteriorate the system behavior. General approaches to disturbance rejection and reference tracking have been elaborated in the framework of geometric control theory, among them are disturbance decoupling control and internal model principles. These approaches, however, assume the state and control of the system to be unconstrained. To take such constraints into account, one usually has to consider optimization problems where the performance index penalizes in some way the system process. Optimization problems in presence of uncertain signals have been addressed in the context of robust control and stochastic control. Standard methods like usually provide only suboptimality of the process; the optimal value can be found for either “worst-case” signal (like in minimax H8-and L1-optimization approaches) or “on average”, assuming the external signals to be stochastic with known spectral density. In a series of his papers published in 1992-2012, Vladimir A. Yakubovich promoted the approach of universal controllers for linear-quadratic regulation (LQR) problems under uncertain signals. The term “universal” emphasizes that the controller renders the solution of the closed-loop system optimal for any external signal. Although this is not possible for arbitrary signals, in some special classes of signals the universal controllers not only exist but may even be chosen linear. The existence of linear optimal controllers has been proved for two important classes of uncertain signals, that is, polyharmonic signals with known spectrum and signals with fast decreasing spectral density. In this paper we extend the results of V.A. Yakubovich to more general classes of systems and quadratic performance indices, arising in problems of optimal oscillation damping, reference tracking and model matching.
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