On the Effect of Non-Linearity on Linear Quadratic Regulator Stability and Performance

This research proposes control method to balance and stabilize an inverted pendulum. A robust control was analyzed and adjusted to the model output with real time feedback. The feedback was obtained using state space equation of the feedback controller. A linear quadratic regulator (LQR) model tuning and control was applied to the inverted pendulum using internet of things (IoT). The system's conditions and performance could be monitored and controlled via personal computer (PC) and mobile phone. Finally, the inverted pendulum was able to be controlled using the LQR controller and the IoT communication developed will monitor to check the all conditions and performance results as well as help the inverted pendulum improved various operations of IoT control is discussed.

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ACTIVE VIBRATION CONTROL OF SEISMICALLY EXCITED STRUCTURES BY ATMDS: STABILITY AND PERFORMANCE ROBUSTNESS PERSPECTIVE

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455410003592 ◽

2010 ◽

Vol 10 (03) ◽

pp. 501-527 ◽

Cited By ~ 9

Author(s):

ARASH MOHTAT ◽

AGHIL YOUSEFI-KOMA ◽

EHSAN DEHGHAN-NIRI

Keyword(s):

Vibration Control ◽

Structural Damage ◽

Fuzzy Logic Controller ◽

Control Strategies ◽

Linear Quadratic Regulator ◽

Pole Placement ◽

Structural Vibration ◽

Linear Quadratic ◽

And Performance ◽

Performance Robustness

This paper demonstrates the trade-off between nominal performance and robustness in intelligent and conventional structural vibration control schemes; and, proposes a systematic treatment of stability robustness and performance robustness against uncertainty due to structural damage. The adopted control strategies include an intelligent genetic fuzzy logic controller (GFLC) and reduced-order observer-based (ROOB) controllers based on pole-placement and linear quadratic regulator (LQR) conventional schemes. These control strategies are applied to a seismically excited truss bridge structure through an active tuned mass damper (ATMD). Response of the bridge-ATMD control system to earthquake excitation records under nominal and uncertain conditions is analyzed via simulation tests. Based on these results, advantages of exploiting heuristic intelligence in seismic vibration control, as well as some complexities arising in realistic conventional control are highlighted. It has been shown that the coupled effect of spill-over (due to reduction and observation) and mismatch between the mathematical model and the actual plant (due to uncertainty and modeling errors) can destabilize the conventional closed-loop system even if each is alone tolerated. Accordingly, the GFLC proves itself to be the dominant design in terms of the compromise between performance and robustness.

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Design and Performance Analysis of LQR Controller for Stabilizing Double Inverted Pendulum System

Circulation in Computer Science ◽

10.22632/ccs-2017-252-45 ◽

2017 ◽

Vol 2 (9) ◽

pp. 1-5

Author(s):

Ghassan A. Sultan ◽

Ziyad K. Farej

Keyword(s):

Inverted Pendulum ◽

Linear Quadratic Regulator ◽

Linear Quadratic ◽

Pendulum System ◽

Inverted Pendulum Model ◽

Inverted Pendulum System ◽

Pendulum Model ◽

Lqr Controller ◽

And Performance ◽

Performance Results

Double inverted pendulum (DIP) is a nonlinear, multivariable and unstable system. The inverted pendulum which continually moves toward an uncontrolled state represents a challenging control problem. The problem is to balance the pendulum vertically upward on a mobile platform that can move in only two directions (left or right) when it is offset from zero stat. The aim is to determine the control strategy that deliver better performance with respect to pendulum's angles and cart's position. A Linear-Quadratic-Regulator (LQR) technique for controlling the linearized system of double inverted pendulum model is presented. Simulation studies conducted in MATLAB environment show that the LQR controller are capable of controlling the multi output double inverted pendulum system. Also better performance results are obtained for controlling heavy driven part DIP system.

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Friction and the Inverted Pendulum Stabilization Problem

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2957631 ◽

2008 ◽

Vol 130 (5) ◽

Cited By ~ 29

Author(s):

Sue Ann Campbell ◽

Stephanie Crawford ◽

Kirsten Morris

Keyword(s):

Small Amplitude ◽

Viscous Friction ◽

Experimental System ◽

Linear Quadratic Regulator ◽

Poor Performance ◽

Friction Model ◽

Linear Quadratic ◽

Stick Slip ◽

And Performance ◽

Friction Parameters

We consider an experimental system consisting of a pendulum, which is free to rotate 360deg, attached to a cart. The cart can move in one dimension. We study the effect of friction on the design and performance of a feedback controller, a linear quadratic regulator, that aims to stabilize the pendulum in the upright position. We show that a controller designed using a simple viscous friction model has poor performance—small amplitude oscillations occur when the controller is implemented. We consider various models for stick slip friction between the cart and the track and measure the friction parameters experimentally. We give strong evidence that stick slip friction is the source of the small amplitude oscillations. A controller designed using a stick slip friction model stabilizes the system, and the small amplitude oscillations are eliminated.

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Polynomial-Chaos-Based Numerical Method for the LQR Problem With Uncertain Parameters in the Formulation

Volume 4: 12th International Conference on Advanced Vehicle and Tire Technologies; 4th International Conference on Micro- and Nanosystems ◽

10.1115/detc2010-28467 ◽

2010 ◽

Cited By ~ 1

Author(s):

Emmanuel Blanchard ◽

Corina Sandu ◽

Adrian Sandu

Keyword(s):

Numerical Method ◽

Polynomial Chaos ◽

Linear Quadratic Regulator ◽

Mean Value ◽

Optimal Controller ◽

Linear Quadratic ◽

Case Scenario ◽

Worst Case ◽

Lqr Problem ◽

And Performance

This paper proposes a polynomial chaos based numerical method providing an optimal controller for the linear-quadratic regulator (LQR) problem when the parameters in the formulation are uncertain, i.e., a controller minimizing the mean value of the LQR cost function obtained for a certain distribution of the uncertainties which is assumed to be known. The LQR problem is written as an optimality problem using Lagrange multipliers in an extended form associated with the polynomial chaos framework, and an iterative algorithm converges to the optimal answer. The algorithm is applied to a simple example for which the answer is already known. Polynomial chaos based methods have the advantage of being computationally much more efficient than Monte Carlo simulations. The Linear-Quadratic Regulator controller is not very well adapted to robust design, and the optimal controller does not guarantee a minimum performance or even stability for the worst case scenario. Stability robustness and performance robustness in the presence of uncertainties are therefore not guaranteed. However, this is a first step aimed at designing more judicious controllers if combined with other techniques in the future. The next logical step would be to extend this numerical method to H2 and then H-infinity problems.

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Design of Optimized PID Controller Based on ABC Algorithm for Buck Converters with Uncertainties

10.5772/intechopen.94907 ◽

2020 ◽

Author(s):

Ibrahim K. Mohammed

Keyword(s):

Pid Controller ◽

Hybrid Control ◽

Control Strategies ◽

Linear Quadratic Regulator ◽

Industrial Applications ◽

Linear Quadratic ◽

Single Input Single Output ◽

Single Output ◽

Hybrid Controller ◽

And Performance

Proportional Integral Derivative (PID) is the most popular controller that is commonly used in wide industrial applications due to its simplicity to realize and performance characteristics. This technique can be successfully applied to control the behavior of single-input single-output (SISO) systems. Extending the using of PID controller for complex dynamical systems has attracted the attention of control engineers. In the last decade, hybrid control strategies are developed by researchers using conventional PID controllers with other controller techniques such as Linear Quadratic Regulator (LQR) controllers. The strategy of the hybrid controller is based on the idea that the parameters of the PID controller are calculated using gain elements of LQR optimal controller. This chapter focuses on design and simulation a hybrid LQR-PID controller used to stabilize elevation, pitch and travel axes of helicopter system. An improvement in the performance of the hybrid LQR-PID controller is achieved by using Genetic Algorithm (GA) which, is adopted to obtain best values of gain parameters for LQR-PID controller.

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Design and Optimization on Active Engine Mounting Systems for Vibration Isolation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.479-480.202 ◽

2013 ◽

Vol 479-480 ◽

pp. 202-209

Author(s):

Pak Kin Wong ◽

Zheng Chao Xie ◽

Yu Cong Cao ◽

Ming Li

Keyword(s):

Analytical Model ◽

Vibration Isolation ◽

Linear Quadratic Regulator ◽

Linear Quadratic ◽

State Equations ◽

Element Analysis ◽

Research Experiences ◽

Design And Optimization ◽

Lumped Parameter ◽

And Performance

In this paper, based on the previous research experiences in the lumped parameter modeling and study of active control mounts model, a test bench model of ACM in powertrain is described and the vibration model is implemented in MATLAB. In order to validate the implementation of the state equations in this work, a finite element analysis (FEA) method is used in ANSYS and compared with analytical model for validate. After the validation, the control strategy is integrated into the analytical model by using the linear quadratic regulator (LQR) method, which is a well know design technique that provides practical feedback gains. Furthermore, this work examines the application of genetic algorithms (GA) in optimizing the weight matrices of LQR. Finally, this work will be useful in improved prediction and performance of vehicle NVH.

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