A Study into the Relationship between the Procedures for the Pole Placement Problem and Linear Quadratic Regulator

2018 ◽  
Author(s):  
Nasko Raychev Atanasov ◽  
Mariela Ivanova Alexandrova ◽  
Ivan Veselinov Grigorov ◽  
Ivelina Yordanova Zlateva
Keyword(s):  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
Linear Quadratic ◽  
Placement Problem ◽  
The Relationship

scholarly journals Mathematical Modelling and Control of a Two-Wheeled PUMA-LikeVehicle

2016 ◽  
Vol 6 (2) ◽  
pp. 11 ◽  
Author(s):  
Khaled M Goher
Keyword(s):  
Mathematical Modelling ◽  
Sliding Mode ◽  
Impact Load ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
The Body ◽  
Pole Placement ◽  
General Motors ◽  
Linear Quadratic ◽  
And Control

<p class="1Body">This paper presents mathematical modelling and control of a two-wheeled single-seat vehicle. The design of the vehicle is inspired by the Personal Urban Mobility and Accessibility (PUMA) vehicle developed by General Motors® in collaboration with Segway®. The body of the vehicle is designed to have two main parts. The vehicle is activated using three motors; a linear motor to activate the upper part in a sliding mode and two DC motors activating the vehicle while moving forward/backward and/or manoeuvring. Two stages proportional-integral-derivative (PID) control schemes are designed and implemented on the system models. The state space model of the vehicle is derived from the linearized equations. Controller based on the Linear Quadratic Regulator (LQR) and the pole placement techniques are developed and implemented. Further investigation of the robustness of the developed LQR and the pole placement techniques is emphasized through various experiments using an applied impact load on the vehicle.</p>

scholarly journals Stabilized controller of a two wheels robot

2020 ◽  
Vol 9 (4) ◽  
pp. 1357-1363
Author(s):  
Ahmad Fahmi ◽  
Marizan Sulaiman ◽  
Indrazno Siradjuddin ◽  
I Made Wirawan ◽  
Abdul Syukor Mohamad Jaya ◽  
...  
Keyword(s):  
Control Method ◽  
Control Function ◽  
Balance Control ◽  
Linear Quadratic Regulator ◽  
Zero Point ◽  
Stability Control ◽  
Pole Placement ◽  
Linear Quadratic ◽  
Balancing Robot ◽  
The Stability

The Segway Human Transport (HT) robot, it is dynamical self-balancing robot type. The stability control is an important thing for the Segway robot. It is an indisputable fact that Segway robot is a natural instability framework robot. The case study of the Segway robot focuses on running balance control systems. The roll, pitch, and yaw balance of this robot are obtained by estimating the Kalman Filter with a combination of the pole placement and the Linear Quadratic Regulator (LQR) control method. In our system configuration, the mathematical model of the robot will be proved by Matlab Simulink by modelling of the stabilizing control system of all state variable input. Furthermore, the implementation of this system modelled to the real-time test of the Segway robot. The expected result is by substitute the known parameters from Gyro, Accelero and both rotary encoder to initial stabilize control function, the system will respond to the zero input curve. The coordinate units of displacement response and inclination response pictures are the same. As our expected, the response of the system can reach the zero point position. 

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

2010 ◽  
Vol 10 (03) ◽  
pp. 501-527 ◽  
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.

Diagonal Recurrent Neural Networks for MDOF Structural Vibration Control

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Z. Q. Gu ◽  
S. O. Oyadiji
Keyword(s):  
Vibration Control ◽  
Control Method ◽  
Control Strategies ◽  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
Structural Vibration ◽  
Stability And Convergence ◽  
Northridge Earthquake ◽  
Linear Quadratic ◽  
Structural Vibration Control

In recent years, considerable attention has been paid to the development of theories and applications associated with structural vibration control. Integrating the nonlinear mapping ability with the dynamic evolution capability, diagonal recurrent neural network (DRNN) meets the needs of the demanding control requirements in increasingly complex dynamic systems because of its simple and recurrent architecture. This paper presents numerical studies of multiple degree-of-freedom (MDOF) structural vibration control based on the approach of the backpropagation algorithm to the DRNN control method. The controller’s stability and convergence and comparisons of the DRNN method with conventional control strategies are also examined. The numerical simulations show that the structural vibration responses of linear and nonlinear MDOF structures are reduced by between 78% and 86%, and between 52% and 80%, respectively, when they are subjected to El Centro, Kobe, Hachinohe, and Northridge earthquake processes. The numerical simulation shows that the DRNN method outperforms conventional control strategies, which include linear quadratic regulator (LQR), linear quadratic Gaussian (LQG) (based on the acceleration feedback), and pole placement by between 20% and 30% in the case of linear MDOF structures. For nonlinear MDOF structures, in which the conventional controllers are ineffective, the DRNN controller is still effective. However, the level of reduction of the structural vibration response of nonlinear MDOF structures achievable is reduced by about 20% in comparison to the reductions achievable with linear MDOF structures.

scholarly journals Inverse optimal control from incomplete trajectory observations

2021 ◽  
pp. 027836492199638
Author(s):  
Wanxin Jin ◽  
Dana Kulić ◽  
Shaoshuai Mou ◽  
Sandra Hirche
Keyword(s):  
Optimal Control ◽  
Objective Function ◽  
Control Algorithm ◽  
Robot Manipulator ◽  
Linear Quadratic Regulator ◽  
Inverse Optimal Control ◽  
Linear Quadratic ◽  
System States ◽  
Segment Data ◽  
The Relationship

This article develops a methodology that enables learning an objective function of an optimal control system from incomplete trajectory observations. The objective function is assumed to be a weighted sum of features (or basis functions) with unknown weights, and the observed data is a segment of a trajectory of system states and inputs. The proposed technique introduces the concept of the recovery matrix to establish the relationship between any available segment of the trajectory and the weights of given candidate features. The rank of the recovery matrix indicates whether a subset of relevant features can be found among the candidate features and the corresponding weights can be learned from the segment data. The recovery matrix can be obtained iteratively and its rank non-decreasing property shows that additional observations may contribute to the objective learning. Based on the recovery matrix, a method for using incomplete trajectory observations to learn the weights of selected features is established, and an incremental inverse optimal control algorithm is developed by automatically finding the minimal required observation. The effectiveness of the proposed method is demonstrated on a linear quadratic regulator system and a simulated robot manipulator.

scholarly journals Performance Evaluation of Pole Placement and Linear Quadratic Regulator Strategies Designed for Mass-Spring-Damper System Based on Simulated Annealing and Ant Colony Optimization

2021 ◽  
Vol 27 (11) ◽  
pp. 15-31
Author(s):  
Huthaifa Al-Khazraji ◽  
Luay T. Rasheed
Keyword(s):  
Performance Evaluation ◽  
Simulated Annealing ◽  
State Feedback ◽  
Linear Quadratic Regulator ◽  
The State ◽  
Ant Colony ◽  
System Stability ◽  
Pole Placement ◽  
Linear Quadratic ◽  
Mass Spring

This paper investigates the performance evaluation of two state feedback controllers, Pole Placement (PP) and Linear Quadratic Regulator (LQR). The two controllers are designed for a Mass-Spring-Damper (MSD) system found in numerous applications to stabilize the MSD system performance and minimize the position tracking error of the system output. The state space model of the MSD system is first developed. Then, two meta-heuristic optimizations, Simulated Annealing (SA) optimization and Ant Colony (AC) optimization are utilized to optimize feedback gains matrix K of the PP and the weighting matrices Q and R of the LQR to make the MSD system reach stabilization and reduce the oscillation of the response. The Matlab software has been used for simulations and performance analysis. The results show the superiority of the state feedback based on the LQR controller in improving the system stability, reducing settling time, and reducing maximum overshoot. Furthermore, AC optimization shows significant advantages for optimizing the parameters of PP and LQR and reducing the fitness value in comparison with SA optimization

scholarly journals Feedback Control Methods for a Single Machine Infinite Bus System

2020 ◽  
Author(s):  
Pratik Vernekar ◽  
Zhongkui Wang ◽  
Andrea Serrani ◽  
Kevin Passino
Keyword(s):  
Single Machine ◽  
Linear Models ◽  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
High Fidelity ◽  
Nonlinear Feedback ◽  
Linear Quadratic ◽  
Reduced Order ◽  
System P ◽  
Single Machine Infinite Bus

In this manuscript, we present a high-fidelity physics-based truth model of a Single Machine Infinite Bus (SMIB) system. We also present reduced-order control-oriented nonlinear and linear models of a synchronous generator-turbine system connected to a power grid. The reduced-order control-oriented models are next used to design various control strategies such as: proportional-integral-derivative (PID), linear-quadratic regulator (LQR), pole placement-based state feedback, observer-based output feedback, loop transfer recovery (LTR)-based linear-quadratic-Gaussian (LQG), and nonlinear feedback-linearizing control for the SMIB system. The controllers developed are then validated on the high-fidelity physics-based truth model of the SMIB system. Finally, a comparison is made of the performance of the controllers at different operating points of the SMIB system.

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