Fractional Order Filter Enhanced LQR for Seismic Protection of Civil Structures

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Abdollah Shafieezadeh ◽  
Keri Ryan ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Ground Motions ◽  
Linear Quadratic Regulator ◽  
Performance Criterion ◽  
Seismic Protection ◽  
State Variables ◽  
Linear Quadratic ◽  
Civil Structures ◽  
Order Filter ◽  
Earthquake Data

This study presents fractional order filters to enhance the performance of the conventional linear quadratic regulator (LQR) method for optimal robust control of a simple civil structure. The introduced filters modify the state variables fed back to the constant gain controller. Four combinations of fractional order filter and LQR are considered and optimized based on a new performance criterion defined in the paper. Introducing fractional order filters is shown to considerably improve the results for both the artificially generated ground motions and previously recorded earthquake data.

scholarly journals Design of Static Output Feedback and Structured Controllers for Active Suspension with Quarter-Car Model

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8231
Author(s):  
Manbok Park ◽  
Seongjin Yim
Keyword(s):  
Output Feedback ◽  
Ride Comfort ◽  
Linear Quadratic Regulator ◽  
Active Suspension ◽  
Static Output Feedback ◽  
State Variables ◽  
Linear Quadratic ◽  
Suspension Control ◽  
Quarter Car ◽  
Static Output

This paper presents a method to design active suspension controllers for a 7-Degree-of-Freedom (DOF) full-car (FC) model from controllers designed with a 2-DOF quarter-car (QC) one. A linear quadratic regulator (LQR) with 7-DOF FC model has been widely used for active suspension control. However, it is too hard to implement the LQR in real vehicles because it requires so many state variables to be precisely measured and has so many elements to be implemented in the gain matrix of the LQR. To cope with the problem, a 2-DOF QC model describing vertical motions of sprung and unsprung masses is adopted for controller design. LQR designed with the QC model has a simpler structure and much smaller number of gain elements than that designed with the FC one. In this paper, several controllers for the FC model are derived from LQR designed with the QC model. These controllers can give equivalent or better performance than that designed with the FC model in terms of ride comfort. In order to use available sensor signals instead of using full-state feedback for active suspension control, LQ static output feedback (SOF) and linear quadratic Gaussian (LQG) controllers are designed with the QC model. From these controllers, observer-based controllers for the FC model are also derived. To verify the performance of the controllers for the FC model derived from LQR and LQ SOF ones designed with the QC model, frequency domain analysis is undertaken. From the analysis, it is confirmed that the controllers for the FC model derived from LQ and LQ SOF ones designed with the QC model can give equivalent performance to those designed with the FC one in terms of ride comfort.

Evolutionary Control Systems

2018 ◽  
pp. 195-237
Author(s):  
Jesús-Antonio Hernández-Riveros ◽  
Jorge Humberto Urrea-Quintero ◽  
Cindy Vanessa Carmona-Cadavid
Keyword(s):  
Control Systems ◽  
Transfer Functions ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
Performance Criterion ◽  
Linear Quadratic ◽  
Tuning Method ◽  
Current Trends ◽  
Lqr Controller ◽  
Process Behavior

In control systems, the actual output is compared with the desired value so a corrective action maintains an established behavior. The industrial controller most widely used is the proportional integral derivative (PID). For PIDs, the process is represented in a transfer function. The linear quadratic regulator (LQR) controller needs a state space model. The process behavior depends on the setting of the controller parameters. Current trends in estimating those parameters optimize an integral performance criterion. In this chapter, a unified tuning method for controllers is presented, the evolutionary algorithm MAGO optimizes the parameters of several controllers minimizing the ITAE index, applied on benchmark plants, operating on servo and regulator modes, and representing the system in both transfer functions and differential equation systems. The evolutionary approach gets a better overall performance comparing with traditional methods. The evolutionary method is indeed better than the classical, eliminating the uncertainty in the controller parameters. Better results are yielded with MAGO algorithm than with optimal PID, optimal-robust PID, and LQR.

Fractional Order LQR for Optimal Robust Control of a Simple Structure

2007 ◽  
Author(s):  
Abdollah Shafieezadeh ◽  
Keri Ryan ◽  
YangQuan Chen
Keyword(s):  
Robust Control ◽  
Control Problem ◽  
Fractional Order ◽  
Simple Structure ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Fractional Damping ◽  
Fractional Order Control

This study combines fractional order control with linear quadratic regulator (LQR) for optimal robust control of a simple civil structure. As a first attempt, the purpose of this paper is to demonstrate that, when fractional damping is introduced, additional benefits can be obtained over the best traditional control method. The control problem of this paper can be used as a simple benchmark example to test new control ideas before applying to more complicated models.

scholarly journals Fractional-Order Fuzzy Control Approach for Photovoltaic/Battery Systems under Unknown Dynamics, Variable Irradiation and Temperature

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1455
Author(s):  
Amirhosein Mosavi ◽  
Sultan Noman Qasem ◽  
Manouchehr Shokri ◽  
Shahab S. Band ◽  
Ardashir Mohammadzadeh
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Fuzzy Logic Systems ◽  
Control Approach ◽  
Operation Conditions ◽  
Battery Systems ◽  
Temperature Variable ◽  
Voltage Management

For this paper, the problem of energy/voltage management in photovoltaic (PV)/battery systems was studied, and a new fractional-order control system on basis of type-3 (T3) fuzzy logic systems (FLSs) was developed. New fractional-order learning rules are derived for tuning of T3-FLSs such that the stability is ensured. In addition, using fractional-order calculus, the robustness was studied versus dynamic uncertainties, perturbation of irradiation, and temperature and abruptly faults in output loads, and, subsequently, new compensators were proposed. In several examinations under difficult operation conditions, such as random temperature, variable irradiation, and abrupt changes in output load, the capability of the schemed controller was verified. In addition, in comparison with other methods, such as proportional-derivative-integral (PID), sliding mode controller (SMC), passivity-based control systems (PBC), and linear quadratic regulator (LQR), the superiority of the suggested method was demonstrated.

A Control Scheme for an Opposed Recumbent Tandem Human-Powered Bicycle

1996 ◽  
Vol 12 (4) ◽  
pp. 480-492
Author(s):  
Scott O. Cloyd ◽  
Mont Hubbard ◽  
LeRoy W. Alaways
Keyword(s):  
Feedback Control ◽  
Linear Quadratic Regulator ◽  
Optimal Feedback Control ◽  
State Variables ◽  
Linear Quadratic ◽  
Lateral Deviation ◽  
Control Scheme ◽  
Control Schemes ◽  
Lean Angle ◽  
Human Powered

Feedback control of a human-powered single-track bicycle is investigated through the use of a linearized dynamical model in order to develop feedback gains that can be implemented by a human pilot in an actual vehicle. The object of the control scheme is to satisfy two goals: balance and tracking. The pilot should be able not only to keep the vehicle upright but also to direct the forward motion as desired. The two control inputs, steering angle and rider lean angle, are assumed to be determined by the rider as a product of feedback gains and “measured” values of the state variables: vehicle lean, lateral deviation from the desired trajectory, and their derivatives. Feedback gains are determined through linear quadratic regulator theory. This results in two control schemes, a “full” optimal feedback control and a less complicated technique that is more likely to be usable by an inexperienced pilot. Theoretical optimally controlled trajectories are compared with experimental trajectories in a lane change maneuver.

scholarly journals Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System

2021 ◽  
Vol 11 (7) ◽  
pp. 3252
Author(s):  
Akihiro Takeshita ◽  
Tomohiro Yamashita ◽  
Natsuki Kawaguchi ◽  
Masaharu Kuroda
Keyword(s):  
Fractional Order ◽  
Linear Quadratic Regulator ◽  
State Observer ◽  
State Equation ◽  
Algebraic Riccati Equation ◽  
Linear Quadratic ◽  
Vibratory System ◽  
Derivative Term ◽  
Numerical Calculation Method ◽  
Order State

The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order to estimate the states originating from the fractional-order derivative term. Fourth, numerical simulations are presented using a numerical calculation method corresponding to a fractional-order state equation. Finally, the numerical simulation results demonstrate that the fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping.

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