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.

Formulation of a State Equation Including Fractional-Order State-Vectors

2007 ◽  
Author(s):  
Masaharu Kuroda
Keyword(s):  
Fractional Calculus ◽  
Control Theory ◽  
Fractional Order ◽  
State Equation ◽  
The State ◽  
Space Representation ◽  
Fractional Dynamics ◽  
Modern Control Theory ◽  
Order State ◽  
Modern Control

In recent years, applications of fractional calculus have flourished in various science and engineering fields. Particularly in engineering, control engineering appears to be expanding aggressively in its applications. Exemplary are the CRONE controller and the PIλDμ controller, which is categorizable into applications of fractional calculus in classical control theory. A state equation can be called the foundation of modern control theory. However, the relationship between fractional derivatives and the state equation has not been examined sufficiently. Consequently, a systematic procedure referred to by every researcher on the fractional-calculus side or control-theory side has not yet been established. For this study, therefore, involvement of fractional-order derivatives into a state equation is demonstrated here for ready comprehension by researchers. First, the procedures are explained generally; then the technique to incorporate the fractional-order state-vector into a conventional state equation is given as an example of the applications. The state-space representation in this study is useful not only for modeling a controlled system with fractional dynamics, but also for design and implementation of a controller to control fractional-order states. After we complete installation of the basic parts, we can apply the benefits of modern control theory, including robust control theories such as H-infinity and μ-analysis and synthesis in their integrities, to this fractional-order state-equation.

scholarly journals Actuator Placement for Active Surge Control in a Multi-Stage Axial Compressor

1996 ◽  
Author(s):  
M. Montazeri-Gh. ◽  
D. J. Allerton ◽  
R. L. Elder
Keyword(s):  
Cost Function ◽  
Mass Flow ◽  
Controller Design ◽  
Axial Compressor ◽  
Minimum Cost ◽  
Linear Quadratic Regulator ◽  
Algebraic Riccati Equation ◽  
Linear Quadratic ◽  
Non Linear ◽  
Actuator Placement

This paper describes an actuator placement methodology for the active control of purely one-dimensional instabilities of a seven-stage axial compressor using an air bleeding strategy. In this theoretical study, using stage-by-stage non-linear modelling based on the conservation equations of mass, momentum, and energy, a scheduling LQR (Linear Quadratic Regulator) controller is designed for several actuator locations in a compressor from the first stage to the plenum. In this controller design, the LQR weighting matrices are selected so that the associated cost function includes only air bleeding mass flow leading to the minimisation of the air bleed. The LQR cost function represents a measure of the consumption of air bleeding and can be calculated analytically using the solution of an Algebraic Riccati Equation. From analysis of the cost at different compressor stages, the location of an air bleeding actuator is selected at the stage with the minimum cost. Finally, using an ACSL simulation program, the scheduling controller has been integrated with a non-linear. stage-by-stage model and the time response of the air bleeding mass flow at different locations has been obtained to confirm the results from the analytical approach. Results are presented to show actively stabilised compressor flow beyond the surge point where the air bleed is minimised. These results also indicate the preferred location of the actuator at the compressor downstream stages for both low and high compressor speeds.

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.

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.

Formulation of A State Equation Including Fractional-Order State Vectors

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Masaharu Kuroda
Keyword(s):  
Fractional Calculus ◽  
Control Theory ◽  
Fractional Order ◽  
State Equation ◽  
The State ◽  
Space Representation ◽  
Fractional Dynamics ◽  
Modern Control Theory ◽  
Order State ◽  
Modern Control

In recent years, applications of fractional calculus have flourished in various science and engineering fields. Particularly in engineering, control engineering appears to be expanding aggressively in their applications. Exemplary are the CRONE controller and the PIλDμ controller, which is categorizable into applications of fractional calculus in classical control theory. A state equation can be called as the foundation of modern control theory. However, the relationship between fractional derivatives and the state equation has not been examined sufficiently. Consequently, a systematic procedure referred to every researcher on the fractional-calculus side or control-theory side has not yet been established. For this study, therefore, involvement of fractional-order derivatives into a state equation is demonstrated here for ready comprehension by researchers. First, the procedures are explained generally; then the technique to incorporate a fractional-order state vector into a conventional state equation is given as an example of the applications. The state-space representation in this study is useful not only to model a controlled system with fractional dynamics but also for design and implementation of a controller to control fractional-order states. After introducing the basic parts, the benefits of modern control theory including robust control theories, such as H∞ and μ-analysis and synthesis in their integrities, can be applied to this fractional-order state equation.

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