Control of a Linear Time-Varying System With a Forward Riccati Formulation in Wavelet Domain

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Biswajit Basu ◽  
Andrea Staino
Keyword(s):  
Linear Time ◽  
Control Strategies ◽  
Linear Quadratic Regulator ◽  
Time Varying ◽  
Wavelet Domain ◽  
Nonlinear Controller ◽  
Linear Quadratic ◽  
Time Frequency ◽  
Future System ◽  
Control Feedback

A wavelet domain forward differential Ricatti formulation is proposed in this paper for control of linear time-varying (LTV) systems. The control feedback gains derived are time-frequency dependent, and they can be appropriately tuned for each wavelet scale or frequency band. The gains in the proposed forward formulation are functions of the present and past states and hence lead to a nonlinear controller. This nonlinear controller does not require information or approximation about future system matrices. The proposed controller is suitable for systems with time-varying (TV) system matrices and also for controlling transient dynamics. The performance of the proposed controller is compared with two other control strategies, namely, a TV linear quadratic regulator (LQR) based on a backward formulation of the differential Ricatti equation (DRE) and a multiscale wavelet-LQR controller based on asymptotic assumptions. Two numerical examples demonstrate promising results on the performance of the controller.

scholarly journals A periodic linear–quadratic controller for suppressing rotor-blade vibration

2019 ◽  
Vol 25 (17) ◽  
pp. 2351-2364 ◽  
Author(s):  
J. F. Camino ◽  
I. F. Santos
Keyword(s):  
Rotor Blade ◽  
Linear Time ◽  
Linear Quadratic Regulator ◽  
Time Varying ◽  
Linear Quadratic ◽  
Blade Vibration ◽  
Linear Quadratic Optimal Control ◽  
Riccati Differential Equation ◽  
Periodic Linear ◽  
Lqr Problem

This paper presents an active control strategy, based on a time-varying linear–quadratic optimal control problem, to attenuate the tip vibration of a two-dimensional coupled rotor-blade system whose dynamics is periodic. First, a periodic full-state feedback controller based on the linear–quadratic regulator (LQR) problem is designed. If all the states are not available for feedback, then an optimal periodic time-varying estimator, using the Kalman–Bucy filter, is computed. Both the Kalman filter gain and the LQR gain are obtained as the solution of a periodic Riccati differential equation (PRDE). Together, these gains provide the observer-based linear–quadratic–Gaussian (LQG) controller. An algorithm to solve the PRDE is also presented. Both controller designs ensure closed-loop stability and performance for the linear time-varying rotor-blade equation of motion. Numerical simulations show that the LQR and the LQG controllers are able to significantly attenuate the rotor-blade tip vibration.

scholarly journals DYNAMICS BASED CONTROL OF A SKID STEERING MOBILE ROBOT

2016 ◽  
Vol 9 (2) ◽  
pp. 70 ◽  
Author(s):  
Osama Elshazly ◽  
Hossam Abbas ◽  
Zakarya Zyada
Keyword(s):  
Mobile Robot ◽  
Inverse Dynamics ◽  
Linear Quadratic Regulator ◽  
Nonlinear Controller ◽  
Linear Quadratic ◽  
Reduced Order ◽  
Lqr Control ◽  
Control Schemes ◽  
Skid Steering ◽  
Drive Model

In this paper, development of a reduced order, augmented dynamics-drive model that combines both the dynamics and drive subsystems of the skid steering mobile robot (SSMR) is presented. A Linear Quadratic Regulator (LQR) control algorithm with feed-forward compensation of the disturbances part included in the reduced order augmented dynamics-drive model is designed. The proposed controller has many advantages such as its simplicity in terms of design and implementation in comparison with complex nonlinear control schemes that are usually designed for this system. Moreover, the good performance is also provided by the controller for the SSMR comparable with a nonlinear controller based on the inverse dynamics which depends on the availability of an accurate model describing the system. Simulation results illustrate the effectiveness and enhancement provided by the proposed controller.

Harmonic Current Distortion Using the Linear Quadratic Regulator for a Grid-Connected Photovoltaic System

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Oscar Andrew Zongo ◽  
Anant Oonsivilai
Keyword(s):  
Control Strategies ◽  
Harmonic Distortion ◽  
Linear Quadratic Regulator ◽  
Photovoltaic System ◽  
Voltage Source ◽  
Linear Quadratic ◽  
Grid Current ◽  
Harmonic Currents ◽  
Low Pass ◽  
Low Pass Filters

This paper presents a comparison between a proportional-integral controller, low pass filters, and the linear quadratic regulator in dealing with the task of eliminating harmonic currents in the grid-connected photovoltaic system. A brief review of the existing methods applied to mitigate harmonic currents is presented. The Perturb & Observe technique was employed for maximum power point tracking. The PI control, low pass filters, and the linear quadratic regulator are discussed in detail in terms of their control strategies. The grid current was analyzed in the system with all three of the controllers applied to control the voltage source inverter of the solar photovoltaic system connected to the grid through an L filter and LCL filter and simulated in MATLAB/SIMULINK. The simulation results obtained have proven the robustness of the linear quadratic regulator over other methods. The technique lowers the grid current total harmonic distortion from 7.85% to 2.13%.

Linear time-varying systems analysis in wavelet domain

2006 ◽  
Vol 89 (8) ◽  
pp. 653-658
Author(s):  
Hasari Karci ◽  
Gulay Tohumoglu
Keyword(s):  
Systems Analysis ◽  
Linear Time ◽  
Time Varying ◽  
Wavelet Domain ◽  
Time Varying Systems

LQG Control Design for Vehicle Active Anti-Roll Bar System

2014 ◽  
Vol 663 ◽  
pp. 146-151 ◽  
Author(s):  
Noraishikin Zulkarnain ◽  
Hairi Zamzuri ◽  
Saiful Amri Mazlan
Keyword(s):  
Ride Comfort ◽  
Simulation Analysis ◽  
Control Strategies ◽  
Dynamic Modelling ◽  
Linear Quadratic Regulator ◽  
Vehicle Body ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Roll Rate ◽  
External Forces

The objective of this paper is to design a linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controllers for an active anti-roll bar system. The use of an active anti-roll bar will be analysed from two different perspectives in vehicle ride comfort and handling performances. This paper proposed the basic vehicle dynamic modelling with four degree of freedom (DOF) on half car model and are described that show, why and how it is possible to control the handling and ride comfort of the car, with the external forces also control strategies on the front anti-roll bar. By simulation analysis, the design model is validity and the performance under control of linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller are achieved. Both two controllers are modeled in MATLAB/SIMULINK environment. It has to be determined which control strategy delivers better performance with respect to roll angle and the roll rate of half vehicle body. The result shows, however, that LQG produced better response compared to a LQR strategy.

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