Control of Ball and Beam with LQR Control Scheme using Flatness Based Approach

2018 ◽  
Author(s):  
Mustansar Shah ◽  
Rahat Ali ◽  
Fahad Mumtaz Malik
Keyword(s):  
Lqr Control ◽  
Control Scheme

FULL-AND REDUCED- ORDER COMPENSATOR FOR INNOSAT ATTITUDE CONTROL

2015 ◽  
Vol 76 (12) ◽  
Author(s):  
Fadzilah Hashim ◽  
Mohd Yusoff Mashor ◽  
Siti Maryam Sharun
Keyword(s):  
State Space ◽  
Attitude Control ◽  
Space Form ◽  
Transfer Functions ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Reduced Order ◽  
Lqr Control ◽  
Best Value ◽  
Control Scheme

This paper presents a study on the estimator based on Linear Quadratic Regulator (LQR) control scheme for Innovative Satellite (InnoSAT). By using LQR control scheme, the controller and the estimator has been derived for state space form in all three axes to stabilize the system’s performance. This study starts by converting the transfer functions of attitude control into state space form.  Then, the step continues by finding the best value of weighting matrices of LQR in order to obtain the best value of controller gain, K. After that, the best value of L is obtained for the estimator gain. The value of K and L is combined in forming full order compensator and in the same time the reduced order compensator is also formed. Lastly, the performance of full order compensator is compared to reduced order compensator. From the simulation, results indicate that both types of estimators have presented good stability and tracking performance. However, reduced order estimator has simpler equation and faster convergence to zero than the full order estimator. This property is very important in developing a satellite attitude control for real-time implementation.

Design and comparison of LQR and a novel robust backstepping controller for supercavitating vehicles

2016 ◽  
Vol 39 (2) ◽  
pp. 149-162 ◽  
Author(s):  
Xiaoyu Zhang ◽  
Yanhui Wei ◽  
Yuntao Han ◽  
Tao Bai ◽  
Kemao Ma
Keyword(s):  
Actuator Saturation ◽  
Control Design ◽  
Linear Quadratic Regulator ◽  
Underwater Vehicles ◽  
Friction Drag ◽  
Linear Quadratic ◽  
Supercavitating Vehicles ◽  
Lqr Control ◽  
Control Scheme ◽  
Backstepping Controller

Traditional underwater vehicles are limited in speed due to dramatic friction drag on the hull. Supercavitating vehicles exploit supercavitation as a means to reduce drag and increase their underwater speed. Compared with fully wetted vehicles, the non-linearity in the modelling of cavitator, fin and in particular the planing force make the control design of supercavitating vehicles more challenging. Dominant non-linearities associated with planing force are taken into account in the model of supercavitating vehicles in this paper. Two controllers are proposed to realize stable system dynamics and tracking responses, a linear quadratic regulator (LQR) control scheme and a robust backstepping control (RBC) scheme. The proposed backstepping procedure, in association with integral filters technique, exploits the possibility of avoiding the overparameterization problem existing in the classical backstepping process. In particular, the achieved stability is robust to modelling errors in supercavitating vehicles. Compared with the LQR control scheme, the RBC scheme is seen to increase the robustness with saturation compensation algorithm, which can be useful for avoiding actuator saturation in magnitude.

scholarly journals Robust LQR-Based Neural-Fuzzy Tracking Control for a Lower Limb Exoskeleton System with Parametric Uncertainties and External Disturbances

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Jyotindra Narayan ◽  
Santosha K. Dwivedy
Keyword(s):  
Lower Limb ◽  
Gait Training ◽  
Lyapunov Theory ◽  
Parametric Uncertainties ◽  
External Disturbances ◽  
Lower Limb Exoskeleton ◽  
Lqr Control ◽  
Control Scheme ◽  
Firing Strength ◽  
Neural Fuzzy

The design of an accurate control scheme for a lower limb exoskeleton system has few challenges due to the uncertain dynamics and the unintended subject’s reflexes during gait rehabilitation. In this work, a robust linear quadratic regulator- (LQR-) based neural-fuzzy (NF) control scheme is proposed to address the effect of payload uncertainties and external disturbances during passive-assist gait training. Initially, the Euler-Lagrange principle-based nonlinear dynamic relations are established for the coupled system. The input-output feedback linearization approach is used to transform the nonlinear relations into a linearized state-space form. The architecture of the adaptive neuro-fuzzy inference system (ANFIS) and used membership function are briefly explained. While varying mass parameters up to 20%, three robust neural-fuzzy datasets are formulated offline with the joint error vector and LQR control input. Thereafter, to deal with external interferences, an error dynamics with a disturbance estimator is presented using an online adaptation of the firing strength matrix. The Lyapunov theory is carried out to ensure the asymptotic stability of the coupled human-exoskeleton system in view of the proposed controller. The gait tracking results for the proposed control scheme (RLQR-NF) are presented and compared with the exponential reaching law-based sliding mode (ERL-SM) controller. Furthermore, to investigate the robustness of the proposed control over LQR control, a comparative performance analysis is presented for two cases of parametric uncertainties and external disturbances. The first case considers the 20% raise in mass values with a trigonometric form of disturbances, and the second case includes the effect of the 30% increment in mass values with a random form of disturbances. The simulation runs have shown the promising gait tracking aspects of the designed controller for passive-assist gait training.

scholarly journals A new algebraic LQR weight selection algorithm for tracking control of 2 DoF torsion system

2017 ◽  
Vol 66 (1) ◽  
pp. 55-75 ◽  
Author(s):  
Vinodh Kumar Elumalai ◽  
Raaja Ganapathy Subramanian
Keyword(s):  
Linear Quadratic Regulator ◽  
High Gain ◽  
Algebraic Riccati Equation ◽  
Selection Algorithm ◽  
Linear Quadratic ◽  
Tracking Errors ◽  
Lqr Control ◽  
Control Scheme ◽  
Design Requirements ◽  
Command Following

Abstract This paper proposes a novel linear quadratic regulator (LQR) weight selection algorithm by synthesizing the algebraic Riccati equation (ARE) with the Lagrange multiplier method for command following applications of a 2 degree of freedom (DoF) torsion system. The optimal performance of LQR greatly depends on the elements of weighting matrices Q and R. However, normally these weighting matrices are chosen by a trial and error approach which is not only time consuming but cumbersome. Hence, to address this issue, blending the design criteria in time domain with the ARE, we put forward an algebraic weight selection algorithm, which makes the LQR design both simple and modular. Moreover, to estimate the velocity of a servo angle, a high gain observer (HGO) is designed and integrated with the LQR control scheme. The efficacy of the proposed control scheme is tested on a benchmark 2 DoF torsion system for a trajectory tracking application. Both the steady state and dynamic characteristics of the proposed controller are assessed. The experimental results accentuate that the proposed HGO based LQR scheme can guarantee the system to attain the design requirements with minimal vibrations and tracking errors.

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