Mathematical Model and Vibration Analysis of Aircraft with Active Landing Gear System using Linear Quadratic Regulator Technique

This paper deals with the active control of a non-linear active landing gear system equipped with oleo pneumatic shock absorber. Runway induced vibration can cause reduction of pilot’s capability of control the aircraft and results the safety problem before take-off and after landing. Moreover, passenger–crew comfort is adversely affected by vertical vibrations of the fuselage. The active landing gears equipped with oleo pneumatic shock absorber are highly non-linear systems. In this study, uncertain polytopic state space representation is developed by modelling the pneumatic shock absorber dynamics as a mechanical system with non-linear stiffness and damping properties. Then, linear matrix inequalities-based robust linear quadratic regulator controller having pole location constraints is designed, since the classical linear quadratic regulator control design is dealing with linearized state space models without considering the non-linearities and uncertainties. Thereafter, numerical simulation studies are carried out to analyse aircraft response during taxiing. Bump- and random-type runway irregularities are used with various runway class and wide range of longitudinal speed. Simulation results revealed that neglecting the non-linear dynamics associated with oleo pneumatic shock absorber results significant performance degradation. Consequently, it is demonstrated that proposed robust linear quadratic regulator controller has a superior performance in terms of passenger–crew comfort and operational safety when compared to classical linear quadratic regulator.

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FULL CAR ACTIVE DAMPING SYSTEM FOR VIBRATION CONTROL

International Journal of Engineering Technologies and Management Research ◽

10.29121/ijetmr.v6.i4.2019.365 ◽

2020 ◽

Vol 6 (4) ◽

pp. 1-17

Author(s):

G. Yakubu ◽

G. Sani ◽

S. B. Abdulkadir ◽

A. A.Jimoh ◽

M. Francis

Keyword(s):

Mathematical Model ◽

Linear Quadratic Regulator ◽

Active Damping ◽

Settling Time ◽

Linear Quadratic ◽

Body Acceleration ◽

The Road ◽

Road Profile ◽

Lqr Controller ◽

Mass Displacement

Full car passive and active damping system mathematical model was developed. Computer simulation using MATLAB was performed and analyzed. Two different road profile were used to check the performance of the passive and active damping using Linear Quadratic Regulator controller (LQR)Road profile 1 has three bumps with amplitude of 0.05m, 0.025 m and 0.05 m. Road profile 2 has a bump with amplitude of 0.05 m and a hole of -0.025 m. For all the road profiles, there were 100% amplitude reduction in Wheel displacement, Wheel deflection, Suspension travel and body displacement, and 97.5% amplitude reduction in body acceleration for active damping with LQR controller as compared to the road profile and 54.0% amplitude reduction in body acceleration as compared to the passive damping system. For the two road profiles, the settling time for all the observed parameters was less than two (2) seconds. The present work gave faster settling time for mass displacement, body acceleration and wheel displacement.

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Swing Vibration Control of Suspended Structure Using Active Rotary Inertia Driver System: Parametric Analysis and Experimental Verification

Applied Sciences ◽

10.3390/app9153144 ◽

2019 ◽

Vol 9 (15) ◽

pp. 3144 ◽

Cited By ~ 12

Author(s):

Chunwei Zhang ◽

Hao Wang

Keyword(s):

Mathematical Model ◽

Control System ◽

Vibration Control ◽

Parametric Analysis ◽

Linear Quadratic Regulator ◽

Shaking Table ◽

Rotary Inertia ◽

System Control ◽

Linear Quadratic ◽

Control Effectiveness

The Active Rotary Inertia Driver (ARID) system is a novel vibration control system that can effectively mitigate the swing vibration of suspended structures. Parametric analysis is carried out using Simulink based on the mathematical model and the effectiveness is further validated by a series of experiments. Firstly, the active controller is designed based on the system mathematical model and the LQR (linear quadratic regulator) algorithm. Next, the parametric analysis is carried out using Simulink to study the key parameters such as the coefficient of the control algorithm, the rotary inertia ratio. Lastly, the ARID system control effectiveness and the parametric analysis results are further validated by the shaking table experiments. The effectiveness and robustness of the ARID system are well verified. The dynamic characteristics of this system are further studied, and the conclusions of this paper provide a theoretical basis for further development of such unique control system.

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Modeling, Simulation, and Optimal Control for Two-Wheeled Self-Balancing Robot

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v7i4.pp2008-2017 ◽

2017 ◽

Vol 7 (4) ◽

pp. 2008 ◽

Cited By ~ 6

Author(s):

Modestus Oliver Asali ◽

Ferry Hadary ◽

Bomo Wibowo Sanjaya

Keyword(s):

Mathematical Model ◽

Inverted Pendulum ◽

Linear Quadratic Regulator ◽

Linear Quadratic ◽

Modeling Simulation ◽

Mathematic Modeling ◽

Lqr Controller ◽

Output System ◽

Balancing Robot ◽

Cart Model

Two-wheeled self-balancing robot is a popular model in control system experiments which is more widely known as inverted pendulum and cart model. This is a multi-input and multi-output system which is theoretical and has been applied in many systems in daily use. Anyway, most research just focus on balancing this model through try-on experiments or by using simple form of mathematical model. There were still few researches that focus on complete mathematic modeling and designing a mathematical model based controller for such system. This paper analyzed mathematical model of the system. Then, the authors successfully applied a Linear Quadratic Regulator (LQR) controller for this system. This controller was tested with different case of system condition. Controlling results was proved to work well and tested on different case of system condition through simulation on matlab/Simulink program.

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Design of Flight Control System for a Novel Tilt-Rotor UAV

Complexity ◽

10.1155/2020/4757381 ◽

2020 ◽

Vol 2020 ◽

pp. 1-14

Author(s):

Zaibin Chen ◽

Hongguang Jia

Keyword(s):

Mathematical Model ◽

Control System ◽

Flight Control ◽

Actuator Saturation ◽

High Reliability ◽

Linear Quadratic Regulator ◽

Control Law ◽

Linear Quadratic ◽

Tilt Rotor ◽

Configuration Scheme

This paper presents the control system design process of a novel tilt-rotor unmanned aerial vehicle (TRUAV). First, a new configuration scheme with the tilting rotors is designed. Then, the detailed nonlinear mathematical model is established, and the parameters are acquired from designed experiments and numerical analyses. For control design purposes, the dynamics equation is linearized around the hovering equilibrium point, and a control allocation method based on trim calculation is developed. To deal with the actuator saturation and uncertain disturbance problems for the novel TRUAV, an improved flight control law based on the combination of the robust servo linear quadratic regulator (RSLQR) optimal control and the extended state observer (ESO) is proposed. The designed flight control law has a simple structure with a high reliability in engineering. Simulations and hovering flight tests are carried out to verify the effectiveness of the mathematical model and the proposed control strategy.

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Linear quadratic regulator and pole placement for stabilizing a cart inverted pendulum system

Bulletin of Electrical Engineering and Informatics ◽

10.11591/eei.v9i3.2017 ◽

2020 ◽

Vol 9 (3) ◽

pp. 914-923

Author(s):

Mila Fauziyah ◽

Zakiyah Amalia ◽

Indrazno Siradjuddin ◽

Denda Dewatama ◽

Rendi Pambudi Wicaksono ◽

...

Keyword(s):

Mathematical Model ◽

System Performance ◽

Inverted Pendulum ◽

Linear Quadratic Regulator ◽

Pole Placement ◽

Underactuated System ◽

Mechanical Transmission ◽

Linear Quadratic ◽

Pendulum System ◽

Inverted Pendulum System

The system of a cart inverted pendulum has many problems such as nonlinearity, complexity, unstable, and underactuated system. It makes this system be a benchmark for testing many control algorithm. This paper presents a comparison between 2 conventional control methods consist of a linear quadratic regulator (LQR) and pole placement. The comparison indicated by the most optimal steps and results in the system performance that obtained from each method for stabilizing a cart inverted pendulum system. A mathematical model of DC motor and mechanical transmission are included in a mathematical model to minimize the realtime implementation problem. From the simulation, the obtained system performance shows that each method has its advantages, and the desired pendulum angle and cart position reached.

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Modeling, simulation and control of a twin-inverted pendulum on a moving cart

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962321500276 ◽

2021 ◽

pp. 2150027

Author(s):

Jasem Tamimi

Keyword(s):

Mathematical Model ◽

Inverted Pendulum ◽

Linear Quadratic Regulator ◽

Euler Method ◽

Linear Quadratic ◽

Highly Nonlinear ◽

Efficient Control ◽

Simple Matrix ◽

And Control ◽

Unstable Dynamics

In this paper, a mathematical model of a twin-inverted pendulum on a moving cart has been derived. This is done using the Lagrange–Euler method and, hence, a highly nonlinear mathematical model is resulted from this derivation. These nonlinear and unstable dynamics are written in a simple matrix form. For this challenging system, we use two types of efficient control approaches to treat the control problem of the twin inverted pendulum, namely, linear quadratic regulator (LQR) and nonlinear model predictive control (NMPC). Simulations with several scenarios are also presented to demonstrate the control performances and the model validity.

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