scholarly journals Active Suspension Control Using an MPC-LQR-LPV Controller with Attraction Sets and Quadratic Stability Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2533
Author(s):  
Daniel Rodriguez-Guevara ◽  
Antonio Favela-Contreras ◽  
Francisco Beltran-Carbajal ◽  
David Sotelo ◽  
Carlos Sotelo
Keyword(s):  
Nonlinear Behavior ◽  
Linear Quadratic Regulator ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Hydraulic Actuator ◽  
Linear Quadratic ◽  
Quadratic Stability ◽  
Quarter Car Model ◽  
Suspension Control ◽  
Automotive Suspension

The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a Linear Parameter Varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In terms of control, a dual controller consisting of a Model Predictive Control (MPC) and a Linear Quadratic Regulator (LQR) is implemented. To ensure stability, Quadratic Stability conditions are imposed in terms of Linear Matrix Inequalities (LMI). Simulation results for quarter-car model over several disturbances are tested in both frequency and time domain to show the effectiveness of the proposed algorithm.

scholarly journals Takagi-Sugeno Fuzzy Modeling and PSO-Based Robust LQR Anti-Swing Control for Overhead Crane

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xuejuan Shao ◽  
Jinggang Zhang ◽  
Xueliang Zhang
Keyword(s):  
Linear Quadratic Regulator ◽  
Pso Algorithm ◽  
Fuzzy Modeling ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Overhead Crane ◽  
Linear Quadratic ◽  
Highly Nonlinear ◽  
The Stability ◽  
Takagi Sugeno

The dynamic model of overhead crane is highly nonlinear and uncertain. In this paper, Takagi-Sugeno (T-S) fuzzy modeling and PSO-based robust linear quadratic regulator (LQR) are proposed for anti-swing and positioning control of the system. First, on the basis of sector nonlinear theory, the two T-S fuzzy models are established by using the virtual control variables and approximate method. Then, considering the uncertainty of the model, robust LQR controllers with parallel distributed compensation (PDC) structure are designed. The feedback gain matrices are obtained by transforming the stability and robustness of the system into linear matrix inequalities (LMIs) problem. In addition, particle swarm optimization (PSO) algorithm is used to overcome the blindness of LQR weight matrix selection in the design process. The proposed control methods are simple, feasible, and robust. Finally, the numeral simulations are carried out to prove the effectiveness of the methods.

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.

scholarly journals Optimization of parameters of a modal active control in a beam of composite material

2018 ◽  
Vol 211 ◽  
pp. 19002
Author(s):  
Camila Albertin Xavier da Silva ◽  
Erik Taketa ◽  
Edson Hideki Koroishi ◽  
Fabian Andres Lara-Molina ◽  
Albert Willian Faria
Keyword(s):  
Composite Material ◽  
Active Control ◽  
Active Vibration Control ◽  
Linear Quadratic Regulator ◽  
Optimization Methods ◽  
Linear Matrix ◽  
Linear Quadratic ◽  
Electromagnetic Actuators ◽  
Optimization Of Parameters ◽  
The Time Domain

The present work proposes the active vibration control in a beam of composite material, using electromagnetic actuators, in order to obtain a reduction in the response of the displacement of the system associated to a reduction in energy consumption. The control theory used was the linear quadratic regulator solved by linear matrix inequalities. The electromagnetic actuator was then linearized using a methodology similar to that used in magnetic bearings. The work also proposes to study the optimization of parameters applied in this active control, by means of the heuristic optimization methods. From numerical simulations, the system´s response was obtained in the time domain that demonstrated the efficiency of the proposed technique in the active control of vibrations.

Tracking Control of an Electro-Hydraulic Actuator System using LQR Controller

2021 ◽  
Vol 20 (2) ◽  
pp. 8-13
Author(s):  
Norlela Ishak ◽  
Ahmad Zikri Kamarudin ◽  
Ramli Adnan
Keyword(s):  
Tracking Control ◽  
High Performance ◽  
Phase Error ◽  
Control Process ◽  
Linear Quadratic Regulator ◽  
Fast Response ◽  
Feedback Controller ◽  
Hydraulic Actuator ◽  
Linear Quadratic ◽  
Lqr Controller

Electro-Hydraulic actuator (EHA) is a one type of application used in industry and building high performance of motion control process. Apparently, dealing with EHA behaviour is quite difficult and make the controlling process complicated. Designing Linear Quadratic Regulator (LQR) controller as a feedback controller require in selecting the weighting parameter Q and R. The result shows that the higher value of Q offers fast response and high stability by referring the placement of close-loop poles. However, the higher value of Q gives a higher error that can make position performance of hydraulic actuator become worst. In order to overcome this problem, the feedforward controller is developed by implementing the zero-phase error tracking control (ZPETC). It shows that both feedforward and feedback controller offers good tracking position performance in reducing gain and phase error.

Mixed Skyhook and Power-Driven-Damper: A New Low-Jerk Semi-Active Suspension Control Based on Power Flow Analysis

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Yilun Liu ◽  
Lei Zuo
Keyword(s):  
Active Control ◽  
Power Flow ◽  
Flow Analysis ◽  
Linear Quadratic Regulator ◽  
Control Algorithms ◽  
Linear Quadratic ◽  
Active Suspensions ◽  
Switching Law ◽  
Suspension Control ◽  
Optimal Linear

In practice, semi-active suspensions provide better tradeoffs between performances and costs than passive or active damping. Many different semi-active control algorithms have been developed, including skyhook (SH), acceleration-driven-damper (ADD), power-driven-damper (PDD), mixed SH and ADD (SH-ADD), and others. Among them, it has been shown that the SH-ADD is quasi-optimal in reducing the sprung mass vibration. In this paper, we analyze the abilities of vehicular suspension components, the shock absorber and the spring, from the perspective of energy transfer between the sprung mass and the unsprung mass, and propose a new sprung mass control algorithm named mixed SH and PDD (SH-PDD). The proposed algorithm defines a switching law that is capable of mixing SH and PDD, and simultaneously carries their advantages to achieve a better suspension performance. As a result, the proposed SH-PDD is effective in reducing the sprung mass vibration across the whole frequency spectrum, similar to SH-ADD and much better than SH, PDD, and ADD, while eliminating the control chattering and high-jerk behaviors as occurred in SH-ADD. The superior characteristics of the SH-PDD are verified in numerical analysis as well as experiments. In addition, the proposed switching law is extended to mix other semi-active control algorithms such as the mixed hard damping and soft damping, and the mixed SH and clipped-optimal linear quadratic regulator (LQR).

Optimal Roll Control of a Single-Unit Lorry

1996 ◽  
Vol 210 (1) ◽  
pp. 45-55 ◽  
Author(s):  
R C Lin ◽  
D Cebon ◽  
D J Cole
Keyword(s):  
Single Unit ◽  
Load Transfer ◽  
Linear Quadratic Regulator ◽  
Lateral Acceleration ◽  
Hydraulic Actuator ◽  
Linear Quadratic ◽  
Mean Power ◽  
Worst Case ◽  
Limited Bandwidth ◽  
Roll Control

Lateral acceleration control and linear quadratic regulator (LQR) theory are used to design active roll control systems for heavy goods vehicles. The suspension consists of a limited bandwidth hydraulic actuator in series with an anti-roll bar. The procedure used to determine suitable controller gains is described. The simulation results show that roll control of a single-unit lorry requires an actuator bandwidth of 6 Hz and mean power of approximately 17 kW for a ‘worst case’ random steering input. The static roll-over threshold of this vehicle is increased by 66 per cent when compared with the same vehicle with passive suspensions and the r.m.s. lateral load transfer is reduced by 34 per cent for a typical random steering input.

Perturbation Analysis of the LMI-Based Continuous-time Linear Quadratic Regulator Problem for Descriptor Systems

2016 ◽  
Vol 14 (1) ◽  
pp. 13-20
Author(s):  
A. Yonchev
Keyword(s):  
Control Problem ◽  
Perturbation Analysis ◽  
Continuous Time ◽  
Linear Quadratic Regulator ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Linear Perturbation ◽  
Linear Quadratic ◽  
Perturbation Bounds ◽  
Lqr Control

Abstract This paper considers an approach to perform perturbation analysis of linear quadratic regulator (LQR) control problem for continuous-time descriptor systems. The investigated control problem is based on solving LMIs (Linear Matrix Inequalities) and applying Lyapunov functions. The paper is concerned with obtaining linear perturbation bounds for the continuous-time LQR control problem for descriptor systems. The computed perturbation bounds can be used to study the effect of perturbations in system and controller on feasibility and performance of the considered control problem. A numerical example is also presented in the paper.

Optimal Controller Design For A Railway Vehicle Suspension System Using Particle Swarm Optimization

2012 ◽  
Author(s):  
Arfah Syahida Mohd Nor ◽  
Hazlina Selamat ◽  
Ahmad Jais Alimin
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Linear Quadratic Regulator ◽  
Active Suspension ◽  
Suspension System ◽  
Railway Vehicle ◽  
Linear Quadratic ◽  
Swarm Optimization ◽  
Suspension Control ◽  
Trial And Error Method

This paper presents the design of an active suspension control of a two–axle railway vehicle using an optimized linear quadratic regulator. The control objective is to minimize the lateral displacement and yaw angle of the wheelsets when the vehicle travels on straight and curved tracks with lateral irregularities. In choosing the optimum weighting matrices for the LQR, the Particle Swarm Optimization (PSO) method has been applied and the results of the controller performance with weighting matrices chosen using this method is compared with the commonly used, trial and error method. The performance of the passive and active suspension has also been compared. The results show that the active suspension system performs better than the passive suspension system. For the active suspension, the LQR employing the PSO method in choosing the weighting matrices provides a better control performance and a more systematic approach compared to the trial and error method. Key words: active suspension control, two–axle railway vehicle, linear quadratic regulator, particle swarm optimization

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