scholarly journals Mathematical Modelling and Control of a Two-Wheeled PUMA-LikeVehicle

2016 ◽  
Vol 6 (2) ◽  
pp. 11 ◽  
Author(s):  
Khaled M Goher
Keyword(s):  
Mathematical Modelling ◽  
Sliding Mode ◽  
Impact Load ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
The Body ◽  
Pole Placement ◽  
General Motors ◽  
Linear Quadratic ◽  
And Control

<p class="1Body">This paper presents mathematical modelling and control of a two-wheeled single-seat vehicle. The design of the vehicle is inspired by the Personal Urban Mobility and Accessibility (PUMA) vehicle developed by General Motors® in collaboration with Segway®. The body of the vehicle is designed to have two main parts. The vehicle is activated using three motors; a linear motor to activate the upper part in a sliding mode and two DC motors activating the vehicle while moving forward/backward and/or manoeuvring. Two stages proportional-integral-derivative (PID) control schemes are designed and implemented on the system models. The state space model of the vehicle is derived from the linearized equations. Controller based on the Linear Quadratic Regulator (LQR) and the pole placement techniques are developed and implemented. Further investigation of the robustness of the developed LQR and the pole placement techniques is emphasized through various experiments using an applied impact load on the vehicle.</p>

Acoustic Control Modeling of Conical Bores With Actuating Boundary Conditions

2001 ◽  
Author(s):  
Kevin M. Farinholt ◽  
Donald J. Leo
Keyword(s):  
Boundary Conditions ◽  
Driving Forces ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
Mode Shapes ◽  
Linear Quadratic ◽  
Acoustic Control ◽  
Average Control ◽  
The One ◽  
And Control

Abstract An investigation of the natural frequencies and mode shapes associated with sealed conical bores having actuating boundary conditions is presented. Beginning with the one dimensional wave equation for spherically expanding waves, modal characteristics are developed as functions of cone geometry and actuator parameters. This paper presents both analytical and experimental comparisons for the purpose of validating model and development techniques. An investigation of the orthogonality and adjointness of the solution is presented. A discussion of incorporating driving forces in the system model for the purpose of coupling control actuators with internal acoustics is also included. Including these driving forces, a state space model of the system is developed for the purpose of applying modern feedback control. This paper concludes with a study on applying Linear Quadratic Regulator techniques to this system, relating tradeoffs between spatially averaged pressure and control voltages. The results of our simulations indicate that pressure reductions of 30% are attainable with average control voltages of 14.4 volts, given an example geometry.

Analysis and Control of Aeromechanical Instabilities in Helicopters

2015 ◽  
Author(s):  
Salini S. Nair ◽  
Ranjith Mohan
Keyword(s):  
Active Control ◽  
Degrees Of Freedom ◽  
Linear Quadratic Regulator ◽  
Pole Placement ◽  
Control Input ◽  
Linear Quadratic ◽  
Stability Margins ◽  
Stiffness Variation ◽  
Wake Model ◽  
And Control

The paper focuses on analysis of aeromechanical instabilities, specifically ground resonance in helicopters and active control methods for improving the existing stability margins. First, a simplified model of coupled rotor-fuselage system with translational fuselage degrees of freedom and blade lead-lag degree of freedom is considered. Anisotropy is introduced through stiffness variation between blades. Depending on the configuration, appropriate methods are used for stability analysis and to determine frequency coalescence. Second, similar analysis is extended to a model with fuselage pitch, roll and blade flap, lag degrees of freedom and incorporates wake model. The analysis brings out effects of collective pitch and lock number on aeromechanical instabilities with the inclusion of wake model. Active control strategy using pole placement technique and Linear Quadratic Regulator (LQR) is applied to the periodic system. Stabilization is done by increasing the aerodynamic damping through control input given either as cyclic or collective pitch.

scholarly journals Robust Linear Quadratic Regulator via Sliding Mode Guidance for Spacecraft Orbiting a Tumbling Asteroid

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Peng Zhang ◽  
Tianhao Ma ◽  
Bo Zhao ◽  
Bo Dong ◽  
Yuanchun Li
Keyword(s):  
Feedback Linearization ◽  
Actuator Saturation ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Transition Process ◽  
The Body ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Control Scheme ◽  
The Stability

Aiming to ensure the stability of the spacecraft with multiuncertainties and mitigate the threat of the initial actuator saturation, a Robust Linear Quadratic Regulator (RLQR) via sliding mode guidance (SMG) for orbiting a tumbling asteroid is proposed in this paper. The orbital motion of the spacecraft near a tumbling asteroid is modelled in the body-fixed frame considering the sun-relative effects, and the orbiting control problem is formulated as a stabilization of a nonlinear time-varying system. RLQR based on the adaptive feedback linearization is proposed to stabilize the spacecraft orbiting with the uncertainties of the asteroid’s rotation and gravitational field. In order to avoid the initial actuator saturation, SMG is applied to generate the transition process trajectory of the closed-loop system. The effectiveness of the proposed control scheme is verified by the simulations of orbiting the asteroid Toutatis 4179.

Multivariable modeling and control of an activated sludge process

1998 ◽  
Vol 37 (12) ◽  
pp. 149-156 ◽  
Author(s):  
Carl-Fredrik Lindberg
Keyword(s):  
Activated Sludge ◽  
Nitrate Concentration ◽  
State Space Model ◽  
Activated Sludge Process ◽  
Invariant State ◽  
Linear Quadratic ◽  
Modeling And Control ◽  
Space Model ◽  
And Control ◽  
Time Invariant

This paper contains two contributions. First it is shown, in a simulation study using the IAWQ model, that a linear multivariable time-invariant state-space model can be used to predict the ammonium and nitrate concentration in the last aerated zone in a pre-denitrifying activated sludge process. Secondly, using the estimated linear model, a multivariable linear quadratic (LQ) controller is designed and used to control the ammonium and nitrate concentration.

Robust stabilization control of a spatial inverted pendulum using integral sliding mode controller

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishan Chawla ◽  
Vikram Chopra ◽  
Ashish Singla
Keyword(s):  
Inverted Pendulum ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Linear Quadratic Regulator ◽  
Humanoid Robots ◽  
Sliding Mode Controller ◽  
Linear Quadratic ◽  
Integral Sliding Mode ◽  
Wide Range ◽  
Lqr Controller

AbstractFrom the last few decades, inverted pendulums have become a benchmark problem in dynamics and control theory. Due to their inherit nature of nonlinearity, instability and underactuation, these are widely used to verify and implement emerging control techniques. Moreover, the dynamics of inverted pendulum systems resemble many real-world systems such as segways, humanoid robots etc. In the literature, a wide range of controllers had been tested on this problem, out of which, the most robust being the sliding mode controller while the most optimal being the linear quadratic regulator (LQR) controller. The former has a problem of non-robust reachability phase while the later lacks the property of robustness. To address these issues in both the controllers, this paper presents the novel implementation of integral sliding mode controller (ISMC) for stabilization of a spatial inverted pendulum (SIP), also known as an x-y-z inverted pendulum. The structure has three control inputs and five controlled outputs. Mathematical modeling of the system is done using Euler Lagrange approach. ISMC has an advantage of eliminating non-robust reachability phase along with enhancing the robustness of the nominal controller (LQR Controller). To validate the robustness of ISMC to matched uncertainties, an input disturbance is added to the nonlinear model of the system. Simulation results on two different case studies demonstrate that the proposed controller is more robust as compared to conventional LQR controller. Furthermore, the problem of chattering in the controller is dealt by smoothening the controller inputs to the system with insignificant loss in robustness.

Optimal Design of Forging Processes With Deformation and Temperature Constraints

1993 ◽  
Author(s):  
R. V. Grandhi ◽  
H. Cheng ◽  
S. S. Kumar
Keyword(s):  
Thermal Analyses ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
Parameter Design ◽  
Linear Quadratic ◽  
Optimal Control Strategy ◽  
Time Control ◽  
Systematic Methodology ◽  
Element Approach ◽  
Nonisothermal Conditions

Abstract This paper presents a systematic methodology for the design of process parameters for nonisothermal forgings. The finite element approach is used for deformation and thermal analyses, and an optimal control strategy is used for the process parameter design. A state-space model is developed for representing the coupled deformation and thermal behavior using rigid viscoplastic formulation. Design constraints on strain-rates and temperature variation are imposed for achieving the desired forging conditions. The linear quadratic regulator (LQR) theory for finite time control is used in designing the ram velocity and initial die temperature. The approach is demonstrated on an axisymmetric disc forging and a plane strain channel section forging, under nonisothermal conditions.

scholarly journals Design of hybrid sliding mode controller based on fireworks algorithm for nonlinear inverted pendulum systems

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668427 ◽  
Author(s):  
Te-Jen Su ◽  
Shih-Ming Wang ◽  
Tsung-Ying Li ◽  
Sung-Tsun Shih ◽  
Van-Manh Hoang
Keyword(s):  
Inverted Pendulum ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Sliding Mode Controller ◽  
Proportional Integral Derivative ◽  
Linear Quadratic ◽  
Pendulum System ◽  
Fireworks Algorithm ◽  
Simulation Process ◽  
Inverted Pendulum System

The objective of this article is to optimize parameters of a hybrid sliding mode controller based on fireworks algorithm for a nonlinear inverted pendulum system. The proposed controller is a combination of two modified types of the classical sliding mode controller, namely, baseline sliding mode controller and fast output sampling discrete sliding mode controller. The simulation process is carried out with MATLAB/Simulink. The results are compared with a published hybrid method using proportional–integral–derivative and linear quadratic regulator controllers. The simulation results show a better performance of the proposed controller.

scholarly journals The linear quadratic regular algorithm-based control system of the direct current motor

2019 ◽  
Vol 10 (2) ◽  
pp. 768
Author(s):  
Trong-Thang Nguyen
Keyword(s):  
Control System ◽  
Direct Current ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
Response Speed ◽  
Dc Motor ◽  
Linear Quadratic ◽  
Lqr Controller ◽  
Mathematical Equations ◽  
Feed Forward Controller

<span>This research aims to propose an optimal controller for controlling the speed of the Direct Current (DC) motor. Based on the mathematical equations of DC Motor, the author builds the equations of the state space model and builds the linear quadratic regulator (LQR) controller to minimize the error between the set speed and the response speed of DC motor. The results of the proposed controller are compared with the traditional controllers as the PID, the feed-forward controller. The simulation results show that the quality of the control system in the case of LQR controller is much higher than the traditional controllers. The response speed always follows the set speed with the short conversion time, there isn't overshoot. The response speed is almost unaffected when the torque impact on the shaft is changed.</span>

Modeling and Control of a Complex Interacting Process

2011 ◽  
Vol 403-408 ◽  
pp. 3758-3762
Author(s):  
Subhajit Patra ◽  
Prabirkumar Saha
Keyword(s):  
Storage System ◽  
Linear Quadratic Regulator ◽  
Model Parameters ◽  
Linear Quadratic ◽  
Modeling And Control ◽  
Dynamic Matrix ◽  
Liquid Storage ◽  
Efficient Control ◽  
And Control

In this paper, two efficient control algorithms are discussed viz., Linear Quadratic Regulator (LQR) and Dynamic Matrix Controller (DMC) and their applicability has been demonstrated through case study with a complex interacting process viz., a laboratory based four tank liquid storage system. The process has Two Input Two Output (TITO) structure and is available for experimental study. A mathematical model of the process has been developed using first principles. Model parameters have been estimated through the experimentation results. The performance of the controllers (LQR and DMC) has been compared to that of industrially more accepted PID controller.

Sign in / Sign up

Export Citation Format

Share Document