Backstepping Controller Design for a 5 DOF Spherical Inverted Pendulum

2019 ◽  
Vol 41 ◽  
pp. 37-50 ◽  
Author(s):  
Soukaina Krafes ◽  
Zakaria Chalh ◽  
Abdelmjid Saka
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Controller Design ◽  
Linear Quadratic Regulator ◽  
Performance Comparison ◽  
Virtual Reality Environment ◽  
Linear Quadratic ◽  
Control Scheme ◽  
Linearized System ◽  
Backstepping Controller

This paper presents a Backstepping controller for five degrees of freedom Spherical Inverted Pendulum. Since the system is nonlinear, unstable, underactuated and MIMO and has a nonsquare form, the classic control design cannot be applied to control it. In order to remedy this problem, we propose in this paper a new method based on hierarchical steps of the Backstepping controller taking into a count the nonlinearities that cannot be neglected. Furthermore, a Linear Quadratic Regulator controller and LQR + PID based on the linearized system model are also designed for performance comparison. Finally, a simulation study is carried out to prove the effectiveness of proposed control scheme and is validated using the virtual reality environment that proves the performance of the Backstepping controller over the linear ones where it brings the pendulum from any initial condition in the upper hemisphere while the base is brought to the origin of the coordinates.

CONTROL OF TWO-WHEELED INVERTED PENDULUM ROBOT USING ROBUST PI AND LQR CONTROLLERS

2020 ◽  
pp. 1-15
Author(s):  
Nguyen Hoai Nam
Keyword(s):  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Pi Controller ◽  
Linear Quadratic ◽  
Control Loops ◽  
Dc Motors ◽  
Wheeled Inverted Pendulum ◽  
Control Scheme ◽  
Lqr Controller ◽  
Heading Angle

In this paper, a robust PI controller in combination with a linear quadratic regulator (LQR) is proposed to control a two-wheeled inverted pendulum robot (TWIPR) such that it is kept balanced while moving. The proposed TWIPR control system consists of two control loops. The inner loop has two PI controllers for two DC motors’ currents, which are separately designed based on a robust PI controller structure. The outer loop contains a LQR controller for the tilt angle, heading angle and position of the TWIPR. The proposed PI controller is compared to the existing method such as the magnitude optimum (MO) and genetic algorithm (GA) methods. The proposed control scheme is verified through simulations and practical tests, and it is also compared to the MO-LQR and GA-LQR strategies.

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 Comparative analysis of observer-based LQR and LMI controllers of an inverted pendulum

2020 ◽  
Vol 9 (6) ◽  
pp. 2244-2252
Author(s):  
Nura Musa Tahir ◽  
Mustapha Muhammad ◽  
Musa Idi ◽  
Salinda Buyamin ◽  
Ladan Maijama’a ◽  
...  
Keyword(s):  
Comparative Analysis ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Absolute Error ◽  
Linear Matrix ◽  
Linear Quadratic ◽  
External Disturbances ◽  
Control Engineering ◽  
Control Scheme ◽  
Lqr Controller

An inverted pendulum is a multivariable, unstable, nonlinear system that is used as a yardstick in control engineering laboratories to study, verify and confirm innovative control techniques. To implement a simple control algorithm, achieve upright stabilization and precise tracking control under external disturbances constitutes a serious challenge. Observer-based linear quadratic regulator (LQR) controller and linear matrix inequality (LMI) are proposed for the upright stabilization of the system. Simulation studies are performed using step input magnitude, and the results are analyzed. Time response specifications, integral square error (ISE), integral absolute error (IAE) and mean absolute error (MAE) were employed to investigate the performances of the proposed controllers. Based on the comparative analysis, the upright stabilization of the pendulum was achieved within the shortest possible time with both controllers however, the LMI controller exhibits better performances in both stabilization and robustness. Moreover, the LMI control scheme is effective and simple.

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.

Stabilizing and Swinging-Up the Inverted Pendulum Using PI and PID Controllers Based on Reduced Linear Quadratic Regulator Tuned by PSO

2015 ◽  
Vol 4 (4) ◽  
pp. 52-69 ◽  
Author(s):  
M. E. Mousa ◽  
M. A. Ebrahim ◽  
M. A. Moustafa Hassan
Keyword(s):  
Pid Controller ◽  
Inverted Pendulum ◽  
Research Work ◽  
Linear Quadratic Regulator ◽  
Nonlinear Problems ◽  
Pid Controllers ◽  
Linear Quadratic ◽  
Swarm Optimization ◽  
Feed Forward ◽  
Forward Gain

The inherited instabilities in the Inverted Pendulum (IP) system make it one of the most difficult nonlinear problems in the control theory. In this research work, Proportional –Integral and Derivative (PID) Controller with a feed forward gain is used with Reduced Linear Quadratic Regulator (RLQR) for stabilizing the Cart Position and Swinging-up the Pendulum angle. Tuning the Controllers' gains is achieved by using Particle Swarm Optimization (PSO) Technique. Obtaining the combined PID controllers' gains with a feed forward gain and RLQR is a multi-dimensions control problem. The Proposed Controllers give minimum Settling Time, Rise Time, Undershoot and Over shoot for both the Cart Position and the Pendulum angle. A disturbance with different amplitudes is applied to the system, and the results showed the robustness of the systems based on the tuned controllers. The overall results are promising.

Lateral Stability Analysis for Car-Trailer Combinations

2016 ◽  
Author(s):  
Eungkil Lee ◽  
Tao Sun ◽  
Yuping He
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Parametric Study ◽  
Degrees Of Freedom ◽  
Linear Quadratic Regulator ◽  
Lateral Stability ◽  
Linear Quadratic ◽  
Lqr Control ◽  
Ct System

This paper presents a parametric study of linear lateral stability of a car-trailer (CT) combination in order to examine the fidelity, complexity, and applicability for control algorithm development for CT systems. Using MATLAB software, a linear yaw-roll model with 5 degrees of freedom (DOF) is developed to represent the CT combination. In the case of linear stability analysis, a parametric study was carried out using eigenvalue analysis based on a linear yaw-roll CT model with varying parameters. Built upon the linear stability analysis, an active trailer differential braking (ATDB) controller was designed for the CT system using the linear quadratic regulator (LQR) technique. The simulation study presented in this paper shows the effectiveness of the proposed LQR control design and the influence of different trailer parameters.

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 Simulation of a Steam Injected Gas Turbine Plant Control System

1997 ◽  
Author(s):  
Shusheng Zang ◽  
Jaqiang Pan
Keyword(s):  
Gas Turbine ◽  
Flow Rate ◽  
Controller Design ◽  
Dynamic Performance ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Turbine Plant ◽  
Fuel Flow ◽  
Lqr Controller ◽  
Gas Turbine Plant

The design of a modern Linear Quadratic Regulator (LQR) is described for a test steam injected gas turbine (STIG) unit. The LQR controller is obtained by using the fuel flow rate and the injected steam flow rate as the output parameters. To meet the goal of the shaft speed control, a classical Proportional Differential (PD) controller is compared to the LQR controller design. The control performance of the dynamic response of the STIG plant in the case of rejection of load is evaluated. The results of the computer simulation show a remarkable improvement on the dynamic performance of the STIG unit.

Optimal Error-Clamping Design for Position-Based Visual Servoing of a 2-DOF Model Helicopter

2011 ◽  
Author(s):  
M. Alizadeh ◽  
C. Ratanasawanya ◽  
M. Mehrandezh ◽  
R. Paranjape
Keyword(s):  
Visual Servoing ◽  
Degrees Of Freedom ◽  
Vision System ◽  
Physical Space ◽  
Linear Quadratic Regulator ◽  
Image Plane ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Feed Forward ◽  
Model Helicopter

A vision-based servoing technique is proposed for a 2 degrees-of-freedom (dof) model helicopter equipped with a monocular vision system. In general, these techniques can be categorized as image- and position-based, where the task error is defined in the image plane in the former and in the physical space in the latter. The 2-dof model helicopter requires a configuration-dependent feed-forward control to compensate for gravitational forces when servoing on a ground target. Therefore, a position-based visual servoing deems more appropriate for precision control. Image information collected from a ground object, with known geometry a priori, is used to calculate the desired pose of the camera and correspondingly the desired joint angles of the model helicopter. To assure a smooth servoing, the task error is parameterized, using the information obtained from the linearaized image Jacobian, and time scaled to form a moving reference trajectory. At the higher level, a Linear Quadratic Regulator (LQR), augmented with a feed-forward term and an integrator, is used to track this trajectory. The discretization of the reference trajectory is achieved by an error-clamping strategy for optimal performance. The proposed technique was tested on a 2-dof model helicopter capable of pitch and yaw maneuvers carrying a light-weight off-the-shelf video camera. The test results show that the optimized controller can servo the model helicopter to a hovering pose for an image acquisition rate of as low as 2 frames per second.

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