scholarly journals Swinging up the Furuta Pendulum and its Stabilization Via Model Predictive Control

2013 ◽  
Vol 64 (3) ◽  
pp. 152-158 ◽  
Author(s):  
Pavol Seman ◽  
Boris Rohal’-Ilkiv ◽  
Martin Juh´as ◽  
Michal Salaj
Keyword(s):  
Predictive Control ◽  
Inverted Pendulum ◽  
Control Law ◽  
Classical Approach ◽  
Second Stage ◽  
Total Potential ◽  
Predictive Controller ◽  
Power Law Function ◽  
Two Stages ◽  
Rotary Inverted Pendulum

This paper deals with certain options on controlling an inverted rotary pendulum also known as the Furuta pendulum. Controlling an inverted pendulum involves two stages. The first stage is the swing up of the pendulum and the second stage is its balancing in the up-right position. The paper describes two possibilities on swinging up the pendulum. First one is the classical approach based on comparing the current total (potential and kinetic) energy of the system with the energy in its stabilized up-right position. The second option uses an exponentiation operation over the pendulum position since the trend of power law function is very convenient for determining the amount of required energy to be delivered to the system. For the purposes of balancing the pendulum in the up-right position a predictive controller based on optimal control law with perturbation was proposed, which is an LQ controller with control signal corrections when constraints are exceeded. The results are illustrated by real-time experiments on a laboratory rotary inverted pendulum setup.

Nonlinear stabilizing control of a rotary double inverted pendulum: a modified backstepping approach

2016 ◽  
Vol 39 (11) ◽  
pp. 1721-1734 ◽  
Author(s):  
Abdul Jabbar ◽  
Fahad Mumtaz Malik ◽  
Shahzad Amin Sheikh
Keyword(s):  
Inverted Pendulum ◽  
Coupled System ◽  
System Model ◽  
Control Law ◽  
Second Stage ◽  
Backstepping Approach ◽  
Stabilizing Control ◽  
Control Scheme ◽  
Backstepping Controller ◽  
Two Stages

Modified backstepping control is proposed for an under-actuated rotary double inverted pendulum. The system has actuated rotary base joint with which two unactuated links are attached. The proposed control design is a three step process for de-coupled system model. In the first stage, a backstepping controller is designed for each of the active and passive joints. In the second stage, compensation is introduced in the respective control efforts to cater for uncertain terms based on Lyapunov function for each joint. Finally, the controllers obtained in the two stages are combined to form a total control law. The performance of the proposed control scheme is evaluated by convergence analysis and simulations.

scholarly journals Nonlinear Model Predictive Control for the Swing-Up of a Rotary Inverted Pendulum

2004 ◽  
Vol 126 (3) ◽  
pp. 666-673 ◽  
Author(s):  
Sooyong Jung ◽  
John T. Wen
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Nonlinear Model ◽  
Inverted Pendulum ◽  
Optimal Solution ◽  
Nonlinear Model Predictive Control ◽  
Prediction Horizon ◽  
Experimental Implementation ◽  
Gradient Based ◽  
Rotary Inverted Pendulum

This paper presents the experimental implementation of a gradient-based nonlinear model predictive control (NMPC) algorithm to the swing-up control of a rotary inverted pendulum. The key attribute of the NMPC algorithm used here is that it only seeks to reduce the error at the end of the prediction horizon rather than finding the optimal solution. This reduces the computation load and allows real-time implementation. We discuss the implementation strategy and experimental results. In addition to NMPC based swing-up control, we also present results from a gradient based iterative learning control, which is the basis our NMPC algorithm.

Model Predictive Control of a Differential-Drive Mobile Robot

2018 ◽  
Vol 10 (1) ◽  
pp. 20-41
Author(s):  
Samir Bouzoualegh ◽  
El-Hadi Guechi ◽  
Ridha Kelaiaia
Keyword(s):  
Mathematical Model ◽  
Model Predictive Control ◽  
Mobile Robot ◽  
Predictive Control ◽  
Control Law ◽  
Input Output ◽  
Linearization Technique ◽  
Differential Drive ◽  
Predictive Controller ◽  
Simulation Results

Abstract This paper presents a model predictive control (MPC) for a differential-drive mobile robot (DDMR) based on the dynamic model. The robot’s mathematical model is nonlinear, which is why an input–output linearization technique is used, and, based on the obtained linear model, an MPC was developed. The predictive control law gains were acquired by minimizing a quadratic criterion. In addition, to enable better tuning of the obtained predictive controller gains, torques and settling time graphs were used. To show the efficiency of the proposed approach, some simulation results are provided.

scholarly journals Predictive Control of aWastewater Treatment Process

2007 ◽  
Vol 2 (2) ◽  
pp. 132 ◽  
Author(s):  
Sergiu Caraman ◽  
Mihaela Sbarciog ◽  
Marian Barbu
Keyword(s):  
Predictive Control ◽  
Internal Model ◽  
Current Practice ◽  
Treatment Process ◽  
Control Structure ◽  
Control Law ◽  
Wastewater Treatment Process ◽  
Prediction Horizon ◽  
Control Objective ◽  
Predictive Controller

The paper deals with the design of a predictive controller for a wastewater treatment process. In the considered process, the wastewater is treated in order to obtain an effluent having the substrate concentration within the standard limits established by law (below 20 mg/l). This goal is achieved by controlling the concentration of dissolved oxygen to a certain value. The predictive controller uses a neural network as internal model of the process and alters the dilution rate in order to fulfill the control objective. This control strategy offers various possibilities for the control law adjustment by means of the following parameters: the prediction horizon, the control horizon, the weights of the error and the command. The predictive control structure has been tested in three functioning regimes, considered essential due to the frequency of their occurrence in current practice.

Nonlinear Parameters and State Estimation for Adaptive Nonlinear Model Predictive Control Design

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Hichem Salhi ◽  
Faouzi Bouani
Keyword(s):  
Model Predictive Control ◽  
State Estimation ◽  
Predictive Control ◽  
Nonlinear Model ◽  
State Space Model ◽  
Nonlinear Model Predictive Control ◽  
Control Law ◽  
Unknown Parameters ◽  
Prediction Horizon ◽  
Predictive Controller

This paper deals with an adaptive nonlinear model predictive control (NMPC) based estimator in cases of mismatch modeling, presence of perturbations and/or parameter variations. Thus, we propose an adaptive nonlinear predictive controller based on the second-order divided difference filter (DDF) for multivariable systems. The controller uses a nonlinear state-space model for parameters and state estimation and for the control law synthesis. Two nonlinear optimization layers are included in the proposed algorithm. The first optimization problem is based on the output error (OE) model with a tuning factor, and it is dedicated to minimize the error between the model and the system at each sample time by estimating unknown parameters when assuming that all system states are available. The second optimization layer is used by the centralized nonlinear predictive controller to generate the control law which minimizes the error between future setpoints and future outputs along the prediction horizon. The proposed algorithm leads to a good tracking performance with an offset-free output and an effectiveness in perturbation attenuation. Practical results on a real setup show the reliability of the proposed approach.

Generalized Predictive Control for Rotary Inverted Pendulum System

2011 ◽  
Vol 130-134 ◽  
pp. 4256-4260 ◽  
Author(s):  
Qiang Gao ◽  
Yi Li
Keyword(s):  
Predictive Control ◽  
Inverted Pendulum ◽  
Mathematic Model ◽  
Generalized Predictive Control ◽  
Matlab Simulation ◽  
Lagrange Method ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Straight Line ◽  
Rotary Inverted Pendulum

Inverted pendulum system is a complex, multivariable, nonlinear, strong-coupling, unstable system of high order. Compared with the straight-line inverted pendulum, rotary inverted pendulum is more complicated and unstable. In this paper, the mathematic model of a rotary inverted pendulum system is analyzed and deduced detailedly by applying the Lagrange method; the control properties and characteristics of generalized predictive control are researched with matlab simulation. Finally, the results of the experiment prove the system controlled by GPC has a better stability and quickness.

scholarly journals Mobile Robot Navigation in a Cluttered Environment via Visual Predictive Control

2020 ◽  
Author(s):  
Adrien Durand-Petiteville ◽  
Viviane Cadenat
Keyword(s):  
Predictive Control ◽  
Mobile Robot Navigation ◽  
Control Law ◽  
Large Set ◽  
Specific System ◽  
Differential Drive ◽  
Cluttered Environment ◽  
Future State ◽  
Predictive Controller ◽  
Differential Drive Robot

This paper presents a Visual Predictive Controller scheme for a differential drive robot navigating in a cluttered environment. We introduce an analytic model predicting the future state for this specific system Moreover, constraints guaranteeing the convergence of the control law, and avoiding occultations and collisions with obstacles are presented. A large set of results obtained in simulations highlights the interest and efficiency of the approach.

scholarly journals Stabilizing a Rotary Inverted Pendulum Based on Logarithmic Lyapunov Function

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Wen ◽  
Yuanhao Shi ◽  
Xiaonong Lu
Keyword(s):  
Lyapunov Function ◽  
Inverted Pendulum ◽  
Control Method ◽  
Quadratic Function ◽  
Control Law ◽  
Logarithmic Function ◽  
Control Laws ◽  
Lyapunov Control ◽  
Comparative Results ◽  
Rotary Inverted Pendulum

The stabilization of a Rotary Inverted Pendulum based on Lyapunov stability theorem is investigated in this paper. The key of designing control laws by Lyapunov control method is the construction of Lyapunov function. A logarithmic function is constructed as the Lyapunov function and is compared with the usual quadratic function theoretically. The comparative results show that the constructed logarithmic function has higher numerical accuracy and faster convergence speed than the usual quadratic function. On this basis, the control law of stabilizing Rotary Inverted Pendulum is designed based on the constructed logarithmic function by Lyapunov control method. The effectiveness of the designed control law is verified by experiments and is compared with LQR controller and the control law designed based on the quadratic function. Moreover, the system robustness is analyzed when the system parameters contain uncertainties under the designed control law.

Predictive Controller and Estimator for NASA Deep Space Network Antennas

1994 ◽  
Vol 116 (2) ◽  
pp. 241-248 ◽  
Author(s):  
W. Gawronski
Keyword(s):  
Predictive Control ◽  
Tracking Control ◽  
Controller Design ◽  
Control Law ◽  
Deep Space ◽  
Linear Quadratic ◽  
Deep Space Network ◽  
Space Network ◽  
Predictive Controller ◽  
Simulation Results

This paper presents a modified output prediction procedure, and a new controller design based on the predictive control law. Also, a predictive estimator is developed for implementing the controller. The predictive controller was designed and simulated for tracking control of the NASA Deep Space Network 70-m antenna. Simulation results show significant improvement in tracking performance compared to the linear quadratic controller and estimator presently in use.

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