Global Stability Study of a Compliant Double-Inverted Pendulum Based on Hamiltonian Modeling

2012 ◽  
Author(s):  
Emmanouil Spyrakos-Papastavridis ◽  
Gustavo Medrano-Cerda ◽  
Jian S. Dai ◽  
Darwin G. Caldwell
Keyword(s):  
Global Stability ◽  
Inverted Pendulum ◽  
Physical Structure ◽  
Stability Study ◽  
Dynamical Model ◽  
Hamiltonian Equations ◽  
Stabilizing Control ◽  
Control Scheme ◽  
Simulation Results ◽  
Insight Into

This paper presents a dynamical model of a compliant double-inverted pendulum that is used to approximate the physical structure of the compliant humanoid (COMAN) robot, using both the Hamiltonian and the Lagrangian approaches. A comparison between the two aims at providing insight into the various advantages and/or disadvantages associated to each approach. Through manipulation of the resulting formulae, it is shown that the Hamiltonian equations possess certain characteristics, such as the allowance of the tracking of global stability, that render this method of representation suitable for legged robotics applications. Finally, an asymptotically stabilizing control scheme is presented together with simulation results.

Nonlinear Control of an Inverted Pendulum on a Cart by a Single Control Law

2013 ◽  
Vol 464 ◽  
pp. 279-284 ◽  
Author(s):  
Aydın Özbey ◽  
Erol Uzal ◽  
Hüseyin Yildiz
Keyword(s):  
Nonlinear Control ◽  
Global Stability ◽  
Mechanical System ◽  
Feedback Linearization ◽  
Numerical Experiments ◽  
Inverted Pendulum ◽  
Vertical Position ◽  
Control Law ◽  
Underactuated Mechanical System ◽  
Control Scheme

Stabilization at the top vertical position of an inverted pendulum on a cart, while bringing the cart to a desired position, by applying a force to the cart is considered. This is an underactuated mechanical system for which the main nonlinear control scheme, feedback linearization, fails. A single control law producing the force on the cart using cart velocity, and position and velocity of the pendulum is developed and shown, by numerical experiments, to asymptotically stabilize the pendulum at the top position while bringing the cart to its origin, although no attemp is made for a proof of global stability.

TPC and Non-TPC Based Topology Control Approaches for QoS Improvement in MR-WMN

2010 ◽  
pp. 304-329
Author(s):  
Vinod Mirchandani ◽  
Ante Prodan ◽  
Olivier Marcé
Keyword(s):  
Topology Control ◽  
Path Length ◽  
Mesh Networks ◽  
Grand Challenge ◽  
Transmit Power Control ◽  
Wireless Mesh ◽  
Control Scheme ◽  
Control Schemes ◽  
Simulation Results ◽  
Insight Into

A grand challenge in Multi-Radio Wireless Mesh Networks (MR-WMN) is to limit the interference such that its net capacity increases without compromising scalability and stability. In this chapter, the authors first provide an insight into the implications of transmit power control (TPC) on the MR-WMN topology and QoS. In this regard, a review of some of the key work is carried out they then explore the approach of non-TPC based topology control schemes for limiting the interference in a static nodes based MR-WMN system that uses a distributed, light-weight, cooperative multiagents. A path reduction (PR) algorithm is the principle behind our topology control scheme and its viability is explained through NetLogo tool based simulation results. The effectiveness of the PR algorithm is shown in terms of improved interference cost reduction and decrease in path length. The focus of this chapter is mainly on non-TPC approach rather than the TPC approach.

Backstepping Control Design on the Dynamics of the Omni-Directional Mobile Robot

2012 ◽  
Vol 203 ◽  
pp. 51-56 ◽  
Author(s):  
Qing Zhu Cui ◽  
Xun Li ◽  
Xiang Ke Wang ◽  
Meng Zhang
Keyword(s):  
Lyapunov Function ◽  
Mobile Robot ◽  
Global Stability ◽  
Model Simulation ◽  
Control Design ◽  
Dynamical Model ◽  
Control Input ◽  
Newtonian Mechanics ◽  
Virtual Control ◽  
Simulation Results

The dynamical model of an omni-directional mobile robot is bulit based on the Newtonian mechanics. Correspondingly, a backstepping-based controller is then proposed with proven global stability by selecting a Lyapunov function and introducing a virtual control input for the built dynamical model. Simulation results show the effectiveness of the proposed controller.

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.

Model development and control of an auto-refrigerated polystyrene polymerization reactor

2021 ◽  
pp. 014233122110251
Author(s):  
Reyhane Mokhtarname ◽  
Ali Akbar Safavi ◽  
Leonhard Urbas ◽  
Fabienne Salimi ◽  
Mohammad M Zerafat ◽  
...  
Keyword(s):  
Temperature Control ◽  
Model Development ◽  
Heat Removal ◽  
Superior Performance ◽  
Polymerization Process ◽  
Vacuum System ◽  
Control Scheme ◽  
Simulation Results ◽  
And Control ◽  
Operating Plant

Dynamic model development and control of an existing operating industrial continuous bulk free radical styrene polymerization process are carried out to evaluate the performance of auto-refrigerated CSTRs (continuous stirred tank reactors). One of the most difficult tasks in polymerization processes is to control the high viscosity reactor contents and heat removal. In this study, temperature control of an auto-refrigerated CSTR is carried out using an alternative control scheme which makes use of a vacuum system connected to the condenser and has not been addressed in the literature (i.e. to the best of our knowledge). The developed model is then verified using some experimental data of the real operating plant. To show the heat removal potential of this control scheme, a common control strategy used in some previous studies is also simulated. Simulation results show a faster dynamics and superior performance of the first control scheme which is already implemented in our operating plant. Besides, a nonlinear model predictive control (NMPC) is developed for the polymerization process under study to provide a better temperature control while satisfying the input/output and the heat exchanger capacity constraints on the heat removal. Then, a comparison has been also made with the conventional proportional-integral (PI) controller utilizing some common tuning rules. Some robustness and stability analyses of the control schemes investigated are also provided through some simulations. Simulation results clearly show the superiority of the NMPC strategy from all aspects.

scholarly journals Design of a Decoupling Fuzzy Control Scheme for Omnidirectional Inverted Pendulum Real-World Control

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 26083-26092
Author(s):  
Chih-Hui Chiu ◽  
Yao-Ting Hung ◽  
Ya-Fu Peng
Keyword(s):  
Fuzzy Control ◽  
Real World ◽  
Inverted Pendulum ◽  
Control Scheme

CONTROLLING THE UNCERTAIN MULTI-SCROLL CRITICAL CHAOTIC SYSTEM WITH INPUT NONLINEAR USING SLIDING MODE CONTROL

2009 ◽  
Vol 23 (16) ◽  
pp. 2021-2034 ◽  
Author(s):  
XINGYUAN WANG ◽  
DA LIN ◽  
ZHANJIE WANG
Keyword(s):  
Chaotic System ◽  
Sliding Mode ◽  
Equilibrium Points ◽  
Dead Zone ◽  
Variable Structure ◽  
Sliding Mode Controller ◽  
Global Stabilization ◽  
Structure Control ◽  
Control Scheme ◽  
Simulation Results

In this paper, control of the uncertain multi-scroll critical chaotic system is studied. According to variable structure control theory, we design the sliding mode controller of the uncertain multi-scroll critical chaotic system, which contains sector nonlinearity and dead zone inputs. For an arbitrarily given equilibrium point of the uncertain multi-scroll chaotic system, we achieve global stabilization for the equilibrium points. Particularly, a class of proportional integral (PI) switching surface is introduced for determining the convergence rate. Furthermore, the proposed control scheme can be extended to complex multi-scroll networks. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Identification and Model Predictive Position Control of Two Wheeled Inverted Pendulum Mobile Robot

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Amir A. Bature ◽  
Salinda Buyamin ◽  
Mohamad N. Ahmad ◽  
Mustapha Muhammad ◽  
Auwalu A. Muhammad
Keyword(s):  
Mathematical Model ◽  
System Identification ◽  
Mobile Robot ◽  
Inverted Pendulum ◽  
Position Control ◽  
Superior Performance ◽  
System A ◽  
Wheeled Inverted Pendulum ◽  
Simulation Results ◽  
Real Plant

In order to predict and analyse the behaviour of a real system, a simulated model is needed. The more accurate the model the better the response is when dealing with the real plant. This paper presents a model predictive position control of a Two Wheeled Inverted Pendulum robot. The model was developed by system identification using a grey box technique. Simulation results show superior performance of the gains computed using the grey box model as compared to common linearized mathematical model. 

A Robust Trajectory Tracking Control Scheme of Two-Link Flexible Manipulator

2011 ◽  
Vol 328-330 ◽  
pp. 2108-2112
Author(s):  
Jing Shuang Lu ◽  
Chun Mei Du ◽  
Rui Zhou ◽  
Na Li
Keyword(s):  
Trajectory Tracking ◽  
Tracking Control ◽  
Vertical Plane ◽  
Flexible Manipulator ◽  
System Model ◽  
Error Signal ◽  
Dynamics Model ◽  
Trajectory Tracking Control ◽  
Control Scheme ◽  
Simulation Results

A simple dynamics model is established based on the two-link flexible manipulator moving within the vertical plane, and a robust simple control scheme is put forward. The advantages of this scheme are simple and good robustness. Only the error signal is needed when designing the control scheme and the acquirement of control signal does not depend on the system model. The simulation results show that this method has a good robustness and stability.

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