Modeling and Control of Elastic Joint Robots

1987 ◽  
Vol 109 (4) ◽  
pp. 310-318 ◽  
Author(s):  
M. W. Spong
Keyword(s):  
Controller Design ◽  
Nonlinear Models ◽  
Integral Manifold ◽  
Equations Of Motion ◽  
Joint Stiffness ◽  
Nonlinear Feedback ◽  
Static State ◽  
Modeling And Control ◽  
Elastic Joint ◽  
And Control

In this paper we study the modeling and control of robot manipulators with elastic joints. We first derive a simple model to represent the dynamics of elastic joint manipulators. The model is derived under two assumptions regarding dynamic coupling between the actuators and the links, and is useful for cases where the elasticity in the joints is of greater significance than gyroscopic interactions between the motors and links. In the limit as the joint stiffness tends to infinity, our model reduces to the usual rigid model found in the literature, showing the reasonableness of our modeling assumptions. We show that our model is significantly more tractable with regard to controller design than previous nonlinear models that have been used to model elastic joint manipulators. Specifically, the nonlinear equations of motion that we derive are shown to be globally linearizable by diffeomorphic coordinate transformation and nonlinear static state feedback, a result that does not hold for previously derived models of elastic joint manipulators. We also detail an alternate approach to nonlinear control based on a singular perturbation formulation of the equations of motion and the concept of integral manifold. We show that by a suitable nonlinear feedback, the manifold in state space which describes the dynamics of the rigid manipulator, that is, the manipulator without joint elasticity, can be made invariant under solutions of the elastic joint system. The implications of this result for the control of elastic joint robots are discussed.

Dynamic modeling and control design for a parallel-mechanism-based meso-milling machine tool

Robotica ◽  
2013 ◽  
Vol 32 (4) ◽  
pp. 515-532 ◽  
Author(s):  
Adam Y. Le ◽  
James K. Mills ◽  
Beno Benhabib
Keyword(s):  
Machine Tool ◽  
Dynamic Modeling ◽  
Design Methodology ◽  
Controller Design ◽  
Convex Combination ◽  
Control Design ◽  
Milling Machine ◽  
Modeling And Control ◽  
Kinematic Mechanisms ◽  
And Control

SUMMARYA novel rigid-body control design methodology for 6-degree-of-freedom (dof) parallel kinematic mechanisms (PKMs) is proposed. The synchronous control of PKM joints is addressed through a novel formulation of contour and lag errors. Robust performance as a control specification is addressed. A convex combination controller design approach is applied to address the problem of simultaneously satisfying multiple closed-loop specifications. The applied dynamic modeling approach allows the design methodology to be extended to 6-dof spatial PKMs. The methodology is applied to the design of a 6-dof PKM-based meso-milling machine tool and simulations are conducted.

Modeling and Control of Interconnected Dimensionless Dynamic Systems

2009 ◽  
Author(s):  
Scott Manwaring ◽  
Andrew Alleyne
Keyword(s):  
Dimensional Analysis ◽  
Dynamic Systems ◽  
Controller Design ◽  
Fluid Power ◽  
Modeling And Control ◽  
Initial Investigation ◽  
And Control ◽  
Insight Into ◽  
Original Dynamic

Previous work has found benefit in using dimensional analysis in the modeling and control of dynamic systems. What has not been explored is how multiple dimensionless dynamic systems would interconnect and interact with one another. This work presents an initial investigation into the interconnection of dimensionless dynamic systems, including an analysis of the differences between interconnecting dimensioned and dimensionless systems. A strategy is developed to interconnect dimensionless dynamic systems and explored using models of multiple fluid power components. The interconnection strategy is tested through controller design and simulation, which reveals insight into the dimensionless transformation of the original dynamic systems.

Modeling and Control of Nonlinear Series Elastic Actuator

2007 ◽  
Author(s):  
Ehsan Basafa ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Nonlinear Models ◽  
Human Gait ◽  
Output Impedance ◽  
Modeling And Control ◽  
Series Elastic Actuator ◽  
Scheduling Method ◽  
Normal Human ◽  
Series Elastic Actuators ◽  
And Control ◽  
Series Elastic

Series Elastic Actuators are force actuators with applications in robotics and biomechanics. In linear Series Elastic Actuators, a large force bandwidth requires a stiff sensor (spring), but the output impedance puts an upper limit on this parameter, therefore selecting the proper spring is difficult in these actuators. In this paper, Series Elastic Actuator is modeled with a nonlinear, stiffening spring and controlled using the Gain Scheduling method. Simulations show that both linear and nonlinear models have similar force bandwidths, but the nonlinear one shows much lower output impedance. Hence, the choice of spring for actuator design is an easier task than that of the linear model. Also, as a force-augmenting device for the knee joint in normal human gait, the nonlinear model acts better in simulations.

Modeling and Control of an Ejector Based Anode Recirculation System for Fuel Cells

2005 ◽  
Author(s):  
Amey Y. Karnik ◽  
Jing Sun
Keyword(s):  
Controller Design ◽  
Design Guidelines ◽  
Operating Conditions ◽  
Feedback Controller ◽  
Modeling And Control ◽  
Recirculation Flow ◽  
Dynamic Representation ◽  
Recirculation System ◽  
Proportional Integral Controller ◽  
And Control

A control oriented analysis of an anode recirculation system that uses an ejector with a variable throat area is presented for a PEMFC system. Two control issues addressed in this paper are (a) achieving desired recirculated flow to meet humidity control requirements, and (b) regulating anode pressure to protect the polymer membrane from deformation. To meet these objectives, a static feedforward controller using the variable throat area is applied to control the recirculation flow rate, while a proportional-integral controller is designed for anode pressure regulation. A dynamic system model comprising of a nonlinear static characterization of the ejector and dynamic representation of the anode recirculation flow path is developed for controller design and evaluation. Linear analysis is used to derive design guidelines for tuning the feedback controller and to analyze the interactions between the feedback and the feedforward controllers. Our analysis shows that the system characteristics are dependent on the operating condition of throat area of ejector. To meet the control objectives for different operating conditions, a gain scheduling scheme is proposed to adjust the feedback controller parameters and the performance is evaluated through simulations. Results for two representative conditions are included.

scholarly journals Diagonally dominant backstepping autopilot for aircraft with unknown actuator failures and severe winds

2014 ◽  
Vol 118 (1207) ◽  
pp. 1009-1038 ◽  
Author(s):  
S. Ismail ◽  
A. A. Pashilkar ◽  
R. Ayyagari ◽  
N. Sundararajan
Keyword(s):  
Dynamic Models ◽  
Controller Design ◽  
Design Method ◽  
Equations Of Motion ◽  
Control Surface ◽  
Actuator Failures ◽  
Time Scale Separation ◽  
Diagonally Dominant ◽  
Trajectory Following ◽  
And Control

Abstract A novel formulation of the flight dynamic equations is presented that permits a rapid solution for the design of trajectory following autopilots for nonlinear aircraft dynamic models. A robust autopilot control structure is developed based on the combination of the good features of the nonlinear dynamic inversion (NDI) method, integrator backstepping method, time scale separation and control allocation methods. The aircraft equations of motion are formulated in suitable variables so that the matrices involved in the block backstepping control design method are diagonally dominant. This allows us to use a linear controller structure for a trajectory following autopilot for the nonlinear aircraft model using the well known loop by loop controller design approach. The resulting autopilot for the fixed-wing rigid-body aircraft with a cascaded structure is referred to as the diagonally dominant backstepping (DDBS) controller. The method is illustrated here for an aircraft auto-landing problem under unknown actuator failures and severe winds. The requirement of state and control surface limiting is also addressed in the context of the design of the DDBS controller.

Instantaneous Center of Rotation-Based Master-Slave Kinematic Modeling and Control

2019 ◽  
Author(s):  
Vikram Ramanathan ◽  
Andy Zelenak ◽  
Mitch Pryor
Keyword(s):  
Feedback Linearization ◽  
Controller Design ◽  
Kinematic Model ◽  
Nonholonomic Constraints ◽  
Kinematic Modeling ◽  
Nonlinear Controller ◽  
Center Of Rotation ◽  
Modeling And Control ◽  
Instantaneous Center ◽  
And Control

Abstract This article presents a novel kinematic model and controller design for a mobile robot with four Centered Orientable Conventional (COC) wheels. When compared to non-conventional wheels, COC wheels perform better over rough terrain, are not subject to vertical chatter and offer better braking capability. However, COC wheels are pseudo-omnidirectional and subject to nonholonomic constraints. Several established modeling and control techniques define and control the Instantaneous Center of Rotation (ICR); however, this method involves singular configurations that are not trivial to eliminate. The proposed method uses a novel ICR-based kinematic model to avoid these singularities, and an ICR-based nonlinear controller for one ‘master’ wheel. The other ‘slave’ wheels simply track the resulting kinematic relationships between the ‘master’ wheel and the ICR. Thus, the nonlinear control problem is reduced from 12th to 3rd-order, becoming much more tractable. Simulations with a feedback linearization controller verify the approach.

scholarly journals Modeling of Autonomous Underwater Vehicles with Multi-Propellers Based on Maximum Likelihood Method

2020 ◽  
Vol 8 (6) ◽  
pp. 407
Author(s):  
Feiyan Min ◽  
Guoliang Pan ◽  
Xuefeng Xu
Keyword(s):  
Maximum Likelihood ◽  
Controller Design ◽  
Autonomous Underwater Vehicles ◽  
Underwater Vehicles ◽  
Likelihood Method ◽  
Hydrodynamic Characteristics ◽  
Identification Algorithm ◽  
Modeling And Control ◽  
Good Convergence ◽  
And Control

The hydrodynamic characteristics of multi-propeller autonomous underwater vehicles (AUV) is usually complicated and it is difficult to obtain an accurate mathematical model. A modeling method based on CFD calculation and maximum likelihood identification algorithm is proposed for this problem. Firstly, rough hydrodynamic parameters of AUV hull are obtained by CFD calculation. Secondly, on the basis of rough parameters, a maximum likelihood identification algorithm is proposed to adjust the parameters and improve the model precision. Besides, the method to improve the convergence of identification algorithm is analyzed by considering the characteristics of AUV model structure. Finally, the identification algorithm and identification results were validated with experimental data. It was found that this method has good convergence and adaptability. In particular, the identification results of turning force and torque parameters are highly consistent in different identification experiments, which indicates that this method can well extract the maneuvering characteristics of AUVs, thus contributing to the controller design of AUVs. The research of this paper has potential application for the modeling and control of multi-propeller AUVs.

Cross term constructed Lyapunov function based two-time scale controller design and vibration suppression for a rotating hub-beam system

2019 ◽  
Vol 42 (3) ◽  
pp. 551-564
Author(s):  
Ghasem Khajepour ◽  
Ramin Vatankhah ◽  
Mohammad Eghtesad ◽  
Mohsen Vakilzadeh
Keyword(s):  
Lyapunov Function ◽  
Vibration Suppression ◽  
Controller Design ◽  
Equations Of Motion ◽  
Angular Position ◽  
Pole Placement ◽  
Cross Term ◽  
Modeling And Control ◽  
Beam System ◽  
Flexible Arm

In this article, modeling and control of a rotating hub-beam system are studied. The system consists of a solid rotating cylinder and an attached flexible arm with a payload at the end. The rotation is supposed to be in the presence of gravity and the flexible arm is assumed to be a Euler-Bernoulli beam. To derive the equations of motion of the system, Lagrange’s method is applied. Moreover, Galerkin’s technique is employed to discretize the equations of motion. Furthermore, designing an appropriate two-time (slow and fast) scale controller in the presence of uncertainties is considered in order to track the desired hub angular position and suppress vibrations of the arm simultaneously. For the so-called slow subsystem, a novel controller design is proposed as two different cases, with and without the presence of uncertainties in system dynamics are considered; and accordingly, a control law for tracking the desired path is introduced based on the idea of using the cross-term constructed Lyapunov function. For the fast subsystem, a pole placement technique is used to suppress vibration of the beam. The simulation results indicate notable effectiveness of the proposed controller.

Three-state switching cell boost converter using H-inf controller

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nivedita Pati ◽  
Babita Panda
Keyword(s):  
Model Order Reduction ◽  
Controller Design ◽  
Order Reduction ◽  
Boost Converter ◽  
Describing Function ◽  
Model Order ◽  
Modeling And Control ◽  
State Switching ◽  
Converter Topology ◽  
And Control

Abstract This paper presents the modeling and control of a non-minimum phase dc-dc boost converter based on the three - state switching cells. In any double stage grid-connected system the converter forms an interface between the photovoltaic source and the inverter. As the control and regulation of the converter output is a vital part of penetration of renewable to grid, therefore, this paper had attempted the control of a converter topology that can reduce the current stress across its switches. But the system becomes highly unstable and complex which has been validated by predicting the limit cycle with a describing function. The Controller design is implemented after reducing the complexity of the system using the Model order reduction principle. H-inf controller being robust in nature is applied for stable and regulated output.

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