scholarly journals A Multivariable Adaptive Control Approach for Stabilization of a Cart-Type Double Inverted Pendulum

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
I. Hassanzadeh ◽  
A. Nejadfard ◽  
M. Zadi
Keyword(s):  
Steady State ◽  
Nonlinear Model ◽  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Feedback Gain ◽  
Practical Implementation ◽  
Model Parameters ◽  
Lagrange Equations ◽  
Control Approach ◽  
Input Structure

This paper considers the design and practical implementation of linear-based controllers for a cart-type double inverted pendulum (DIPC). A constitution of two linked pendulums placed on a sliding cart, presenting a three Degrees of Freedom and single controlling input structure. The controller objective is to keep both pendulums in an up-up unstable equilibrium point. Modeling is based on the Euler-Lagrange equations, and the resulted nonlinear model is linearized around up-up position. First, the LQR method is used to stabilize DIPC by a feedback gain matrix in order to minimize a quadratic cost function. Without using an observer to estimate the unmeasured states, in the next step we make use of LQG controller which combines the Kalman-Bucy filter estimation and LQR feedback control to obtain a better steady-state performance, but poor robustness. Eventually, to overcome the unknown nonlinear model parameters, an adaptive controller is designed. This controller is based on Model Reference Adaptive System (MRAS) method, which uses the Lyapunov function to eliminate the defined state error. This controller improves both the steady-state and disturbance responses.

scholarly journals Modeling and Optimal Controller Based on Disturbance Detector for the Stabilization of a Three-link Inverted Pendulum Mobile Robot

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1821
Author(s):  
Luis Alfonso Jordán-Martínez ◽  
Maricela Guadalupe Figueroa-García ◽  
José Humberto Pérez-Cruz
Keyword(s):  
Mathematical Model ◽  
Mobile Robot ◽  
Nonlinear Model ◽  
Direct Current ◽  
Inverted Pendulum ◽  
Experimental Tests ◽  
Optimal Controller ◽  
Stabilization Problem ◽  
Lagrange Equations ◽  
Direct Measurements

This work presents the realization of a complicated stabilization problem for a three inverted pendulum links-based mobile robot. The actuators of the mobile robot are direct current motors that have tachometer couplings to measure both the position and speed of the wheels and links. Using direct measurements under load and analyzing the deceleration curve, the motor parameters are determined experimentally. A mathematical model of the robot is obtained via the Euler–Lagrange equations. Next, the nonlinear model is linearized and discretized. Based on this discrete LTI model, an optimal controller is designed. The states and disturbances are estimated using a robust detector. Both the controller and detector are implemented in the robot processor. Numerical simulations and experimental tests show a good performance of the controller despite the presence of disturbances.

Experimental Validation of a Nonlinear Model Calibration Method Based on Multiharmonic Frequency Responses

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Yousheng Chen ◽  
Andreas Linderholt ◽  
Thomas J. S. Abrahamsson
Keyword(s):  
Steady State ◽  
Frequency Response ◽  
Test Data ◽  
Nonlinear Model ◽  
Model Calibration ◽  
Experimental Validation ◽  
Calibration Method ◽  
Model Parameters ◽  
Response Data ◽  
Starting Point

Correlation and calibration using test data are natural ingredients in the process of validating computational models. Model calibration for the important subclass of nonlinear systems which consists of structures dominated by linear behavior with the presence of local nonlinear effects is studied in this work. The experimental validation of a nonlinear model calibration method is conducted using a replica of the École Centrale de Lyon (ECL) nonlinear benchmark test setup. The calibration method is based on the selection of uncertain model parameters and the data that form the calibration metric together with an efficient optimization routine. The parameterization is chosen so that the expected covariances of the parameter estimates are made small. To obtain informative data, the excitation force is designed to be multisinusoidal and the resulting steady-state multiharmonic frequency response data are measured. To shorten the optimization time, plausible starting seed candidates are selected using the Latin hypercube sampling method. The candidate parameter set giving the smallest deviation to the test data is used as a starting point for an iterative search for a calibration solution. The model calibration is conducted by minimizing the deviations between the measured steady-state multiharmonic frequency response data and the analytical counterparts that are calculated using the multiharmonic balance method. The resulting calibrated model's output corresponds well with the measured responses.

scholarly journals Scaling and similarity of a stream-power incision and linear diffusion landscape evolution model

2018 ◽  
Vol 6 (3) ◽  
pp. 779-808 ◽  
Author(s):  
Nikos Theodoratos ◽  
Hansjörg Seybold ◽  
James W. Kirchner
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Degrees Of Freedom ◽  
Landscape Evolution ◽  
Initial Conditions ◽  
Evolution Model ◽  
Model Parameters ◽  
Stream Power ◽  
Linear Diffusion ◽  
Characteristic Scales

Abstract. The scaling and similarity of fluvial landscapes can reveal fundamental aspects of the physics driving their evolution. Here, we perform a dimensional analysis of the governing equation of a widely used landscape evolution model (LEM) that combines stream-power incision and linear diffusion laws. Our analysis assumes that length and height are conceptually distinct dimensions and uses characteristic scales that depend only on the model parameters (incision coefficient, diffusion coefficient, and uplift rate) rather than on the size of the domain or of landscape features. We use previously defined characteristic scales of length, height, and time, but, for the first time, we combine all three in a single analysis. Using these characteristic scales, we non-dimensionalize the LEM such that it includes only dimensionless variables and no parameters. This significantly simplifies the LEM by removing all parameter-related degrees of freedom. The only remaining degrees of freedom are in the boundary and initial conditions. Thus, for any given set of dimensionless boundary and initial conditions, all simulations, regardless of parameters, are just rescaled copies of each other, both in steady state and throughout their evolution. Therefore, the entire model parameter space can be explored by temporally and spatially rescaling a single simulation. This is orders of magnitude faster than performing multiple simulations to span multidimensional parameter spaces. The characteristic scales of length, height and time are geomorphologically interpretable; they define relationships between topography and the relative strengths of landscape-forming processes. The characteristic height scale specifies how drainage areas and slopes must be related to curvatures for a landscape to be in steady state and leads to methods for defining valleys, estimating model parameters, and testing whether real topography follows the LEM. The characteristic length scale is roughly equal to the scale of the transition from diffusion-dominated to advection-dominated propagation of topographic perturbations (e.g., knickpoints). We introduce a modified definition of the landscape Péclet number, which quantifies the relative influence of advective versus diffusive propagation of perturbations. Our Péclet number definition can account for the scaling of basin length with basin area, which depends on topographic convergence versus divergence.

scholarly journals Scaling and similarity of a stream-power incision and linear diffusion landscape evolution model

2018 ◽  
Author(s):  
Nikos Theodoratos ◽  
Hansjörg Seybold ◽  
James W. Kirchner
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Characteristic Length ◽  
Initial Conditions ◽  
Model Parameters ◽  
Length Scale ◽  
Characteristic Length Scale ◽  
Stream Power ◽  
Linear Diffusion ◽  
Characteristic Scales

Abstract. Scaling and similarity of fluvial landscapes can reveal fundamental aspects of the physics driving their evolution. Here we perform dimensional analysis on a widely used landscape evolution model (LEM) that combines stream-power incision and linear diffusion laws. Our analysis assumes that length and height are conceptually distinct dimensions, and uses characteristic scales that depend only on the model parameters (incision coefficient, diffusion coefficient, and uplift rate) rather than on the size of the domain or of landscape features. We use a previously defined characteristic length scale, but introduce new characteristic height and time scales. We use these characteristic scales to non-dimensionalize the LEM, such that it includes only dimensionless variables and no parameters. This significantly simplifies the LEM by removing all parameter-related degrees of freedom. The only remaining degrees of freedom are in the boundary and initial conditions. Thus, for any given set of dimensionless boundary and initial conditions, all simulations, regardless of parameters, are just re-scaled copies of each other, both in steady state and throughout their evolution. Therefore, the entire model parameter space can be explored by temporally and spatially re-scaling a single simulation. This is orders of magnitude faster than performing multiple simulations to span multi-dimensional parameter spaces. The characteristic length, height, and time scales are geomorphologically interpretable; they define relationships between topography and the relative strengths of landscape-forming processes. The characteristic height scale specifies how drainage areas and slopes must be related to curvatures for a landscape to be in steady state, and leads to methods for defining valleys, estimating model parameters, and testing whether real topography follows the LEM. The characteristic length scale is roughly equal to the scale of the transition from diffusion-dominated to advection-dominated propagation of topographic perturbations (e.g., knickpoints). We introduce a modified definition of the landscape Péclet number, which quantifies the relative influence of advective versus diffusive propagation of perturbations. Our Péclet number definition can account for the scaling of basin length with basin area, which depends on topographic convergence versus divergence.

Feedback Control Sensitivity Calculations Using Computational Differentiation

2015 ◽  
Author(s):  
Ahmad Bani Younes ◽  
James Turner
Keyword(s):  
Feedback Control ◽  
Parameter Uncertainty ◽  
Taylor Series Expansion ◽  
Higher Order ◽  
Optimal Feedback Control ◽  
Feedback Gain ◽  
Model Parameters ◽  
Nonlinear Feedback ◽  
Partial Derivatives ◽  
Control Approach

Feedback control is a powerful methodology for handling model and parameter uncertainty in real-world applications. Given a useful nominal plant model for developing the control approach, it is well-known that optimal solutions only perform well for a limited range of model and parameter uncertainty. A higher-order optimal nonlinear feedback control strategy is presented where the feedback control is augmented with feedback gain sensitivity partial derivatives for handling model uncertainties. The computational differentiation (CD) toolbox is used for automatically generating higher-order partial derivatives for the feedback gain differential equations. An estimator is assumed to be available for predicting the model parameter changes. The optimal gain is computed as a Taylor series expansion in the gains, where the feedback gains are expanded as a function of the system model parameters. Derivative enhanced optimal feedback control is shown to be robust to large changes in the model parameters. Numerical examples are presented that demonstrate the effectiveness of the proposed methodology.

Independent Identification of Friction Characteristics for Parallel Manipulators

2006 ◽  
Vol 129 (3) ◽  
pp. 294-302 ◽  
Author(s):  
Houssem Abdellatif ◽  
Martin Grotjahn ◽  
Bodo Heimann
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Friction Model ◽  
Rigid Body Dynamics ◽  
Model Parameters ◽  
Friction Modeling ◽  
Friction Characteristics ◽  
Experimental Identification ◽  
Kinematic Coupling

The compensation for friction or joint losses in robotic manipulators contributes to an important improvement of the control quality. Besides appropriate friction modeling, experimental identification of the model parameters is fundamental toward better control performance. Conventionally steady-state friction characteristics are investigated for mechanical systems in the first step. However, and due to the high kinematic coupling, such procedure is already complicated for complex multiple closed-loop mechanisms, like parallel manipulators. Actuation friction of such mechanisms becomes configuration dependent. This paper presents a methodology that deals with such challenge. The kinematic coupling is regarded in the friction model and therefore in the design of the experimental identification. With the proposed strategy, it is possible to identify the steady-state friction parameters independently from any knowledge about inertial or rigid-body dynamics. Friction models for sensorless passive joints can also be provided. Besides, the method is kept very practical, since there is no need for any additional hardware devices or interfaces than a standard industrial control. The suitability for the industrial field is proven by experimental application to PaLiDA that is a six degrees of freedom parallel manipulator equipped with linear directly driven actuators.

scholarly journals Investigation of a multi-ball, automatic dynamic balancing mechanism for eccentric rotors

2007 ◽  
Vol 366 (1866) ◽  
pp. 705-728 ◽  
Author(s):  
K Green ◽  
A.R Champneys ◽  
M.I Friswell ◽  
A.M Muñoz
Keyword(s):  
Numerical Simulation ◽  
Experimental Investigation ◽  
Steady State ◽  
Transient Response ◽  
Nonlinear Model ◽  
Practical Implementation ◽  
Dynamic Balancing ◽  
Qualitative And Quantitative ◽  
Simulation Results ◽  
Experimental Rig

This paper concerns an analytical and experimental investigation into the dynamics of an automatic dynamic balancer (ADB) designed to quench vibration in eccentric rotors. This fundamentally nonlinear device incorporates several balancing masses that are free to rotate in a circumferentially mounted ball race. An earlier study into the steady state and transient response of the device with two balls is extended to the case of an arbitrary number of balls. Using bifurcation analysis allied to numerical simulation of a fully nonlinear model, the question is addressed of whether increasing the number of balls is advantageous. It is found that it is never possible to perfectly balance the device at rotation speeds comparable with or below the first natural, bending frequency of the rotor. When considering practical implementation of the device, a modification is suggested where individual balls are contained in separate arcs of the ball race, with rigid partitions separating each arc. Simulation results for a partitioned ADB are compared with those from an experimental rig. Close qualitative and quantitative match is found between the theory and the experiment, confirming that for sub-resonant rotation speeds, the ADB at best makes no difference to the imbalance, and can make things substantially worse. Further related configurations worthy of experimental and numerical investigation are proposed.

Model-Reference Based Adaptive Control for Enhancing Lateral Stability of Car-Trailer Systems

2016 ◽  
Author(s):  
Smitha Vempaty ◽  
Eungkil Lee ◽  
Yuping He
Keyword(s):  
Adaptive Control ◽  
Degrees Of Freedom ◽  
Reference Model ◽  
Model Reference Adaptive Control ◽  
Operating Conditions ◽  
Model Parameters ◽  
Lateral Stability ◽  
Model Reference ◽  
Control Approach ◽  
Model Reference Adaptive

This paper presents a model reference adaptive control (MRAC) approach to enhance the lateral stability of car-trailer systems. To this end, a 3 degrees of freedom (DOF) linear yaw-plane car-trailer model was developed as a “reference model”. The yaw rate of leading and trailing units of the reference model were used as the target states to control and stabilize a virtual vehicle plant represented by a 5 DOF linear yaw-roll car-trailer model. A Lyapunov-based controller was designed to handle the lateral stability of the car-trailer dynamical system. The model parameters and operating conditions of the system were predefined while designing the controller. The effectiveness of the adaptive controller for improving the lateral stability of car-trailer systems was demonstrated under a simulated multiple cycle sine-wave steering input maneuver. It was observed that the lateral stability of car-trailer system was improved by controlling respective yaw rates of the car and the trailer, using model reference adaptive control approach in conjunction with Lyapunov stability criterion.

Holdup and holdup profiles in the reciprocating plate extractor VPE

1990 ◽  
Vol 55 (11) ◽  
pp. 2648-2661 ◽  
Author(s):  
Helena Sovová ◽  
Vladislav Bízek ◽  
Jaroslav Procházka
Keyword(s):  
Steady State ◽  
Experimental Results ◽  
Model Parameters ◽  
Dispersed Phase ◽  
Pulse Form ◽  
Sieve Plates

In this work measurements of mean holdup of dispersed phase, of axial holdup profiles and of flooding points in a reciprocating plate contactor with both the VPE-type plates and the sieve plates were carried out. The experimental results were compared with a monodisperse model of steady-state column hydrodynamics and the model parameters were evaluated. Important differences in the behaviour of the two plate types could be identified. Comparison was also made between two reciprocating drives of different pulse form.

scholarly journals Improvement of hand functions of spinal cord injury patients with electromyography-driven hand exoskeleton: A feasibility study

2020 ◽  
Vol 1 ◽  
Author(s):  
Youngmok Yun ◽  
Youngjin Na ◽  
Paria Esmatloo ◽  
Sarah Dancausse ◽  
Alfredo Serrato ◽  
...  
Keyword(s):  
Spinal Cord ◽  
Spinal Cord Injury ◽  
Degrees Of Freedom ◽  
Standardized Test ◽  
Hand Function ◽  
Severe Disabilities ◽  
Finger Movements ◽  
Control Approach ◽  
Cord Injury ◽  
Hand Exoskeleton

Abstract We have developed a one-of-a-kind hand exoskeleton, called Maestro, which can power finger movements of those surviving severe disabilities to complete daily tasks using compliant joints. In this paper, we present results from an electromyography (EMG) control strategy conducted with spinal cord injury (SCI) patients (C5, C6, and C7) in which the subjects completed daily tasks controlling Maestro with EMG signals from their forearm muscles. With its compliant actuation and its degrees of freedom that match the natural finger movements, Maestro is capable of helping the subjects grasp and manipulate a variety of daily objects (more than 15 from a standardized set). To generate control commands for Maestro, an artificial neural network algorithm was implemented along with a probabilistic control approach to classify and deliver four hand poses robustly with three EMG signals measured from the forearm and palm. Increase in the scores of a standardized test, called the Sollerman hand function test, and enhancement in different aspects of grasping such as strength shows feasibility that Maestro can be capable of improving the hand function of SCI subjects.

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