Validation of an Instrumented Walkway Designed for Estimation of the Ankle Impedance in Sagittal and Frontal Planes

2016 ◽  
Author(s):  
Evandro M. Ficanha ◽  
Guilherme Ribeiro ◽  
Mohammad Rastgaar Aagaah
Keyword(s):  
Mechanical Impedance ◽  
Time Varying ◽  
Camera System ◽  
Ankle Impedance ◽  
Actuation System ◽  
Ankle Kinematics ◽  
Preliminary Validation ◽  
Time Varying Systems ◽  
Similar Accuracy ◽  
Time Invariant

Recently, the authors designed and fabricated an Instrumented Walkway for the estimation of the ankle mechanical impedance in the sagittal and frontal planes during walking in arbitrary directions [1]. It consists of a powered platform; therefore, the users do not need to wear or carry any measurement device or actuation system other than reflective markers used to record the ankle kinematics with a motion capture camera system. This paper describes the continuous development of the Instrumented Walkway and presents an experimental preliminary validation of its capability to estimate the impedance of a system with time-varying dynamics. To validate the system, a mockup with mechanical characteristics similar to a human lower-leg and controllable time-varying stiffness was used. The stiffness of the mockup was estimated with fixed and time-varying stiffness. With fixed stiffness, a stochastic system identification method was used to estimate the mockup’s impedance. When the mockup presented a time-varying stiffness, a second order parametric model was used. The RMS error between the two methods was 2.81 Nm/rad (maximum 4.12 Nm/rad and minimum of −3.41 Nm/rad). The results show that the proposed approach can estimate the stiffness of systems with time-varying dynamics or static dynamics with similar accuracy. Since the setup was already validated for systems with time-invariant dynamics, it concluded the system’s applicability for time-varying systems such as the human ankle-foot during the stance phase.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

Floquet Experimental Modal Analysis for System Identification of Linear Time-Periodic Systems

2007 ◽  
Author(s):  
Matthew S. Allen
Keyword(s):  
System Identification ◽  
Linear Time ◽  
Time Varying ◽  
Response Model ◽  
State Matrix ◽  
Linear Time Invariant ◽  
Response Data ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Periodic

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotorbearing systems, wind turbines, satellite systems, etc… A number of powerful techniques have been presented in the past few decades, so that one might expect to model or control an LTP system with relative ease compared to time varying systems in general. However, few, if any, methods exist for experimentally characterizing LTP systems. This work seeks to produce a set of tools that can be used to characterize LTP systems completely through experiment. While such an approach is commonplace for LTI systems, all current methods for time varying systems require either that the system parameters vary slowly with time or else simply identify a few parameters of a pre-defined model to response data. A previous work presented two methods by which system identification techniques for linear time invariant (LTI) systems could be used to identify a response model for an LTP system from free response data. One of these allows the system’s model order to be determined exactly as if the system were linear time-invariant. This work presents a means whereby the response model identified in the previous work can be used to generate the full state transition matrix and the underlying time varying state matrix from an identified LTP response model and illustrates the entire system-identification process using simulated response data for a Jeffcott rotor in anisotropic bearings.

Instrumented Walkway for Estimation of the Ankle Impedance in Dorsiflexion-Plantarflexion and Inversion-Eversion During Standing and Walking

2015 ◽  
Author(s):  
Evandro M. Ficanha ◽  
Guilherme Ribeiro ◽  
Mohammad Rastgaar Aagaah
Keyword(s):  
Degrees Of Freedom ◽  
Force Plate ◽  
Mechanical Impedance ◽  
Standing Position ◽  
Camera System ◽  
Ankle Impedance ◽  
System A ◽  
Human Ankle ◽  
Applied Forces ◽  
And Inversion

This paper describes in detail the fabrication of an instrumented walkway for estimation of the ankle mechanical impedance in both dorsiflexion-plantarflexion (DP) and in inversion-eversion (IE) directions during walking in arbitrary directions and standing. The platform consists of two linear actuators, each capable of generating ±351.3 N peak force that are mechanically coupled to a force plate using Bowden cables. The applied forces cause the force plate to rotate in two degrees of freedom (DOF) and transfer torques to the human ankle to generate DP and IE rotations. The relative rotational motion of the foot with respect to the shin is recorded using a motion capture camera system while the forces applied to the foot are measured with the force plate, from which the torques applied to the ankle are calculated. The analytical methods required for the estimation of the ankle torques, rotations, and impedances are presented. To validate the system, a mockup with known stiffness was used, and it was shown that the developed system was capable of properly estimating the stiffness of the mockup in two DOF with less than 5% error. Also, a preliminary experiment with a human subject in standing position was performed, and the estimated quasi-static impedance of the ankle was estimated at 319 Nm/rad in DP and 119 Nm/rad in IE.

Observer and Controller Design Using Time-Varying Gains: Duality and Distinctions

2004 ◽  
Vol 127 (2) ◽  
pp. 267-274
Author(s):  
Vladimir Polotski
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Dual Problem ◽  
Controller Design ◽  
Time Varying ◽  
Feedback Controllers ◽  
Observer Error ◽  
Time Varying Systems ◽  
Error Dynamics ◽  
Time Invariant

Stabilization of linear systems by state feedback is an important problem of the controller design. The design of observers with appropriate error dynamics is a dual problem. This duality leads, at first glance, to the equivalence of the responses in the synthesized systems. This is true for the time-invariant case, but may not hold for time-varying systems. We limit ourselves in this work by the situation when the system itself is time invariant, and only the gains are time varying. The possibility of assigning a rapidly decaying response without peaking is analyzed. The solution of this problem for observers using time-varying gains is presented. Then we show that this result cannot be obtained for state feedback controllers. We also analyze the conditions under which the observer error dynamics and the response of the closed loop time-varying controllers are equivalent. Finally we compare our results to recently proposed observer converging in finite time and Riccati-based continuous observer with limited overshoots.

Robust Adaptive Controllers for Interconnected Mechanical Systems: Influence of Types of Interconnections on Time-Invariant and Time-Varying Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 456-473 ◽  
Author(s):  
Sunil K. Singh ◽  
Lin Shi
Keyword(s):  
State Space ◽  
High Speed ◽  
Linear Time ◽  
Direct Method ◽  
Time Varying ◽  
Adaptive Controllers ◽  
First Order ◽  
Time Varying Systems ◽  
Robust Adaptive ◽  
Time Invariant

We investigate robust adaptive controller designs for interconnected systems when no exact knowledge about the structure of the nonlinear interconnections between various subsystems is available. In this study, we concentrate on several different types of systems. We deal with both linear time-invariant (LTI) and linear time-varying (LTV) systems with nonlinear interconnections. For LTI systems, we examine the following types of interconnections: • interconnections that are bounded by first order polynomials in state space; • slowly time varying interconnections; • interconnections bounded by higher-order polynomials in state-space together with input channel interconnections. For LTV systems we deal with interconnections bounded by first-order polynomials in state space. We show that the nature of the nonlinear interactions influences the adaptation laws. We use the direct method of Lyapunov for the design of adaptive controllers for tracking in such systems. We investigate issues such as stability, transient performance and steady-state errors, and derive quantitative estimates and analytical bounds for various different adaptive controllers. For time-varying systems, we analyze the effect of the time variations of parameters and interactions and propose a modified adaptive control scheme with better performance. Simulation results are presented to validate our conclusions. We also investigate these results experimentally on a two-link robot manipulator. Experimental results validate theoretical conclusions and demonstrate the usefulness of such robust adaptive controllers for high-speed motions in uncertain systems.

scholarly journals Quantized State Based Simulation of Time Invariant and Time Varying Continuous Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Xiao Song ◽  
Yaofei Ma ◽  
Wei Zhang ◽  
Jiangyun Wang
Keyword(s):  
Computer Simulation ◽  
State Space ◽  
Continuous System ◽  
Continuous Systems ◽  
Practical Case ◽  
Time Varying ◽  
Aircraft Control ◽  
Novel Approach ◽  
Time Varying Systems ◽  
Time Invariant

Continuous system can be discretized for computer simulation. Quantized state systems (QSS) method has been used to discretize time invariant systems based on the discretization of the state space. A HLA based QSS method is proposed in this paper to address issues of real-time advancements in simulation and an aircraft control example was introduced to illustrate our method. Moreover, to simulate time varying systems, a novel approach is also proposed and exemplified with a practical case.

scholarly journals Impedance of the Human Ankle During Standing for Posture Control

2018 ◽  
Author(s):  
G. A. Ribeiro ◽  
E. Ficanha ◽  
L. Knop ◽  
M. Rastgaar
Keyword(s):  
Mechanical Impedance ◽  
Posture Control ◽  
Resultant Force ◽  
Order System ◽  
Time Varying ◽  
Ankle Impedance ◽  
Impedance Modulation ◽  
Human Ankle ◽  
Stiffness And Damping ◽  
Antagonistic Muscles

The stiffness and damping of anatomical joints can be modulated by muscle co-contraction, where antagonistic muscles contract simultaneously, increasing both the joint’s stiffness and damping. In a second order system, the mechanical impedance, or simply impedance, is a function of the system’s inertia, damping, and stiffness. The ankle impedance can be defined as the resultant force due to an external motion perturbation. The impedance modulation of the human ankle is required for stable walking. The estimation of the time-varying impedance modulation of the human ankle is the focus of research by different groups [1,2].

scholarly journals On a continuity of characteristic exponents of linear discrete time-varying systems

2012 ◽  
Vol 22 (1) ◽  
pp. 17-27 ◽  
Author(s):  
Adam Czornik ◽  
Piotr Mokry ◽  
Michał Niezabitowski
Keyword(s):  
Linear System ◽  
Lyapunov Exponents ◽  
Discrete Time ◽  
Sufficient Condition ◽  
Time Varying ◽  
Characteristic Exponents ◽  
Time Varying Systems ◽  
Time Invariant

On a continuity of characteristic exponents of linear discrete time-varying systemsIn this paper we present a sufficient condition for continuity of Lyapunov exponents of discrete time-varying linear system. Basing on this result we show that Lyapunov exponents of time-invariant systems depend continuously on the time-varying perturbations.

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