Design of Extended Kalman Filter for a Shape Memory Alloy Manipulator

2003 ◽  
Author(s):  
Mohammad H. Elahinia ◽  
Hashem Ashrafiuon ◽  
Mehdi Ahmadian ◽  
William T. Baumann
Keyword(s):  
Kalman Filter ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Extended Kalman Filter ◽  
State Space Model ◽  
Angular Position ◽  
The State ◽  
State Variables ◽  
Time Step ◽  
Noisy Measurements

This paper presents an Extended Kalman Filter (EKF) for estimation of the state variables of a single degree of freedom rotary manipulator actuated by Shape Memory Alloy (SMA). A state space model for the SMA manipulator is presented. The model includes nonlinear dynamics of the manipulator, constitutive model of Shape Memory Alloy, and the electrical and heat transfer behavior of SMA wire. In the experimental setup, angular position of the arm is the only state variable that is measured. The other state variables of the system are arm’s angular velocity, SMA wire’s stress, temperature and the Martensite factor, which are not available experimentally due to measurement difficulties. Hence, a model-based state estimator that works with noisy measurements is presented based on the Extended Kalman Filter. This estimator predicts the state vector at each time step and corrects its prediction based on the angular position of the arm which can be measured experimentally. The state variables collected through model simulations are also used to evaluate the performance of the EKF. Several EKF simulations are presented that show accurate, and robust performance of the estimator for different types of inputs.

Application of the Extended Kalman Filter to Control of a Shape Memory Alloy Arm

2003 ◽  
Author(s):  
Mohammad H. Elahinia ◽  
Hashem Ashrafiuon ◽  
Mehdi Ahmadian ◽  
Daniel J. Inman
Keyword(s):  
Kalman Filter ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Extended Kalman Filter ◽  
State Vector ◽  
Angular Position ◽  
The State ◽  
State Variables ◽  
Time Step ◽  
State Variable

This paper presents a robust nonlinear control that uses a state variable estimator for control of a single degree of freedom rotary manipulator actuated by Shape Memory Alloy (SMA) wire. A model for SMA actuated manipulator is presented. The model includes nonlinear dynamics of the manipulator, a constitutive model of the Shape Memory Alloy, and the electrical and heat transfer behavior of SMA wire. The current experimental setup allows for the measurement of only one state variable which is the angular position of the arm. Due to measurement difficulties, the other three state variables, arm angular velocity and SMA wire stress and temperature, cannot be directly measured. A model-based state estimator that works with noisy measurements is presented based on the Extended Kalman Filter (EKF). This estimator predicts the state vector at each time step and corrects its prediction based on the angular position measurements. The estimator is then used in a nonlinear and robust control algorithm based on Variable Structure Control (VSC). The VSC algorithm is a control gain switching technique based on the arm angular position (and velocity) feedback and EKF estimated SMA wire stress and temperature. The state vector estimates help reduce or avoid the undesirable and inefficient overshoot problem in SMA one-way actuation control.

scholarly journals A Temperature-based Controller for a Shape Memory Alloy Actuator

2005 ◽  
Vol 127 (3) ◽  
pp. 285-291 ◽  
Author(s):  
Mohammad H. Elahinia ◽  
Hashem Ashrafiuon ◽  
Mehdi Ahmadian ◽  
Hanghao Tan
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
State Vector ◽  
Angular Position ◽  
Variable Structure ◽  
The State ◽  
State Variables ◽  
Time Step ◽  
State Variable ◽  
Control Gain

This paper presents a robust nonlinear control that uses a state variable estimator for control of a single degree of freedom rotary manipulator actuated by shape memory alloy (SMA) wire. A model for SMA actuated manipulator is presented. The model includes nonlinear dynamics of the manipulator, a constitutive model of the shape memory alloy, and the electrical and heat transfer behavior of SMA wire. The current experimental setup allows for the measurement of only one state variable which is the angular position of the arm. Due to measurement difficulties, the other three state variables, arm angular velocity and SMA wire stress and temperature, cannot be directly measured. A model-based state estimator that works with noisy measurements is presented based on the extended Kalman filter (EKF). This estimator estimates the state vector at each time step and corrects its estimation based on the angular position measurements. The estimator is then used in a nonlinear and robust control algorithm based on variable structure control (VSC). The VSC algorithm is a control gain switching technique based on the arm angular position (and velocity) feedback and EKF estimated SMA wire stress and temperature. Using simulation it is shown that the state vector estimates help reduce or avoid the undesirable and inefficient overshoot problem in SMA one-way actuation control.

scholarly journals The Extended Kalman Filter in the Dynamic State Estimation of Electrical Power Systems

Enfoque UTE ◽  
2018 ◽  
Vol 9 (4) ◽  
pp. 120-130
Author(s):  
Holger Ignacio Cevallos Ulloa ◽  
Gabriel Intriago ◽  
Douglas Plaza ◽  
Roger Idrovo
Keyword(s):  
Kalman Filter ◽  
Power Systems ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Electrical Power ◽  
The State ◽  
Dynamic State ◽  
State Variables ◽  
Electrical Power Systems ◽  
Error Index

The state estimation and the analysis of load flow are very important subjects in the analysis and management of Electrical Power Systems (EPS). This article describes the state estimation in EPS using the Extended Kalman Filter (EKF) and the method of Holt to linearize the process model and then calculates a performance error index as indicators of its accuracy. Besides, this error index can be used as a reference for further comparison between methodologies for state estimation in EPS such as the Unscented Kalman Filter, the Ensemble Kalman Filter, Monte Carlo methods, and others. Results of error indices obtained in the simulation process agree with the order of magnitude expected and the behavior of the filter is appropriate due to follows adequately  the true value of the state variables. The simulation was done using Matlab and the electrical system used corresponds to the IEEE 14 and 30 bus test case systems. State Variables to consider in this study are the voltage and angle magnitudes.

InSAR Adaptive Extended Kalman Filter Phase Unwrapping Algorithm

2013 ◽  
Vol 798-799 ◽  
pp. 493-496
Author(s):  
Hua Dong Hao ◽  
Ting Yi Bai ◽  
Guo Lin Liu
Keyword(s):  
Kalman Filter ◽  
State Space ◽  
Extended Kalman Filter ◽  
State Space Model ◽  
Model Error ◽  
Phase Unwrapping ◽  
The State ◽  
Observation Equation ◽  
Space Model ◽  
The One

Phase Unwrapping (PU) is the key step in the image processing for Interferometric Synthetic Aperture Radar (InSAR). In the Extended Kalman Filter (EKF) model of PU, due to the state space model is not taken into account the terrain factors, it is often resulted in unwrapping error delivery as the pixel to the next when the state changes rapidly in steep terrain. The observation equation is nonlinear and usually applied in PU through linear processing, requiring the system model and noise statistics known. But in fact the mathematical model or statistical noise is completely or partially unknown; the results have been inevitably lead to the declining of valuation accuracy and filter divergence. If directly applied in phase unwrapping, it is made impossible to retrieve surface deformation. In order to solve this problem and fully consider the terrain effect and model error, an adaptive EKF PU algorithm (AEKFPU) for InSAR is presented. On the one hand, it is achieved local adaptive estimation of image fringe frequency through 2D FFT and Chirp-Z Transform (CZT) joint method, by considering the impact of terrain factors on unwrapping results; On the one hand, the fading factor is calculated by innovation covariance and adaptively adjusted with the error covariance so as to suppress the memory length of the filter, compensating the effect of incomplete information on unwrapping. The experimental results are proved the proposed method is effective, it can be dealt with phase unwrapping and filtering simultaneously, and can be adaptively considered terrain factors in state space model and compensated for model error in observation equation model, ultimately improving the accuracy of phase unwrapping.

Development of an Extended Kalman Filter for Self-Sensing Application of Shape Memory Alloy Wire Actuator

2015 ◽  
Author(s):  
H. Gurung ◽  
S. Karmakar ◽  
A. Banerjee
Keyword(s):  
Heat Transfer ◽  
Kalman Filter ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Convective Heat Transfer ◽  
Extended Kalman Filter ◽  
Convective Heat ◽  
Electrical Resistance ◽  
System Response ◽  
Sensing Application

This paper presents the development of an Extended Kalman Filter (EKF) for self-sensing application of Shape Memory Alloy (SMA) wire actuator. The EKF is used to estimate the end displacement of a SMA wire actuated compliant link using the electrical resistance variation of SMA. The model of the system is developed by coupling the stress-deformation relation of the link along the direction of the SMA actuator with the phenomenological model of the SMA wire. In EKF, the stress and temperature of SMA comprise the state vector and its electrical resistance is considered as output. The developed EKF is validated, by comparing the estimated system response with that of the model for a given input signal. The effects of the process and measurement noise on the estimation error have also been studied. An experimental setup is developed to measure the change in electrical resistance of the SMA wire, voltage drop across the same, and the associated end-displacement of the compliant link. Using the measured data, the end-displacement of the link is estimated using EKF and compared with the experimentally measured end-displacement. Significant qualitative agreement is observed. It is noted, that the convective heat transfer coefficient significantly affects the quantitative discrepancy. Thus the coefficient of convective heat transfer is determined, so as to minimize the gap between the two responses for a particular applied voltage. The coefficient is then used for different set of experiments, revealing the true potential of the EKF based approach to harness the self-sensing capability of SMA.

scholarly journals A Kalman particle filter for online parameter estimation with applications to affine models

2021 ◽  
Author(s):  
Jian He ◽  
Asma Khedher ◽  
Peter Spreij
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
State Space ◽  
Outer Layer ◽  
Posterior Distribution ◽  
State Space Model ◽  
The State ◽  
State Variables ◽  
Unknown Parameters ◽  
Space Model

AbstractIn this paper we address the problem of estimating the posterior distribution of the static parameters of a continuous-time state space model with discrete-time observations by an algorithm that combines the Kalman filter and a particle filter. The proposed algorithm is semi-recursive and has a two layer structure, in which the outer layer provides the estimation of the posterior distribution of the unknown parameters and the inner layer provides the estimation of the posterior distribution of the state variables. This algorithm has a similar structure as the so-called recursive nested particle filter, but unlike the latter filter, in which both layers use a particle filter, our algorithm introduces a dynamic kernel to sample the parameter particles in the outer layer to obtain a higher convergence speed. Moreover, this algorithm also implements the Kalman filter in the inner layer to reduce the computational time. This algorithm can also be used to estimate the parameters that suddenly change value. We prove that, for a state space model with a certain structure, the estimated posterior distribution of the unknown parameters and the state variables converge to the actual distribution in $$L^p$$ L p with rate of order $${\mathcal {O}}(N^{-\frac{1}{2}}+\varDelta ^{\frac{1}{2}})$$ O ( N - 1 2 + Δ 1 2 ) , where N is the number of particles for the parameters in the outer layer and $$\varDelta $$ Δ is the maximum time step between two consecutive observations. We present numerical results of the implementation of this algorithm, in particularly we implement this algorithm for affine interest models, possibly with stochastic volatility, although the algorithm can be applied to a much broader class of models.

Application of the extended Kalman filter to control of a shape memory alloy arm

2006 ◽  
Vol 15 (5) ◽  
pp. 1370-1384 ◽  
Author(s):  
Mohammad H Elahinia ◽  
Mehdi Ahmadian
Keyword(s):  
Kalman Filter ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Extended Kalman Filter

scholarly journals Scalable Output Linear Actuators, a Novel Design Concept Using Shape Memory Alloy Wires Driven by Fluid Temperature

Machines ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 14
Author(s):  
Andres Osorio Salazar ◽  
Yusuke Sugahara ◽  
Daisuke Matsuura ◽  
Yukio Takeda
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Angular Position ◽  
Scale Factor ◽  
Design Concept ◽  
Fluid Temperature ◽  
Step Size ◽  
Simple Method ◽  
Output Characteristics ◽  
Novel Design

In this paper, the concept of scalability for actuators is introduced and explored, which is the capability to freely change the output characteristics on demand: displacement and force for a linear actuator, angular position and torque for a rotational actuator. This change can either be used to obtain power improvement (with a constant scale factor), or to improve the usability of a robotic system according to variable conditions (with a variable scale factor). Some advantages of a scalable design include the ability to adapt to changing environments, variable resolution of step size, ability to produce designs that are adequate for restricted spaces or that require strict energy efficiency, and intrinsically safe systems. Current approaches for scalability in actuators have shortcomings: the method to achieve scalability is complex, so obtaining a variable scaling factor is challenging, or they cannot scale both output characteristics simultaneously. Shape Memory Alloy (SMA) wire-based actuators can overcome these limitations, because its two output characteristics, displacement and force, are physically independent from each other. In this paper we present a novel design concept for linear scalable actuators that overcome SMA design and scalability limitations by using a variable number of SMA wires mechanically in parallel, immersed in a liquid that transmits heat from a separate heat source (wet activation). In this concept, more wires increase the maximum attainable force, and longer wires increase the maximum displacement. Prototypes with different number of SMA wires were constructed and tested in isometric experiments to determine force vs. temperature behavior and time response. The heat-transmitting liquid was either static or flowing using pumps. Scalability was achieved with a simple method in all tested prototypes with a linear correlation of maximum force to number of SMA wires. Flowing heat transmission achieved higher actuation bandwidth.

Comparisons Between the Extended Kalman Filter and the State-Dependent Riccati Estimator

2014 ◽  
Vol 37 (5) ◽  
pp. 1556-1567 ◽  
Author(s):  
Andrew Berman ◽  
Paul Zarchan ◽  
Brian Lewis
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
The State ◽  
State Dependent
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