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.

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.

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.

Position Sensorless Control Based on Augmented Extended Kalman Filter for Permanent Magnet Linear Synchronous Motor

2011 ◽  
Vol 88-89 ◽  
pp. 350-354
Author(s):  
Hua Cai Lu ◽  
Ming Jiang ◽  
Li Sheng Wei ◽  
Bing You Liu
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Sensorless Control ◽  
Estimation Method ◽  
Estimation Algorithm ◽  
The State ◽  
State Variable ◽  
Detailed Explanation ◽  
System States ◽  
Position Sensorless

In order to achieve position sensorless control for PMLSM drive system, speed and position of the motor must be estimated. A novel sensorless position and speed estimation algorithm was designed for PMLSM drive by measuring terminal voltages and currents. That was state augmented extended Kalman filter (AEKF) estimation method. The resistance of the motor was augmented to the state variable. Then, the speed, position and the resistance were estimated simultaneously through extended Kalman filter (EKF). The influence of the resistance on the state estimation results could be reduced. As well as giving a detailed explanation of the new algorithm, experimental results were presented. It shows that the AEKF is capable of estimating system states accurately and reliability, and the proposed sensorless control system has a good dynamic response.

scholarly journals COMPARISON OF GPS SMOOTHENING METHODS BETWEEN EXTENDED KALMAN FILTER AND PARTICLE FILTER FOR UAV

2017 ◽  
Keyword(s):  
Numerical Simulation ◽  
Kalman Filter ◽  
Particle Filter ◽  
Extended Kalman Filter ◽  
Kalman Filtering ◽  
Particle Filtering ◽  
State Vector ◽  
The State ◽  
Gps Data ◽  
Extended Kalman Filtering

This paper presents a method for smoothing GPS data from a UAV using Extended Kalman filtering and particle filtering for navigation or position control. A key requirement for navigation and control of any autonomous flying or moving robot is availability of a robust attitude estimate. Consider a dynamic system such as a moving robot. The unknown parameters, e.g., the coordinates and the velocity, form the state vector. This time dependent vector may be predicted for any instant time by means of system equations. The predicted values can be improved or updated by observations containing information on some components of the state vector. The whole procedure is known as Kalman filtering. On the other hand, the particle filtering algorithm is to perform a recursive Bayesian filter by Monte Carlo simulations. The key is to represent the required posterior density function by a set of random samples, which is called particles with associated weights, and to compute estimates based on these samples as well as weights. We compare the two GPS smoothening methods: Extended Kalman Filter and Particle Filter for mobile robots applications. Validity of the smoothing methods is verified from the numerical simulation and the experiments. The numerical simulation and experimental results show the good GPS data smoothing performance using Extended Kalman filtering and particle filtering.

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 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.

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