scholarly journals Approximate Model-based State Estimation in Simplified Receding Horizon Control

2021 ◽  
Vol 15 ◽  
pp. 114-124
Author(s):  
Hemza Redjimi ◽  
József K. Tar
Keyword(s):  
Approximate Model ◽  
The State ◽  
Control Signal ◽  
Measured Quantity ◽  
State Variables ◽  
Receding Horizon ◽  
Applied Model ◽  
State Variable ◽  
Multiple Variable ◽  
And Control

Multiple variable systems often have to be so controlled that in the lack of appropriate sensors no satisfactory information is available for the complete estimation of their state variables. Normally only their certain components are kept under observation and control, while the other ones evolve according to the consequences of the exerted control signal. In control-based treatment of patients suffering from "Type 1 Diabetes Mellitus (T1DM)", the only directly measured quantity is the subcutaneous glucose concentration in the blood controlled by a single control signal, the insulin ingress rate. The applied model may use several components in the state variable. The traditional "Receding Horizon Controller (RHC)" requires the estimation of the complete state variable for the calculation of the control signal. In this paper preliminary simulations are persented in which the operation of the RHC is studied in the control of two vertically connected, oscillating masspoints so coupled by springs that only the state of the upper one is observed and directly controlled. Instead sensor-based observations, the lower point’s coordinate is calculated by the use of an available "rough" model. Preliminary calculations were made for a particular human glucose-insulin model, too. In the implementation of the RHC special simplifications were introduced. In our further work we wish to apply this method for investigating various T1DM treatment models.

scholarly journals Exploring the Limits of Floating-Point Resolution for Hardware-In-the-Loop Implemented with FPGAs

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 219 ◽  
Author(s):  
Alberto Sanchez ◽  
Elías Todorovich ◽  
Angel de Castro
Keyword(s):  
The State ◽  
Floating Point ◽  
Hardware In The Loop ◽  
State Variables ◽  
Numerical Resolution ◽  
Digital Devices ◽  
State Variable ◽  
Simulation Step ◽  
Field Programmable ◽  
The Difference

As the performance of digital devices is improving, Hardware-In-the-Loop (HIL) techniques are being increasingly used. HIL systems are frequently implemented using FPGAs (Field Programmable Gate Array) as they allow faster calculations and therefore smaller simulation steps. As the simulation step is reduced, the incremental values for the state variables are reduced proportionally, increasing the difference between the current value of the state variable and its increments. This difference can lead to numerical resolution issues when both magnitudes cannot be stored simultaneously in the state variable. FPGA-based HIL systems generally use 32-bit floating-point due to hardware and timing restrictions but they may suffer from these resolution problems. This paper explores the limits of 32-bit floating-point arithmetics in the context of hardware-in-the-loop systems, and how a larger format can be used to avoid resolution problems. The consequences in terms of hardware resources and running frequency are also explored. Although the conclusions reached in this work can be applied to any digital device, they can be directly used in the field of FPGAs, where the designer can easily use custom floating-point arithmetics.

Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Eric Donald Dongmo ◽  
Kayode Stephen Ojo ◽  
Paul Woafo ◽  
Abdulahi Ndzi Njah
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
The State ◽  
State Variables ◽  
State Variable ◽  
New Type ◽  
The Difference ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

scholarly journals Effects of relaxation on anxiety and salivary IgA levels in puerperae

2008 ◽  
Vol 16 (1) ◽  
pp. 36-41 ◽  
Author(s):  
Cândida Caniçali Primo ◽  
Maria Helena Costa Amorim
Keyword(s):  
Statistical Tests ◽  
Immunoglobulin A ◽  
Maternity Hospital ◽  
The State ◽  
Relaxation Techniques ◽  
State Variables ◽  
State Trait Anxiety Inventory ◽  
Salivary Iga ◽  
And Control ◽  
Experimental Group

This experimental study aimed to evaluate the effect of relaxation techniques on anxiety levels, and the relation between anxiety and the concentration of Immunoglobulin A. The study was carried out in a maternity hospital in a city of the State of Espírito Santo, Brazil. The sample was composed of 60 puerperae. The information on the variables: age, education, marital status, type of childbirth, and parity were collected with a specific form; the trait and state of anxiety were based on the State Trait Anxiety Inventory (STAI/IDATE); and the level of salivary IgA was obtained through immunoturbidimetry. The application of the Mann-Whitney, Wilcoxon, and Pearson's correlation statistical tests showed a significant reduction in the levels of the state of anxiety in the experimental group (p = 0.01); there was no correlation between the trait and state variables of anxiety and the salivary IgA level; both groups (experimental and control) showed trait and state of medium-intensity anxiety.

Evaluation of state variable interface between the Activated Sludge Models and Anaerobic Digestion Model no 1

2008 ◽  
Vol 57 (6) ◽  
pp. 901-907 ◽  
Author(s):  
H. Yasui ◽  
K. Komatsu ◽  
R. Goel ◽  
Y. Y. Li ◽  
T. Noike
Keyword(s):  
Activated Sludge ◽  
State Of The Art ◽  
Degradation Kinetics ◽  
The State ◽  
State Variables ◽  
Anaerobic Conditions ◽  
State Variable ◽  
Kinetics Of ◽  
Aerobic And Anaerobic ◽  
Aerobic And Anaerobic Conditions

For plant wide modelling of wastewater treatment, it is necessary to develop a suitable state variables interface for integrating state of the art models of ASM and ADM1. ADM1 currently describes such an interface, however, its suitability needs to be experimentally evaluated. In this study, we characterised activated sludge under aerobic and anaerobic conditions to obtain representative state variables for both models. ASM state variables of XS, XH and XI (as obtained from aerobic tests) and ADM1 state variables of XC and XI (as obtained from anaerobic tests) were then correlated to assess the suitability of current interface. Based on the seven datasets of this study and seven datasets from literatures, it was found that in general ASM state variables were well correlated to the state variables of ADM1. The ADM1 state variable of XC could be correlated to the sum of state variables of XS and XH, while XI in both the models showed direct correspondence. It was also observed that the degradation kinetics of XC under anaerobic condition could be better described by individual degradation kinetics of XS and XH. Therefore, to establish a one to one correspondence between ASM and ADM1 state variables and better description of degradation kinetics in ADM1, replacing the composite variable of XC by the state variables of XS and XH is recommended.

scholarly journals STACK with state

2017 ◽  
Vol 15 (2) ◽  
pp. 60 ◽  
Author(s):  
Matti Harjula ◽  
Jarmo Malinen ◽  
Antti Rasila
Keyword(s):  
Finite State Machine ◽  
State Machine ◽  
The State ◽  
Point Of View ◽  
State Variables ◽  
State Variable ◽  
Finite State ◽  
Input Event ◽  
Single Input ◽  
The Right

The question model of STACK provides an easy way for building automatically assessable questions with mathematical content, but it requires that the questions and their assessment logic depend only on the current input, given by the student at a single instant. However, the present STACK question model already has just the right form to be extended with state variables that would remove this limitation. In this article, we report our recent work on the state-variable extension for STACK, and we also discuss combining the use of state variables with our previous work on conditional output processing. As an outcome, we propose an expansion to the STACK question model, allowing the questions to act as state machines instead of pure functions of a single input event from the studentWe present a model question using the state variable extension of STACK that demonstrates some of the new possibilities that open up for the question author. This question is based on a finite state machine in its assessment logic, and it demonstrates aspects of strategic planning to solve problems of recursive nature. The model question also demonstrates how the state machine can interpret the solution path taken by the student, so as to dynamically modify the question behaviour and progress by, e.g., asking additional questions relevant to the path. We further explore the future possibilities from the point of view of learning strategic competencies in mathematics (Kilpatrick et al., 2001; Rasila et al., 2015).

A Probabilistic Theory for Balance Dynamics

2008 ◽  
Vol 65 (9) ◽  
pp. 2949-2960 ◽  
Author(s):  
Gregory J. Hakim
Keyword(s):  
Gravity Wave ◽  
Potential Vorticity ◽  
Joint Probability ◽  
The State ◽  
State Variables ◽  
Control Variables ◽  
Height Control ◽  
Gaussian Statistics ◽  
And Control ◽  
Balance Dynamics

Abstract Balance dynamics are proposed in a probabilistic framework, assuming that the state variables and the master, or control, variables are random variables described by continuous probability density functions. Balance inversion, defined as recovering the state variables from the control variables, is achieved through Bayes’ theorem. Balance dynamics are defined by the propagation of the joint probability of the state and control variables through the Liouville equation. Assuming Gaussian statistics, balance inversion reduces to linear regression of the state variables onto the control variables, and assuming linear dynamics, balance dynamics reduces to a Kalman filter subject to perfect observations given by the control variables. Example solutions are given for an elliptical vortex in shallow water having unity Rossby and Froude numbers, which produce an outward-propagating pulse of inertia–gravity wave activity. Applying balance inversion to the potential vorticity reveals that, because potential vorticity and divergence share well-defined patterns of covariability, the inertia–gravity wave field is recovered in addition to the vortical field. Solutions for a probabilistic balance dynamics model applied to the elliptical vortex reveal smaller errors (“imbalance”) for height control compared to potential vorticity control. Important attributes of the probabilistic balance theory include quantification of the concept of balance manifold “fuzziness,” and clear state-independent definitions of balance and imbalance in terms of the range of the probabilistic inversion operators. Moreover, the theory provides a generalization of the notion of balance that may prove useful for problems involving moist physics, chemistry, and tropical circulations.

Sensor Synthesis for Control of Manufacturing Processes

1992 ◽  
Vol 114 (2) ◽  
pp. 158-174 ◽  
Author(s):  
G. Chryssolouris ◽  
M. Domroese ◽  
P. Beaulieu
Keyword(s):  
The State ◽  
Process Models ◽  
State Variables ◽  
Test Bed ◽  
Control Approach ◽  
State Variable ◽  
Sensor Signals ◽  
Multiple Sensor ◽  
Sensor Information ◽  
Basic Approaches

When a human controls a manufacturing process he or she uses multiple senses to monitor the process. Similarly, one can consider a control approach where measurements of process variables are performed by several sensing devices which in turn feed their signals into process models. Each of these models contains mathematical expressions based on the physics of the process which relate the sensor signals to process state variables. The information provided by the process models should be synthesized in order to determine the best estimates for the state variables. In this paper two basic approaches to the synthesis of multiple sensor information are considered and compared. The first approach is to synthesize the state variable estimates determined by the different sensors and corresponding process models through a mechanism based on training such as a neural network. The second approach utilizes statistical criteria to estimate the best synthesized state variable estimate from the state variable estimates provided by the process models. As a “test bed” for studying the effectiveness of the above sensor synthesis approaches turning has been considered. The approaches are evaluated and compared for providing estimates of the state variable tool wear based on multiple sensor information. The robustness of each scheme with respect to noisy and inaccurate sensor information is investigated.

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.

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