scholarly journals Some New Trajectory Patterns and Periodic Behaviors of Unstable Second-Order Digital Filter with Two's Complement Arithmetic

2003 ◽  
Vol 13 (08) ◽  
pp. 2361-2368 ◽  
Author(s):  
Wing-Kuen Ling ◽  
Kwong-Shum Tam
Keyword(s):  
Periodic Orbit ◽  
Digital Filter ◽  
State Vector ◽  
Initial Conditions ◽  
Second Order ◽  
The State ◽  
Simulation Results ◽  
The Stability ◽  
Straight Lines

This Letter shows some counter-intuitive simulation results that for some filter parameters in the extended boundaries of the stability triangle, the state vector will converge to a periodic orbit after some iterations, no matter what the initial conditions. Also, a new pattern, which looks like a rotated letter "X", is found. The center of the rotated letter is located at the origin and the slopes of the "straight lines" of the rotated letter are equal to the values of the pole locations.

scholarly journals CHAOTIC BEHAVIORS OF A DIGITAL FILTER WITH TWO'S COMPLEMENT ARITHMETIC AND ARBITRARY INITIAL CONDITIONS AND ORDER

2004 ◽  
Vol 14 (07) ◽  
pp. 2425-2430 ◽  
Author(s):  
BINGO WING-KUEN LING ◽  
WAI-FUNG HUNG ◽  
PETER KWONG-SHUM TAM
Keyword(s):  
Digital Filter ◽  
Initial Conditions ◽  
The State ◽  
State Variables ◽  
System Matrix ◽  
Symbolic Sequences ◽  
Simulation Results

This letter shows some counter-intuitive simulation results that the symbolic sequences and the state variables of a digital filter with two's complement arithmetic and arbitrary initial conditions and order will be eventually zero when all the filter parameters are even numbers, no matter the system matrix of the filter is stable or not.

An Improved Adaptive Algorithm for INS/GPS System

2013 ◽  
Vol 397-400 ◽  
pp. 1606-1610 ◽  
Author(s):  
Li Dong Wang ◽  
Ying Zhao ◽  
Ni Zhang
Keyword(s):  
Adaptive Filtering ◽  
Adaptive Filter ◽  
Adaptive Algorithm ◽  
Initial Conditions ◽  
Forgetting Factor ◽  
Kalman Filter Algorithm ◽  
Simulation Results ◽  
The Stability ◽  
Gps System

In INS/GPS system, the changing of initial conditions and the quality of the data can affect the convergence of the conventional Kalman filter algorithm. Sage-Husa adaptive filter algorithm is adopted in the INS/GPS system in this paper. The effecting of the forgetting factor to the improved Sage-Husa adaptive filter algorithm is studied and the simulation results show that when the forgetting factor taken near 0.97, the adaptive filtering result is best, the stability of the system is guaranteed and the convergent speed of error can be reduced.

DISCRETIZATION CHAOS IN THE SWITCHING CONTROL SYSTEM WITH FINITE SWITCHING VALUES

1995 ◽  
Vol 05 (06) ◽  
pp. 1749-1755 ◽  
Author(s):  
XING HUO YU
Keyword(s):  
Control System ◽  
Initial Conditions ◽  
Switching Control ◽  
Second Order ◽  
Periodic Motions ◽  
Theoretical Investigations ◽  
Simulation Results

A case study is presented to demonstrate the discretization chaos in the switching control system with only finite switching values. It is proved that for the second order oscillator, with several classes of sampling periods, discrete switching control enables periodic motions around the desired equilibrium. The pattern of the discretized system is determined by the initial conditions as well as the sampling periods. Simulation results are presented to confirm the theoretical investigations.

On Dynamic Tooth Load and Stability of a Spur-Gear System Using the State-Space Approach

1985 ◽  
Vol 107 (1) ◽  
pp. 54-60 ◽  
Author(s):  
A. S. Kumar ◽  
T. S. Sankar ◽  
M. O. M. Osman
Keyword(s):  
State Space ◽  
Dynamic Load ◽  
Initial Conditions ◽  
Gear Tooth ◽  
Spur Gear ◽  
The State ◽  
Gear System ◽  
Computational Time ◽  
Steady State Condition ◽  
The Stability

In this study, a new approach using the state-space method is presented for the dynamic load analysis of spur gear systems. This approach gives the dynamic load on gear tooth in mesh as well as information on the stability of the gear system. Also a procedure is given for the selection of proper initial conditions that enable the steady-state condition to be reached faster, conditions that result in considerable savings in computational time. The variations in the dynamic load with respect to changes in contact position, operating speed, backlash, damping, and stiffness are also investigated. In addition, the stability of the gear system is studied, using the Floquet theory and the well-known stability conditions of difference systems.

scholarly journals A new feature parametrization for monocular SLAM using line features

Robotica ◽  
2014 ◽  
Vol 33 (3) ◽  
pp. 513-536 ◽  
Author(s):  
Liang Zhao ◽  
Shoudong Huang ◽  
Lei Yan ◽  
Gamini Dissanayake
Keyword(s):  
State Vector ◽  
Bundle Adjustment ◽  
The State ◽  
Minimal Representation ◽  
Monocular Slam ◽  
Reprojection Error ◽  
Line Features ◽  
New Feature ◽  
Slam Algorithm ◽  
Straight Lines

SUMMARYThis paper presents a new monocular SLAM algorithm that uses straight lines extracted from images to represent the environment. A line is parametrized by two pairs of azimuth and elevation angles together with the two corresponding camera centres as anchors making the feature initialization relatively straightforward. There is no redundancy in the state vector as this is a minimal representation. A bundle adjustment (BA) algorithm that minimizes the reprojection error of the line features is developed for solving the monocular SLAM problem with only line features. A new map joining algorithm which can automatically optimize the relative scales of the local maps is used to combine the local maps generated using BA. Results from both simulations and experimental datasets are used to demonstrate the accuracy and consistency of the proposed BA and map joining algorithms.

Generalized Stability-Triangle for Guaranteeing the Stability-Margin of the Second-Order Digital Filter

2016 ◽  
Vol 25 (08) ◽  
pp. 1650094 ◽  
Author(s):  
Tian-Bo Deng
Keyword(s):  
Digital Filter ◽  
Upper Bound ◽  
Digital Filters ◽  
Stability Margin ◽  
Second Order ◽  
Recursive Digital Filter ◽  
The Stability ◽  
Special Case ◽  
Recursive Digital Filters ◽  
Generalized Stability

In the design of recursive digital filters, the stability of the recursive digital filters must be guaranteed. Furthermore, it is desirable to add a certain amount of margin to the stability so as to avoid the violation of stability due to some uncertain perturbations of the filter coefficients. This paper extends the well-known stability-triangle of the second-order digital filter into more general cases, which results in dented stability-triangles and generalized stability-triangle. The generalized stability-triangle can be viewed as a special case of the dented stability-triangles if the two upper bounds on the radii of the two poles are the same, which is a generalized version of the existing conventional stability-triangle and can guarantee the radii of the two poles of the second-order recursive digital filter below some prescribed upper bound. That is, it is able to provide a prescribed stability-margin in terms of the upper bound of the pole radii. As a result, the generalized stability-triangle increases the flexibility for guaranteeing a prescribed stability-margin. Since the generalized stability-triangle is parameterized by using the upper bound of pole radii, i.e., the stability-margin is parameterized as a function of the upper bound, the proposed generalized stability-triangle facilitates the stability-margin guarantee in the design of the second-order as well as high-order recursive digital filters.

Synthesis of Tracking Algorithms for Linear Objects with a Generative Model of the Reference Signal

2019 ◽  
Vol 20 (2) ◽  
pp. 72-79
Author(s):  
Ju. I. Myshljaev ◽  
Pyi Kyaw Khaung ◽  
Ja. А. Dolgov
Keyword(s):  
State Vector ◽  
Reference Model ◽  
Initial Conditions ◽  
Tracking Error ◽  
Reference Signal ◽  
Control Object ◽  
The State ◽  
Control Goal ◽  
Scalar Input ◽  
Stationary Objects

In the article the class of linear stationary objects with a scalar input is considered. The purpose of control is formulated in the form of tracking the output of the control object for a given input reference. At the same time, the principle of the internal model is used to form a generating model of the input reference. The solution of the representation subtask with a predetermined finite precision of a time-discretized input reference in the form of a linear expansion on the basic functions corresponding to the roots of the desired characteristic polynomial of a discrete linear dynamic system (generator) is considered. By using the continualization, a continuous, linear generating model of the input reference with non-zero initial conditions and input is constructed in the state space, coinciding in dimension with the model of the control object. The generating model makes it possible to formulate the control goal in the form of tracking the state vector of a closed system with the state vector of the generating model. In general, the generating model may not be stable. Therefore, the desired rate of convergence of the tracking error vector is given by the Hurwitz reference model. The developed method of generating the generating model is considered in the context of solving the general problem of the synthesis of the tracking algorithm.

Sub-fixed-time control for a class of second order system

2020 ◽  
pp. 014233122092100
Author(s):  
Boyan Jiang ◽  
Hua Chen ◽  
Bo Li ◽  
Xuewu Zhang
Keyword(s):  
Initial Conditions ◽  
Equilibrium Points ◽  
Fixed Time ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
Time Stability ◽  
Time Control ◽  
Initial States ◽  
The Stability

In this paper, a new concept “sub-fixed-time stability” (SFTS) is proposed and studied, which means the states can converge to a region of equilibrium points in a fixed time for any initial states’ values. Then, a sufficient condition for it is given and proven. Though SFTS is similar to “practical fixed-time stability” (PFTS), they are not the same, and the sufficient condition for SFTS is much clearer and simpler than PFTS. Next, a sub-fixed-time controller is proposed for a class of second order system. The stability analyses are given in the case without disturbance and with disturbance, respectively. Finally, to illustrate the robustness of the proposed sub-fixed-time controller to different initial conditions, 100 numerical simulations are conducted for 100 initial states’ values.

Shimmy model for electric vehicle with independent suspensions

2017 ◽  
Vol 232 (3) ◽  
pp. 330-340 ◽  
Author(s):  
Tian Mi ◽  
Gabor Stepan ◽  
Denes Takacs ◽  
Nan Chen
Keyword(s):  
Electric Vehicle ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Structural Parameters ◽  
Contact Point ◽  
Dynamic Responses ◽  
Simulation Results ◽  
The Stability ◽  
Linearized Model ◽  
Wheel Shimmy

A 5-degrees-of-freedom shimmy model is established to analyse the dynamic responses of an electric vehicle with independent suspensions. Tyre elasticity is considered by means of Pacejka’s magic formula. Under the nonslip assumption for the leading contact point, tyre–road constraint equations are derived. Numerical simulation is conducted with different structural parameters and initial conditions to observe the shimmy phenomenon. Simulation results indicate that Hopf bifurcation occurs at a certain vehicle forward speed. Moreover, suspension structural parameters, such as caster angle, affect wheel shimmy. The linearized model of the system presents the stability boundaries, which agree with the simulation results. The results of this study not only provide a theoretical reference for shimmy attenuation, but also validate the effectiveness of the provided model, which can be used in further dynamic analysis of vehicle shimmy.

scholarly journals Invariant, Decoupling and Blocking Zeros of Fractional Linear Systems

2018 ◽  
Vol 12 (1) ◽  
pp. 44-48
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
State Vector ◽  
Transfer Functions ◽  
Initial Conditions ◽  
The State ◽  
Input Output ◽  
Fractional System ◽  
Controllability And Observability

AbstractThe notions of invariant, decoupling and blocking zeros are extended to the fractional linear systems. It is shown that: 1) The zeros are closely connected with the controllability and observability of the linear systems and their transfer functions matrices. 2) The state vector of the fractional system for any input and zero initial conditions is independent of the input decoupling zeros of the system. 3) The output of the fractional system for any input and zero initial conditions is independent of the input-output decoupling zeros of the system.

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