scholarly journals Cascade Delayed Controller Design for a Class of Underactuated Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
G. Ochoa-Ortega ◽  
R. Villafuerte-Segura ◽  
A. Luviano-Juárez ◽  
M. Ramírez-Neria ◽  
N. Lozada-Castillo
Keyword(s):  
Fourth Order ◽  
Controller Design ◽  
Local Controllability ◽  
Order System ◽  
System Response ◽  
Joint System ◽  
Linearization Technique ◽  
Exponential Decay Rate ◽  
Cascade Connection ◽  
Controllability Property

In this paper, a delayed control strategy for a class of nonlinear underactuated fourth-order systems is developed. The proposal is based on the implementation of the tangent linearization technique, differential flatness, and a study of the σ-stabilization of the characteristic equation of the closed-loop system. The tangent linearization technique allows obtaining a local controllability property for the analyzed class of systems. Also, it can reduce the complexity of the global control design, through the use of a cascade connection of two second-order controllers instead of designing a global controller of the fourth-order system. The stabilizing behavior of the delayed controller design is supported by the σ-stability criterion, which provides the controller parameter selection to reach the maximum exponential decay rate on the system response. To illustrate the efficiency of the theoretical results, the proposal is experimentally assessed in two cases of study: a flexible joint system and a pendubot.

scholarly journals Lead and lag controller design in fractional-order control systems

2019 ◽  
Vol 52 (7-8) ◽  
pp. 1017-1028
Author(s):  
Tufan Dogruer ◽  
Nusret Tan
Keyword(s):  
Control System ◽  
Control Systems ◽  
Fractional Order ◽  
Fourth Order ◽  
Controller Design ◽  
Design Method ◽  
Performance Criteria ◽  
Order System ◽  
Fractional Order Control ◽  
Minimum Error

This paper presents a controller design method using lead and lag controllers for fractional-order control systems. In the presented method, it is aimed to minimize the error in the control system and to obtain controller parameters parametrically. The error occurring in the system can be minimized by integral performance criteria. The lead and lag controllers have three parameters that need to be calculated. These parameters can be determined by the simulation model created in the Matlab environment. In this study, the fractional-order system in the model was performed using Matsuda’s fourth-order integer approximation. In the optimization model, the error is minimized by using the integral performance criteria, and the controller parameters are obtained for the minimum error values. The results show that the presented method gives good step responses for lead and lag controllers.

Controller Design for Linear Multivariable Systems

1972 ◽  
Vol 5 (5) ◽  
pp. 188-191
Author(s):  
P H Walker ◽  
J W Green
Keyword(s):  
Fourth Order ◽  
Controller Design ◽  
Reference Model ◽  
Point Of View ◽  
The Other ◽  
Order System ◽  
Multivariable Systems ◽  
System State ◽  
State Variables ◽  
Model Point

A method of designing controllers for multivariable systems is described which regards the problem from an implicit reference model point of view. The rules for the design are found to be very simple to apply and involve only proportional and integral terms if all the system state variables are available. The method is demonstrated by means of two examples, one being a second order system with two inputs and two outputs, the other being a fourth order system also with two inputs and two outputs.

Controllability Ellipsoid to Evaluate the Performance of Mobile Manipulators for Manufacturing Tasks

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Stephen L. Canfield ◽  
Reabetswe M. Nkhumise
Keyword(s):  
Time Domain ◽  
Controller Design ◽  
Control Design ◽  
Quantitative Measure ◽  
Space Representation ◽  
System Response ◽  
Geometric Representation ◽  
Mobile Manipulators ◽  
Control Parameters ◽  
The Time Domain

This paper develops an approach to evaluate a state-space controller design for mobile manipulators using a geometric representation of the system response in tool space. The method evaluates the robot system dynamics with a control scheme and the resulting response is called the controllability ellipsoid (CE), a tool space representation of the system’s motion response given a unit input. The CE can be compared with a corresponding geometric representation of the required motion task (called the motion polyhedron) and evaluated using a quantitative measure of the degree to which the task is satisfied. The traditional control design approach views the system response in the time domain. Alternatively, the proposed CE views the system response in the domain of the input variables. In order to complete the task, the CE must fully contain the motion polyhedron. The optimal robot arrangement would minimize the total area of the CE while fully containing the motion polyhedron. This is comparable to minimizing the power requirements of robot design when applying a uniform scale to all inputs. It will be shown that changing the control parameters changes the eccentricity and orientation of the CE, implying a preferred set of control parameters to minimize the design motor power. When viewed in the time domain, the control parameters can be selected to achieve desired stability and time response. When coupled with existing control design methods, the CE approach can yield robot designs that are stable, responsive, and minimize the input power requirements.

Fourth‐order finite‐difference P-SV seismograms

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1425-1436 ◽  
Author(s):  
Alan R. Levander
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Fourth Order ◽  
Equations Of Motion ◽  
Dispersion Analysis ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Order System ◽  
Surface Boundary ◽  
Lamb’S Problem

I describe the properties of a fourth‐order accurate space, second‐order accurate time, two‐dimensional P-SV finite‐difference scheme based on the Madariaga‐Virieux staggered‐grid formulation. The numerical scheme is developed from the first‐order system of hyperbolic elastic equations of motion and constitutive laws expressed in particle velocities and stresses. The Madariaga‐Virieux staggered‐grid scheme has the desirable quality that it can correctly model any variation in material properties, including both large and small Poisson’s ratio materials, with minimal numerical dispersion and numerical anisotropy. Dispersion analysis indicates that the shortest wavelengths in the model need to be sampled at 5 gridpoints/wavelength. The scheme can be used to accurately simulate wave propagation in mixed acoustic‐elastic media, making it ideal for modeling marine problems. Explicitly calculating both velocities and stresses makes it relatively simple to initiate a source at the free‐surface or within a layer and to satisfy free‐surface boundary conditions. Benchmark comparisons of finite‐difference and analytical solutions to Lamb’s problem are almost identical, as are comparisons of finite‐difference and reflectivity solutions for elastic‐elastic and acoustic‐elastic layered models.

scholarly journals A New Asymptotic Treatment of g-modes of a Star

1995 ◽  
Vol 155 ◽  
pp. 285-286
Author(s):  
P. Smeyers ◽  
T. Van Hoolst ◽  
I. De Boeck ◽  
L. Decock
Keyword(s):  
Singular Perturbation ◽  
Fourth Order ◽  
Asymptotic Expansions ◽  
Equilibrium Model ◽  
Asymptotic Representation ◽  
Radial Displacement ◽  
Low Frequency ◽  
Order System ◽  
Oscillation Modes ◽  
Perturbation Problems

An asymptotic representation of low-frequency, linear, isentropic g-modes of a star is developed without the usual neglect of the Eulerian perturbation of the gravitational potential. Our asymptotic representation is based on the use of asymptotic expansions adequate for solutions of singular perturbation problems (see, e.g., Kevorkian & Cole 1981).Linear, isentropic oscillation modes with frequency different from zero are governed by a fourth-order system of linear, homogeneous differential equations in the radial parts of the radial displacement ξ(r) and the divergence α(r). These equations take the formThe symbols have their usual meaning. N2 is the square of the frequency of Brunt-Väisälä. The functions K1 (r), K2 (r), K3 (r), K4 (r), depend on the equilibrium model, e.g.,We introduce the small expansion parameterand assume, for the sake of simplification, N2 to be positive everywhere in the star so that the star is everywhere convectively stable.

scholarly journals Linearization of symmetrical and asymmetrical two-way Doherty amplifier

2012 ◽  
Vol 25 (2) ◽  
pp. 161-170 ◽  
Author(s):  
Aleksandar Atanaskovic ◽  
Natasa Males-Ilic ◽  
Bratislav Milovanovic
Keyword(s):  
Fourth Order ◽  
Linearization Technique ◽  
The Third ◽  
Simulation Process ◽  
Input And Output ◽  
Carrier Cell ◽  
Fifth Order ◽  
Doherty Amplifier

The linearization effects on two-way Doherty amplifiers are presented in this paper. Symmetrical Doherty amplifier with the additional circuit for linearization has been realized and measurements of the linearization influence on the third- and fifth-order intermodulation products have been carried out. Asymmetrical Doherty amplifier has been designed and effects of the applied linearization technique have been considered through the simulation process. The linearization approach uses the fundamental signals? second harmonics and fourth-order nonlinear signals that are extracted at the output of the peaking cell, adjusted in amplitude and phase and injected at the input and output of the carrier cell in Doherty amplifier.

Use of Temporal Irreversibility of Symbolic Time Series for Early Detection of Extinction in Thermal Pulse Combustors

2006 ◽  
Author(s):  
Subhashis Datta ◽  
Achintya Mukhopadhyay ◽  
Dipankar Sanyal
Keyword(s):  
Time Series ◽  
Fourth Order ◽  
Time Series Data ◽  
Order System ◽  
Series Data ◽  
Thermal Pulse ◽  
Pulse Combustor ◽  
The Difference ◽  
Symbol Sequences ◽  
System Approaches

A nonlinear fourth-order dynamic model of a thermal pulse combustor has been developed. In this work, the time series data generated by solution of the fourth order system is converted into a set of symbols based on the values of pressure variables. The key step to symbolization involves transformation of the original values to a stream of discretised symbols by partitioning the range of observed values into a finite number of regions and then assigning a symbol to each measurement based on the region in which it falls. Once all the measured values are symbolized, a symbol sequence vector consisting of L successive temporal observations is defined and its relative frequency is determined. In this work, the relative frequencies of different symbol sequences are computed by scanning the time series data in forward and reverse directions. The difference between the relative frequencies obtained in forward and reverse scanning is termed as "irreversibility" of the process. It is observed that for given alphabet and word sizes, the "irreversibility" increases as the system approaches extinction. The effects of different choices of alphabet and word sizes are also considered.

scholarly journals Assessment of Patellar Tendon Reflex Responses Using Second-Order System Characteristics

2016 ◽  
Vol 2016 ◽  
pp. 1-4 ◽  
Author(s):  
Brett D. Steineman ◽  
Pavan Karra ◽  
Kiwon Park
Keyword(s):  
Decay Rate ◽  
Natural Frequency ◽  
Patellar Tendon ◽  
Exponential Decay ◽  
Second Order ◽  
Order System ◽  
Sample Population ◽  
Exponential Decay Rate ◽  
Tendon Reflex ◽  
Patellar Tendon Reflex

Deep tendon reflex tests, such as the patellar tendon reflex (PTR), are widely accepted as simple examinations for detecting neurological disorders. Despite common acceptance, the grading scales remain subjective, creating an opportunity for quantitative measures to improve the reliability and efficacy of these tests. Previous studies have demonstrated the usefulness of quantified measurement variables; however, little work has been done to correlate experimental data with theoretical models using entire PTR responses. In the present study, it is hypothesized that PTR responses may be described by the exponential decay rate and damped natural frequency of a theoretical second-order system. Kinematic data was recorded from both knees of 45 subjects using a motion capture system and correlation analysis found that the meanR2value was 0.99. Exponential decay rate and damped natural frequency ranges determined from the sample population were −5.61 to −1.42 and 11.73 rad/s to 14.96 rad/s, respectively. This study confirmed that PTR responses strongly correlate to a second-order system and that exponential decay rate and undamped natural frequency are novel measurement variables to accurately measure PTR responses. Therefore, further investigation of these measurement variables and their usefulness in grading PTR responses is warranted.

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