The Solution of a Problem of Speed of Response on Output Coordinate for Linear Dynamic Systems

2019 ◽  
Vol 20 (9) ◽  
pp. 532-541 ◽  
Author(s):  
V. I. Lovchakov ◽  
O. A. Shibyakin
Keyword(s):  
Control System ◽  
Closed Loop ◽  
Transfer Functions ◽  
Algebraic Method ◽  
Control Signal ◽  
Transient Processes ◽  
Linear Control Systems ◽  
Feedback Signal ◽  
Transient Time ◽  
Speed Of Response

The solution of the so-called problem of speed of response in one coordinate, which has important theoretical and practical importance, is investigated. It is formulated with reference to linear one-dimensional high-order control objects described by a system of ordinary differential equations in a certain phase space. The transient time tnn of the system designed is understood in a sense of the classical control theory in reference to one (output) coordinate of the object and is determined by using the zone Δ = σ* = 4.321 %, which equals the given (desirable) value of the overshoot of the system synthesized. This overshoot corresponds with the speed of response oscillating second-order element with a damping coefficient ζ= = 2 2 0,7071 / . It is indispensable to mention here that the equation Δ = σ is one of the necessary conditions for the maximum speed of response of the system with the oscillating character of transient processes. In accordance to this the task of the speed of response by one coordinate can be described by the following generalized formulation: one must find the linear algorithm of the feedback signal, which provides a preset order of the astatism na for the closed-loop control system and converts the control object from a zero state into a final state, which is determined by the constant signal of the input, with a minimal time value of the transient processes of the system tnn and the preset value of the overshoot σ m σ* while fulfilling the constraint of the control signal |u(t)| m umax. Nowadays the task mentioned is approximately solved by the algebraic method of the synthesis of linear control systems with the determination of a desirable transfer function of the designed closed-loop system based on model normalized transfer functions (NTF). In the works by Kim D. P. there was carried out the analysis of four types of normalized transfer functions characterized by the increased speed of response. In this work two additional types of normalized transfer functions are suggested, in comparison with mentioned NTF they have the increased speed of response in case of the preset value of the overregulation σ* = 4.321 %. On their basis and using the methodology of the modal control the method of the synthesis of the controller is suggested; this method ensures the transient time of the designed system to be close to the minimum in case of the preset constraint of the overregulation and the value of the control signal. It needs to be emphasized that in contrast to the algebraic method of the synthesis, this method is applied to a wider range of control objects: as to minimal-phased objects as to non-minimum-phased ones; as to the objects containing zeros as to those without them. The method is illustrated by an example of synthesis of control system speed of response of the fourth order, containing the results of its modeling.

Kinematics, Dynamics, and Control of Tendon-Driven Mechanisms Using Signal Flow Graphs

1998 ◽  
Author(s):  
Meng-Sang Chew ◽  
Theeraphong Wongratanaphisan
Keyword(s):  
Control System ◽  
Transfer Function ◽  
Closed Loop ◽  
Transfer Functions ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Loop Transfer Function ◽  
Dynamics And Control ◽  
Flow Graphs ◽  
And Control

Abstract This paper presents the analysis of the kinematics, dynamics and controls of tendon-driven mechanism under the framework of signal flow graphs. For decades, the signal flow graphs have been applied in many areas, particularly in controls, for determining the closed-loop transfer function of a control system. The tendon-driven mechanism considered here consists of several subsystems including actuator-controller dynamics, mechanism kinematics and mechanism dynamics. Each subsystem will be derived and represented by signal flow graphs. The representation of the whole system can be carried out by connecting the graphs of subsystems at the corresponding nodes. Transfer functions can then be obtained by using Mason’s rules. A 3-DOF robot finger utilizing tendon-driven mechanism is used as an illustrative example.

Automatic Positioning Closed-Loop Control Cystem Design of Linear Time Grating Sensor

2011 ◽  
Vol 328-330 ◽  
pp. 2121-2124
Author(s):  
Tian Heng Zhang ◽  
Dong Lin Peng ◽  
Ji Sen Yang ◽  
Xian Quan Wang ◽  
Chun Dong
Keyword(s):  
Control System ◽  
High Precision ◽  
Closed Loop ◽  
Linear Time ◽  
Stepper Motor ◽  
Feedback Signal ◽  
Closed Loop Control ◽  
Positioning System ◽  
Loop Control ◽  
Automatic Positioning

A high-precise automatic positioning system for data sample of linear time grating sensor is designed. In order to achieve linear time grating sensor of data sample, improve measure work efficiency, an ARM MCU is used as a major chip to control the stepper motor to rotate. In this way, the stepper motor drives the ball screw, the moving probe of linear time grating sensor and reading head of linear grating to move synchronously. A high-precision automatic positioning of the system hardware is designed. In addition, ARM controlling circuits and stepper motor driving circuits are designed. Therefore, the special communication interface is designed for the high-precision automatic positioning system, receiving the feedback signal from time grating sensor, forming a high-precision closed loop control system, and communicating with upper computer by serial. Experiment results prove that the positioning precision of control system can reach 0.1 um.

Model Reduction and Control System Design by Shifted Legendre Polynomial Functions

1983 ◽  
Vol 105 (1) ◽  
pp. 52-55 ◽  
Author(s):  
Rong-Yeu Chang ◽  
Maw-Ling Wang
Keyword(s):  
Control System ◽  
Model Reduction ◽  
Transfer Functions ◽  
Legendre Function ◽  
Operational Matrix ◽  
Algebraic Method ◽  
Recursive Formula ◽  
Legendre Series ◽  
Model Reduction Technique ◽  
And Control

A method of model reduction for reducing a higher order transfer function to its lower order model is developed based on the shifted Legendre function approximation. The expansion coefficients of the shifted Legendre series which represents the approximate responses of transfer functions are computed by the recursive formula, via operational matrix approach. The significances of applying shifted Legendre function to model reduction problem are that the method is simple, straightforward and the computational results obtained are accurate as well as the final time of the control system can be adjustable without any restriction. Based on the model reduction technique, a new algebraic method is proposed for the design of a feedback control system to satisfy specifications. Illustrative examples are given and satisfactory results are obtained.

scholarly journals Use of a Secondary Current Sensor in Plasma during Electron-Beam Welding with Focus Scanning for Process Control

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Dmitriy Trushnikov ◽  
Elena Krotova ◽  
Elena Koleva
Keyword(s):  
Electron Beam ◽  
Control System ◽  
Closed Loop ◽  
Electron Beam Welding ◽  
Current Sensor ◽  
Feedback Signal ◽  
Secondary Current ◽  
The Stability ◽  
Phase Relationships ◽  
Pilot Tests

We consider questions of building a closed-loop focus control system for electron-beam welding. As a feedback signal, we use the secondary current in the plasma that forms above the welding zone. This article presents a model of a secondary current sensor in plasma during electron-beam welding with focus scanning. A comparison of modeled results with experimental data confirms the adequacy of the model. We show that the best results for focus control are obtained when using phase relationships rather than amplitude relationships. We outline the principles for building an EBW focus control system based on parameters of the secondary current in plasma. We simulate the work of a control system’s circuits and demonstrate the stability of the synthesized system. We have conducted pilot tests on an experimental prototype.

scholarly journals Studies on Closed-loop Interaction in a Multi-loop Single Tank Control System

2018 ◽  
Vol 7 (3.26) ◽  
pp. 38
Author(s):  
Abhijeet Chourdhary ◽  
Amit Jain
Keyword(s):  
Control System ◽  
Closed Loop ◽  
Transfer Functions ◽  
Test Method ◽  
Step Test ◽  
Flow Loop ◽  
Array Analysis ◽  
Relative Gain ◽  
Relative Gain Array ◽  
Tank System

This paper investigates the interaction between level and flow loop in a single tank system. The data generated is used to generate all transfer functions via step test method. The model generated is then simulated on MATLAB-Simulink and the obtained results are then compared with experimental results for verification. A Relative Gain Array analysis is performed to check the interaction and comment on the pairing.  

Modelling, Identification and Control of Thermal Deformation of Machine Tool Structures, Part 4: A Multi-Variable Closed-Loop Control System

1999 ◽  
Vol 121 (3) ◽  
pp. 509-516 ◽  
Author(s):  
S. Fraser ◽  
M. H. Attia ◽  
M. O. M. Osman
Keyword(s):  
Control System ◽  
Machine Tool ◽  
Thermal Deformation ◽  
Closed Loop ◽  
Transfer Functions ◽  
Closed Loop Control ◽  
Loop Control ◽  
Closed Loop Control System ◽  
Loop Control System ◽  
Machine Tool Structures

A multi-variable closed-loop control system is proposed to compensate for the thermal deformation of machine tool structures. The control system recognizes the fact the relative thermal displacement between the tool and workpiece is not accessible for direct measurement. Using the generalized thermoelastic transfer functions of the structure, which provide satisfactory input-output dynamic dependencies, the heat input to the structure and thermal displacements are estimated in real time. Artificial heating elements are used as the actuation mechanism of the control system, since they provide an economical solution for retrofitting existing conventional machine tools, and can also be combined with NC controllers to effect the desired compensation of the expansion and bending modes of deformation. Computer simulation test results indicated that even when the random temperature measurement and power actuation errors are taken in consideration, an accuracy of better than 2.5 μm and a control cycle of the order of 1 second are achievable.

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