Synthesis of control systems based on approximation to a third-order system

1958 ◽  
Vol 77 (5) ◽  
pp. 415-421
Author(s):  
C. R. Hausenbauer ◽  
G. V. Lago
Keyword(s):  
Control Systems ◽  
Order System ◽  
Third Order

scholarly journals ALGORITHM FOR SYNTHESIS OF QUASI-OPTIMAL IN SPEED THIRD-ORDER SYSTEMS WITH APERIODIC SLIDING MODE

2021 ◽  
Vol 1 (38) ◽  
pp. 48-56
Author(s):  
O. Derets ◽  
O. Sadovoi ◽  
H. Derets
Keyword(s):  
Control System ◽  
Control Systems ◽  
Electric Drive ◽  
Sliding Mode ◽  
Block Diagram ◽  
Order System ◽  
Practical Implementation ◽  
Third Order ◽  
Relay Control ◽  
Electric Drives

The relevance of the work is due to the growing requirements for the dynamic characteristics of electric drives. In particular, together with the requirements of ensuring high accuracy and maximum at given speed limits, a typical task of designing such systems is the mandatory formation of transition diagrams in the form of monotonic time functions. The purpose of this study is to develop an adaptive algorithm for the synthesis of the third-order sliding mode control systems based on the method of N-i switching. Changing the shape of transient trajectory depends on the magnitude of the movement, which requires adaptation of the settings of the control system of the electric drive to the features of the current positioning mode. On the basis of the N-i switching method, an algorithm for synthesizing the parameters of a re-lay control system with cascade-subordinated structure, ensures non-oscillatory initiation of a sliding mode at various positioning modes, has been created. It is constructed by integrating the results of a number of previous works, in which the synthesis of relay control systems based on the analysis of the roots of the sliding equation of the position regulator is performed. This algorithm cannot be formally considered as an optimization tool due to the incompatibility of this problem with the aperiodization taken as the purpose, which comes about for certain forms of transient trajectories. But for such cases, the loss of performance relatively optimal one is negligible. Thus, the result of the application of the proposed algorithm in most practically significant cases is an optimal third-order system with aperiodic entry into the sliding mode. When controlling the electric drive, such a system will ensure the monotonous nature of the movement of the working body of the electromechanical system. The developed block diagram is focused on the practical implementation of the algorithm by the software of controllers of precision electric drives.

On the stability properties of a third order system

1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina
Keyword(s):  
Order System ◽  
Third Order ◽  
Stability Properties ◽  
The Stability

Sychronisation of Chua's Oscillator via the State Observer Technique

2003 ◽  
Vol 40 (1) ◽  
pp. 36-44
Author(s):  
Xiaogen Yin ◽  
Y. J. Cao
Keyword(s):  
Control Theory ◽  
Control Systems ◽  
Chaotic Dynamics ◽  
State Observer ◽  
Dynamical Behaviour ◽  
Simple Approach ◽  
Nonlinear Circuit ◽  
Third Order ◽  
Rich Variety ◽  
Chua’S Oscillator

Chua's oscillator is a simple autonomous third-order nonlinear circuit with a rich variety of dynamical behaviour. This paper presents a simple approach to synchronisation of Chua's oscillators using a state observer in control theory, which can be used as an interesting example for educational purposes in control systems, showing the students a simple way of coping with chaotic dynamics.

scholarly journals Control solutions in mechatronics systems

2005 ◽  
Vol 18 (3) ◽  
pp. 379-394
Author(s):  
Radu-Emil Precup ◽  
Stefan Preitl
Keyword(s):  
Fuzzy Control ◽  
Control Systems ◽  
Third Order ◽  
Fuzzy Controllers ◽  
Real World Application ◽  
Conventional Solution ◽  
Extended Symmetrical Optimum Method ◽  
Theoretical Results ◽  
Iterative Feedback ◽  
Fuzzy Solutions

This paper presents control solutions dedicated to a class of controlled plants widely used in mechatronics systems, characterized by simplified mathematical models of second-order and third-order plus integral type. The conventional control solution is focused on the Extended Symmetrical Optimum method proposed by the authors in 1996. There are proposed six fuzzy control solutions employing PI-fuzzy controllers. These solutions are based on the approximate equivalence in certain conditions between fuzzy control systems and linear ones, on the application of the modal equivalence principle, and on the transfer of results from the continuous-time conventional solution to the fuzzy solutions via a discrete-time expression of the controller where Prof. Milic R. Stojic's book [1] is used. There is performed the sensitivity analysis of the fuzzy control systems with respect to the parametric variations of the controlled plant, which enables the development of the fuzzy controllers. In addition, the paper presents aspects concerning Iterative Feedback Tuning and Iterative Learning Control in the framework of fuzzy control systems. The theoretical results are validated by considering a real-world application.

scholarly journals Modeling and Designing a Hydrostatic Transmission With a Fixed-Displacement Motor

1998 ◽  
Vol 120 (1) ◽  
pp. 45-49 ◽  
Author(s):  
N. D. Manring ◽  
G. R. Luecke
Keyword(s):  
Order System ◽  
Axial Piston Pump ◽  
Third Order ◽  
Stability Range ◽  
Hydrostatic Transmission ◽  
Control Gain ◽  
Variable Displacement ◽  
Linearized System ◽  
The Stability ◽  
Axial Piston

This study develops the dynamic equations that describe the behavior of a hydrostatic transmission utilizing a variable-displacement axial-piston pump with a fixed-displacement motor. In general, the system is noted to be a third-order system with dynamic contributions from the motor, the pressurized hose, and the pump. Using the Routh-Hurwitz criterion, the stability range of this linearized system is presented. Furthermore, a reasonable control-gain is discussed followed by comments regarding the dynamic response of the system as a whole. In particular, the varying of several parameters is shown to have distinct effects on the system rise-time, settling time, and maximum percent-overshoot.

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.

Controllability of fractional order system with nonlinear term having integral contractor

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Surendra Kumar ◽  
Nagarajan Sukavanam
Keyword(s):  
Control Systems ◽  
Fractional Order ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Lipschitz Continuity ◽  
Fractional Order System ◽  
Order System ◽  
Semilinear Control Systems

AbstractIn this paper, controllability results for a class of semilinear control systems of fractional order are established. The nonlinear term is assumed to have an integral contractor which is a weaker condition than the Lipschitz continuity. The existence and uniqueness of mild solution is also proved.

Periodic Behavior of a Nonlinear Third Order Vibrating System

2002 ◽  
Author(s):  
Gholamreza Nakhaie Jazar ◽  
Mohammad H. Alimi ◽  
Mohammad Mahinfalah ◽  
Ali Khazaei
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Ad Hoc ◽  
Order Differential Equation ◽  
Second Order ◽  
Order System ◽  
Third Order ◽  
Modeling Process ◽  
Third Order Differential Equation ◽  
Second Order Systems

In modeling of dynamical systems, differential equations, either ordinary or partial, are a common outcome of the modeling process. The basic problem becomes the existence of solution of these deferential equations. In the early days of the solution of deferential equations at the beginning of the eighteenth century the methods for determining the existence of nontrivial solution were so limited and developed very much on an ad hoc basis. Most of the efforts on dynamical system are related to the second order systems, derived by applying Newton equation of motion to dynamical systems. But, behavior of some dynamical systems is governed by equations falling down in the general nonlinear third order differential equation x″′+f(t,x,x′,x″)=0, sometimes as a result of combination of a first and a second order system. It is shown in this paper that these equations could have nontrivial solutions, if x, x′, x″, and f(t,x,x′,x″) are bounded. Furthermore, it is shown that the third order differential equation has a τ-periodic solution if f(t,x,x′,x″) is an even function with respect to x′. For this purpose, the concept of Green’s function and the Schauder’s fixed-point theorem has been used.

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